ElectricalandElectronicsMeasurementsandInstrumentation

AbouttheAuthors

PrithwirajPurkaitobtainedhisBEE,MEEandPhDdegreesfromJadavpurUniversity,Kolkata.HeworkedwithM/sCromptonGreavesLtd,Mumbai,asaDesignEngineerforone year. He was involved in post-doctoral research in the University of Queensland,Australia,during2002-2003,andasVisitingAcademicResearchFellowduring2005and2007.Presently,heisProfessor,DepartmentofElectricalEngineeringandDean,SchoolofEngineering,atHaldiaInstituteofTechnology,Haldia,WestBengal.Hiscurrentareasof interest include PC/DSP based instruments, motion and industrial process control,insulation-condition assessment techniques and advanced signal-processing applications.DrPurkaithaspublishedextensivelyininternationaljournalsandconferenceproceedingsonvarioustopicsrelatedtohisresearchparadigm.

BudhadityaBiswasobtainedhisBEEandMEEfromUniversityofKalyani,NadiaandBengalEngineeringandScienceUniversity(BESU),Shibpur,intheyears2002and2006respectively.HestartedhiscareerasalecturerinHaldiaInstituteofTechnology,Haldia,in2006.Atpresent,heisworkingasAssistantProfessorattheDepartmentofElectricalEngineeringinRCCInstituteofInformationTechnology,Kolkata.Hehasbeenteachingforover6yearsandhisareasofinterestincludepowersystems,especiallythedesignofmicrocontroller-based numerical adaptive relay, digital instrumentation, and dataacquisition. He has to his credit publications in international and national conferenceproceedingsonvarioustopicsrelatedtohisresearchdomain.

Santanu Das obtained his BEE and MEE from Bengal Engineering and ScienceUniversity, Howrah, West Bengal. He has submitted his PhD thesis (in electricalengineering)toJadavpurUniversity,Kolkata,forevaluation.Earlier,Prof.Dasworkedat

Asansol Engineering College, Asansol, as Lecturer. Presently, he holds the post ofAssociate Professor andHead,Department ofElectricalEngineeringHaldia Institute ofTechnology, Haldia. He has published more than 20 research papers in internationaljournalsandconferenceproceedingsontopicsrelatedtohisresearchdomains.Hiscurrentfields of research interest include fault diagnosis and condition monitoring of electricmotors,PLCandmicrocontroller-basedmotioncontrol,powerelectronicsanddrives.

ChiranjibKoleyobtainedhisB.TechfromHIT,Haldia,M.TechfromIITDelhiandPhDfrom JadavpurUniversity,Kolkata.He received theEFIPScholarship in 2001 from theGovernment of India. Presently, he is Associate Professor in Department of ElectricalEngineering,NationalInstituteofTechnology,Durgapur,WestBengal.Hiscurrentareasof interest include signal processing, machine learning, and measurement andinstrumentation.Hehaspublishedextensively innationalandinternational journals,andconferenceproceedingsonvarioustopicsrelatedtohisresearchareas.

ElectricalandElectronicsMeasurementsandInstrumentation

PrithwirajPurkaitProfessor

DepartmentofElectricalEngineeringand

Dean,SchoolofEngineering

HaldiaInstituteofTechnology

Haldia,WestBengal

BudhadityaBiswasAssistantProfessor

DepartmentofElectricalEngineering

RCCInstituteofInformationTechnology

Kolkata,WestBengal

SantanuDasAssociateProfessor

DepartmentofElectricalEngineering

HaldiaInstituteofTechnology

Haldia,WestBengal

ChiranjibKoleyAssociateProfessor

ElectricalEngineeringDepartment

NationalInstituteofTechnology(NIT)Durgapur

Durgapur,WestBengal

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ContentsPreface

GuidedTour

1.ConceptofMeasurementSystems1.1Introduction

1.2FundamentalandDerivedUnits

1.3StandardsandtheirClassifications

1.4MethodsofMeasurement

1.5MeasurementSystemanditsElements

1.6ClassificationofInstruments

1.7DefinitionsofSomeStaticCharacteristics

1.8MeasurementofErrors

1.9LoadingEffects

Exercise

2.AnalogMeters2.1Introduction

2.2ClassificationofAnalogInstruments

2.3PrincipleofOperation

2.4OperatingTorques

2.5ConstructionalDetails

2.6PermanentMagnetMovingCoilInstrument

2.7ExtensionofRangeofPMMCInstruments

2.8Moving-IronInstruments

2.9Electrodynamometer-TypeInstruments

2.10ElectrostaticInstruments

2.11Induction-typeInstruments

2.12ElectrothermalInstruments

2.13Rectifier-typeInstruments

2.14TruermsVoltmeter

2.15ComparisonbetweenDifferentTypesofInstruments

Exercise

3.InstrumentTransformers3.1Introduction

3.2AdvantagesofInstrumentTransformers

3.3CurrentTransformers(CT)

3.4TheoryofCurrentTransformers

3.5ErrorsIntroducedbyCurrentTransformers

3.6OperationalCharacteristicsofCurrentTransformers

3.7DesignandConstructionalFeaturesofCurrentTransformers

3.8PrecautionsinUseofCurrentTransformer

3.9PotentialTransformers(PT)

3.10TheoryofPotentialTransformers

3.11ErrorsIntroducedbyPotentialTransformers

3.12OperationalCharacteristicsofPotentialTransformers

3.13DesignandConstructionalFeaturesofPotentialTransformers

3.14DifferencesbetweenCTandPT

Exercise

4.MeasurementofResistance4.1Introduction

4.2MeasurementofMediumResistances

4.3MeasurementofLowResistances

4.4MeasurementofHighResistances

4.5LocalisationofCableFaults

Exercise

5.Potentiometers5.1Introduction

5.2ABasicdcPotentiometer

5.3Crompton’sdcPotentiometers

5.4ApplicationsofdcPotentiometers

5.5ACPotentiometers

5.6ClassificationofACPotentiometers

5.7AdvantagesandDisadvantagesofACPotentiometers

5.8ApplicationsofACPotentiometer

Exercise

6.ACBridges6.1Introduction

6.2SourcesandDetectorsinACBridges

6.3GeneralBalanceEquationforFour-ArmBridge

6.4MeasurementofSelf-Inductance

6.5MeasurementofCapacitance

6.6MeasurementofFrequency

6.7WagnerEarthingDevice

Exercise

7.PowerMeasurement7.1Introduction

7.2PowerMeasurementindcCircuits

7.3PowerMeasurementinacCircuits

7.4ElectrodynamometerTypeWattmeter

7.5Induction-typeWattmeter

7.6PowerMeasurementinPolyphaseSystems

7.7PowerMeasurementinThree-PhaseSystems

7.8ReactivePowerMeasurements

7.9PowerMeasurementwithInstrumentTransformers

Exercise

8.MeasurementofEnergy8.1Introduction

8.2Single-PhaseInduction-typeEnergyMeter

8.3ErrorsinInduction-typeEnergyMetersandTheirCompensation

8.4TestingofEnergyMeters

Exercise

9.CathodeRayOscilloscope9.1Introduction

9.2BlockDiagramofaCathodeRayTube(CRT)

9.3ElectrostaticDeflection

9.4TimeBaseGenerator

9.5VerticalInputandSweepGeneratorSignalSynchronisation

9.6MeasurementofElectricalQuantitieswithCRO

9.7MeasurementofVoltageandCurrent

9.8MeasurementofFrequency

9.9MeasurementofPhaseDifference

9.10SamplingOscilloscope

9.11StorageOscilloscope

9.12Multi-InputOscilloscopes

9.13FrequencyLimitationofCRO

Exercise

10.ElectronicInstruments10.1Introduction

10.2MeritsandDemeritsofDigitalInstrumentsoverAnalogOnes

10.3PerformanceCharacteristicsofDigitalMeters

10.4DigitalMultimeter

10.5DigitalFrequencyMeter

10.6DigitalVoltmeters(DVMs)

10.7SignalGenerators

Exercise

11.SensorsandTransducers11.1Introduction

11.2ElectricalTransducers

11.3LinearVariabledifferentialTransformer(LVDT)

11.4StrainGauges

11.5ElectromagneticFlowMeter

11.6TemperatureTransducers

11.7PressureMeasurement

Exercise

12.MagneticMeasurements12.1Introduction

12.2TypesofMagneticMeasurements

12.3TheBallisticGalvanometer

12.4Fluxmeter

12.5UsesofBallisticGalvanometerandFluxmeter

12.6MeasurementofFluxDensity

12.7MeasurementofMagnetisingForce(H)

12.8DeterminationofMagnetisingCurve

12.9DeterminationofHysteresisLoop

12.10TestingofSpecimensintheFormofRodsorBars

12.11Permeameters

12.12MeasurementofMagneticLeakage

12.13MagneticTestingwithAlternatingCurrent

12.14BridgeandacPotentiometerMethods

12.15MagneticShielding

Exercise

13.SignalGeneratorsandAnalysers13.1Introduction

13.2Oscillators

13.3HartleyOscillator

13.4ColpittsOscillators

13.5TheRCOscillator

13.6WienBridgeOscillators

13.7CrystalOscillators

13.8PierceOscillator

13.9MicroprocessorClocks

13.10SquareWaveandPulseGenerators

13.11TriangularWaveGenerator

13.12Sine-WaveGenerator

13.13FunctionGenerators

13.14RFSignalGenerator

13.15SweepFrequencyGenerator

13.16WaveAnalyser

13.17HarmonicDistortionAnalysers

13.18SpectrumAnalyser

Exercise

14.DataAcquisitionSystem14.1Introduction

14.2BasicComponentsofDataAcquisitionSystems

14.3ComponentsofaTypicalPC-basedDataAcquisitionSystem

14.4AnalogInputSubsystem

14.5AnalogOutputSubsystem

14.6DigitalInputandOutputSubsystem

14.7IEEE488Interface

Exercise

15.Recording,StorageandDisplayDevices15.1Introduction

15.2AnalogRecorders

15.3DigitalRecorders

15.4DisplaySystem

Exercise

16.ProgrammableLogicControllers16.1Introduction

16.2AdvantagesofPLCs

16.3TheControlProgram

16.4FunctionofeachPartinPLC

16.5HardwareofPLC

16.6SystemAddressing

16.7PLCOperationandProgramScan

16.8ImplementationofControlProgramsinPLC

16.9MoreinLadderLogic

Exercise

17.MicrowaveandRFMeasurement17.1IntroductiontoRFandWirelessCommunicationSystem

17.2RadioFrequencyandMicrowaveSpectralAnalysis

17.3RadioFrequencySpectrumAnalyser

17.4RFScalarandVectorNetworkAnalyser

17.5Modulation

17.6CommunicationSystems

17.7RFVoltageandPowerMeasurement

Exercise

18.FibreOpticMeasurements18.1Introduction

18.2HowdoesanOpticalFibreWork?

18.3SourcesandDetectors

18.4FibreOpticPowerMeasurement

Exercise

AppendixATableofSIUnits

AppendixBNumberSystems

AppendixCWestenFrequencyMeter

SolvedSampleQuestionPapers

Index

PrefaceOverviewThis book can be used as a textbook for the course in electrical and electronicsmeasurementsandinstrumentation.Itpresentsacomprehensivetreatmentofthesubjectofelectrical and electronics measurements and instrumentation as taught to theundergraduatestudentsofB.Tech/BEinElectricalEngineering,ElectricalandElectronicsEngineering, Instrumentation Engineering, and allied branches. The book thus aims atmaintaining balance between these diverse fields of engineering disciplines by drawingexamplesfromvariousapplications.Theprerequisiteonthepartofthereaderisthatheorsheshouldhavehadintroductorycoursesonlinearalgebra,basiccalculus,vector/phasoranalysis, transform theory, circuit analysis and elementarymechanics. For the students’interest,appendicesonnumbersystemsandunitconversionsareaddedattheend.

AimWhile conceptualising the text, the authors felt that the scope andmethod of treatmentcould, with advantage, be augmented to suit the requirements of various branches ofengineering.Owingtotherapidadvancementstakingplaceinmodernelectricalandalliedindustries, and their interconnection with power systems, the subject of electrical andelectronicsmeasurementsisgaininganever-increasingimportance.

AbouttheBookAs a subject of study, electrical measurement is one of the more traditional fields ofelectrical and allied engineering disciplines. However, with progress in technology andmanufacturingexpertise,measurementsofphysicalparametershavegainednewheightsintermsofstate-of-the-artconceptsandtechnologies.Thisbookaimsatbridgingtraditionalconcepts with modern technologies of electrical and electronics measurements andinstrumentation.

The text is designed for an undergraduate course in electrical and electronicsmeasurements. Since the basic concepts cut across disciplines—such as electrical,mechanical, electronics, instrumentation and control engineering—this book presents aproper balance between theoretical and analytical approach, as well as practicalillustrations along with computational approach for solving various kinds of numericalproblems. Some of the subjects dealt with are essentially mathematical in nature, andcannot be treated otherwise, but themathematics throughout the bookhas been kept assimpleaspossiblesothatitisfollowedeasilybymostreaders.Thetheoryofmostofthemeasurement techniques and measuring instruments has been dealt with in sufficientdetail,butinmostcasesconciseformshavebeenusedforsuchtheoreticaldiscussions,sothat readers may skip them, if desired, and consider only the resulting expressions.Photographs of real systems have been used in places where schematic representationneededtobeaugmented.

Themainthemeofthisbookhasbeentocatertoundergraduatestudents.Alltopicsindifferentchaptershavebeendevelopedwithampleandadequatedetailwithoutsubjectingstudents to unwanted complicacies.As a textbook, this contribution is expected to help

students not only in building up their knowledge of physical concepts of the systemsdescribed,butalsoasareadyandconcisereference.

SalientFeaturesCoveragebridgestraditionalconceptswithmoderntechnologiesinthesubjectarea

Comprehensivediscussionsonelectronicmeasurementsystemsandrelatedcomponentsincludinganalysers,dataacquisitionsystems,etc.

Special-purposemeasurementsandapplicationssuchasmagneticmeasurementsandfibreopticmeasurementscovered

DedicatedchapteronSensorsandTransducers

Inclusionofreal-lifephotographstoaugmentschematicdiagramswherevernecessary

Solvedquestionpapersfrom9universities

Richpedagogy

•Illustrations:400

•SolvedExamples:100

•Objective-typeQuestions:236

•Short-Answer-TypeQuestions:164

•Long-Answer-TypeQuestions:119

ChapterOrganisationThe entire text is organised into 18 chapters. Chapter organisation has been primarilybased on the electrical and electronicmeasurement syllabi inBE/B.Tech undergraduatecoursesofuniversitiesaroundthecountry.Theoutlineofthebookcanbeorganisedinthefollowingfourmajorparts:

1. Generalconceptsofmeasurement2. Electricalmeasurementtechniquesandclassicalmeasuringinstruments3. Modernmeasurementtechniquesandinstruments4. Briefconceptsofsensorsandtransducers5. Electronicmeasurementsystemsandrelatedcomponentsincludingsignalgenerators,

analysers, data acquisition systems, storage anddisplaydevices andprogrammablelogiccontrollers

6. Applications of the concepts of electrical and electronic measurement systems inspecial-purpose measurements including magnetic measurements, fibre opticmeasurements,RFandmicrowavemeasurements.

Within this framework,amore in-depthbreakdowncanbeobtainedfromthe tableofcontents.Detailinginthetableofcontentwillbeusefulfortheinstructorsandstudentstoselectpartsof the text thatmightbeappropriate for thespecificneedathand. Inplaceswhereillustrationsandexplanationshavebeensummarised,theadequatelistofreferenceattheendwillenableenthusiasticreaderstoprobefurther.Thefluidflowoftextdealing

withdifferenttopicshasbeenwellthoughtoutbytheauthorswhohaveseveralyearsofexperience in teaching the subject directly to undergraduate students. Illustrations,examples,questions,highlights,exercises,numericalproblemsareextremelyrelevantandappropriate for studentsaswellas instructors.Themainstrengthof thebook thus is itsstrong focus towards students’ readability and understanding with the scope forindependentstudyandproblem-solvingskilldevelopment.Theauthorsareconfidentthatthedepthofthisbookhasbeenjudiciouslydevelopedsothatstudentsnotonlytreatthisasatextbook,but,inaddition,canalsogatherenoughpracticalandtheoreticalknowledgetoappearinnational-levelcompetitiveexaminationsandinterviews.

WebSupplementsThe text is supplemented with an exhaustive Online Learning Center, which can beaccessedathttps://www.mhhe.com/purkait/eemi

ItcontainsPowerPointlectureslidesandtheSolutionManual.

AcknowledgementsWearethankfultoallthosewhohavedirectlyorindirectlyhelpedusinbringingoutthisbook. First, we would like to thank the reviewers who through various instances haveprovidedcommentsthathaveshapedthisbook.Theirnamesaregivenbelow:

NileshChaurasia SriVaishnavInstituteofTechnologyandScience,Indore,MadhyaPradesh

SaurabhBasu GLAUniversity,Mathura,UttarPradesh

PraveenTiwari IMITCollege,Meerut,UttarPradesh

SBLSeksena NationalInstituteofTechnology(NIT)Jamshedpur,Jharkhand

SuvenduNaryanMishra VeerSurendraSaiUniversityofTechnology(VSSUT),Burla,Odisha

SamirEkbote DattaMegheCollegeofEngineering,NaviMumbai,Mumbai,Maharashtra

VGSarode XavierInstituteofEngineering,Mumbai,Maharashtra

CDKapse WatmullInstituteofEngineeringandComputerTechnology,Mumbai,Maharashtra

RubanN VelloreInstituteofTechnology(VIT)University,Vellore,TamilNadu

SubhashKrishnamoorthy NationalInstituteofTechnology(NIT),Calicut,TamilNadu

RSVaradhan ICFAIInstituteofTechnology&Science,Hyderabad,AndhraPradesh

KESrinivasMurthy SriVenkateswaraInstituteofTechnology,Ananthapur,AndhraPradesh

CHMadhuri SriInduCollegeofEngineering,Hyderabad,AndhraPradesh

ThanksarealsoduetothestaffatMcGrawHillEducation(India)forbringingoutthisbookinsuchashorttime.Finally,wewouldliketothankourrespectivefamilymemberswhose patience and lovewas a source of encouragement during the preparation of thismanuscript.

Suggestionsforimprovementswillalwaysbewelcome.

PRITHWIRAJPURKAIT

BUDHADITYABISWAS

SANTANUDAS

CHIRANJIBKOLEY

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1.1 INTRODUCTION

Measurement is the act, or the result, of a quantitative comparison between a givenquantityandaquantityofthesamekindchosenasaunit.Theresultofthemeasurementisexpressed by a pointer deflection over a predefined scale or a number representing theratiobetweentheunknownquantityandthestandard.Astandardisdefinedasthephysicalpersonification of the unit of measurement or its submultiple or multiple values. Thedevice or instrument used for comparing the unknown quantity with the unit ofmeasurement or a standard quantity is called ameasuring instrument. The value of theunknownquantitycanbemeasuredbydirectorindirectmethods.Indirectmeasurementmethods, the unknown quantity is measured directly instead of comparing it with astandard.Examplesofdirectmeasurementarecurrentbyammeter,voltagebyvoltmeter,resistancebyohmmeter,powerbywattmeter,etc. In indirectmeasurementmethods, thevalue of the unknown quantity is determined by measuring the functionally relatedquantityandcalculatingthedesiredquantityratherthanmeasuringitdirectly.Supposetheresistanceas(R)ofaconductorcanbemeasuredbymeasuringthevoltagedropacrosstheconductor and dividing the voltage (V) by the current (I) through the conductors, byOhm’s

1.2 FUNDAMENTALANDDERIVEDUNITS

At the time of measuring a physical quantity, we must express the magnitude of thatquantityintermsofaunitandanumericalmultiplier,i.e.,

Magnitudeofaphysicalquantity=(Numericalratio)×(Unit)

Thenumericalratioisthenumberoftimestheunitoccursinanygivenamountofthesamequantityand,therefore,iscalledthenumberofmeasures.Thenumericalratiomaybecallednumericalmultiplier.However,inmeasurements,weareconcernedwithalargenumber of quantities which are related to each other, through established physicalequations, and therefore the choice of size of units of these quantities cannot be donearbitrarily and independently. In thisway,we can avoid the use of awkward numericalconstants when we express a quantity of one kind which has been derived frommeasurementofanotherquantity.

Inscienceandengineering,twokindsofunitsareused:

•Fundamentalunits

•Derivedunits

Thefundamentalunitsinmechanicsaremeasuresoflength,massandtime.Thesizesofthe fundamental units, whether foot or metre, pound or kilogram, second or hour arearbitraryandcanbeselectedtofitacertainsetofcircumstances.Sincelength,massandtimeare fundamental tomostotherphysicalquantitiesbesides those inmechanics, theyarecalled theprimary fundamental units.Measures of certain physical quantities in thethermal,electricalandilluminationdisciplinesarealsorepresentedbyfundamentalunits.These units are used only when these particular classes are involved, and they maythereforebedefinedasauxiliaryfundamentalunits.

All other units which can be expressed in terms of the fundamental units are calledderivedunits.Everyderivedunitoriginatesfromsomephysicallawdefiningthatunit.Forexample,thearea(A)ofarectangleisproportionaltoitslength(l)andbreadth(b),orA=lb. if themetre has been chosen as the unit of length then the area of a rectangle of 5metresby7metresis35m2.Notethatthenumbersofmeasurearemultipliedaswellastheunits.Thederivedunitforarea(A)isthenthemetresquare(m2).

Aderivedunit isrecognizedbyitsdimensions,whichcanbedefinedas thecompletealgebraicformulaforthederivedunit.Thedimensionalsymbolsforthefundamentalunitsof length,mass and time areL,M andT respectively.The dimensional symbol for thederivedunitofareaisL2andthatforvolumeisL3.Thedimensionalsymbolfortheunitof force isMLT ,which follows from thedefining equation for force.Thedimensionalformulasofthederivedunitsareparticularlyusefulforconvertingunitsfromonesystemto another. For convenience, some derived units have been given new names. Forexample,thederivedunitofforceintheSIsystemiscalledthenewton(N),insteadofthedimensionallycorrectkg-m/s2.

1.3 STANDARDSANDTHEIRCLASSIFICATIONS

Astandardofmeasurementisaphysicalrepresentationofaunitofmeasurement.Aunitisrealisedbyreferencetoanarbitrarymaterialstandardortonaturalphenomenaincludingphysical and atomic constants. The term ‘standard’ is applied to a piece of equipmenthavingaknownmeasureofphysicalquantity.Forexample,thefundamentalunitofmassintheSIsystemisthekilogram,definedasthemassofthecubicdecimetreofwateratitstemperatureofmaximumof4°C.Thisunitofmassisrepresentedbyamaterialstandard;themassoftheinternationalprototypekilogramconsistingofaplatinum–iridiumhollowcylinder.This unit is preserved at the InternationalBureau ofWeights andMeasures atSevres, nearParis, and is thematerial representation of the kilogram.Similar standardshavebeendevelopedforotherunitsofmeasurement,includingfundamentalunitsaswellasforsomeofthederivedmechanicalandelectricalunits.

Theclassificationsofstandardsare

1.Internationalstandards

2.Primarystandards

3.Secondarystandards

4.Workingstandards

5.Currentstandards

6.Voltagestandards

7.Resistancestandards

8.Capacitancestandards

9.Timeandfrequencystandards

1.3.1InternationalStandardsTheinternationalstandardsaredefinedbyinternationalagreement.Theyrepresentcertainunitsofmeasurement to the closestpossible accuracy thatproductionandmeasurementtechnology allow. International standards are periodically checked and evaluated byabsolutemeasurementsintermsofthefundamentalunits.ThesestandardsaremaintainedattheInternationalBureauofWeightsandMeasuresandarenotavailabletotheordinaryuserofmeasuringinstrumentsforpurposesofcomparisonorcalibration.Table1.1showsbasicSIUnits,QuantitiesandSymbols.

Table1.1BasicQuantities,SIUnitsandSymbols

1.3.2PrimaryStandardsTheprimarystandardsaremaintainedbynationalstandardslaboratoriesindifferentplacesof theworld.TheNationalBureauofStandards(NBS) inWashington is responsibleformaintenance of the primary standards in North America. Other national laboratoriesinclude the National Physical Laboratory (NPL) in Great Britain and the oldest in theworld, the Physikalisch Technische Reichsanstalt in Germany. The primary standards,again representing the fundamental units and some of the derived mechanical andelectrical units, are independently calibrated by absolute measurements at each of thenational laboratories. The results of thesemeasurements are comparedwith each other,leading to a world average figure for the primary standard. Primary standards are notavailableforuseoutside thenational laboratories.Oneof themainfunctionsofprimarystandardsistheverificationandcalibrationofsecondarystandards.

1.3.3SecondaryStandardsSecondarystandardsarethebasicreferencestandardsusedintheindustrialmeasurementlaboratories.These standards aremaintainedby theparticular involved industry andare

checked locally against other reference standards in the area. The responsibility formaintenanceandcalibrationrestsentirelywiththeindustrial laboratoryitself.Secondarystandards are generally sent to the national standards laboratory on a periodic basis forcalibrationandcomparisonagainst theprimary standards.Theyare then returned to theindustrial user with a certification of their measured value in terms of the primarystandard.

1.3.4WorkingStandardsWorkingstandardsaretheprincipletoolsofameasurementlaboratory.Theyareusedtocheck and calibrate general laboratory instruments for accuracy and performance or toperformcomparisonmeasurementsinindustrialapplications.Amanufacturerofprecisionresistances,forexample,mayuseastandardresistorinthequalitycontroldepartmentofhis plant to checkhis testing equipment. In this case, themanufacturer verifies that hismeasurementsetupperformswithintherequiredlimitsofaccuracy.

1.3.5CurrentStandardThefundamentalunitofelectriccurrent(Ampere)isdefinedbytheInternationalSystemof Units (SI) as the constant current which, if maintained in two straight parallelconductorsofinfinitelengthandnegligiblecircularcrosssectionplaced1meterapartinvacuum,willproducebetweentheseconductorsaforceequalto2×10-7newtonpermeterlength.Earlymeasurementsoftheabsolutevalueoftheampereweremadewithacurrentbalancewhichmeasuredtheforcebetweentwoparallelconductors.Thesemeasurementswere rather crude and the need was felt to produce a more practical and reproduciblestandard for the national laboratories. By international agreement, the value of theinternationalamperewasbasedontheelectrolyticdepositionofsilverfromasilvernitratesolution.Theinternationalamperewasthendefinedasthatcurrentwhichdepositssilverat the rate of 1.118 mg/s from a standard silver nitrate solution. Difficulties wereencountered in the exact measurement of the deposited silver and slight discrepanciesexisted between measurements made independently by the various National StandardLaboratories.Later,theinternationalamperewassupersededbytheabsoluteampereanditisnowthefundamentalunitofelectriccurrentintheSIandisuniversallyacceptedbyinternationalagreement.

1.3.6VoltageStandardInearlytimes,thestandardvoltwasbasedonanelectrochemicalcellcalledthesaturatedstandardcellorsimplystandardcell.Thesaturatedcellhastemperaturedependence,andthe output voltage changes about -40 µV/°C from the nominal of 1.01858 volt. Thestandard cell suffers from this temperature dependence and also from the fact that thevoltageisafunctionofachemicalreactionandnotrelateddirectlytoanyotherphysicalconstants.In1962,basedontheworkofBrianJosephson,anewstandardforthevoltwasintroduced. A thin-film junction is cooled to nearly absolute zero and irradiated withmicrowave energy. A voltage is developed across the junction, which is related to theirradiatingfrequencybythefollowingrelationship:

where,h=Planck’sconstant=6.63×10-34J-s

e=chargeofanelectron=1.602×10-19C

f=frequencyofthemicrowaveirradiation

In Eq. (1.1), the irradiation frequency is the only variable, thus the standard volt isrelated to the standard of time/frequency.When themicrowave irradiating frequency islockedtoanatomicclockorabroadcastfrequencystandardsuchasWWVB,theaccuracyofthestandardvolt,includingallofthesysteminaccuracies,isonepartin108.

Themajormethod of transferring the volt from the standard based on the Josephsonjunction to secondary standards used for calibration of the standard cell. This device iscalled the normal or saturatedWeston cell. TheWeston cell has a positive electrode ofmercuryandanegativeelectrodeofcadmiumamalgam(10%cadmium).Theelectrolyteis a solution of cadmium sulfate. These components are placed in an H-shaped glasscontainerasshowninFigure1.1.

Figure1.1Standardcellofemfof1.0183voltat20°C(Courtesy,physics.kenyon.edu)

1.3.7ResistanceStandardIntheSIsystem,theabsolutevalueofohmisdefinedintermsofthefundamentalunitsoflength, mass and time. The absolute measurement of the ohm is carried out by theInternationalBureauofWeightsandMeasuresinSevresandalsobythenationalstandardlaboratories,whichpreserveagroupofprimaryresistancestandards.TheNBSmaintainsa group of those primary standards (1 ohm standard resistors) which are periodicallycheckedagainsteachotherandareoccasionallyverifiedbyabsolutemeasurements.Thestandardresistorisacoilofwireofsomealloylikemanganinwhichhasahighelectricalresistivityandalowtemperaturecoefficientofresistance.Theresistancecoilismountedin a double walled sealed container as shown in Figure 1.2 to prevent changes in

resistanceduetomoistureconditionsintheatmosphere.Withasetoffourorfive1-ohmresistorsinthistype,theunitresistancecanberepresentedwithaprecisionofafewpartsin107overseveralyears.

Figure1.2Resistancestandard

Secondary standards and working standards are available from some instrumentmanufacturesinawiderangeofvalues,usuallyinmultiplesof10ohms.Thesestandardresistorsaresometimescalledtransferresistorandaremadeofalloyresistancewire,suchasmanganinorEvanohm.Theresistancecoilofthetransferresistorissupportedbetweenpolyesterfilmstoreducestressesonthewireandtoimprovethestabilityoftheresistor.Thecoilisimmersedinmoisturefreeoilandplacedinasealedcontainer.Theconnectionsto thecoilare silver soldered,and the terminalhooksaremadeofnickel-platedoxygenfreecopper.Thetransferresistorischeckedforstabilityandtemperaturecharacteristicsatitsratedpowerandaspecifiedoperatingtemperature(usually25°C).Acalibrationreportaccompanying the resistor specifies its traceability toNBSstandards and includes theaand β temperature coefficients. Although the selected resistance wire provides almostconstantresistanceoverafairlywidetemperaturerange,theexactvalueoftheresistanceatanytemperaturecanbecalculatedfromtheformula

Rt=R25°C+α(t—25)+β(t—25)2

whereRt=resistanceattheambienttemperaturet

R25°C=reisitanceat25°c

α,β=temperaturecoefficients

Temperaturecoefficientaisusuallylessthan10×10- ,andcoefficientβliesbetween-3×10-to-6×10-7.Thismeansthatachangeintemperatureof10°Cfromthespecifiedreferencetemperatureof25°Cmaycauseachangeinresistanceof30to60ppmfromthenominalvalue.

1.3.8CapacitanceStandardMany electrical and magnetic units may be expressed in terms of these voltage and

resistancestandardssincetheunitofresistanceisrepresentedbythestandardresistorandthe unit of voltage by standardWeston cell. The unit of capacitance (the farad) can bemeasuredwithaMaxwelldccommutatedbridge,wherethecapacitanceiscomputedfromtheresistivebridgearmsandthefrequencyofthedccommutation.ThebridgeisshowninFigure1.3.CapacitorC is alternately charged and discharged through the commutatingcontactandresistorR.BridgebalanceisobtainedbyadjustingtheresistanceR3,allowingexact determination of the capacitance value in terms of the bridge arm constants andfrequency of commutation. Although the exact derivation of the expression forcapacitanceintermsoftheresistancesandthefrequencyisratherinvolved,itmaybeseenthatthecapacitorcouldbemeasuredaccuratelybythismethod.Sincebothresistanceandfrequency can be determined very accurately, the value of the capacitance can bemeasured with great accuracy. Standard capacitors are usually constructed frominterleavedmetalplateswithairasthedielectricmaterial.Theareaoftheplatesandthedistance between them must be known very accurately, and the capacitance of the aircapacitorcanbedeterminedfromthesebasicdimensions.TheNBSmaintainsabankofaircapacitorsasstandardsandusesthemtocalibratethesecondaryandworkingstandardsofmeasurementlaboratoriesandindustrialusers.

Figure1.3Commutateddcmethodformeasuringcapacitance

1.3.9TimeStandardandFrequencyStandardIn early centuries the time reference usedwas the rotation of the earth around the sunaboutitsaxis.Later,preciseastronomicalobservationshaveshownthattherotationoftheearth around the sun is very irregular, owing to secular and irregular variations in therotationalspeedoftheearth.Sothetimescalebasedonthisapparentsolartimehadtobechanged.Meansolartimewasthoughttogiveamoreaccuratetimescale.Ameansolardayistheaverageofalltheapparentdaysintheyear.Ameansolarsecondisthenequalto1/86400ofthemeansolarday.Themeansolarsecondisstillinappropriatesinceitisbasedontherotationoftheearthwhichisnon-uniform.

Intheyear1956,theephemerissecondhasbeendefinedbytheInternationalBureauofWeights andMeasures as the fraction 1/31556925.99747 of the tropical year for 1900January01at12hET(EphemerisTime),andadoptedasthefundamentalinvariableunitof time.Adisadvantageof theuseof theephemeris second is that it canbedeterminedonlyseveralyearsinarrearsandthenonlyindirectly,byobservationsofthepositionsofthesunandthemoon.Forphysicalmeasurements,theunitoftimeintervalhasnowbeendefinedintermsofanatomicstandard.Theuniversalsecondandtheephemeris second,however, will continue to be used for navigation, geodetic surveys and celestialmechanics.TheatomicunitsofthetimewasfirstrelatedtoUT(UniversalTime)butwas

laterexpressedintermsofET.TheInternationalCommitteeofWeightsandMeasureshasnowdefinedthesecondintermsoffrequencyofthecesiumtransition,assigningavalueof9192631770Hztothehyperfinetransitionofthecesiumatomunperturbedbyexternalfields.Theatomicdefinitionofsecondrealisesanaccuracymuchgreaterthanthatachievedby

astronomicalobservations, resulting inamoreuniformandmuchmoreconvenient timebase. Determinations of time intervals can now be made in a few minutes to greateraccuracythanwaspossiblebeforeinastronomicalmeasurementsthattookmanyyearstocomplete.Anatomicclockwithaprecisionexceeding1µsperday is inoperationasaprimary frequency standard at the NBS. An atomic time scale, designated NBS-A, ismaintainedwiththisclock.

Time and frequency standards are unique in that they may be transmitted from theprimary standard at NBS to other locations via radio or television transmission. EarlystandardtimeandfrequencytransmissionwereintheHighFrequency(HF)portionoftheradiospectrum,but these transmissionssufferedfromDopplershiftsdue to thefact thatradio propagation was primarily ionospheric. Transmission of time and frequencystandards via low frequency and very low frequency radio reduces this Doppler shiftbecausethepropagationisstrictlygroundwave.TwoNBSoperatedstations,WWVLandWWVB, operate 20 and 60 kHz, respectively, providing precision time and frequencytransmissions.

1.4 METHODSOFMEASUREMENT

Asdiscussedabove,themeasurementmethodscanbeclassifiedas

•Directcomparisonmethods

•Indirectcomparisonmethods

1.4.1DirectComparisonMethodsIn direct measurement methods, the unknown quantity is measured directly. Directmethods ofmeasurement are of two types, namely,deflectionmethods and comparisonmethods.

Indeflectionmethods,thevalueoftheunknownquantityismeasuredbythehelpofameasuringinstrumenthavingacalibratedscaleindicatingthequantityundermeasurementdirectly,suchasmeasurementofcurrentbyanammeter.

In comparison methods, the value of the unknown quantity is determined by directcomparison with a standard of the given quantity, such as measurement of emf bycomparisonwiththeemfofastandardcell.Comparisonmethodscanbeclassifiedasnullmethods, differential methods, etc. In null methods of measurement, the action of theunknownquantityupontheinstrumentisreducedtozerobythecounteractionofaknownquantityofthesamekind,suchasmeasurementofweightbyabalance,measurementofresistance,capacitance,andinductancebybridgecircuits.

1.4.2IndirectComparisonMethodsInindirectmeasurementmethods,thecomparisonisdonewithastandardthroughtheuseofacalibratedsystem.Thesemethodsformeasurementareusedinthosecaseswherethedesiredparameter tobemeasured isdifficult tobemeasureddirectly,but theparameterhasgotsomerelationwithsomeotherrelatedparameterwhichcanbeeasilymeasured.

Forinstance,theeliminationofbacteriafromsomefluidisdirectlydependentuponitstemperature.Thus, thebacteriaeliminationcanbemeasuredindirectlybymeasuringthetemperatureofthefluid.

In indirect methods of measurement, it is general practice to establish an empiricalrelationbetweentheactualmeasuredquantityandthedesiredparameter.

ThedifferentmethodsofmeasurementaresummarisedwiththehelpofatreediagraminFigure1.4.

Figure1.4Differentmethodsofmeasurement

1.5 MEASUREMENTSYSTEMANDITSELEMENTS

Ameasurementsystemmaybedefinedasasystematicarrangementforthemeasurementordeterminationofanunknownquantityandanalysisofinstrumentation.Thegeneralisedmeasurementsystemanditsdifferentcomponents/elementsareshowninFigure1.5.

Figure1.5Generalisedmeasurementsystem

The operation of a measurement system can be explained in terms of functional

elementsofthesystem.Everyinstrumentandmeasurementsystemiscomposedofoneormore of these functional elements and each functional element is made of distinctcomponents or groups of components which performs required and definite steps inmeasurement.Thevariouselementsarethefollowing:

1.5.1PrimarySensingElementsIt is an element that is sensitive to themeasured variable. The physical quantity undermeasurement, called the measurand, makes its first contact with the primary sensingelementofameasurement system.Themeasurand isalwaysdisturbedby theactof themeasurement,butgoodinstrumentsaredesignedtominimisethiseffect.Primarysensingelementsmayhaveanon-electricalinputandoutputsuchasaspring,manometerormayhaveanelectricalinputandoutputsuchasarectifier.Incasetheprimarysensingelementhasanon-electricalinputandoutput,thenitisconvertedintoanelectricalsignalbymeansofatransducer.Thetransducerisdefinedasadevice,whichwhenactuatedbyoneformofenergy,iscapableofconvertingitintoanotherformofenergy.

Many a times, certain operations are to be performedon the signal before its furthertransmissionsothat interferingsourcesareremovedinorderthat thesignalmaynotgetdistorted. The process may be linear such as amplification, attenuation, integration,differentiation, addition and subtraction or nonlinear such as modulation, detection,sampling,filtering,choppingandclipping,etc.Theprocessiscalledsignalconditioning.Soasignalconditionerfollowstheprimarysensingelementortransducer,asthecasemaybe. The sensing element senses the condition, state or value of the process variable byextractingasmallpartofenergyfromthemeasurand,andthenproducesanoutputwhichreflectsthiscondition,stateorvalueofthemeasurand.

1.5.2VariableConversionElementsAfter passing through the primary sensing element, the output is in the form of anelectricalsignal,maybevoltage,current,frequency,whichmayormaynotbeacceptedtothe system. For performing the desired operation, it may be necessary to convert thisoutputtosomeothersuitableformwhileretainingtheinformationcontentoftheoriginalsignal.Forexample,iftheoutputisinanalogformandthenextstepofthesystemacceptsonly in digital form then an analog-to-digital converter will be employed. Manyinstrumentsdonotrequireanyvariableconversionunit,whilesomeothersrequiremorethanoneelement.

1.5.3ManipulationElementsSometimes it is necessary to change the signal level without changing the informationcontained in it for the acceptance of the instrument. The function of the variablemanipulationunitistomanipulatethesignalpresentedtoitwhilepreservingtheoriginalnature of the signal. For example, an electronic amplifier converts a small low voltageinputsignalintoahighvoltageoutputsignal.Thus,thevoltageamplifieractsasavariablemanipulation unit. Some of the instruments may require this function or some of theinstrumentsmaynot.

1.5.4DataTransmissionElements

The data transmission elements are required to transmit the data containing theinformation of the signal from one system to another. For example, satellites arephysicallyseparatedfromtheearthwherethecontrolstationsguidingtheirmovementarelocated.

1.5.5DataPresentationElementsThefunctionofthedatapresentationelementsistoprovideanindicationorrecordinginaformthatcanbeevaluatedbyanunaidedhumansenseorbyacontroller.Theinformationregarding measurand (quantity to be measured) is to be conveyed to the personnelhandling the instrument or the system for monitoring, controlling or analysis purpose.Such a devicemay be in the form of analog or digital format. The simplest form of adisplaydeviceisthecommonpanelmeterwithsomekindofcalibratedscaleandpointer.Incasethedataistoberecorded,recorderslikemagnetictapesormagneticdiscsmaybeused.Forcontrolandanalysispurpose,computersmaybeused.

Thestagesofa typicalmeasurementsystemaresummarisedbelowwiththehelpofaflowdiagraminFigure1.6.

Figure1.6Stepsofatypicalmeasurementsystem

1.6 CLASSIFICATIONOFINSTRUMENTS

Themeasuringinstrumentsmaybeclassifiedasfollows:

1.6.1AbsoluteandSecondaryInstruments

1.AbsoluteInstruments

The instruments of this type give the value of the measurand in terms of instrumentconstant and its deflection. Such instruments do not require comparisonwith any otherstandard.Theexampleofthistypeofinstrumentistangentgalvanometer,whichgivesthevalue of the current to be measured in terms of tangent of the angle of deflectionproduced, the horizontal component of the earth’s magnetic field, the radius and thenumberofturnsofthewireused.Rayleighcurrentbalanceandabsoluteelectrometerareotherexamplesofabsoluteinstruments.Absoluteinstrumentsaremostlyusedinstandardlaboratories and in similar institutions as standardising. The classification ofmeasuringinstrumentsisshowninFigure1.7.

Figure1.7Classificationofmeasuringinstruments

2.SecondaryInstruments

These instruments are so constructed that the deflection of such instruments gives themagnitude of the electrical quantity to be measured directly. These instruments arerequiredtobecalibratedbycomparisonwitheitheranabsoluteinstrumentorwithanothersecondaryinstrument,whichhasalreadybeencalibratedbeforetheuse.Theseinstrumentsaregenerallyusedinpractice.

Secondaryinstrumentsarefurtherclassifiedas

•Indicatinginstruments

•Integratinginstruments

•Recordinginstruments(i)IndicatingInstruments

Indicatinginstrumentsarethosewhichindicatethemagnitudeofanelectricalquantityatthetimewhenitisbeingmeasured.Theindicationsaregivenbyapointermovingoveracalibrated (pregraduated) scale. Ordinary ammeters, voltmeters, wattmeters, frequencymeters,powerfactormeters,etc.,fallintothiscategory.(ii)IntegratingInstruments

Integrating instruments are those whichmeasure the total amount of either quantity ofelectricity (ampere-hours) or electrical energy supplied over a period of time. Thesummation,givenbysuchaninstrument,istheproductoftimeandanelectricalquantityundermeasurement.Theampere-hourmetersandenergymetersfallinthisclass.(iii)RecordingInstruments

Recording instruments are thosewhichkeepa continuous recordof thevariationof themagnitudeofanelectricalquantitytobeobservedoveradefiniteperiodoftime.Insuchinstruments, the moving system carries an inked pen which touches lightly a sheet ofpaperwrappedoveradrummovingwithuniformslowmotioninadirectionperpendiculartothatofthedirectionofthepointer.Thus,acurveistracedwhichshowsthevariationsinthemagnitudeoftheelectricalquantityunderobservationoveradefiniteperiodoftime.Such instruments are generally used in powerhouseswhere the current, voltage, power,etc.,aretobemaintainedwithincertainacceptablelimit.

1.6.2AnalogandDigitalInstruments

1.AnalogInstruments

Thesignalsofananalogunitvaryinacontinuousfashionandcantakeoninfinitenumberofvaluesinagivenrange.Fuelgauge,ammeterandvoltmeters,wristwatch,speedometerfallinthiscategory.

2.DigitalInstruments

Signals varying in discrete steps and taking on a finite number of different values in agiven range are digital signals and the corresponding instruments are of digital type.Digital instruments have some advantages over analog meters, in that they have highaccuracyandhighspeedofoperation.Iteliminatesthehumanoperationalerrors.Digitalinstrumentscanstoretheresultforfuturepurposes.Adigitalmultimeteristheexampleofadigitalinstrument.

1.6.3Mechanical,ElectricalandElectronicsInstruments

1.MechanicalInstruments

Mechanicalinstrumentsareveryreliableforstaticandstableconditions.Theyareunabletorespondrapidlytothemeasurementofdynamicandtransientconditionsduetothefactthattheyhavemovingpartsthatarerigid,heavyandbulkyandconsequentlyhavealarge

mass.Masspresentsinertiaproblemsandhencetheseinstrumentscannotfaithfullyfollowthe rapid changes which are involved in dynamic instruments. Also, most of themechanicalinstrumentscausesnoisepollution.AdvantagesofMechanicalInstruments

•Relativelycheaperincost

•Moredurableduetoruggedconstruction

•Simpleindesignandeasytouse

•Noexternalpowersupplyrequiredforoperation

•ReliableandaccurateformeasurementofstableandtimeinvariantquantityDisadvantagesofMechanicalInstruments

•Poorfrequencyresponsetotransientanddynamicmeasurements

•Largeforcerequiredtoovercomemechanicalfriction

•Incompatiblewhenremoteindicationandcontrolneeded

•Causenoisepollution

2.ElectricalInstruments

Whentheinstrumentpointerdeflectioniscausedbytheactionofsomeelectricalmethodsthenitiscalledanelectricalinstrument.Thetimeofoperationofanelectricalinstrumentismore rapid than that of amechanical instrument.Unfortunately, an electrical systemnormally depends upon a mechanical measurement as an indicating device. Thismechanical movement has some inertia due to which the frequency response of theseinstrumentsispoor.

3.ElectronicInstruments

Electronic instruments use semiconductor devices.Most of the scientific and industrialinstrumentations require very fast responses. Such requirements cannot bemetwith bymechanical and electrical instruments. In electronic devices, since the only movementinvolved is that of electrons, the response time is extremely small owing to very smallinertia of the electrons.With the use of electronic devices, a very weak signal can bedetectedbyusingpre-amplifiersandamplifiers.AdvantagesofElectrical/ElectronicInstruments

•Non-contactmeasurementsarepossible

•Theseinstrumentsconsumelesspower

•Compactinsizeandmorereliableinoperation

•Greaterflexibility

•Goodfrequencyandtransientresponse

•Remoteindicationandrecordingpossible

•Amplificationproducedgreaterthanthatproducedinmechanicalinstruments

1.6.4ManualandAutomaticInstrumentsIn case of manual instruments, the service of an operator is required. For example,measurement of temperature by a resistance thermometer incorporating a Wheatstonebridgeinitscircuit,anoperatorisrequiredtoindicatethetemperaturebeingmeasured.

Inanautomatic typeof instrument,nooperator is requiredall the time.Forexample,measurementoftemperaturebymercury-in-glassthermometer.

1.6.5Self-operatedandPower-operatedInstrumentsSelf-operated instrumentsare those inwhichnooutsidepower is requiredforoperation.The output energy is supplied wholly or almost wholly by the input measurand. Dial-indicatingtypeinstrumentsbelongtothiscategory.

The power-operated instruments are those in which some external power such aselectricity,compressedair,hydraulic supply is required foroperation. In suchcases, theinputsignalsuppliesonlyaninsignificantportionoftheoutputpower.ElectromechanicalinstrumentsshowninFigure1.8fallinthiscategory.

Figure1.8Electromechanicalmeasurementsystem

1.6.6DeflectionandNullOutputInstrumentsInadeflection-typeinstrument,thedeflectionoftheinstrumentindicatesthemeasurementof the unknownquantity.Themeasurand quantity produces somephysical effectwhichdeflectsorproducesamechanicaldisplacement in themovingsystemof theinstrument.An opposite effect is built in the instrument which opposes the deflection or themechanicaldisplacementofthemovingsystem.Thebalanceisachievedwhenopposingeffectequalstheactuatingcauseproducingthedeflectionorthemechanicaldisplacement.The deflection or the mechanical displacement at this point gives the value of theunknown input quantity. These type of instruments are suited for measurement underdynamic condition. PermanentMagnetMoving Coil (PMMC),Moving Iron (MI), etc.,typeinstrumentsareexamplesofthiscategory.

In null-type instruments, a zero or null indication leads to determination of themagnitudeofthemeasurandquantity.Thenullconditiondependsuponsomeotherknownconditions.Thesearemoreaccurateandhighlysensitiveascomparedtodeflection-typeinstruments.Adcpotentiometerisanull-typeinstrument.

1.7 DEFINITIONSOFSOMESTATICCHARACTERISTICS

1.Accuracy

Accuracyistheclosenesswithwhichtheinstrumentreadingapproachesthetruevalueofthe variable under measurement. Accuracy is determined as the maximum amount bywhich the result differs from the true value. It is almost impossible to determineexperimentallythetruevalue.Thetruevalueisnotindicatedbyanymeasurementsystemduetotheloadingeffect,lagsandmechanicalproblems(e.g.,wear,hysteresis,noise,etc.).

Accuracyofthemeasuredsignaldependsuponthefollowingfactors:

•Intrinsicaccuracyoftheinstrumentitself;

•Accuracyoftheobserver;

•Variationofthesignaltobemeasured;and

•Whetherornotthequantityisbeingtrulyimpressedupontheinstrument.

2.Precision

Precision is a measure of the reproducibility of the measurements, i.e., precision is ameasure of the degree to which successive measurements differ from one another.Precision is indicated from the number of significant figures in which it is expressed.Significant figures actually convey the information regarding the magnitude and themeasurementprecisionofaquantity.Moresignificant figures implygreaterprecisionofthemeasurement.

3.Resolution

Iftheinputisslowlyincreasedfromsomearbitraryvalueitwillbenoticedthattheoutputdoesnotchangeatalluntiltheincrementexceedsacertainvaluecalledtheresolutionordiscriminationoftheinstrument.Thus,theresolutionordiscriminationofanyinstrumentis the smallest change in the input signal (quantity under measurement) which can bedetected by the instrument. Itmay be expressed as an accrual value or as a fraction orpercentage of the full scale value. Resolution is sometimes referred as sensitivity. Thelargestchangeofinputquantityforwhichthereisnooutputoftheinstrumentiscalledthedeadzoneofthatinstrument.

Thesensitivitygivestherelationbetweentheinputsignaltoaninstrumentorapartoftheinstrumentsystemandtheoutput.Thus,thesensitivityisdefinedastheratioofoutputsignal or response of the instrument to a change of input signal or the quantity undermeasurement.

Example1.1

A moving coil ammeter has a uniform scale with 50divisions and gives a full-scale reading of 5 A. TheinstrumentcanreaduptoVthofascaledivisionwithafairdegree of certainty. Determine the resolution of theinstrumentinmA.

SolutionFull-scalereading=5A

Numberofdivisionsonscale=50

4.SpeedofResponse

The quickness of an instrument to read the measurand variable is called the speed ofresponse.Alternately,speedofresponseisdefinedasthetimeelapsedbetweenthestartofthemeasurement to the reading taken. This time depends upon themechanicalmovingsystem,friction,etc.

1.8 MEASUREMENTOFERRORS

Inpractice,itisimpossibletomeasuretheexactvalueofthemeasurand.Thereisalwayssome difference between the measured value and the absolute or true value of theunknownquantity(measurand),whichmaybeverysmallormaybelarge.Thedifferencebetweenthetrueorexactvalueandthemeasuredvalueoftheunknownquantityisknownastheabsoluteerrorofthemeasurement.

IfδAbetheabsoluteerrorofthemeasurement,AmandAbethemeasuredandabsolutevalueoftheunknownequantitythenδAmaybeexpressedas

Sometimes,δAisdenotedbyε0.

Therelativeerroristheratioofabsoluteerrortothetruevalueoftheunknownquantitytobemeasured,

When the absolute error ε0 (=δA) is negligible, i.e.,when the difference between thetrue value A and the measured value Am of the unknown quantity is very small ornegligiblethentherelativeerrormaybeexpressedas,

The relative error is generally expressed as a fraction, i.e., 5 parts in 1000 or inpercentagevalue,

Themeasuredvalueof theunknownquantitymaybemore thanor less than the truevalue of the measurand. So the manufacturers have to specify the deviations from thespecifiedvalueof a particular quantity in order to enable thepurchaser tomakeproper

selection according to his requirements. The limits of these deviations from specifiedvalues are defined as limiting or guarantee errors. The magnitude of a given quantityhaving a specifiedmagnitudeAm and amaximum or a limiting error ±δAmust have amagnitudebetweenthelimits

Forexample,themeasuredvalueofaresistanceof100Ωhasalimitingerrorof±0.5Ω.Thenthetruevalueoftheresistanceisbetweenthelimits100±0.5,i.e.,100.5and99.5Ω.

Example1.2A0-25Aammeterhasaguaranteedaccuracyof1percentof full scale reading. The current measured by thisinstrument is 10 A. Determine the limiting error inpercentage.

SolutionThemagnitudeoflimitingerroroftheinstrumentfromEq.(1.1),δA=εr×A=0.01×25=0.25A

Themagnitudeofthecurrentbeingmeasuredis10A.Therelativeerroratthiscurrentis

Therefore,thecurrentbeingmeasuredisbetweenthelimitof

A=Am(1±εr)=10(1±0.025)=10±0.25A

Example1.3The inductance of an inductor is specified as 20 H ± 5percent by a manufacturer. Determine the limits ofinductancebetweenwhichitisguaranteed.

Solution

Limitingvalueofinductance,A=Am±δA

=Am±εrAm=Am(1±εr)

=20(1±0.05)=20±1H

Example1.4A0-250V voltmeter has a guaranteed accuracy of 2%offull-scalereading.Thevoltagemeasuredbythevoltmeteris150volts.Determinethelimitingerrorinpercentage.

SolutionThemagnitudeofthelimitingerroroftheinstrument,δA=εrV=0.02ˣ250=5.0V

Themagnitudeofthevoltagebeingmeasuredis150V.

Thepercentagelimitingerroratthisvoltage

Example1.5

The measurand value of a resistance is 10.25 Ω, whereas its value is10.22Ω.Determinetheabsoluteerrorofthemeasurement.

SolutionMeasurandvalueAm=10.25Ω

TruevalueAm=10.22Ω

Absoluteerror,δA=Am-A=10.25-10.22=0.03Ω

Example1.6 Themeasuredvalueofacapacitoris205.3fiF,whereasitstruevalueis201.4fiF.Determinetherelativeerror.

Solution

MeasuredvalueAm=205.3×10-6F

Truevalue,A=201.4×10-6F

Absoluteerror,ε0=Am-A

=205.3×10-6—201.4×10-6

=3.9×10-6F

=3.9×10-6F

Example1.7

Awattmeterreads25.34watts.Theabsoluteerrorinthemeasurementis–0.11watt.Determinethetruevalueofpower.

SolutionMeasuredvalueAm=25.34W

AbsoluteerrorδA=–0.11W

TruevalueA=Measuredvalue-Absoluteerror

=25.34–(–0.11),

=25.45W

1.8.1TypesofErrorsTheoriginationoferrormaybeinavarietyofways.Theyarecategorisedinthreemaintypes.

•Grosserror

•Systematicerror

•Randomerror

1.GrossError

Theerrorsoccurbecauseofmistakes inobserved readings, orusing instruments and inrecording and calculating measurement results. These errors usually occur because ofhuman mistakes and these may be of any magnitude and cannot be subjected tomathematical treatment. One common gross error is frequently committed duringimproperuseofthemeasuringinstrument.Anyindicatinginstrumentchangesconditionsto some extentwhen connected in a complete circuit so that the reading ofmeasurandquantity is altered by the method used. For example, in Figure (1.9)(a) and (b), twopossibleconnectionsofvoltageandcurrentcoilofawattmeterareshown.

InFigure1.9(a), the connection shown is usedwhen the applied voltage is high andcurrentflowinginthecircuitislow,whiletheconnectionshowninFigure1.9(b)isusedwhen the applied voltage is low and current flowing in the circuit is high. If theseconnections of wattmeter are used in opposite order then an error is liable to enter inwattmeterreading.Anotherexampleofthistypeoferrorisintheuseofawell-calibratedvoltmeter formeasurement of voltage across a resistance of very high value.The samevoltmeter, when connected in a low resistance circuit, may give a more dependablereading because of very high resistance of the voltmeter itself. This shows that thevoltmeterhasaloadingeffectonthecircuit,whichalterstheoriginalsituationduringthemeasurement.

Figure1.9Differentconnectionsofwattmeter

For another example, a multirange instrument has a different scale for each range.During measurements, the operator may use a scale which does not correspond to thesettingof therangeselectorof the instrument.Grosserrormayalsobe therebecauseofimpropersettingofzerobeforethemeasurementandthiswillaffectallthereadingstakenduring measurements. The gross error cannot be treated mathematically, so great careshouldbetakenduringmeasurementtoavoidthiserror.Pictorial illustrationofdifferenttypesofgrosserrorisshowninFigure1.10.

Figure1.10Differenttypesofgrosserrors

Ingeneral, toavoidgrosserror,at least two, threeormorereadingsof themeasurandquantity should be taken by different observers. Then if the readings differ by anunacceptably large amount, the situation can be investigated and the more erroneousreadingseliminated.

2.SystematicError

Thesearetheerrorsthatremainconstantorchangeaccordingtoadefinitelawonrepeatedmeasurementofthegivenquantity.Theseerrorscanbeevaluatedandtheir influenceonthe results ofmeasurement can be eliminated by the introduction of proper correction.Therearetwotypesofsystematicerrors:

•Instrumentalerror

•Environmentalerror

Instrumental errors are inherent in the measuring instruments because of theirmechanicalstructureandcalibrationoroperationof theapparatusused.Forexample, inD’Arsonvalmovement, friction in bearings of various componentsmay cause incorrectreadings.Improperzeroadjustmenthasasimilareffect.Poorconstruction,irregularspringtensions, variations in the air gapmay also cause instrumental errors. Calibration errormayalsoresultintheinstrumentreadingeitherbeingtoolowortoohigh.

Suchinstrumentalerrorsmaybeavoidedby

•Selectingapropermeasuringdevicefortheparticularapplication

•Calibratingthemeasuringdeviceorinstrumentagainstastandard

•Applyingcorrectionfactorsafterdeterminingthemagnitudeofinstrumentalerrors

Environmentalerrorsaremuchmoretroublesomeastheerrorschangewithtimeinanunpredictablemanner.Theseerrorsareintroducedduetousinganinstrumentindifferentconditions than inwhich itwas assembledandcalibrated.Change in temperature is themajorcauseofsucherrorsas temperatureaffects thepropertiesofmaterials indifferentways,includingdimensions,resistivity,springeffectandmanymore.Otherenvironmentalchangesalsoeffecttheresultsgivenbytheinstrumentssuchashumidity,altitude,earth’smagnetic field, gravity, stray electric and magnetic field, etc. These errors can beeliminatedorreducedbytakingthefollowingprecautions:

•Usethemeasuringinstrumentinthesameatmosphericconditionsinwhichitwasassembledandcalibrated.

•Iftheaboveprecautionisnotpossiblethendeviationinlocalconditionsmustbedeterminedandsuitablecompensationsareappliedintheinstrumentalreading.

•Automaticcompensation,employingsophisticateddevicesforsuchdeviations,isalsopossible.

3.RandomErrors

Theseerrorsareofvariablemagnitudeandsignanddonotmaintainanyknownlaw.Thepresenceofrandomerrorsbecomeevidentwhendifferentresultsareobtainedonrepeatedmeasurementsofoneandthesamequantity.Theeffectofrandomerrorsisminimisedbymeasuring thegivenquantitymany timesunder thesameconditionsandcalculating thearithmeticalmeanoftheresultsobtained.Themeanvaluecanjustlybeconsideredasthemostprobablevalueofthemeasuredquantitysincerandomerrorsofequalmagnitudebutopposite sign are of approximately equal occurrence when making a great number ofmeasurements.

1.9 LOADINGEFFECTS

Underidealconditions,anelementusedforsignalsensing,conditioning,transmissionanddetectionshouldnotchange/distorttheoriginalsignal.Thesensingelementshouldnotuseanyenergyortakeleastenergyfromtheprocesssoasnottochangetheparameterbeingmeasured.However,underpracticalconditions,ithasbeenobservedthattheintroductionofanyelementinasystemresultsinvariablyinextractionoftheenergyfromthesystem,thereby distorting the original signal. This distortionmay take the form of attenuation,waveformdistortion,phaseshift,etc.,andconsequently,theidealmeasurementsbecomeimpossible.

Theincapabilityofthesystemtofaithfullymeasuretheinputsignalinundistortedformiscalledloadingeffect.Thisresultsinloadingerror.

Theloadingeffects,inameasurementsystem,notonlyoccurinthedetector–transducerstage but also occur in signal conditioning and signal presentation stages as well. Theloadingproblemiscarriedrightdowntothebasicelementsthemselves.Theloadingeffect

may occur on account of both electrical and mechanical elements. These are due toimpedancesof thevariouselementsconnected ina system.Themechanical impedancesmaybetreatedsimilartoelectricalimpedances.

Sometimesloadingeffectoccursduetotheconnectionofmeasuringinstrumentsinanimproperway.Supposeavoltmeter isconnectedwithparallelofaveryhigh resistance.Duetothehighresistanceofthevoltmeteritself, thecircuitcurrentchanges.Thisis theloading effect of a voltmeter when they are connected in parallel with a very highresistance.Similarly,anammeterhasaverylowresistance.Soifanammeterisconnectedin series with a very low resistance, the total resistance of the circuit changes, and insuccession,thecircuitcurrentalsochanges.Thisistheloadingeffectofammeterswhentheyareconnectedinserieswithverylowresistance.

EXERCISE

Objective-typeQuestions1.Anull-typeinstrumentascomparedtoadeflection-typeinstrumenthas

(a)alowersensitivity

(b)afasterresponse

(c)ahigheraccuracy

(d)alloftheabove

2.Inameasurementsystem,thefunctionofthesignalmanipulatingelementisto

(a)changethemagnitudeoftheinputsignalwhileretainingitsidentity

(b)changethequantityundermeasurementtoananalogoussignal

(c)toperformnon-linearoperationlikefiltering,choppingandclippingandclamping

(d)toperformlinearoperationlikeadditionandmultiplication

3.Themeasurementofaquantity

(a)isanactofcomparisonofanunknownquantitywithapredefinedacceptablestandardwhichisaccuratelyknown

(b)isanactofcomparisonofanunknownquantitywithanotherquantity

(c)isanactofcomparisonofanunknownquantitywithaknownquantitywhoseaccuracymaybeknownormaynotbeknown

(d)noneofthese

4.Purelymechanicalinstrumentscannotbeusedfordynamicmeasurementsbecausetheyhave

(a)largetimeconstant

(b)higherresponsetime

(c)highinertia

(d)alloftheabove

5.Amodifyinginputtoameasurementsystemcanbedefinedasaninput

(a)whichchangestheinput–outputrelationshipfordesiredaswellasinterferinginputs

(b)whichchangestheinput–outputrelationshipfordesiredinputsonly

(c)whichchangestheinput–outputrelationshipforinterferinginputsonly

(d)noneoftheabove

6.Inmeasurementsystems,whichofthefollowingstaticcharacteristicsaredesirable?

(a)Sensitivity

(b)Accuracy

(c)Reproducibility

(d)Alloftheabove

7.Inmeasurementsystems,whichofthefollowingareundesirablestaticcharacteristics?

(a)Reproducibilityandnonlinearity

(b)Drift,staticerroranddeadzone

(c)Sensitivityandaccuracy

(d)Drift,staticerror,deadzoneandnonlinearity

8.Insometemperaturemeasurement,thereadingisrecordedas25.70°C.Thereadinghas

(a)fivesignificantfigures

(b)foursignificantfigures

(c)threesignificantfigures

(d)noneoftheabove

9. In thecentreofazeroanalogammeterhavinga rangeof -10A to+10A, there isadetectablechangeof thepointerfromitszeropositiononeithersideofthescaleonlyasthecurrentreachesavalueof1A(oneitherside).Theammeterhasa

(a)deadzoneof1A

(b)deadzoneof2A

(c)resolutionof1A

(d)sensitivityof1A

10.Adccircuitcanberepresentedbyaninternalvoltagesourceof50Vwithanoutputresistanceof100kW.Inordertoachieve99%accuracyforvoltagemeasurementacrossitsterminals,thevoltagemeasuringdeviceshouldhave

(a)aresistanceofatleast10W

(b)aresistanceof100kW

(c)aresistanceofatleast10MW

(d)noneoftheabove

11.Inaccircuits,theconnectionofmeasuringinstrumentscauseloadingerrorswhichmayaffect

(a)onlythephaseofthequantitybeingmeasured

(b)onlythemagnitudeofthequantitybeingmeasured

(c)boththephaseandthemagnitudeofthequantity

(d)magnitude,phaseandalsothewaveformofthequantitybeingmeasured

12.Apressuregaugeiscalibratedform0–50kN/m2.Ithasauniformscalewith100scaledivisions.Onefifthofthescaledivisioncanbereadwithcertainty.Thegaugehasa

(a)deadzoneof0.2kN/m2

(b)resolutionof0.1kN/m2

(c)resolutionof0.5kN/m2

(d)thresholdof0.1kN/m2

13.Apressuremeasurementinstrumentiscalibratedbetween10barand260bar.Thescalespanoftheinstrumentis

(a)10bar

(b)260bar

(c)250bar

(d)270bar

14.AWheatstonebridgeisbalancedwithallthefourresistancesequalto1kWeach.Thebridgesupplyvoltageis100V.Thevalueofoneoftheresistanceischangedto1010W.Theoutputvoltageismeasuredwithavoltagemeasuringdeviceofinfiniteresistance.Thebridgesensitivityis

(a)2.5mV/W

(b)10V/W

(c)25mV/W

(d)noneoftheabove

15.Themainadvantageofthenullbalancetechniqueofmeasurementisthat

(a)itgivesaquickmeasurement

(b)itdoesnotloadthemedium

(c)itgivesacentrezerovalueatitsinput

(d)itisnotaffectedbytemperaturevariation

16.Thesmallestchangeinameasuredvariabletowhichaninstrumentwillrespondis

(a)resolution

(b)precision

(c)sensitivity

(d)accuracy

17.Thedesirablestaticcharacteristicsofameasurementare

(a)precision

(b)accuracy

(c)sensitivity

(d)allofthese

18.Theerrorsmainlycausedbyhumanmistakesare

(a)systematicerror

(b)instrumentalerror

(c)observationalerror

(d)grosserror

19.Systematicerrorsare

(a)environmentalerror

(b)observationalerror

(c)instrumentalerror

(d)alloftheabove

20.Ananalogammeteris

(a)anabsoluteinstrument

(b)anindicatinginstrument

(c)acontrollinginstrument

(d)arecordinginstrument

Short-answerQuestions1.Comparetheadvantagesanddisadvantagesofelectricalandmechanicalmeasurementsystems.

2.Explainthevariousclassesofmeasuringinstrumentswithexamples.

3.Differentiateclearlybetweenabsoluteandsecondaryinstruments.

4.Explainanaloganddigitalmodesofoperation.Whyarethedigitalinstrumentsbecomingpopularnow?WhatismeantbyADCandDAC?

5.Brieflydefineandexplainallthestaticcharacteristicsofmeasuringinstruments.

6.Explainloadingeffectinmeasurementsystems.

7.Explainthetermsaccuracy,sensitivityandresolutionasusedforindicatinginstruments.

8.Whatarethedifferenttypesoferrorsinameasuringinstrument?Describetheirsourcebriefly.

9.Whatarefundamentalandderivedunits?Brieflyexplainthem.

10.Whatarethedifferencesbetweenprimaryandsecondarystandards?

Long-answerQuestions1.(a)Whatismeasurement?Whatismeantbythetermmeasurand?Whatisameasuringinstrument?

(b)Writedowntheimportantprecautionsthatshouldbetakenwhilecarryingoutelectricalmeasurements.

(c)Withanexample,explainthetermloadingeffectinameasurementsystem.

2.(a)Explaintheterms:

(i) Measurement(ii) Accuracy(iii) Precision(iv) Sensitivity(v) Reproducibility

(b)Definerandomerrorsandexplainhowtheyareanalysedstatistically.

3.(a)Whatareenvironmental,instrumentalandobservationalerrors?Brieflyexplaineachofthem.

(b)Threeresistorshavethefollowingratings:

R1=47W±4%,R2=65W±4%,R3=55W±4%

Determinethemagnitudeandlimitingerrorsinohmsandinpercentageoftheresistanceoftheseresistorsconnectedinseries.

4.(a)Whatisthenecessityofunitsinmeasurements?WhatarevariousSIunits?

(b)Definethetermsunits,absoluteunits,fundamentalunitsandderivedunitswithsuitableexamples.

(c)Whatissystematicerrorandhowcanwereduceit?

5.(a)Distinguishbetweeninternational,primary,secondaryandworkingstandards.

(b)Whataretheprimarystandardsfortimeandfrequency?Brieflydiscusseachofthem.

(c)Describetheworkingprinciple,operationandconstructionaldetailofaprimarystandardofemf.

2.1 INTRODUCTION

Ananalogdevice isone inwhich theoutputordisplay isacontinuousfunctionof timeandbearsaconstantrelationtoitsinput.Measuringinstrumentsareclassifiedaccordingtoboththequantitymeasuredbytheinstrumentandtheprincipleofoperation.Threegeneralprinciples of operation are available: (i) electromagnetic, which utilises the magneticeffectsofelectriccurrents;(ii)electrostatic,whichutilisestheforcesbetweenelectricallychargedconductors;(iii)electro-thermal,whichutilisestheheatingeffect.

Electric measuring instruments andmeters are used to indicate directly the value ofcurrent,voltage,powerorenergy.In thischapter,wewillconsideranelectromechanicalmeter (input is as an electrical signalwhich results inmechanical forceor torque as anoutput) that canbe connectedwith additional suitable components in order to act as anammeterandavoltmeter.Themostcommonanaloginstrumentormeteristhepermanentmagnetmovingcoilinstrumentanditisusedformeasuringadccurrentorvoltageofanelectric circuit. On the other hand, the indications of alternating current ammeters andvoltmetersmustrepresentthermsvaluesofthecurrent,orvoltage,respectively,appliedtotheinstrument.

2.2 CLASSIFICATIONOFANALOGINSTRUMENTS

Inabroadsense,analoginstrumentsmaybeclassifiedintotwoways:

1.Absoluteinstruments

2.Secondaryinstruments

Absoluteinstrumentsgivethevalueoftheelectricalquantitytobemeasuredintermsofthe constants of the instruments and to its deflection, no comparison with anotherinstrumentbeingrequired.Forexample, thetangentgalvanometergivesthevalueofthecurrenttobemeasuredintermsofthetangentoftheangleofdeflectionproducedbythecurrent, the radius and the number of turns of galvanometer coil, and the horizontalcomponent of the earth’s magnetic field. No calibration of the instrument is thusnecessary.

Secondary instruments are so constructed that the value of current, voltage or otherquantitytobemeasuredcanbedeterminedfromthedeflectionoftheinstruments,onlyifthe latter has been calibrated by comparisonwith either an absolute instrument or onewhich has already been calibrated. The deflection obtained ismeaningless until such acalibrationhasbeenmade.

Thisclassofinstrumentsisinmostgeneraluse,absoluteinstrumentbeingseldomusedexceptinstandardlaboratoriesandsimilarinstitutions.

Thesecondaryinstrumentsmaybeclassifiesas

1.Indicatinginstruments

2.Recordinginstruments

3.Integratinginstruments

Indicatinginstrumentsareinstrumentswhichindicatethemagnitudeofaquantitybeingmeasured.Theygenerallymakeuseofadialandapointerforthispurpose.

Recordinginstrumentsgiveacontinuousrecordofthequantitybeingmeasuredoveraspecified period. The variation of the quantity being measured are recorded by a pen(attached to themovingsystemof the instrument; themovingsystemisoperatedby thequantitybeingmeasured)onasheetofpaperthatmovesperpendiculartothemovementofthepen.

Integrating instruments record totalised events over a specified period of time. Thesummation,which they give, is the product of time and an electrical quantity.Amperehourandwatthour(energy)metersareexamplesofthiscategory.

2.3 PRINCIPLEOFOPERATION

Analoginstrumentsmaybeclassifiedaccordingtotheprincipleofoperationtheyutilise.Theeffectstheyutiliseare

1.Magneticeffect

2.Heatingeffect

3.Electrostaticeffect

4.Electromagneticeffect

5.Halleffect

The majority of analog instruments including moving coil, moving iron andelectrodynamicutilisethemagneticeffect.Theeffectoftheheatproducedbyacurrentinaconductorisusedinthermocoupleandhotwireinstruments.Electrostaticeffectisusedin electrostatic voltmeters. The electromagnetic induction effect is used in inductionwattmetersandinductionenergymeters.

2.4 OPERATINGTORQUES

Threetypesoftorquesareneededforsatisfactoryoperationofanyindicatinginstrument.Theseare

•Deflectingtorque

•Controllingtorque

•Dampingtorque

2.4.1DeflectingTorque/ForceAny instrument’s deflection is found by the total effect of the deflecting torque/force,controltorque/forceanddampingtorque/force.Thedeflectingtorque’svalueisdependentupontheelectricalsignaltobemeasured;thistorque/forcehelpsinrotatingtheinstrumentmovementfromitszeroposition.Thesystemproducingthedeflectingtorqueiscalledthedeflectingsystem.

2.4.2ControllingTorque/ForceTheactofthistorque/forceisoppositetothedeflectingtorque/force.Whenthedeflectingand controlling torques are equal in magnitude then the movement will be in definiteposition or in equilibrium. Spiral springs or gravity is usually given to produce thecontrolling torque. The system which produces the controlling torque is called thecontrollingsystem.Thefunctionsofthecontrollingsystemare

•Toproduceatorqueequalandoppositetothedeflectingtorqueatthefinalsteadypositionofthepointerinordertomakethedeflectionofthepointerdefiniteforaparticularmagnitudeofcurrent

•Tobringthemovingsystembacktoitszeropositionwhentheforcecausingtheinstrumentmovingsystemtodeflectisremoved

Thecontrollingtorqueinindicatinginstrumentsisalmostalwaysobtainedbyaspring,muchlesscommonly,bygravity.

2.4.3DampingTorque/ForceAdampingforcegenerallyworksinanoppositedirectiontothemovementofthemovingsystem. This oppositemovement of the damping force,without any oscillation or verysmalloscillationbringsthemovingsystemtorestat thefinaldeflectedpositionquickly.Air friction, fluid friction and eddy currents provide the damping torque/force to act. Itmustalsobenotedthatnotalldampingforceaffectsthesteady-statedeflectioncausedbyagivendeflecting forceor torque.With the angularvelocityof themoving system, theintensityofthedampingforcerises;therefore,itseffectisgreatestwhenitrotatesrapidlyand zero when the system rotation is zero. In the description of various types ofinstruments, detailed mathematical expressions for the damping torques are taken intoconsideration.

When thedeflecting torque ismuchgreater than thecontrolling torque, the system iscalledunderdamped.Ifthedeflectingtorqueisequaltothecontrollingtorque,itiscalledcriticallydamped.When deflecting torque ismuch less than the controlling torque, thesystemisunderoverdampedcondition.Figure2.1shows thevariationofdeflection(d )withtimeforunderdamped,criticallydampedandoverdampedsystems.

Figure2.1Dampingtorquecurve

2.5 CONSTRUCTIONALDETAILS

2.5.1MovingSystemThemovingsystemshouldhavethefollowingproperties:

•Themovingpartsshouldbelight.

•Thefrictionalforceshouldbeminimum.

Theserequirementsshouldbefulfilled inorder thatpowerrequiredby the instrumentforitsoperationissmall.Thepowerisproportionaltotheweightofthemovingpartsandthe frictional forces opposing themovement.Themoving system can bemade light byusing aluminium as far as possible. The frictional forces are reduced by using spindle-mountedjewelbearingsandbycarefullybalancingthesystem.

The force or torque developed by themoving element of an electrical instrument isnecessarilysmallinorderthatthepowerconsumptionoftheinstrumentiskeptlowsothattheintroductionoftheinstrumentintoacircuitmaycauseminimumchangeintheexistingcircuitconditions.Becauseoflowpowerlevels,theconsiderationsofvariousmethodsofsupporting themoving elements becomes of vital importance.With the operating forcebeingsmall, thefrictionalforcemustbekept toaminimuminorder that the instrumentreadscorrectlyandisnoterraticinactionandisreliable.Supportsmaybeofthefollowingtypes:

•Suspension

•Tautsuspension

•Pivotandjewelbearings

1.Suspension

Itconsistofa fine, ribbon-shapedmetal filament for theuppersuspensionandacoiloffinewireforthelowerpart.Theribbonismadeofaspringmateriallikeberylliumcopperor μHosphor bronze. This coiling of lower part of suspension is done in order to give

negligiblerestrainonthemovingsystem.Thetypeofsuspensionrequirescarefullevelingof the instrument, so that the moving system hangs in correct vertical position. Thisconstructionis,therefore,notsuitedtofielduseandisemployedonlyinthoselaboratoryapplicationsinwhichverygreatsensitivityisrequired.Inordertopreventshockstothesuspension during transit, etc., a clamping arrangement is employed for supporting themovingsystem.

2.TautSuspension

Asuspensiontypeofinstrumentcanonlybeusedinverticalposition.Thetautsuspensionhasaflatribbonsuspensionbothaboveandbelowthemovingelement,withsuspensionkept under tensionby a spring arrangement (Figure2.2).The advantage of this type ofsuspension is that exact levelling is not required if the moving system is properlybalanced.

Suspension and taut suspension are customarily used in instruments of galvanometerclasswhichrequiresa lowfrictionandhighsensitivitymechanism.Butactually there isno strict line of demarcation between a galvanometer and other indicating instruments.Somesensitivewattmetersandelectrostaticvoltmetersuseflexiblesuspension.

Ribbonsuspension, inadditiontosupportingthemovingelement,exertsacontrollingtorquewhentwisted.Thus,theuseofsuspensionresultsineliminationofpivots,jewels,controlspringsandtherefore,pivotlessinstrumentsarefreefrommanydefects.

Figure2.2Tautsuspension

3.PivotandJewelBearings

Themovingsystemismountedonaspindlemadeofhardenedsteel.Thetwoendsofthespindlearemadeconicalandthenpolishedtoformpivots.Theseendsfitconicalholesinjewels located in the fixed part of instruments (Figure 2.3). These jewels, which arepreferablymadeofsapphire,formbearings.

Figure2.3(a)Spring-loadedjewelbearing(b)Jewelbearing(c)Pivot

Ithasbeenfoundthatthefrictionaltorque,forjewelbearings,isproportionaltotheareaofcontactbetweenthepivotandjewel.Thus,thecontactareabetweenapivotandjewelshouldbesmall.Thepivot isgroundtoaconeandits tip isroundedtoahemisphericalsurfaceofsmallarea.Thejewelisgroundtoaconeofsomewhatlargerangle.

4.Torque/WeightRatio

The frictional torque in an instrument depends upon theweight ofmoving parts. If theweight of the moving parts is large, the frictional torque will be large. The frictionaltorqueexertsaconsiderableinfluenceontheperformanceofanindicatinginstrument.Ifthefrictionaltorqueislargeandiscomparabletoaconsiderablefractionofthedeflectingtorque, thedeflectionof themovingsystemwilldependuponthefrictional torquetoanappreciable extent. Also, the deflection will depend on the direction from which theequilibrium position is approached and will be uncertain. On the other hand, if thefrictionaltorqueisverysmallcomparedwiththedeflectingtorque,itseffectondeflectionis negligible. Thus, the ratio of deflecting torque to frictional torque is a measure ofreliability of the instrument indications and is the inherent quality of the design.Hence(deflecting) torque/weight ratio of an instrument is an index of its performance. Thehighertheratio,thebetterwillbeitsperformance.

2.5.2ControllingSystemThecontrollingtorqueisprovidedbyaspringorsometimesbygravity.

1.SpringControl

A hair-spring, usually of phosphor-bronze attached to the moving system, is used inindicating instruments for control purpose, the schematic arrangement being shown inFigure2.4(a)andtheactualcontrollingspringusedintheinstrumentisshowninFigure2.4(b).

Togiveacontrollingtorquewhichisdirectlyproportionaltotheangleofdeflectionofthemovingsystem, thenumberof turnson thespringshouldbefairly large,so that thedeflectionperunitlengthissmall.Thestressinthespringmustbelimitedtosuchavaluethatthereisnopermanentset.

Figure2.4(a)Springcontrol

Figure2.4(b)Springcontrolinaninstrument

Suppose that a spiral spring is made up of a total lengthL m of strip whose cross-sectionisrectangular,theradialthicknessbeingtmandthedepthbm.LetEbeYoung’smodulus(N/m2)forthematerialofthespring.Then,ifθradiansbethedeflectionofthemoving system towhichoneendof the spring isbeingattached, theexpression for thecontrollingtorqueis

Thus,controllingtorque∞θ∞instrumentdeflection.

2.GravityControl

Inagravity-controlledinstrument,asmallweightisattachedtothemovingsysteminsuchawaythatitproducesarestoringorcontrollingtorquewhenthesystemisdeflected.Thisis illustrated inFigure2.5.Thecontrolling torque,when thedeflection isθ, isωl sinθ,whereWisthecontrolweightand l itsdistancefromtheaxisofrotationof themovingsystem,anditis,therefore,proportionalonlytothesineoftheangleofdeflection,insteadof,aswithspringcontrol,beingdirectlyproportionaltotheangleofdeflection.Gravity-controlled instruments must obviously be used in a vertical position in order that thecontrolmayoperate.

Figure2.5Gravitycontrol

3.ComparisonofSpringandGravityControl

Gravitycontrolhasthefollowingadvantageswhencomparedwithspringcontrol:

•Itischeaper

•Independentoftemperature

•Doesnotdeterioratewithtime

ConsideraninstrumentinwhichthedeflectingtorqueTDisdirectlyproportionaltothecurrent(say)tobemeasured.

Thus,ifIisthecurrent,

If the instrument is spring-controlled, the controlling torque being TC, when thedeflectionisθ,

TC=ksθ(ksisspringconstant)

Also, TC=TDor ksθ=kI

Thus,thedeflectionisproportionaltothecurrentthroughoutthescale.

Nowifthesameinstrumentisgravitycontrolled,

TC=kgsinθ (kg is a constant that depends upon the control weight and its

distancefromtheaxisofrotationofthemovingsystem).

And TC=TD=kI

Thus,agravity-controlledinstrumentwouldhaveascalewhichis‘cramped’atitslowerend instead of being uniformly divided, though the deflecting torque is directlyproportionaltothequantitytobemeasured.

2.5.3DampingSystemTherearethreesystemsofdampinggenerallyused.Theseareasfollows:

•Air-frictiondamping

•Fluid-frictiondamping

•Eddy-currentdamping

1.Air-FrictionDamping

Inthismethod,alightaluminiumpistonisattachedtothemovingsystemandmovesinanairchamberclosedatoneend,asshowninFigure2.6.Thecross-sectionofthischambermaybeeithercircularorrectangular.Theclearancebetweenthepistonandthesidesofthechambershouldbesmallanduniform. If thepiston ismovingrapidly into thechamber,theairintheclosedspaceiscompressedandthepressureopposesthemotionofthepiston(and,therefore,ofthewholemovingsystem).Ifthepistonismovingoutofthechamberrapidly, the pressure in the closed space falls, and the pressure on the open side of thepistonisgreaterthanthatontheoppositeside.Motionisthusagainopposed.Sometimesinstead of a piston, a vane,mounted on the spindle of themoving system,moves in a

closed-sector-shapedboxasshowninFigure2.7.

Figure2.6Open-endairfrictiondamping

Figure2.7Air-frictiondampingusingvane

2.Fluid-FrictionDamping

Inthistypeofdamping,alightvane,attachedtothespindleofthemovingsystem,dipsinto a pot of damping oil and should be completely submerged by the oil. This isillustrated in Figure 2.8(a). The frictional drag in the disc is always in the directionopposing motion. There is no friction force when the disc is stationary. In the secondsystem[Figure2.8(b)],increaseddampingisobtainedbytheuseofvanes.

Figure2.8Fluid-frictiondamping

3.Eddy-CurrentDamping

Whenasheetofconductingmaterialmovesinamagneticfieldsoastocutthroughlinesofforce,eddycurrentsaresetup in itandaforceexistsbetween thesecurrentsand themagnetic field, which is always in the direction opposing the motion. The force isproportional to the magnitude of the current and to the strength of the field. The

magnitudeofthecurrentisproportionaltothevelocityofmovementoftheconductor,andthus,ifthemagneticfieldisconstant,thedampingforceisproportionaltothevelocityofthemovingsystemandiszerowhenthereisnomovementofthesystem.

(i) Eddy-Current Damping Torque of Metal Former Figure 2.9 shows a metallicformermovinginthefieldofapermanentmagnet.

Figure2.9Eddy-currentdampingonametalformer

Let,

B=strengthofmagneticfield;(wb/m2)

ω=asngularspeedofformer;(rad/s)

l=lengthofformer;(m)

t=thicknessofformer;(m)

b=widthofformer;(m)

d=breadthofformer;(m)

ρ=resistivityofmaterialofformer;(Wm)

[sincelinearvelocity=radius×angularvelocity]

Dynamicallygeneratedemfintheformer

(ii)Eddy-CurrentDampingTorqueofMetalDiscFigure2.10showsametallicdisc

rotatinginthefieldofapermanentmagnet.

Figure2.10Eddy-currentdampingonmetallicdisc2

Let, B= fluxdensityofmagneticfield;(wb/m2)

ω=angularspeedofdisc;(rad/s)

t=thicknessofdisc;(m)

b=widthofpermanentmagnet;(m)

d=lengthofpermanentmagnet;(m)

ρ=resistivityofmaterialofdisc;(Ωm)

R=radiusmeasuredfromcentreofpoletocentreofdisc;(m)

Considering the emf is induced in the disc under the pole face only, therefore, emfinducesintheportionbelowthemagnet

[since‘l’,lengthoftheportionofthediscunderthemagneticfield=d]

Actualpathforeddycurrentisnotlimitedtotheportionofthediscunderthemagnetbutisgreaterthanthis.Therefore,totakethisfactorintoaccount,theactualresistanceistakenasktimesof .

wherekisaconstantwhichdependsuponradialpositionofthediscandpoles.

2.6 PERMANENTMAGNETMOVINGCOILINSTRUMENT

Basicrange:10μA-100mA

Coilresistance:10Ω-1kΩ

Usage:

-dcPMMCammetersandvoltmeters

-acPMMCammetersandvoltmeters(withrectifiers)

2.6.1PrincipleofOperationTheprincipleonwhichaPermanentMagnetMovingCoil(PMMC)instrumentoperatesisthat a torque is exerted on a current-carrying coil placed in the field of a permanentmagnet.APMMCinstrumentisshowninFigure2.11.ThecoilChasanumberofturnsofthininsulatedwireswoundonarectangularaluminiumformerF.TheframeiscarriedonaspindleSmountedinjewelbearingsJ1,J2.ApointerPRisattachedtothespindlesothatit moves over a calibrated scale. The whole of themoving system ismade as light inweightaspossibletokeepthefrictionatthebearingtoaminimum.

Thecoilisfreetorotateinairgapsformedbetweentheshapedsoft-ironpolepiece(pp)ofapermanentmagnetPMandafixedsoft-ironcylindricalcoreIC[Figure2.11(b)].Thecoreservestwopurposes;(a)itintensifiesthemagneticfieldbyreducingthelengthoftheairgap,and(b)itmakesthefieldradialanduniformintheairgap.

Thus,thecoilalwaysmovesatrightanglestothemagneticfield[Figure2.11(c)].Modernpermanentmagnetsaremadeofsteelalloyswhicharedifficulttomachine.Soft-ironpolepieces(pp)areattachedtothepermanentmagnetPMforeasymachininginordertoadjustthelengthoftheairgap.Figure2.11(d)showstheinternalpartsandFigure2.11(e)showsschematicofinternalpartsofamoving-coilinstrument.

Asoft-ironyoke(Y)isusedtocompletethefluxpathandtoprovideshieldingfromstrayexternalfields.

Permanentmagnetmovingcoilinstrument

PhotographofdifferentcomponentsofaPMMCinstrument

InternalconstructionofPMMCinstrumentsFigure2.11

2.6.2DeflectingTorqueEquationofPMMCInstrumentLet,B=fluxdensityintheairgap(wb/m2)

i=currentinthecoil(A)

l=effectiveaxiallengthofthecoil(m)

b=breadthofthecoil(m)

n=numberofturnsofthecoil.

Forceononesideofthecoilis

Torqueoneachsideofthecoil,

Totaldeflectingtorqueexertedonthecoil,

Forapermanentmagnet,Bisconstant.Also,foragivencoil l,bandnareconstantsandthustheproduct(Blnb)isalsoaconstant,sayk1.

1.ControlTorqueThecontrolonthemovementofthepointeroverthescaleisprovidedbytwospirallywound,phosphor-bronzespringsS1andS2,oneateachendofthespindleS.Sometimesthesespringsalsoconductthecurrentintoandoutofthecoil.Thecontroltorqueofthespringsisproportionaltotheangleθturnedthroughbythecoil.

whereTCisthecontroltorqueandksisthespringconstant.

Atfinalsteadystateposition,Controltorque=Deflectingtorque

So, angular deflection of the pointer is directly proportional to the current. Thus thescaleoftheinstrumentislinearoruniformlydivided.

2.DampingTorqueWhenthealuminiumformer(F)moveswiththecoilinthefieldofthe permanentmagnet, a voltage is induced, causing eddy current to flow in it. Thesecurrent exerts a force on the former. By Lenz’s law, this force opposes the motionproducingit.Thus,adampingtorqueisobtained.Suchadampingiscallededdy-currentdamping.

2.6.3SwampingResistor

The coil of the instrument ismade of copper. Its resistance varieswith temperature.Aresistor of low temperature coefficients, called the swamping resistor, is connected inserieswiththecoil.Itsresistancepracticallyremainsconstantwithtemperature.Hencetheeffectoftemperatureoncoilresistanceisswampedbythisresistor.

AdvantagesofPMMCInstruments

1.Sensitivetosmallcurrent

2.Veryaccurateandreliable

3.Uniformscaleupto270°ormore

4.Veryeffectivebuiltindamping

5.Lowpowerconsumption,variesfrom25µWto200µW

6. Free from hysteresis and not effected by external fields because its permanentmagnetshieldsthecoilfromexternalmagneticfields

7.Easilyadoptedasamultirangeinstrument

DisadvantagesofPMMCInstruments

1.Thistypeofinstrumentcanbeoperatedindirectcurrentonly.Inalternatingcurrent,theinstrumentdoesnotoperatebecauseinthepositivehalf,thepointerexperiencesaforceinonedirectionandinthenegativehalfthepointerexperiencestheforceintheoppositedirection.Duetotheinertiaofthepointer,itretainsit’szeroposition.

2.Themovingsystemisverydelicateandcaneasilybedamagedbyroughhandling.

3.Thecoilbeingveryfine,cannotwithstandprolongedoverloading.

4.Itiscostlier.

5.Theageingoftheinstrument(permanentmagnetandcontrolspring)mayintroducesomeerrors.

Example2.1

ThecoilofaPMMCinstrumenthas60turns,onaformerthat is 18 mm wide, the effective length of the conductorbeing25mm.Itmovesinauniformfieldoffluxdensity0.5Tesla.Thecontrolspringconstantis1.5×10-6Nm/degree.Calculate the current required to produce a deflection of100degree.

Solution Totaldeflectingtorqueexertedonthecoil,

Td=Bilnb(N-m)

=0.5×ix25×10-3×60×18×10-3

Thecontroltorqueofthespringsis

TC=ks×θ

=1.5×10-6×100

Atequilibrium,Td=TC

=0.5×ix18×10-3×25×10-3×60=1.5×10-6×1001.5×10-6×100

Example2.2

APMMCinstrumenthasacoilofdimensions15mm×12mm.Thefluxdensityintheairgapis1.8×10-3wb/m2andthespringconstant is0.14×10-6N-m/rad.Determine thenumberof turnsrequiredtoproduceanangulardeflectionof90°whenacurrentof5mAisflowingthroughthecoil.

SolutionTotaldeflectingtorqueexertedonthecoil,Td=Bilnb(N-m)

=1.8×10-3×5×10-3×15×10-3×12×10-3×n

Thecontroltorqueofthespringsis

TC=ks×6

=0.14×10-6×90×π/180

Atequilibrium,Td=TC

1.8×10-3×5×10-3×15×10-3×12×10-3×n=0.14×10-6×90×π/180

Example2.3

APMMCvoltmeterwitharesistanceof20Ωgivesa full-scaledeflectionof120°whenapotentialdifferenceof100mVisappliedacrossit.Themovingcoilhasdimensionsof30mm×25mmandiswoundwith100turns.Thecontrolspring constant is 0.375×10-6N-m/degree. Find the fluxdensity in the air gap. Find also the dimension of copperwireofcoilwinding if30%of the instrumentresistance isduetocoilwinding.Thespecificresistanceofcopperis1.7×10-8Ωm.

Solution Full-scaledeflectingcurrent

Totaldeflectingtorqueexertedonthecoil,

Td=Bilnb(N-m)

=B×5×10-3×30×10-3×25×10-3×100

Thecontroltorqueofthespringsis

TC=ks×θ

=0.375×10-6×120

Atequilibrium,Td=TC

B×5×10-3×30×10-3×25×10-3×100=0.375×10-6×120

Coilwindingresistance=20×0.3=6Ω

Ifthecopperwirehasacross-sectionalareaofamthen

Example2.4

Thecoilofamoving-coilvoltmeteris40mmlongand30mmwideandhas100turnsonit.Thecontrolspringexertsatorqueof240×10-6N-mwhenthedeflectionis100divisionsonfullscale.Ifthefluxdensityofthemagneticfieldintheairgapis1wb/m2,estimatetheresistancethatmustbeputinserieswiththecoiltogiveonevoltperdivision.Theresistanceofthevoltmetercoilmaybeneglected.

Solution LetthefullscaledeflectingcurrentbeIamp.

Totaldeflectingtorqueexertedonthecoil,

Td=Bilnb(N-m)

=1×I×40×10-3×30×10-3×100

ThecontroltorqueofthespringsisTc=ks×θ

=240×10-6

Atequilibrium,Td=TC

1×I×40×10-3×30×10-3×100=240×10-6

2.7 EXTENSIONOFRANGEOFPMMCINSTRUMENTS

2.7.1AmmeterShuntsThemoving-coil instrumenthasacoilwoundwithveryfinewire. ItcancarryonlyfewmAsafelytogivefull-scaledeflection.Formeasuringhighercurrent,alowresistanceisconnected inparallel to the instrument tobypass themajorpartof thecurrent.The lowresistanceconnectedinparallelwiththecoiliscalledashunt.Figure2.12showsashuntresistanceRshconnectedinparallelwiththebasicmeter.

Figure2.12ExtensionofPMMCammeterusingshunt

Theresistanceoftheshuntcanbecalculatedusingconventionalcircuitanalysis.

Rsh=shuntresistance(Ω)

Rm=coilresistance(Ω)

Im=Ifs=full-scaledeflectioncurrent(A)

1sh=shuntcurrent(A)

I=currenttobemeasured(A)

Thevoltagedropacross theshuntand themetermustbesameas theyareconnected inparallel.

FromEq.(2.25),

The ratio of the total current to the current in themeter is calledmultiplying power ofshunt.Multiplyingpower,

2.7.2VoltmeterMultipliers

Formeasuringhighervoltages,ahighresistanceisconnectedinserieswiththeinstrumenttolimitthecurrentinthecoiltoasafevalue.Thisvalueofcurrentshouldneverexceedthecurrentrequiredtoproducethefullscaledeflection.Thehighresistanceconnectedinserieswiththeinstrumentiscalledamultiplier.InFigure2.13,Rscisthemultiplier.

Figure2.13ExtensionofPMMCvoltmeterusingmultiplier

Thevalueofmultiplierrequiredtoextendthevoltagerange,iscalculatedasunder:

Rsc=multiplierresistance(Ω)

Rm=meterresistance(Ω)

Im=Ifs=fullscaledeflectioncurrent(A)

v=voltageacrossthemeterforproducingcurrentIm(A)

V=voltagetobemeasured(A)

V=ImRm

V=Im(Rm+Rsc)

Nowmultiplyingfactorformultiplier

Sensitivity Themoving-coil instrument is a very sensitive instrument. It is, therefore,widelyused formeasuringcurrentandvoltage.Thecoilof the instrumentmayrequireasmallamountofcurrent (in the rangeofµA) for full-scaledeflection.Thesensitivity issometimesexpressedinohm/volt.Thesensitivityofavoltmeterisgivenby

where Ifs is the full-scale deflecting current. Thus, the sensitivity depends upon on thecurrenttogivefull-scaledeflection.

Example2.5

A moving-coil voltmeter has a resistance of 100 Ω. Thescaleisdividedinto150equaldivisions.Whenapotentialdifferenceof1Visappliedtotheterminalsofthevoltmetera deflection of 100 divisions is obtained.Explain how theinstrumentcouldbeusedformeasuringupto300V.

SolutionLetRscbe themultiplier resistance thatwouldbeconnected inserieswith thevoltmeter.

Volt/division=1/100

Voltageacrossthemeterforproducingthefull-scaledeflectingcurrentv=150×1/100=1.5V

FullscalemetercurrentIm=1.5/100amp

MeterresistanceRm=100Ω

Example2.6Amovingcoilinstrumenthasaresistanceof5Ωandgivesa full scale deflection of 10mv. Showhow the instrumentmay be used to measure (a) voltage up to 50 v, and (b)currentupto10A.

SolutionFullscaledeflectionof10mv

Fullscaledeflectioncurrent=10×10-3/5=2mA

(a)Formeasuringthevoltageupto50VweneedtoconnectamultiplierresistanceRSCinserieswiththeinstrument

(b)Formeasuringthecurrentupto10Aweneedtoconnectashuntresistanceinparalleltotheinstrument.

Example2.7

Amoving-coilammeterhasafixedshuntof0.02Ω.WithacoilresistanceofR=1000Ωandapotentialdifferenceof500mVacross it.Full-scale deflection is obtained. (a)Towhatshuntedcurrentdoesitcorrespond?(b)CalculatethevalueofRtogivefull-scaledeflectionwhenshuntedcurrentI is (i)10A,and(ii)75A, (c)WithwhatvalueofR,40%deflectionobtainedwithI=100A.

Solution

(a)CurrentthroughshuntIsh=500×10-3/0.02=25A.

(b)(i)Voltageacrossshuntforacurrentof10A=0.02×10=0.2V.

Therefore,resistanceofmeterforacurrentof10Atogivefullscaledeflection=0.2/(0.5×10-3)=400Ω

(ii) Voltageacrossshuntforacurrentof75A=0.02×75=1.5V.Therefore,resistance of meter for a current of 75 A to give full scale deflection =1.5/(0.5×10-3)=3000Ω

(c)Now40%deflectionisobtainedwith100A.Therefore,currenttogivefull-scaledeflection=100/0.4=250AVoltageacrossshuntforacurrentof250A=0.02×250=5V

Resistanceofmeterforacurrentof100Atogive40%offullscaledeflection=5/(0.5×10-3)=10,000Ω

Example2.8

A simple shunted ammeter using a basicmetermovementwith an internal resistance of 1800 Ω and a full-scaledeflection current of 100 pA is connected in a circuit andgivesreadingof3.5mAonit’s5mAscale.Thereadingischeckedwitharecentlycalibrateddcammeterwhichgivesa reading of 4.1mA. The implication is that the ammeterhas a faulty shunt on it’s 5 mA range. Calculate (a) theactual value of faulty shunt, and (b) the current shunt forthe5mArange.

Solution

(a)5mAscaledeflectioncorrespondsto100µA.

Therefore,3.5mAcorrespondsto

As theshuntand themeterareconnected inparallel, thedropacross theshuntshouldbeequaltothevoltagedropacrossthemeter.Metercurrent=7×10-5AShuntcurrent=(4.1×10—3–7×10—5)ATherefore,actualvalueof faultyshunt,

Rsh×(4.1×10—3—7×10—5)=1800×7×10—5

(b)5mAscaledeflectioncorrespondsto100µA.

Therefore,4.1mAcorrespondsto =82×10-6A

Astheshuntandthemeterareconnectedinparallel,thenthedropacrosstheshuntshouldbeequaltothevoltagedropacrossthemeter.

Metercurrent=82×10—6A

Shuntcurrent=(4.1×10—3–82×10—6)ATherefore,actualvalueoffaultyshunt,

Rsh×(4.1×10—3–82×10—6)=1800×82×10—6

Example2.9

Amoving-coil instrument gives the full-scale deflection of10mAwhenthepotentialdifferenceacrossitsterminalsis100mV.Calculate (a) the shunt resistance fora full-scaledeflection corresponding to 100 A, and (b) the seriesresistanceforfullscalereadingwith1000V.Calculatethepowerdissipationineachcase.

Solution

(a)MeterresistanceRm=100mV/10mA=10Ω

Theshuntresistancecorrespondsto100Afull-scaledeflection

NowRmandRshareconnectedinparallel,theequivalentresistanceis

PowerdissipationP=12R=1002×0.00099=9.9W

(b)Theseriesresistancecorrespondsto1000V,

NowRmandRscareconnectedinseries,theequivalentresistanceis

R=Rsh+Rm=99,990+10=100,000Ω

PowerdissipationP=V2/R=10002/100,000=10W

Example2.10

Amoving-coilinstrumenthasaresistanceof75Ωandgivesafull-scaledeflectionof100-scaledivisionsforacurrentof1mA.Theinstrumentisconnectedinparallelwithashuntof25Ωresistanceandthecombinationisthenconnectedinserieswitha loadandasupply.What is thecurrent in theload when the instrument gives an indication of 80 scaledivisions?

Solution For80scaledivisions,currentthroughthemeteris×1=0.8mA

2.8 MOVING-IRONINSTRUMENTS

Basicrange:10mA-100A

Usage:

•dcMIammetersandvoltmeters

•acMIammetersandvoltmeters

Moving-IronorMIinstrumentscanbeclassifiedas

•Attraction-typemoving-ironinstruments

•Repulsion-typemoving-ironinstruments

Thecurrenttobemeasured,ingeneral,ispassedthroughacoilofwireinthemoving-ironinstruments.Incaseofvoltagemeasurement,thecurrentwhichisproportionaltothevoltage is measured. The number of turns of the coil depends upon the current to bepassed through it. For operation of the instrument, a certain number of ampere turns isrequired. These ampere turns can be produced by the product of few turns and largecurrentorreverse.

2.8.1Attraction-typeMoving-IronInstrumentsTheattractiontypeofMIinstrumentdependsontheattractionofanironvaneintoacoilcarryingcurrenttobemeasured.Figure2.14showsaattraction-typeMIinstrument.AsoftironvaneIVisattachedtothemovingsystem.Whenthecurrenttobemeasuredispassedthrough the coil C, a magnetic field is produced. This field attracts the eccentricallymountedvaneonthespindletowardsit.Thespindleissupportedatthetwoendsonapairofjewelbearings.Thus,thepointerPR,whichisattachedtothespindleSofthemovingsystemisdeflected.Thepointermovesoveracalibratedscale.

ThecontroltorqueisprovidedbytwohairspringsS1andS2inthesamewayasforaPMMC instrument; but in such instruments springs are not used to carry any current.Gravity control can also be used for vertically mounted panel type MI meters. ThedampingtorqueisprovidedbythemovementofathinvaneVinaclosedsector-shapedboxB,orsimplybyavaneattachedtothemovingsystem.Eddycurrentdampingcannotbe used in MI instruments owing to the fact that any permanent magnet that will berequired to produce Eddy current damping can distort the otherwise weak operatingmagneticfieldproducedbythecoil.

Ifthecurrentinthefixedcoilisreversed,thefieldproducedbyitalsoreverses.Sothepolarityinducedonthevanereverses.Thuswhateverbethedirectionofthecurrentinthecoilthevaneisalwaysbemagnetizedinsuchawaythatitisattractedintothecoil.Hencesuchinstrumentcanbeusedforbothdirectcurrentaswellasalternatingcurrent.

Figure2.14Attraction-typemovingiron(MI)instrument

2.8.2Repulsion-typeMoving-IronInstrumentsIn the repulsion type, there are twovanes inside the coil.One is fixed and the other ismovable. These are similarly magnetised when the current flows through the coil and

there is a force of repulsion between the two vanes resulting in the movement of themovingvane.

Twodifferentdesignsformovingironinstrumentscommonlyusedareasfollows:

1.RadialVaneTypeInthistype,thevanesareradialstripsofiron.Thestripsareplacedwithin thecoilasshowninFigure2.15(a).Thefixedvane isattached to thecoilandthemovableonetothespindleoftheinstrument.Theinstrumentpointerisattachedtothemovingvanespindle.

As current flows through the coil, the generated magnetic field induces identicalpolaritiesonboththefixedandmovingvane.Thus,evenwhenthecurrentthroughthecoilisalternating(forACmeasurement),thereisalwaysarepulsionforceactingbetweenthelikepolesoffixedandmovingvane.Hencedeflectionofthepointerisalwaysinthesamedirection irrespective of the polarity of current in the coil. The amount of deflectiondependsontherepulsionforcebetweenthevaneswhichinturndependsontheamountofcurrentpassing through the coil.The scale can thusbe calibrated to read the currentorvoltagedirectly.

Figure2.15Re-pulsion-typeMovingIron(MI)instruments

2.Co-axialVaneTypeIInthesetypeofinstruments,thefixedandmovingvanesare sections of coaxial cylinders as shown in Figure 2.15(b). Current in the coilmagnetizesboththevaneswithsimilarpolarity.Thusthemovablevanerotatesalongthespindle axis due to this repulsive force. Coaxial vane type instruments are moderatelysensitiveascomparedtoradialvanetypeinstrumentsthataremoresensitive.

Moving iron instruments have their deflection is proportional to the square of thecurrent flowing through thecoil.These instrumentsare thussaid to followasquare lawresponseandhavenon-uniformscalemarking.Deflectionbeingproportionaltosquareofthe current,whatever be the polarity of current in the coil, deflection of amoving ironinstrumentisinthesamedirection.Hence,movingironinstrumentscanbeusedforbothDCandACmeasurements.

2.8.3TorqueEquationofMoving-IronInstrumentsTodeducetheexpressionfortorqueofamovingironinstrument,energyrelationcanbeconsidered for a small increment in current supplied to the instrument. This result in asmall deflection dθ and somemechanical work will be done. Let Td be the deflectingtorque.

Thereforemechanicalworkdone=torque×angulardisplacement

Due to the change in inductance there will be a change in the energy stored in themagneticfield.

LetIbetheinitialcurrent,Lbetheinstrumentinductanceandθisthedeflection.IfthecurrentincreasesbydlthenitcausesthechangeindeflectiondθandtheinductancebydL.Inorder to involvetheincrementdI in thecurrent, theappliedvoltagemustbe increaseby:

[substitutethevalueofedtfromequation(2.28)]

ThecurrentischangesfromIto(I+dI),andtheinductorLto(L+dL)

Thereforethestoredenergychangesfrom

As dI anddL are very small, neglecting the second and higher order terms in smallquantities,this

becomes

Fromtheprincipleofconservationofenergy,

Electricalenergysupplied=Increaseinstoredenergy+Mechanicalworkdone.

whereTdisinnewton-metre,Iisinampere,Lisinhenryandθisinradians.

ThemovingsystemisprovidedwithcontrolspringsandinturnthedeflectingtorqueTdisbalancedbythecontrollingtorqueTC=kθ

wherekisthecontrolspringconstant(N-m/rad)andθisthedeflectioninradians.

Atfinalsteadyposition,TC=Td

Hence,thedeflectionisproportionaltosquareofthermsvalueoftheoperatingcurrent.The deflection torque is, therefore, unidirectional whatever may be the polarity of thecurrent.

AdvantagesofMIInstruments1.Robustconstructionandrelativelycheap

2.Suitableformeasuringbothdcandac

3.Canwithstandoverloadmomentarily

DisadvantagesofMIInstruments

1. As the deflection is proportional to I 2, hence the scale of the instrument is notuniform.Itiscrampedinthelowerendandexpandedintheupperportion.

2.Itisaffectedbystraymagneticfields.

3.Thereishysteresiserrorintheinstrument.Thehysteresiserrormaybeminimizedbyusingthevanesofnickel-ironalloy.

4.Whenusedformeasuringacthereadingmaybeaffectedbyvariationoffrequencydue to the change in reactance of the coil, which has some inductance.With theincreaseinfrequencyironlosesandcoilimpedanceincreases.

5.SincelargeamountofpowerisconsumedtosupplyI2Rlossinthecoilandmagneticlossesinthevanes,itisnotaverysensitiveinstrument.

Example2.11

Theinductanceofamoving-ironammeterwithafull-scaledeflectionof90°at1.5AisgivenbyL=(200+40θ-4θ2-θ3) μH where θ is the deflection in radian from the zeroposition.Estimatetheangulardeflectionofthepointerforacurrentof1A.

SolutionForanMIinstrument,

Aftersolvingforθandtakingonlythepositivevalue

θ=1.00712rad=57.7°

Example2.12Thelawofdeflectionofamoving-ironammeterisgivenbyI=4θnampere,whereθisthedeflectioninradianandnisa constant. The self-inductancewhen themeter current iszerois10mH.Thespringconstantis0.16N-m/rad.

(a)Determineanexpressionforself-inductanceofthemeterasafunctionofθandn.

(b)Withn=0.75,calculatethemetercurrentandthedeflectionthatcorrespondstoaself-inductanceof60mH.

Solution

2.9 ELECTRODYNAMOMETER-TYPEINSTRUMENTS

The electrodynamometer is a transfer-type instrument.A transfer-type instrument is onethatmaybecalibratedwithadcsourceandthenusedwithoutmodificationtomeasureac.Thisrequiresthetransfertypeinstrumentstohavesameaccuracyforbothdcandac.

The electrodynamic or dynamometer-type instrument is amoving-coil instrument butthemagneticfield,inwhichthecoilmoves,isprovidedbytwofixedcoilsratherthanbypermanent magnets. The schematic diagram of electrodynamic instrument is shown inFigure2.16(a)andapracticalmeter isshowninFigure2.16(b). Itconsistsof twofixedcoils,whicharesymmetricallysituated.Itwouldhaveatorqueinonedirectionduringonehalfofthecycleandanequaleffectinoppositedirectionduringtheotherhalfofthecycle.If,however,weweretoreversethedirectionofthefluxeachtimethecurrentthroughthemovable coil reverses, a unidirectional torquewouldbeproduced for bothpositivehalfandnegative half of the cycle. In electrodynamic instruments, the field can bemade toreversesimultaneouslywiththecurrentinthemovablecoilifthefixedcoilisconnectedinserieswiththemovablecoil.

1.ControllingTorqueThecontrollingtorqueisprovidedbytwocontrolsprings.Thesespringsactasleadstothemovingcoil.

Figure2.16Electrodynamometer-typeinstrument

2.DampingAir-frictiondampingisemployedfortheseinstrumentsandisprovidedbyapair of aluminiumvanes, attached to the spindle at the bottom.These vanesmove in asector-shapedchamber.

2.9.1TorqueEquationofElectrodynamometer-typeInstruments

Let,i1=instantaneousvalueofcurrentinthefixedcoils,(A)

i2=instantaneousvalueofcurrentinthemovingcoils,(A)

L1=self-inductanceoffixedcoils,(H)

L2=self-inductanceofmovingcoil,(H)

M=mutualinductancebetweenfixedandmovingcoils(H)

FluxlinkageofCoil1,ψ1=L1i1+Mi2FluxlinkageofCoil2,ψ2=L2i2+Mi1Electricalinputenergy,

Energystoredinthemagneticfield

Changeinenergystored=

Fromtheprincipleofconservationofenergy,

Totalelectricalinputenergy=Changeinenergyinenergystored+mechanicalenergyThemechanicalenergycanbeobtainedbysubtractingEq.(2.35)fromEq.(2.34).

Therefore,mechanicalenergy=

Now,theself-inductancesL1andL1areconstantsand,therefore,dL2anddL2bothareequaltozero.Hence,mechanicalenergy=i1i2dM

SupposeTi is the instantaneous deflecting torque anddθ is the change in deflection,then,Mechanicalenergy=workdone=Tidθ

Thuswehave

1.OperationwithdcLet,I1=currentinthefixedcoils,I2=currentinthemovingcoil

So deflecting torqueTd = I1I2 . This shows that the deflecting torque depends ingeneralontheproductofcurrentI1andI2andtherateofchangeofmutualinductance.

Thisdeflectingtorquedeflectsthemovingcoiltosuchapositionwherethecontrollingtorque of the spring is equal to the deflecting torque. Suppose θ be the final steadydeflection.

ThereforecontrollingtorqueTC=kθwherek=springconstant(N-m/rad)

AtfinalsteadypositionTd=TC

Ifthetwocoilsareconnectedinseriesformeasurementofcurrent,thetwocurrentsI1andI2areequal.

Say, I1=I2=I

Thus,deflectionofthepointeris

For dc use, the deflection is thus proportional to square of the current andhence thescalenon-uniformandcrowdedattheends.

2.OperationwithacLet, i1and i2be the instantaneousvaluesofcurrentcarriedby thecoils.Therefore,theinstantaneousdeflectingtorqueis:

If the two coils are connected in series for measurement of current, the twoinstantaneouscurrentsi1andi2areequal.

Say, ii=i2=i

Thus,instantaneoustorqueonthepointerisTi=i2

Thus, for ac use, the instantaneous torque is proportional to the square of theinstantaneous current. As the quantity i2 is always positive, the current varies and theinstantaneous torquealsovaries.But themovingsystemdue to its inertiacannot followsuchrapidvariationsintheinstantaneoustorqueandrespondsonlytotheaveragetorque.

Theaveragedeflectingtorqueoveracompletecycleisgivenby:

whereTisthetimeperiodforonecompletecycle.

AtfinalsteadypositionTd=TC

Thus,deflectionofthepointeris

Deflectionisthusafunctionofthemeanofthesquareofthecurrent.Ifthepointerscaleiscalibratedintermsofsquarerootofthisvalue,i.e.squarerootofthemeanofthesquareof current value, then rms value of the ac quantity can be directly measured by thisinstrument.

3.SinusoidalCurrent If currents i1 and i2 are sinusoidal and are displaced by a phaseanglej,i.e.

i1=im1sinωtandi2=Im1sin(wt-j)

Theaveragedeflectingtorque

where I1 and I2 are the rms values of the currents flowing through the coils. Atequilibrium,Td=TC

Aswasinthecasewithacmeasurement,withsinusoidalcurrentalsothedeflectionisafunctionofthemeanofthesquareofthecurrent.Ifthepointerscaleiscalibratedintermsof square rootof thisvalue, i.e. square rootof themeanof the squareof currentvalue,thenRMSvalueoftheacquantitycanbedirectlymeasuredbythisinstrument.

1.ElectrodynamicAmmeter In an electrodynamic ammeter, the fixed and movingcoils are connected in series as shown in Figure 2.17.A shunt is connected across themovingcoil for limiting thecurrent.The reactance–resistance ratioof theshuntand themoving coil is keptnearly same for independenceof themeter readingwith the supplyfrequency.Sincethecoilcurrentsarethesame,thedeflectingtorqueisproportionaltothemeansquarevalueofthecurrent.Thus,thescaleiscalibratedtoreadthermsvalue.

2. Electrodynamic Voltmeter The electrodynamic instrument can be used as avoltmeterbyconnectingalargenoninductiveresistance(R)oflowtemperaturecoefficientinserieswiththeinstrumentcoilasshowninFigure2.18.

Figure2.17Electrodynamometerammeter

Figure2.18Electrodynamometervoltmeter

3.ElectrodynamicWattmeterTheelectrodynamicwattmeterconsistoftwofixedcoils‘a’and ‘b’placedsymmetrical toeachotherandproducingauniformmagnetic field.TheyareconnectedinserieswiththeloadandarecalledtheCurrentCoils(CC).Thetwofixedcoils can be connected in series or parallel to give two different current ratings. The

currentcoilscarrythefull-loadcurrentorafractionoffullloadcurrent.Thusthecurrentinthecurrentcoilsisproportionaltotheloadcurrent.Themovingcoil‘c’,inserieswithahighnoninductiveresistanceRvisconnectedacrossthesupply.Thusthecurrentflowinginthemovingcoilisproportionalto,andpracticallyinphasewiththesupplyvoltage.Themoving coil is also called the voltage coil or Pressure Coil (PC). The voltage coil iscarriedonapivotedspindlewhichcarriesthepointer,thepointermovedoveracalibratedscale.

Twohairspringsareusedforprovidingthecontrollingtorqueandfor leadingcurrentintoandoutof themovingcoil.Dampingisprovidedbyairfriction.Figure2.20showsthebasicarrangementofaelectrodynamicwattmeter.

Figure2.19Electrodynamicwattmeter

4.TorqueEquation

Let,if=currentinthefixedcoil

im=currentinthemovingcoil

i=loadcurrent

v=loadvoltage

Tin=instantaneousvalueofthedeflectingtorque

p=instantaneouspowerTinxifim

Thus, the instantaneous value of the deflecting torque is proportional to theinstantaneous power. Owing to the inertia of themoving system, the pointer reads theaveragepower. Indccircuits, thepower isgivenby theproductofvoltageandcurrent,andhencethetorqueisdirectlyproportionaltothepower.Thus,theinstrumentindicatesthepower.

Forac,theinstrumentindicatestheaveragepower.Thiscanbeprovedasfollows:Tin∞Vi

Averagedeflectingtorque×averagepower

Let, v=Vmsind

I=Imsin(θ-Ф)

Averagedeflectingtorque∞averagevalueofVmsind×Imsin(θ-Ф)∞VIcosθIfTdbetheaveragetorque,then

wherePisthetruepowerandkistheconstant.

ForspringcontrolTC=ksθ1whereTCisthecontroltorque,ksisthespringconstantandθ1istheangleofdeflectionofthepointer.

Forsteadydeflection,

Hence,incaseofacalsothedeflectionisproportionaltothetruepowerinthecircuit.Thescaleoftheelectrodynamometerwattmeteristhereforeuniform.

AdvantagesofElectrodynamometer-typeInstruments

1.Theycanbeusedonacaswellasdcmeasurements.

2.Theseinstrumentsarefreefromeddycurrentandhysteresiserror.

3. Electrodynamometer-type instruments are very useful for accurate measurement of rms values of voltagesirrespectiveofwaveforms.

4. Because of precision grade accuracy and same calibration for ac and dcmeasurements these instruments areusefulastransfertypeandcalibrationinstruments.

DisadvantagesofElectrodynamometer-typeInstruments

1.Astheinstrumenthassquarelawresponse,thescaleisnon-uniform.

2.Theseinstrumentshavesmalltorque/weightratio,sothefrictionalerrorisconsiderable.

3.MorecostlythanPMMCandMItypeofinstruments.

4.Adequatescreeningofthemovementsagainststraymagneticfieldsisessential.

5.Powerconsumptioniscomparablyhighbecauseoftheirconstruction.

Theinductanceofa25Aelectrodynamicammeterchangesuniformly at the rate of 0.0035 mH/radian. The spring

Example2.13 constant is 10-6N-m/radian. Determine the angulardeflectionatfullscale.

Nowthedeflection

AngulardeflectionatfullscalecurrentofI=25Aisgivenby:

Example2.14

Inanelectrodynamic instrument the total resistanceof thevoltage coil circuit is 8200 Ω and the mutual inductancechangesuniformlyfrom-173μHatzerodeflectionto+175μH at full scale. The angle of full scale being 95°. If apotential differenceof 100V is appliedacross the voltagecircuit and a current of 3 A at a power factor of 0.75 ispassedthroughthecurrentcoil,whatwillbethedeflection.Springconstantoftheinstrumentis4.63×10-6N-m/rad.

SolutionChangeinmutualinductancedM=175–(–173)=348µHDeflectionθ=95°=1.66rad

Rateofchangeofmutualinductance

CurrentthroughthecurrentcoilI1=3A

Currentthroughthevoltagecoil

Powerfactorcos6=0.75

Deflection

Example2.15

A 50 V range spring-controlled electrodynamic voltmeterhasaninitialinductanceof0.25H,thefullscaledeflectiontorqueof0.4×10-4Nmandfullscaledeflectioncurrentof50mA.Determinethedifferencebetweendcand50Hzacreading at 50 volts if the voltmeter inductance increasesuniformlyoverthefullscaleof90°.

Solution

Full-scaledeflection6=90°

Full-scaledeflectingtorque,Td=0.4×10-4Nm

Full-scaedeflectioncurrent,I=50mA=0.05A

Initialinduction,M=0.25H

Sincedeflectingtorque,

Soforfull-scaledeflection04×10-4=(005)2

or,

Totalchangeininductanceforfull-scaledeflection,

Totalmutualinductance,M=0.25+0.0251=0.2751H

Theresistanceofvoltmeter,

Theimpedancewhilemeasuringthevoltageof50Vat50HzAC

Andvoltmeterreading,=

Therefore,differenceinreading=50–49.8=0.2V

2.10 ELECTROSTATICINSTRUMENTS

Inelectrostaticinstruments,thedeflectingtorqueisproducedbyactionofelectricfieldoncharged conductors. Such instruments are essentially voltmeters, but theymay be usedwiththehelpofexternalcomponentstomeasurethecurrentandpower.Theirgreatestuseinthelaboratoryisformeasurementofhighvoltages.

Figure2.20Linearmotionofelectrostaticinstruments

Figure2.21Rotarymotionofelectrostaticinstruments

Rotarymotionofelectrostaticinstruments

Therearetwowaysinwhichtheforceacts:1.Onetypeinvolvestwooppositelychargedelectrodes.Oneofthemisfixedandtheotherismovable.Duetoforce

ofattraction,themovableelectrodeisdrawntowardsthefixedone.

2.Intheothertype,thereisforceofattractionorrepulsionbetweentheelectrodeswhichcausesrotarymotionofthemovingelectrode.

Inboththecases,themechanismresemblesavariablecapacitorandtheforceortorqueis due to the fact that the mechanism tends to move the moving electrode to such apositionwheretheenergystoredismaximum.

2.10.1ForceandTorqueEquation1. LinearMotionReferring to Figure 2.20, plateA is fixed andB ismovable. Theplatesareoppositelychargedandarerestrainedbyaspringconnectedtothefixedpoint.LetapotentialdifferenceofVvoltbeapplied to theplates; thena forceofattractionFNewtonexistsbetweenthem.PlateBmovestowardsAuntiltheforceisbalancedbythespring.ThecapacitancebetweentheplatesisthenCfaradandthestoredenergyis½CVjoules.

NowlettherebeasmallincrementdVintheappliedvoltage,thentheplateBmovesasmall distance dx towardsA. when the voltage is being increased a capacitive currentflows.Thiscurrentisgivenby

Theinputenergyis

Changeinstoredenergy=

(neglectingthehigherordertermsastheyaresmallquantities)

Fromtheprincipleofconservationofenergy,

Inputelectricalenergy=increaseinstoredenergy+mechanicalworkdone

2.RotationalMotionTheforgoingtreatmentcanbeappliedtotherotationalmotionby writing an angular displacement θ in place of linear displacement x and deflectingtorqueTdinsteadofforceF(Figure2.21).

Deflectingtorque

Iftheinstrumentisspringcontrolledorhasasuspensionthen

ControllingtorqueTC=k&,wherek=springconstant

θ=deflection

Hence,deflection

Since the deflection is proportional to the square of the voltage to bemeasured, theinstrumentcanbeusedonbothacanddc.Theinstrumentexhibitsasquarelawresponseandhencethescaleisnon-uniform.

AdvantagesofElectrostaticInstrumentss

1.Theseinstrumentsdrawsnegligibleamountofpowerfromthemains.

2.Theymaybeusedonbothacanddc.

3.Theyhavenofrequencyandwaveformerrorsasthedeflectionisproportionaltosquareofvoltageandthereisnohysteresis.

4.Therearenoerrorscausedbythestraymagneticfieldastheinstrumentworksontheelectrostaticprinciple.

5.Theyareparticularlysuitedforhighvoltage.

DisadvantagesofElectrostaticInstruments

1. The use of electrostatic instruments is limited to certain special applications, particularly in ac circuits ofrelatively high voltage, where the current drawn by other instrumentswould result in erroneous indication. Aprotective resistor isgenerallyused inserieswith the instrument inorder to limit thecurrent incaseofashortcircuitbetweenplates.

2.Theseinstrumentsareexpensive,largeinsizeandarenotrobustinconstruction.

3.Theirscaleisnotuniform.

4.Theoperatingforceissmall.

2.11 INDUCTION-TYPEINSTRUMENTS

Induction-type instruments areusedonly for acmeasurement and canbeused either asammeter, voltmeter or wattmeter. However, the induction principle finds its widest

application as a watt-hour or energy meter (for details, refer Chapter 8). In suchinstruments,thedeflectingtorqueisproducedduetothereactionbetweenthefluxofanacmagnetandtheeddycurrentsinducedbyanotherflux.

2.11.1PrincipleofOperationTheoperationsof induction-type instrumentsdependon theproductionof torquedue totheinteractionbetweenafluxΦ1(whosemagnitudedependsonthecurrentorvoltagetobemeasured)andeddycurrentinducedinametaldiscordrumbyanotherfluxΦ2(whosemagnitudealsodependsonthecurrentorvoltagetobemeasured).Sincethemagnitudeofeddy current also depends on the flux producing them, the instantaneous value of thetorqueisproportionaltothesquareofcurrentorvoltageundermeasurementandthevalueofmeantorqueisproportionaltothemeansquarevalueofthiscurrentorvoltage.

ConsiderathinaluminiumorcopperdiscDfreetorotateaboutanaxispassingthroughits centre as shown in Figure 2.22. Two electromagnets P1 and P2 produce alternatingfluxesΦ1andΦ2 respectivelywhichcuts thisdisc.Consideranyannularportionof thediscaroundP1withcentreoftheaxisofPl.ThisportionwillbelinkedbyfluxΦ1andsoanalternatingemfΦ1beinducedinit.Φ2willinduceanemfe2whichwillfurtherinduceaneddycurrenti2inanannularportionofthediscaroundPl.Thiseddycurrentsi2flowsunderthepolePl.

Letustakethedownwarddirectionsoffluxesaspositiveandfurtherassumethatattheinstantunderconsideration,bothΦ1andΦ2are increasing.ByapplyingLenz’s law, thedirectionoftheinducedcurrentsi1andi2canbefoundasindicatedinFigure2.22(b).

The portion of the disc which is traversed by flux Φ1 and carries eddy currents i2experiences a force F1 along the direction as indicated. AsF = Bil, force F1 ∞ Φ1i2.Similarly, the portion of the disc lying under flux Φ2 and carrying eddy current i1experiencesaforceΦ2∞F2ij.

It isassumedthat theconstantk is thesame inboth thecasesdue to thesymmetricalpositionofP1andP2withrespecttothedisc.

Ifrbe theeffectiveradiusatwhich theseforcesacts, thennet instantaneous torqueTactingonthediscbeingequaltothedifferentofthetwotorques,itisgivenby

Figure2.22Principleofoperationofinduction-typeinstrument

Letthealternatingfluxφ1begivenbyφ1=φ1msinωt.Thefluxφ2whichisassumedtolagφ1byananglearadianisgivenbyφ2=φ2msin(ωt-a)

Inducedemfe1 (φ1msinωt)=ωφ1mcosωt

AssumingtheeddycurrentpathtobepurelyresistiveandofvalueR,thenthevalueofeddycurrentis

similarly,

Substitutingthesevaluesofi1andi2inEq.(2.48),wegetkw

Thefollowingisobserved:1.Ifα=0,i.e.,iftwofluxesareinphase,thennettorqueiszero.If,ontheotherhand,a=90°,thenettorqueis

maximumforagivenvaluesofφ1mandφ2m.

2. Thenet torque is suchadirectionas to rotate thedisc from thepolewith leading flux, towards thepolewithlaggingflux.

3.Sincetheexpressionfortorquedoesnotinvolvet,itisindependentoftime,i.e.,ithasasteadyvalueatalltimes.

4.ThetorqueTisinverselyproportionaltoR;theresistanceoftheeddycurrentpath.Hence,itismadeofcopperormoreoften,ofaluminium.

2.12 ELECTROTHERMALINSTRUMENTS

Mainlytherearetwotypesofthermalinstruments:

•Hot-wiretype

•Thermocoupleinstrument

Hot-wireandthermocouplemetermovementsusetheheatingeffectofcurrentflowingthrougharesistancetocausemeterdeflection.Eachusesthiseffectinadifferentmanner.Sincetheiroperationdependonlyontheheatingeffectofcurrentflow,theymaybeusedtomeasurebothdirectandalternatingcurrentsofanyfrequencyonasinglescale.

2.12.1Hot-wireInstrumentThehot-wiremetermovementdeflectiondependson theexpansionofahigh resistancewirecausedbytheheatingeffectofthewireitselfascurrentflowsthroughit.Aresistancewireisstretchedbetweenthetwometerterminals,withathreadattachedatarightanglesto the centre of thewire.A spring connected to the opposite endof the thread exerts aconstanttensionontheresistancewire.Currentflowheatsthewire,causingittoexpand.Thismotionistransferredtothemeterpointerthroughthethreadandapivot.Figure2.23showsthebasicarrangementofahotwiretypeinstrument.

Figure2.23Hot-wireinstruments

AdvantagesofHot-wire-typeInstruments

1. The deflection depends upon only the rms value of the current flowing through the wire, irrespective if itswaveformandfrequency.Hence,theinstrumentcanusedforacaswellasdcsystem.

2.Thecalibrationissameforacaswellasdcmeasurement.Soitisatransfer-typeinstrument.

3.Theyarefreefromstraymagneticfieldsbecausenomagneticfieldisusedtocausetheiroperation.

4.Itischeapincostandsimpleinconstruction.

5.Withsuitableadjustments,errorduetotemperaturevariationcanbemadenegligible.

6.Thistypeofinstrumentsarequitesuitableforveryhighfrequencymeasurement.

DisadvantagesofHot-wire-typeInstruments

1.Powerconsumptionisrelativelyhigh.

2.Nonuniformscale.

3.Theseareverysluggishinactionastimeistakeninheatingupthewire.

4.Thedeflectionoftheinstrumentisnotthesameforascendinganddescendingvalues.

5.Thereadingdependsupontheatmospherictemperature.

2.12.2Thermocouple-TypeInstrumentWhen two metals having different work functions are placed together, a voltage isgeneratedatthejunctionwhichisnearlyproportionaltothetemperatureofthejunction.This junction is called a thermocouple.This principle is used to convert heat energy toelectricalenergyatthejunctionoftwoconductorsasshowninFigure2.24.

Theheatatthejunctionisproducedbytheelectricalcurrentflowingintheheaterelementwhile the thermocoupleproducesanemfat itsoutput terminals,whichcanbemeasuredwiththehelpofaPMMCmeter.Theemfproducedisproportionaltothetemperatureandhencetothermsvalueofthecurrent.Therefore, thescaleofthePMMCinstrumentcancalibrate to read the current passing through the heater. The thermocouple type ofinstrument canbeused forboth ac anddc applications.Themost effective featureof athermocoupleinstrumentisthattheycanbeusedformeasurementofcurrentandvoltagesatveryhighfrequency.Infact,theseinstrumentsareveryaccuratewellaboveafrequencyof50MHz.

Figure2.24Circuitdiagramofthermocoupleinstrument

AdvantagesofThermocouple-typeInstruments

1.Thesearenotaffectedbystraymagneticfields.

2.Theyhaveveryhighsensitivity.

3.Theindicationoftheseinstrumentsarepracticallyunaffectedbythefrequencyandwaveformofthemeasuringquantity.Hencetheseinstrumentscanbeusedformeasurementofcurrentsuptofrequenciesof50MHzandgiveaccuracyashighas1%.

4.Theseinstrumentsareveryusefulastransferinstrumentsforcalibrationofdcinstrumentsbypotentiometerandastandardcell.

DisadvantagesofThermocouple-TypeInstruments

1.Considerablepowerlossesduetopoorefficiencyofthermalconversion.

2. Lowaccuracyofmeasurementandsensitivity tooverloads,as theheateroperatesat temperaturesclose to thelimitvalues.Thus,theoverloadcapacityofsuchinstrumentisapproximately1.5timesoffull-scalecurrent.

3.Themulti-voltmetersusedwiththermo-elementsmustbenecessarilymoresensitiveanddelicatethanthoseusedwithshunts,andtherefore,requirescarefulhandling.

2.13 RECTIFIER-TYPEINSTRUMENTS

Thebasicarrangementofarectifiertypeofinstrumentusingafull-waverectifiercircuitisshowninFigure2.25.Ifthisinstrumentisusedformeasuringacquantitythenfirsttheacsignalisconvertedtodcwiththehelpoftherectifier.ThenthisdcsignalismeasuredbythePMMCmeter.ThemultiplierresistanceRs,isusedtolimitthevalueofthecurrentinorderthatitdoesnotexceedthecurrentratingofthePMMCmeter.

Thesetypesofinstrumentsareusedforlightcurrentworkwherethevoltageislowandresistanceshigh.

Figure2.25Rectifier-typeinstrument

2.13.1SensitivityofRectifier-TypeInstrumentThedcsensitivityofarectifier-typeinstrumentis

whereIfsisthecurrentrequiredtoproducefull-scaledeflection.

1.SensitivityofaHalf-waveRectifierCircuit

Figure2.26Half-waverectifier

Figure 2.26 shows a simple half-wave rectifier circuit along with the input and output

waveform.Theaveragevalueofvoltage/currentforhalf-waverectifier,

Hence, the sensitivity of a half-wave rectifier instrument with ac is 0.45 times itssensitivity with dc and the deflection is 0.45 times that produces with dc of equalmagnitudeV.

2.SensitivityofaFull-waveRectifierCircuits

Figure2.27Full-waverectifier

Figure2.27showsafull-waverectifiercircuitalongwiththeinputandoutputwaveform.Averagevalueofvoltage/currentforfull-waverectifier,

So the deflection is 0.9 times in a full-wave rectifier instrumentwith an ac than thatproducedwithdcofequalmagnitudeV.

Sensitivityofafull-waverectifierinstrumentwithanacis0.9timesitssensitivitywithdc.

2.13.2ExtensionofRangeofRectifierInstrumentasVoltmeterSupposeit is intendedtoextendtherangeofarectifierinstrumentwhichusesaPMMCinstrumenthavingadcsensitivityofSdc.

Let,v=voltagedropacrossthePMMCinstrument

V=appliedvoltage

Therefore, fordcoperation, thevaluesof series resistance (multiplier)neededcanbecalculatedfromFigure2.28as

V=RS.Ifs+Rd.Ifs+Rm.Ifs

Figure2.28Rangeextensionofrectifiervoltmeter

whereRm=meterresistance

Rd=diodeforwardresistance

Foracvoltmeter,

Limitations

1.Rectifierinstrumentsareonlyaccurateonthewaveformsonwhichtheyarecalibrated.Sincecalibrationassumespuresinewaves,thepresenceofharmonicsgiveserroneousreadings.

2. Therectifier is temperaturesensitive,and therefore, the instrument readingsareaffectedby largevariationsoftemperature.

Applications

1.Therectifierinstrumentisverysuitableformeasuringalternatingvoltagesintherangeof50–250V.

2.Therectifierinstrumentmaybeusedasamicrometerorlowmilliammeter(upto10–15mA).Itisnotsuitableformeasuring large currents because for larger currents the rectifier becomes too bulky and providing shunts isimpracticableduetorectifiercharacteristics.

3.Rectifierinstrumentsfindtheirprincipalapplicationinmeasurementinhigh-impedancecircuitsatlowandaudiofrequencies.Theyarecommonlyusedincommunicationscircuitsbecauseoftheirhighsensitivityandlowpowerconsumption.

2.14 TRUErmsVOLTMETER

Thecommonlyavailablemultimetersareaverageorpeakreadinginstruments,andthermsvaluestheydisplayarebasedonthesignalmeanvalue.Theymultiplytheaveragevaluewith some factor to convert it to the rms reading. For this reason, conventionalmultimetersareonlysuitedforsinusoidalsignals.Formeasuringrmsvalueofavarietyofsignalsoverawiderangeoffrequencies,anewkindofvoltmeter—calledtheTrueRMS(TRMS)voltmeterhasbeendeveloped.Sincethesevoltmetersdonotmeasurermsvalueofasignalbasedonitsaveragevalue,theyaresuitedforanykindofwaveforms(suchassinewave,squarewaveorsawtoothwave).

Theconventionalmoving-ironvoltmeterhasitsdeflectionproportionaltothesquareofthecurrentpassingthroughitscoil.Thus,ifthescaleiscalibratedintermsofsquarerootof themeasured value,moving-iron instruments can give true rms value of any signal,

independentof itswave shape.However,due to large inertiaof themechanicalmovingpartspresent in suchamoving iron instrument, the frequencybandwidthof sucha truerms voltmeter is limited. Similar is the case for electrodynamometer type instrumentswhich once again have their deflecting torque proportional to the current through theiroperatingcoil.Butonceagain,thoughelectrodynamometer-typeinstrumentscangivetruermsindicationofasignalofanywaveform,theirfrequencybandwidthisalsolimitedduetotheirmechanicalmovingparts.Modern-day true rms reading voltmeters aremade to respond directly to the heating

value of the input signal. Tomeasure rms value of any arbitrary waveform signal, theinputsignal isfedtoaheatingelementanda thermocoupleisplacedverycloseto it.Athermocoupleisajunctionoftwodissimilarmetalswhosecontactpotentialisafunctionofthetemperatureofthejunction.Theheatingvalueisproportionaltothesquareoftherms value of the input signal. The heater raises the temperature of the heater and thethermocoupleproducesanoutputvoltagethatisproportionaltothepowerdeliveredtotheheater by the input signal. Power being proportional to the square of the current (orvoltage) under measurement, the output voltage of the thermocouple can be properlycalibrated to indicate truermsvalueof the inputsignal.Thisway,sucha thermaleffectinstrument permits the determination of true rms value of an unknown signal of anyarbitrarywaveform.Bandwidthisusuallynotaproblemsincethiskindofprinciplecanbeused accurately even beyond 50 MHz. Figure 2.28 shows such an arrangement ofthermocouplebasedtruermsreadingvoltmeter.

Figure2.28Thermocouplebasedtruermsreadingvoltmeter

2.15COMPARISONBETWEENDIFFERENTTYPESOFINSTRUMENTS

EXERCISE

Objective-typeQuestions1.Aspringproducesacontrollingtorqueof16x10-6Nmforadeflectionof120Y.Ifthewidthandlengthbecome

twotimestheiroriginalvaluesandthethicknessishalved,thevalueofcontrollingtorqueforthesamedeflectionwillbe

(a)16×10-6N

(b)8x10-6Nm(c)2x10-6Nm

(d)32x10-6Nm

2.Theshuntresistanceinanammeterisusually

(a)lessthanmeterresistance

(b)equaltometerresistance

(c)morethanmeterresistance

(d)ofanyvalue

3.Avoltageof200Vproducesadeflectionof90°inaPMMCspring-controlledinstrument.Ifthesameinstrumentisprovidedwithgravitycontrol,whatwouldbethedeflection?

(a)45°

(b)65°

(c)90°

(d)cannotbedeterminedbythegivendata

4.Acurrent-carryingconductorisshowninFigure(a).IfitisbroughtinamagneticfieldshowninFigure(b)

(a)itwillexperienceaforcefromlefttoright.

(b)itwillexperienceaforcefromrighttoleft.

(c)itwillexperienceaforcefromtoptobottom.

(d)itwillexperiencenoforce.

5.Thehightorquetoweightratioinananalogindicatinginstrumentindicates

(a)highfrictionloss

(b)nothingasregardsfrictionloss

(c)lowfrictionloss

(d)noneoftheabove

6.Swampingresistanceisconnected

(a)inserieswiththeshunttoreducetemperatureerrorinshuntedammeter

(b)inserieswiththeammeterstoreduceerrorsonaccountoffriction

(c)inserieswithmeterandhaveahighresistancetemperaturecoefficientinordertoreducetemperatureerrorsinammeters.

(d)inserieswiththemeterandhaveanegligibleresistanceco-efficientinordertoreducetemperatureerrorsinshuntedammeters

7.Moving-ironinstrumentswhenmeasuringvoltagesorcurrents

(a)indicatethesamevaluesofthemeasurementforbothascendinganddescendingvalues

(b)indicatehighervalueofmeasurandforascendingvalues

(c)indicatehighervalueofmeasurandfordescendingvalues

(d)noneoftheabove

8.Amoving-irontypeofinstrumentcanbeusedas

(a)standardinstrumentsforcalibrationofotherinstruments

(b)transfer-typeinstruments

(c)indicator-typeinstrumentsasonpanels

(d)alloftheabove

9.Inspring-controlledmovingironinstruments,thescaleis

(a)uniform

(b)crampedatthelowerendandexpandedattheupperend

(c)expandedatthelowerendandcrampedattheupperend

(d)crampedbothatthelowerandtheupperends

10.Thermocoupleinstrumentscanbeusedforafrequencyrange

(a)upto500Hz

(b)upto5MHz

(c)upto100Hz

(d)upto1MHz

11.Thereasonwhyeddy-currentdampingcannotheusedinamoving-ironinstrument,is

(a)theyhaveastrongoperatingmagneticfield

(b)theyarenotnormallyusedinverticalposition

(c)theyneedalargedampingforcewhichcanonlyheprovidedbyairfriction

(d)theyhaveaveryweakoperatingmagneticfieldandintroductionofapermanentmagnetrequiredforeddycurrentdampingwoulddistorttheoperatingmagneticfield

12.Anelectrodynamometertypeofinstrumentfindsitsmajoruseas

(a)standardinstrumentonly

(b)bothasstandardandtransferinstrument

(c)transferinstrumentonly

(d)indicator-typeinstrument

13.Thefrequencyrangeofmoving-ironinstrumentsis

(a)audio-frequencyband20Hzto20kHz

(b)verylow-frequencyband10Hzto30kHz

(c)low-frequencyband30Hzto300kHz

(d)powerfrequencies0to125Hz.

14.Avoltageof200Vat5Hzisappliedtoanelectrodynamometertypeofinstrumentwhichisspringcontrolled.Theindicationontheinstrumentsis

(a)200V

(b)0V

(c)theinstrumentfollowsthevariationsinvoltageanddoesnotgiveasteadyresponse

(d)noneoftheabove

15.Spring-controlledmoving-ironinstrumentsexhibitasquarelawresponseresultinginanon-linearscale.Theshapeofthescalecanbemadealmostlinearby

(a)keepingrateofchangeofinductance,L,withdeflection,θ,asconstant

(b)keeping asconstant

(c)keeping asconstant

(d)keeping asconstant,wherekisthespringconstant

16.Electrostatic-typeinstrumentsareprimarilyusedas

(a)ammeters

(b)voltmeters

(c)wattmeters

(d)ohmmeters

17.ThesensitivityofaPMMCinstrumentis10CkZ/V.Ifthisinstrumentisusedinarectifier-typevoltmeterwithhalfwaverectification.Whatwouldbethesensitivity?

(a)10kΩ/V

(b)4.5kΩ/V

(c)9kΩ/V

(d)22.2kΩ/V

18.Theheaterwireofthermocoupleinstrumentismadeverythininorder

(a)tohaveahighvalueofresistance

(b)toreduceskineffectsathighfrequencies

(c)toreducetheweightoftheinstrument

(d)todecreasetheover-rangingcapacityoftheinstrument

19.Whichinstrumenthasthehighestfrequencyrangewithaccuracywithinreasonablelimits?

(a)PMMC

(b)Movingiron

(c)Electrodynamometer

(d)Rectifier

20.Whichmeterhasthehighestaccuracyintheprescribedlimitoffrequencyrange?

(a)PMMC

(b)Movingiron

(c)Electrodynamometer

(d)Rectifier

Short-answerQuestions1.Describethevariousoperatingforcesneededforproperoperationofananalogindicatinginstrument.

2. Sketch thecurves showingdeflectionversus time for analog indicating instruments forunderdamping, criticaldampingandoverdamping.

3.Whatarethedifferencebetweenrecordingandintegratinginstruments?Givesuitableexamplesineachcase.

4.DerivetheequationfordeflectionofaPMMCinstrumentiftheinstrumentisspringcontrolled.

5.HowcanthecurrentrangeofaPMMCinstrumentbeextendedwiththehelpofshunts?

6.Derivetheequationfordeflectionofaspring-controlledmoving-coilinstrument.

7.Describetheworkingprincipleofarectifier-typeinstrument.Whatisthesensitivityofsuchaninstrument?

8.WhataretheadvantagesanddisadvantagesofaPMMCinstrument?

9.Describetheworkingprincipleandconstructionaldetailsofanattraction-typemovingironinstrument.

10.Derivetheexpressionfordeflectionforarotary-typeelectrostaticinstrumentusingspringcontrol.

11.Whatisswampingresistance?Forwhatpurposeisswampingresistanceused?

12.Howmanywayscanthedampingbeprovidedinanindicatinginstrument?

Long-answerQuestions1.(a)Howmanyoperatingforcesarenecessaryforsuccessfuloperationofanindicatinginstrument?Explainthe

methodsofprovidingtheseforces.

(b)Amoving-coilinstrumenthasthefollowingdata:numberofturns=100,widthofcoil=20mm,depthofcoil=30mm,fluxdensityinthegap=0.1Wb/m2.Calculatethedeflectingtorquewhencarryingacurrentof10mA.Alsocalculatethedeflectionifthecontrolspringconstantis2×10-6N-m/degree.

[Ans.60×10-6Nm,30°]

2.(a)Whataretheadvantagesanddisadvantagesofmoving-coilinstruments?

(b)Amoving-coilvoltmeterhasaresistanceof200Wandthefullscaledeflectionisreachedwhenapotentialdifferenceof100mVisappliedacrosstheterminals.Themovingcoilhaseffectivedimensionsof30mm×25mmandiswoundwith100turns.Thefluxdensityinthegapis0.2Wb/m2.Determinethecontrolconstantofthespringifthefinaldeflectionis100°andasuitablediameterofcopperwireforthecoilwindingif20%ofthetotalinstrumentresistanceisduetothecoilwinding.Resistivityofcopperis1.7×10-8Ωm.

[Ans.0.075×10-6Nm/degree;0.077mm]

3. (a) Derivetheexpressionfor thedeflectionofaspringcontrolledpermanentmagnetmovingcoil instrument.Whynotthisinstrumentabletomeasuretheacquantity?

(b) Thecoilofamovingcoilvoltmeter is40mm×30mmwideandhas100turnswoundon it.Thecontrolspringexertsatorqueof0.25×10-3Nmwhenthedeflectionis50divisionsonthescale.Ifthefluxdensityofthemagneticfieldintheair-gapis1Wb/m2,findtheresistancethatmustbeputinserieswiththecoiltogive1voltperdivision.Resistanceofthevoltmeteris10000Ω.

[Ans.14000Q]

4.(a)Amoving-coilinstrumenthasatnormaltemperaturearesistanceof10Wandacurrentof45mAgivesfullscale deflection. If its resistance rises to 10.2Ω due to temperature change, calculate the readingwhen acurrent of 2000 A is measured by means of a 0.225 × 10-3. A shunt of constant resistance.What is thepercentageerror?

[Ans.44.1mA,-1.96%]

(b)Theinductanceofacertainmoving-ironammeteris pH,where0isthedeflectioninradianfrom

thezeroposition.Thecontrol spring torque is12×10-6Nm/rad.Calculate thescaleposition in radian forcurrentof5A.

[2.04rad]

5. (a) Discuss theconstructionaldetailsofa thermocouple-type instrumentusedatveryhighfrequencies.Writetheiradvantagesanddisadvantages.

(b)Thecontrolspringofamoving-ironammeterexertsatorqueof0.5×10-Nm/degreewhenthedeflectionis52°.Theinductanceofthecoilvarieswithpointerdeflectionaccordingto

deflection(degree)20406080

inductance(|mH)659702752792

Determinethecurrentpassingthroughthemeter.

[0.63A]

6. (a) Describe the constructional details of an attraction-typemoving iron instrumentwith the help of a neatdiagram.Derivetheequationfordeflectionifspringcontrolisusedandcommentupontheshapeofscale.

(b) Derive a general equation for deflection for a spring-controlled repulsion-type moving-iron instrument.Commentupontheshareofthescale.Explainthemethodsadoptedtolinearisethescale.

3.1 INTRODUCTION

Instrument transformers are used in connection with measurement of voltage, current,energyandpower inaccircuits.Thereareprincipally tworeasonsforuseof instrumenttransformers in measurement: first, to extend (multiply) the range of the measuringinstrumentandsecond,toisolatethemeasuringinstrumentfromahigh-voltageline.

Inpowersystems,levelsofcurrentsandvoltageshandledareveryhigh,and,therefore,directmeasurementswithconventionalinstrumentsisnotpossiblewithoutcompromisingoperatorsafety,andsizeandcostof instrument. Insuchacase, instrument transformerscanbeeffectivelyusedtostepdownthevoltageandcurrentwithinrangeoftheexistingmeasuring instruments of moderate size. Instrument transformers are either (a) currenttransformerorCT,or (b)voltageorpotential transformersorPT.The former isused toextendcurrentrangesofinstrumentsandthelatterforincreasingthevoltageranges.

Instrument transformers have their primarywinding connected to the power line andsecondarywindingsto themeasuringinstrument.Inthisway, themeasuringinstrumentsareisolatedfromthehighpowerlines.Inmostapplications,itisnecessarytomeasurethecurrent and voltage of large alternators, motors, transformers, buses and other powertransmissionequipments formeteringaswellas for relayingpurposes.Voltages in suchcasesmay range from 11,000 to even 330,000V. It would be out of question to bringdown these high-voltage lines directly to the metering board. This will require hugeinsulation and pose great danger for operating personnel otherwise. In such a case,instrumenttransformerscangreatlysolvethisproblembysteppingdownthehighvoltagetosafelevelsformeasurement.

3.2 ADVANTAGESOFINSTRUMENTTRANSFORMERS

Shuntandmultipliersusedforextensionofinstrumentrangesaresuitablefordccircuitsandtosomeextent,forlowpower,lowaccuracyaccircuits.Instrumenttransformershavecertain distinguishing characteristics as compared to shunts and multipliers, as listedbelow.

1.Usingshuntsforextensionofrangeonammetersinaccircuitswillrequirecarefuldesigning of the reactance and resistance proportions for the shunt and themeter.Anydeviationfromthedesignedtimeconstantsoftheshuntandthemetermayleadto errors in measurement. This problem is not present with CT being used withammeter.

2.Shuntscannotbeusedforcircuitsinvolvinglargecurrent;otherwisethepowerlossintheshuntitselfwillbecomeprohibitablyhigh.

3. Multipliers, once again, due to inherent leakage current, can introduce errors inmeasurement,andcanalsoresultinunnecessaryheatingduetopowerloss.

4. Measuring circuits involving shunts ormultipliers, being not electrically isolatedfrom the power circuit, are not only safe for the operator, but also insulationrequirementsareexceedinglyhighinhigh-voltagemeasurementapplications.

5. High voltages can be stepped down by the PT to a moderate level as can bemeasuredbystandardinstrumentswithoutposingmuchdangerfortheoperatorandalsonotrequiringtoomuchinsulationforthemeasuringinstrument.

6. Single range moderate size instruments can be used to cover a wide range ofmeasurement,whenusedwithasuitablemulti-rangeCTorPT.

7. Clamp-on type or split-core type CT’s can be very effectively used to measurecurrentwithouttheneedforbreakingthemaincircuitfor insertingtheCTprimarywinding.

8.Instrumenttransformerscanhelpinreducingoverallcost,sincevariousinstruments,including metering, relaying, diagnostic, and indicating instruments can all beconnectedtothesameinstrumenttransformer.

3.3 CURRENTTRANSFORMERS(CT)

Theprimarywindingofacurrenttransformerisconnectedinserieswiththelinecarryingthe main current. The secondary winding of the CT, where the current is many timesstepped down, is directly connected across an ammeter, formeasurement of current; oracrossthecurrentcoilofawattmeter,formeasurementofpower;oracrossthecurrentcoilof a watt-hour meter for measurement of energy; or across a relay coil. The primarywindingofaCThasonlyfewturns,suchthatthereisnoappreciablevoltagedropacrossit,andthemaincircuitisnotdisturbed.ThecurrentflowingthroughtheprimarycoilofaCT,i.e.,themaincircuitcurrentisprimarilydeterminedbytheloadconnectedtothemaincircuitandnotbytheload(burden)connectedtotheCTsecondary.UsesofCTforsuchapplicationsareschematicallyshowninFigure3.1.

Figure3.1CTfor(a)current,and(b)powermeasurement

OneoftheterminalsoftheCTisnormallyearthedtopreventanyaccidentaldamagetotheoperatingpersonnelintheeventofanyincumbentinsulationbreakdown.

WhenatypicalnameplateratingofaCTshows500/1A5VA5P20itindicatesthattheCT rated primary and secondary currents are 500 A and 1 A respectively, its ratedsecondaryburdenis5VA, it isdesignedtohave5%accuracyanditcancarryupto20timeshighercurrentthanitsratedvaluewhileconnectedinlinetodetectfaultconditions,etc.

3.4 THEORYOFCURRENTTRANSFORMERS

Figure 3.2 represents the equivalent circuit of a CT and Figure 3.3 plots the phasordiagramunderoperatingconditionoftheCT.

Figure3.2EquivalentcircuitofaCT

Figure3.3PhasordiagramofaCT

VP=primarysupplyvoltage

EP=primarywindinginducedvoltage

VS=secondaryterminalvoltage

ES=secondarywindinginducedvoltage

IP=primarycurrent

IS=secondarycurrent

I0=no-loadcurrent

IC=corelosscomponentofcurrent

IM=magnetisingcomponentofcurrent

rP=resistanceofprimarywinding

xP=reactanceofprimarywinding

rS=resistanceofsecondarywinding

xS=reactanceofsecondarywinding

RC=imaginaryresistancerepresentingcorelosses

XM=magnetisingreactance

re =resistanceofexternal load(burden) includingresistanceofmeters,currentcoils,etc.

xE = reactance of external load (burden) including reactance ofmeters, current coils,etc.

NP=primarywindingnumberofturns

NS=secondarywindingnumberofturns

n=turnsratio=NS/NPφ=workingfluxoftheCT

θ=the“phaseangle”oftheCT

δ =phaseanglebetweensecondarywindinginducedvoltageandsecondarywindingcurrent(i.e.phaseangleoftotalburden,includingsecondarywinding)

β=phaseangleofsecondaryload(burden)circuitonly

α=phaseanglebetweenno-loadcurrentI0andfluxφ

Thefluxφisplotalongthepositivex-axis.MagnetisingcomponentofcurrentIMisinphasewiththeflux.ThecorelosscomponentofcurrentIc,leadsbyIM90°.SummationofICandIMproducestheno-loadcurrentI0,whichisαangleaheadoffluxφ.

Theprimarywinding inducedvoltageEP is in the samephasewith the resistive coreloss component of the current IC.As per transformer principles, the secondarywindinginducedvoltageESwillbe180°outofphasewith theprimarywinding inducedvoltageEP.ThesecondarycurrentISlagsthesecondaryinducedvoltageESbyangleδ.

The secondary output terminal voltageVS is obtained by vectorically subtracting thesecondarywinding resistiveand reactivevoltagedrops IS rSand ISxS respectively fromthesecondaryinducedvoltageES.ThephaseangledifferencebetweensecondarycurrentISandsecondaryterminalvoltageVSisβ,whichisthephaseangleoftheload(burden).

The secondary current IS,when reflected back to primary, can be represented by the180° shifted phasor indicated by nIS, where n is the turns ratio. The primary windingcurrent IP is thephasorsummationof this reflectedsecondarycurrent (loadcomponent)nISandtheno-loadcurrentI0.

ThephaseangledifferenceθbetweentheprimarycurrentIPandthereflectedsecondarycurrentnISiscalledphaseangleoftheCT.

3.4.1CurrentTransformationRatioofCTRedrawing expanded view of the phasor diagram of Figure 3.3, we obtain the phasordiagramofFigure3.4.

Figure3.4ExpandedviewofasectionofFigure3.3

Fromtheright-angletrianglepqr,weget

pr=I0pq=I0∙cos(90°-δ-α)=I0∙sin(δ+α)

qr=I0∙sin(90°-δ-α)=I0∙cos(δ+α)

Now, (or)2=(op+pq)2+(qr)2

Or, (Ip)2=(nIS+I0∙sin(δ+α))2+(I0.cos(δ+α))2

=n2IS2+I02∙sin2(δ+α)+2nISI0.sin(δ+α)+I02.cos2(δ+α)

=n2IS2+2nISI0.sin(δ+α)+I02(sin2(δ+a)+cos2(δ+α))

=n2IS2+2nISI0∙sin(δ+a)+I02

Inawell-designedCT,theno-loadcurrentI0ismuchlessascomparedtotheprimarycurrentIporeventhereflectedsecondarycurrent(whichisnominallyequaltotheprimarycurrent)nIS.

i.e., I0<<nIsEquation(3.1)canthusnowbeapproximatedas

IP=

Hence,Ip=nIS+I0.sin(δ+α)

CTtransformationratiocannowbeexpressedas

Though approximate, Eq. (3.2) is sufficiently accurate for practical estimation ofCTtransformationratio.Theaboveequation,however,istrueforonlywhenthepowerfactoroftheburdenislagging,whichismostlytrueinallpracticalinductivemetercoilsbeingusedasburden.

Equation(3.2)canbefurtherexpandedas

or,transformationratio

[since,IM=I0cosαandIC=I0sinα]

3.4.2PhaseAngleofCTAscanbeseenfromthephasordiagraminFigure3.3, thesecondarycurrentofaCTisalmost 180° out of phase from the primary current. If the anglewas exactly 180° thentherewouldhavebeennophaseangleerror introduced in theCTwhen it is tobeusedalongwithwattmeterforpowermeasurements.Inreality,however,duetopresenceoftheparallel circuit branches, namely, themagnetising and the core loss branches, thephaseangle difference is usually less than 180°. This causes some error in phase to beintroducedwhileCToperationinpractice.

Theanglebywhichthesecondarycurrentphasor,whenreversed,i.e.,thereflectedsecondarycurrentphasornIS,differsinphasefromtheprimarycurrentIP,iscalledthephaseangleoftheCT.Thisangleistakenaspositivewhenthereversedsecondary

currentleadstheprimarycurrent,inothercaseswhenthereversedsecondarycurrentlagstheprimarycurrent,theCTphaseangleistakenasnegative.

FromthephasordiagraminFigure3.4,

Forverysmallangles,

ThisexpressioncanstillbesimplifiedwiththeassumptionI0<<nIS.

rad

Or, rad

Or,phaseangleofCT degree

3.5 ERRORSINTRODUCEDBYCURRENTTRANSFORMERS

When used for currentmeasurement, the only essential requirement of a CT is that itssecondarycurrentshouldbeapre-definedfractionoftheprimarycurrenttobemeasured.This ratio should remain constant over the entire range of measurement, such that noerrors are introduced in themeasurement. However, from Eq. (3.3), it is clear that thetransformation ratioR of the CT differs from the turns ratio n . This difference is notconstant,butdependson themagnitudeofmagnetisingand losscomponentsofno-loadcurrent, and also on the secondary winding load current and its phase angle. Thesecondarywindingcurrentthusisneveraconstantfractionoftheprimarywindingcurrentunder all conditions of load and of frequency. This introduces considerable amount oferrorincurrentmeasurement.

Whilepowermeasurements,itisrequiredthatthesecondarycurrentofCTisdisplacedexactlyby180° from theprimary current.As seen fromEq. (3.6), this condition is notfulfilled,buttheCThasaphaseangleerrorθ.Thiswillintroduceappreciableerrorduringpowermeasurements.

3.5.1RatioErrorRatioerrorisdefinedas

Inpractice,theCTburdenislargelyresistivewithasmallvalueofinductance,thusthesecondaryphaseangleδispositiveandgenerallysmall.ThenominalratioKn,issometimeslooselytakenequaltotheturnsration.Thisassumption,aswillbedescribedinlatersections,istrueinthecasewhenturnscompensationisnotusedinCT.

Thus,sinδ≈0andcosδ≈1.Therefore,Eq.(3.3)canbeapproximatedas

Accordingly,percentageratioerrorcanbeapproximatedas

Percentageratioerror=

3.5.2Phase-AngleErrorErrorinphaseangleisgivenfollowingEq.(3.6)as

Inpractice,theCTburdenislargelyresistivewithasmallvalueofinductance,thusthesecondaryphaseangleδispositiveandgenerallysmall.

Thus,sinδ≈0andcosδ≈1.Therefore,Eq.(3.10)canbeapproximatedas

3.5.3CausesofErrorsinCTInanidealCT,theactualtransformationratioshouldhavebeenexactlyequaltotheturnsratio and the phase angle should have been zero. However, due to inherent physicallimitationsinherenttotheelectricandmagneticcircuitsoftheCT,practicalperformancedeviatesfromtheseidealbehaviorsanderrorsareintroducedinmeasurement.Thereasonsfortheseerrorsaregivenhere.

1. Primary winding always needs some magnetising MMF to produce flux and,therefore,theCTdrawsthemagnetisingcurrentIM.

2.CTno-loadcurrentmusthaveacomponentIcthathastosupplythecorelosses,i.e.,theeddycurrentlossandthehysteresisloss.

3.OncetheCTcorebecomessaturated,thefluxdensityinthecorenolongerremainsalinearfunctionofthemagnetisingforce,thismayintroducefurthererrors.

4.Primaryandsecondaryfluxlinkagesdifferduetounavoidablefluxleakages.

3.5.4ReducingErrorsinCTErrorsareproducedintheratioandphaseangleofaCTowingtothepresenceoftheno-load component of the primary current. Improvement of accuracy, then, depends upon

minimisingthiscomponentornullifyinginsomewayitseffectsinintroducingerrors.Themost obvious idea would be to attempt to keep the magnetising current component assmallaspossible.Thiscanbeachievedbyacombinationofthefollowingschemes:

1.LowFluxDensity

The magnetising component of current may be restricted by using low values of fluxdensity.Thismaybeachievedbyusinglargecross-sectionforcore.Forthisreason,CTsare normally designedwithmuch lower flux densities as compared to a normal powertransformer.

2.HighPermeabilityCoreMaterial

Themagnetisingcomponentofcurrentmaybemadesmallbytheuseofhighpermeabilitycorematerial. Some special corematerials, such as Permalloy, are even better than thehighestgradesiliconsteelwithrespecttopermeability,particularlyatlowerfluxdensities.Hipernik (50% Fe + 50% Ni) has high permeability at low flux densities along withreasonably high saturation density value. It is used frequently as core material formanufacturingCTs.

3.ModificationofTurnsRatio

Theaccuracyofcurrenttransformersmaybeimproved,atleastintermsoftransformationratio, by suitablymodifying the actual numberof turns. Insteadofusing thenumberofturnsinexactaccordancewiththedesirednominalratio,achangeinfewnumbersofturnsmaybemadeinthesecondarywinding.Primarynumberofturnsitselfbeingsoless,anychangeinnumberofturnsintheprimarymayresultinwidevariationoftheturnsratio.Fornormaloperatingconditions,theusualsecondarycurrentisfoundtobelessthanthenominalvalueduetotheno-loadcurrent.Correctioninsuchcases,thus,maybemadebyasmallreductioninthesecondarynumberofturns.Thiscorrectioncan,however,beexactonlyforparticularvalueofcurrentandburdenimpedance.CTsinsuchcasesarenormallymarkedas‘compensated’forthatparticularoperatingcondition.

4.UseofShunts

If the secondary current is found to be too high, it may be reduced by a shunt placedacrossprimaryorsecondary.Thismethodcanmakeanexactcorrection,onceagain,onlyfor a particular value and type of burden. Use of shunts can also help in reducing thephase-angleerror.

5.Wound-CoreConstruction

AnimprovementinthemagnetisationcharacteristicsoftheCTcoremaybeachievedbytheuseofwound-coreconstruction.Thistypeofconstructionforthecorehasbeeninuseforsometimeindistributiontransformers.Byspecialtreatmentofthesiliconsteeltobeused as core material, and by using it to carry flux always in the direction of grainorientation(rollingthesheetsteelinproperway),magneticpropertiesofthecorecanbe

largelyimproved.ThisimprovementmaybeutilisedinCTstoreducetheratioandphaseangleerrors.

3.6OPERATIONALCHARACTERISTICSOFCURRENTTRANSFORMERS

Characteristics of current transformers under different operating conditions may beestimatedfromthephasordiagramasshowninFigure3.3.

3.6.1EffectofChangeinBurdenonSecondaryCircuitBurdenconnectedwiththeCTsecondarymayincludeammeters,wattmetercurrentcoils,relay coils, and so forth. All these being connected in series, carry the same currentthrough them. In a current transformer, since the current depends solelyon theprimarycurrent,an increase in theburden impedancewillnotchange thesecondarycurrent,butwill demand more voltage in the secondary terminals. This will increase volt-ampereburdenofthesecondary.Withmoreinstrumentsinthecircuit,ahighervoltageisrequiredtomakethecurrentflowandthis,inturn,requiresmorefluxtoflowthroughthecoreandhence a greater magnetising component of the primary current. This will result in anincrease in the ratio and phase angle error of the current transformer. Figure 3.5summarisesthevariationsofratioandphaseangleerrorsinatypicalcurrenttransformeratdifferentvaluesofthesecondaryburdenVA.

Figure3.5Effectsofsecondaryburdenvariationon(a)CTratioerror,and(b)CTphase-angleerror

3.6.2EffectofChangeinPowerFactorofSecondaryBurden

1.RatioError

AscanbeobservedfromthephasordiagramofacurrenttransformerinFigure3.3,forallinductive burdens, the secondarywinding current IS lags behind the secondary inducedvoltageES,sothatthephaseangledifferenceδispositive.Undertheseconditions,fromEq. (3.2), the actual transformation ratio is alwaysgreater than the turns ratio, and thusaccordingtoEq.(3.9),ratioerrorisalwaysnegativeforinductive(laggingpowerfactor)burdens.

Forhighlycapacitiveburdens,thehesecondarywindingcurrentISleadsthesecondaryinducedvoltageES, so that thephaseangledifferenceδ isnegative. In suchacase, theactualtransformationratiomayevenbecomelessthantheturnsratioandratioerrormaythusbecomepositive.

2.Phase-AngleError

FromEq. (3.5) it is observed that for inductive burdens, the phase angle error remains

positive till a certain low value of power factor is reached at highly inductive burdenswhenthephaseangleerrorcrossesovertheaxistoturnnegative.Forcapacitiveburdens,however,thephase-angleerroralwaysremainspositive.

Figure 3.6 shows the variations of ratio and phase-angle errors in a typical currenttransformeratdifferentvaluesofthesecondaryburdenpowerfactor.ThesevariationsaredescribedwiththeassumptionofsecondaryburdenVAtoremainconstant.

Figure3.6Effectsofsecondaryburdenpowerfactorvariationon(a)CTratioerror,and(b)CTphase-angleerror

3.6.3EffectofChangeinPrimaryWindingCurrentAstheprimarywindingcurrentIpchanges,thesecondarywindingcurrentIsalsochangesproportionately.WithlowervaluesofIp(andIs),themagnetisingandlosscomponentsofno-load current become comparatively higher, and, therefore, both of ratio and phaseangleerrorsbecomehigher.AstheprimarycurrentIpincreases,thesecondarycurrentISalso increases, thereby reducing theproportionsofmagnetising and loss components ofcurrents, which reduces the ratio and phase angle errors. These observations can beverifiedfollowingEqs(3.2)and(3.5).

Such variations of CT errors with changing primary (and hence secondary) currentunderatypicalunitypowerfactorburdenareshowninFigure3.7.

Figure3.7Effectsofprimarycurrentvariationon(a)CTratioerror,and(b)CTphase-angleerror

3.7DESIGNANDCONSTRUCTIONALFEATURESOFCURRENTTRANSFORMERS

3.7.1DesignFeatures

1.NumberofPrimaryAmpere-Turns(AT)

One of the primary conditions for restricting ratio and phase-angle errors is that themagnetising ampere-turns in the primary shall be only a small proportion of the totalprimary ampere turns. To satisfy this condition, inmost practical cases, the number ofprimaryampere-turnsmaybeestimatedastobeintherange5000–10000.InthecaseofCTshavingasinglebarastheirprimarywinding,thenumberofprimaryampereturnsis,of course, determined by the primary current. For most practical purposes, withcommerciallyavailablemagneticmaterialsatthecoreoftheCT,primarycurrentsnotlessthan 100 A have proved to be necessary for producing satisfactory amount of ampereturns.

2.Core

To satisfy the condition of achieving low magnetising ampere-turns, the core materialmusthavealowreluctanceandlowironloss.Thefluxdensityinthecorealsoneedstoberestricted to low values. Core materials such as Mumetal (an alloy of iron and nickelcontainingcopper)haspropertiesofhighpermeability,lowloss,andlowretentivity—allofwhichareadvantageousforbeingusedinCTs.Mumetal,however,hasthedisadvantageofhavinglowsaturationfluxdensities.

Thelengthofmagneticpathinthecoreshouldbeassmallaspermissiblefromthepointof viewofmechanical construction andwith proper insulation requirements in order toreduce the core reluctance. For similar reasons, core joints should be avoided as far as

practicable, or in other case, core joints must be as efficient as possible by carefulassembly.

3.Windings

Primary and secondarywindings should be placed close together to reduce the leakagereactance; otherwise the ratio errorwill go up. Thin SWGwires are normally used forsecondary winding, whereas copper strips are generally used for primary winding,dimensionsofwhichdepend,obviously,upontheprimarycurrent.

Thewindingsneedtobedesignedforproperrobustnessandtightbracingwithaviewtowithstand high mechanical forces without damage. Such mechanical forces my getdevelopedduetosuddenshortcircuitsinthesystemwheretheCTisconnected.

4.Insulation

Lowervoltage ratingapplicationsallowwindings tobe insulatedwith tapeandvarnish.Higher voltage applications, however, require oil-immersed insulation arrangements forthewinding.Stillhighvoltagesmayrequireuseofsolidcompoundinsulationsystems.

3.7.2ConstructionalFeatures

1.IndoorTypeCTs

Forindoortable/panelmountedapplications,windingconstructioncanbeoftwotypesinaCT:(i)woundtype,and(ii)bartype.

Inwound-typewinding,theprimarywindingconsistsofafewturnsofheavyconductortowhoseprojectedends,theprimaryconductor,cableorbusbarisbolted.Thesecondarywinding,which composes of a large number of turns, iswound over aBakelite formeraroundacentralcore.Theheavyprimaryconductoriseitherwounddirectlyontopofthesecondarywinding,suitableinsulationbeingfirstappliedoverthesecondarywinding,ortheprimaryiswoundentirelyseparately,insulatedwithsuitabletapeandthenassembledwiththesecondarywindingonthecore.Theentiresystemishoused,normally,withinamoldedinsulationcover.Figure3.8(a)showsaschematicdiagramofthecrosssectionofawound-typeCT.Figure3.8(b)showsaphotographofsuchawound-typeCT.

Figure3.8(a)Crosssectionofwound-typeCT(b)Butyl-moldedwoundprimarytypeindoorCT(CourtesyofGeneralElectricCompany)

The bar-typeCT includes the laminated core and secondarywinding but no primarywinding as such. The primary consists of the bus-bar or conductor, which is passedthroughtheopeningintheinsulatingsleevethroughthesecondarywinding.Theprimarywinding(bar)here formsan integralpartof theCT.SuchCTsaresometimes termedassingle-turnprimary-typeCT.Theexternaldiameterofthebartypeprimarymustbelargeenoughtokeepthevoltagegradientinthedielectricatitssurface,toanacceptablevaluesuchthatcoronaeffectcanbeavoided.Figure3.9showsaschematicdiagramofthecross-sectionofabar-typeCT.Figure3.10showphotographofsuchbar-typeCTs.

Figure3.9Crosssectionofbar-typeCT

Figure3.10(a)Butyl-moldedbarprimary-typeindoorCTfor200–800Aand600Vrangecircuit(CourtesyofGeneralElectricCompany)(b)Singleconductor(bartype)primaryCT

2.Clamp-onTypeorPortableTypeCTs

By the use of a construction with a suitably split and hinged core, upon which thesecondary winding is wound, it is possible to measure the current in a heavy-currentconductororbus-barwithoutbreakingthecurrentcircuit.ThesplitcoreoftheCTalongwiththesecondarywindingissimplyclampedaroundthemainconductor,whichactsastheprimarywindingoftheCT.Whenusedwithrangeselectableshuntsandacalibratedammeter, clamp on type CTs can be very conveniently used for direct and quickmeasurementofcurrent.Figure3.11showsphotographofsuchaclamp-ontypeCT.

Figure3.11Multi-rangeclamp-ontypeCT(CourtesyofMetravi)

Aportable-typeCTinwhichhighandlargelyadjustablecurrentrangescanbeobtainedby actuallywinding the primary turns through the core opening is illustrated in Figure3.12. For example, if one turn of the primary conductor through the opening gives acurrentratioof800/5,thentwoprimaryturnsthroughthesameopeningwillgiveacurrentratioof400/5,andsoon.

Figure3.12Multi-rangeportabletypeCT(CourtesyofYokogawa)

3.Bushing-typeCTs

The bushing-type CT is similar in concept to the bar type in the sense that core andsecondarywindingaremountedaroundthesingleprimaryconductor.Ithasacircularcorethatcarries thesecondarywoundover itandformingaunit thatmaybe installed in thehigh-voltagebushingofacircuitbreakerorapowertransformer.The‘primarywinding’insuchacaseissimplythemainconductor in thebushing.Figure3.13shows theviewofsuchabushing-typeCT.

Figure3.13Bushing-typeCT(CourtesyofWestinghouseElectricCorporation)

3.8 PRECAUTIONSINUSEOFCURRENTTRANSFORMER

3.8.1OpenCircuitingofCTSecondaryCurrent transformersarealwaysusedwith itssecondarycircuitclosed throughvery lowresistanceloadssuchasammeters,wattmetercurrentcoils,orrelaycoils.Insuchacase,acurrent transformer should never have its secondary terminals open circuitedwhile theprimarycircuitisstillenergised.

OnedifferencebetweenanormalpowertransformerandacurrenttransformeristhatinaCT,theprimarycurrentisindependentofthecurrentflowinginthesecondary,primarywinding being connected in series with the main load, carries the line current. Thus,primarycurrentisinnowaycontrolledbytheconditionsofthesecondarywindingcircuitoftheCT.

Undernormaloperatingconditions, thesecondarycurrentproducesaso-called‘back-mmf’thatalmostbalancestheprimarywindingampereturnsandrestrictsthefluxinthecore.Thissmallmmfis responsibleforproducingflux in thecoreandsupplies the ironlosses.This resultant fluxbeing small, the voltage induced in the secondarywinding isalsolow.

If by any reason whatsoever, the secondary winding gets open circuited, then thesecondaryreversemmfvanishes.Thedemagnetisingeffectofthesecondarymmfisnowabsent and the core carries the high flux created due to the primary ampere-turns only.Thislargefluxgreatlyincreasesfluxdensityinthecoreandpushesittowardssaturation.Thislargeflux,whenlinkswiththelargenumberofsecondaryturns,producesaveryhighvoltage, thatcouldbedamaging for thewinding insulationaswell asdangerous for theoperator.Thetransformerinsulationmaygetdamagedundersuchhighvoltagestress.

Inadditiontothis,increasedhysteresisandeddycurrentlossesathigherfluxdensitiesmayoverheatthetransformercore.

Moreover, the highmagnetising forces acting on the corewhile secondary conditiontend tomagnetise themagneticmaterial to high values. If the open circuit condition issuddenly removed, the accuracy of the CT may be seriously impaired by the residualmagnetism remaining in the core in case theprimary circuit is brokenor the secondarycircuitisre-energised.Thisresidualeffectcausesthetransformertooperateatadifferentoperatingpointonthemagnetisationcurve,whichaffectsthepermeabilityandhencethecalibration.Thismayleadtoanaltogetherdifferentvaluesofratioandphase-angleerrors,obtained after such an open circuit, as compared to the corresponding values before itoccurred. A transformer so treated, must first be demagnetised and then recalibratedbeforecanbeusedreliably.

Forthesereasons,caremustbetakentoensurethat,evenwhennotinuseformeasurementpurposes,thesecondarycircuitisclosedatanytimewhentheprimarycircuitisenergised.Inthoseidleperiods,thesecondarycircuitcould(andshould)be

safelyshortcircuitedquitesafely,sincewhilebeingusedformeasurementitispracticallyshortcircuitedbytheammeter,orwattmetercurrentcoils,impedancesofwhicharemerelyappreciable.

3.8.2PermanentMagnetisationofCoreCorematerialofaCTmayundergopermanentmagnetisationduetooneormoreof thefollowingreasons:

1.Asdiscussedearlier,ifbyanychancethesecondarywindingisopencircuitedwiththe primarywinding still energised, then the large fluxwill tend tomagnetise thecore to high values. If such a condition is abruptly removed, then there is a goodpossibilitythatalargeresidualmagnetismwillremaininthecore.

2.AswitchingtransientpassingthroughtheCTprimarymayleavebehindappreciableamountofresidualmagnetisminthecore.

3. Permanentmagnetisationmayresult fromflowofdccurrent througheitherof thewinding.Thedccurrentmaybeflownthroughthewindingforcheckingresistanceorcheckingpolarity.

4.PermanentmagnetisationmayalsoresultfromtransientshortcircuitcurrentflowingthroughthelinetowhichtheCTisconnected.Suchtransientcurrentsarefoundtohavedccomponentsalongwithaccounterparts.

Thepresenceofpermanentmagnetisationinthecoremayalterthepermeabilityofthematerial resulting in lossof calibration and increase inboth ratio error andphase angleerror.Thus,forreliableoperationoftheCT,theresidualmagnetismmustberemovedandthe CT be restored back to its original condition. There are several methods ofdemagnetisingthecoreasdescribedbelow:

1. Onemethod is topassacurrent through theprimarywindingequal to thecurrentthatwasflowingduringtheperiodwhentheCTsecondarywasopencircuited.TheCTsecondarycircuitisleftopen.Thevoltagesupplytotheprimaryisthengraduallyreduced to zero.TheCTcore thusundergoes several cycles of gradually reducingmagnetisationtillitfinishesdowntozero.

2. Inthesecondmethod,theprimarywindingissuppliedfromasourcesothatratedcurrent flows in the primarywinding.Avariable resistor of value certain hundredohms is connected across the secondary winding. This simulates almost the CTsecondary open circuit condition. The variable resistance is then gradually anduniformly reduced down to zero. In this way, the magnetisation of the CT coregraduallyreduceddownfromitsinitialhighvaluetonormaloriginalvalues.

Example3.1

Acurrent transformerhas single-turnprimaryanda100-turn secondarywinding. The secondarywinding of purelyresistive burden of 1.5 W draws a current of 6 A. Themagnetising ampere-turns is 60A. Supply frequency is 50Hzandcorecross-sectionalareais800mm2.CalculatetheratioandphaseangleoftheCT.Alsofindthefluxdensityin

the core. Neglect flux leakage, iron losses and copperlosses.

Solution Neglecting copper losses and flux leakage implies that secondary windingresistanceandreactancearenotbeconsidered.Theburdenof1.5Ωthuscanbeassumedtobetheburdenoftheentiresecondarycircuit.

Secondaryinducedvoltage

ES=Secondarycurrent×Secondaryburden=6×1.5=9V

Asthesecondaryburdenispurelyresistive,thesecondarycurrentisinphasewiththesecondaryinducedvoltage,i.e.,thephaseangledifferencebetweenESandIS,δ=0,andpowerfactorisunity.

Giventhatironlosses,andhencethelosscomponentofcurrentcanbeneglected,i.e.,IC=0.

No-load current in this case is thus simply equal to the magnetising component ofcurrent,i.e.,I0=IMNow,magnetisingcomponentofno-loadcurrentisgivenby

SecondarywindingcurrentIS=6A

Turnsratio=n=100/1=100

Reflectedsecondarywindingcurrent=nIS=100×6=600A

Referring to the phasor diagram shown in the fi gure, the primary current can becalculatedas

actualtransformationratio

FromtherelationES=4.44fφmNS,themaximumfluxφMinthecorecanbecalculatedas

Given,areaofcore=800mm2=800×10-6m2

maximumfluxdensity

Example3.2

AringcoretypeCThasaratioof2000/10.Whenoperatingat rated primary current with a secondary burden ofnoninductive resistance value of 2 Ω, takes a no-loadcurrentof2Aatpowerfactorof0.3.Calculate(i)thephaseangle difference between primary and secondary currents,and(ii)theratioerroratfullload.

Solution Phasordiagramfor thecorrespondingsituationwithpurelyresistiveburdenisshowninthefigure.

The burden being purely resistive, the secondary current IS and secondary inducedvoltageESwillbeinthesamephaseasshowninthefigure.Therefore,secondarywindingpowerfactorwillbeunityandthephaseangledifferencebetweenISandES,δ=0.

Give,no-loadcurrentI0=2A,atpowerfactorof0.3.

cos(90°–α)=0.3orα=17.46°

Nominalratio

Withoutanyturnscompensation,nominalratioequalstheturnsratio,thusn=KnUnderfullloadratedcondition,primarycurrent=2000Aandsecondarycurrent=10A.

transformationratio

Example3.3

A 1500/5 A, 50 Hz single-turn primary type CT has asecondaryburdencomprisingofapureresistanceof1.5Ω.Calculatefluxinthecore,ratioerrorandphase-angleerroratfullload.Neglectleakagereactanceandassumetheironloss in the core to be 3 W at full load. The magnetisingampere-turnsis150.

SolutionPhasordiagramforthecorrespondingsituationwithpurelyresistiveburdenisshowninthefigure.

The burden being purely resistive, the secondary current IS and secondary inducedvoltageESwillbeinthesamephaseasshowninthefigure.Therefore,secondarywindingpowerfactorwillbeunityandthephaseangledifferencebetweenISandES,δ=0.

Nominalratio

Withoutanyturnscompensation,nominalratioequalstheturnsratio,thusn=Kn=300

Given,primarynumberofturnsNP=1

Hence,secondarynumberofturnsNS=n.NP=300

Given,secondaryburdenresistance=1.5Ω.

Neglecting leakage flux and hence neglecting secondary leakage reactance, the totalimpedanceofsecondarycircuit=1.5Ω

Underfullloadratedcondition,primarycurrent=1500Aandsecondarycurrent=5A.

secondaryinducedvoltageES=5×1.5=7.5V

And,primaryinducedvoltageEP=ES/n=7.5/300=0.025V

Fromtherelation,ES=4.44fφmNS,themaximumfluxcanbecalculatedas

Given,ironlossatfullload=3W

losscomponentofcurrent

Magnetisingcomponentofcurrent

Notingthefactthatforpurelyresistiveburdenδ=0

transformationratio

Percentageratioerror

Phase-angleerror

Example3.4

Abar-typeCThas400turnsinthesecondarywinding.Theimpedanceofthesecondarycircuitis(2+j1.5)W.With4Aflowinginthesecondary,themagnetisingmmfis80Aandthe iron loss is 1 W. Determine ratio and phase-angleerrors.

Solution Phasor diagram for the corresponding situation with resistive plus inductiveburdeninthewholesecondarycircuitisshowninthefigure.

Given,forbar-typeCT,primarynumberofturnsNP=1

SecondarynumberofturnsNS=400

turnsration=NS/NP=400

Secondarycircuitburdenimpedance

Secondarycircuitpowerfactor

SecondaryinducedvoltageES=IS×ZS=4×2.5=10V

PrimaryinducedvoltageEP=ES/n=10/400=0.025V

Losscomponentofcurrent

Magnetisingmmf80Magnetisingcurrent

transformationratio

or,

Percentageratioerror

Phase-angleerror

or,

Example3.5

Abar-typeCThas300turnsinthesecondarywinding.Anammeterconnectedtothesecondaryhasaresistanceof1Ωand reactance of 0.8 W, and the secondary windingimpedance is (0.5 + j0.6)Ω. The magnetising MMFrequirementforthecoreis60Aandtosupplytheironlossthecurrentrequiredis25A.(a)Findtheprimarywindingcurrent and also determine the ratio error when theammeter in the secondary winding shows 5 A. (b) Howmany turns should be reduced in the secondary to bringdownratioerrortozeroatthiscondition?

Solution

(a)Totalresistanceofsecondarycircuit=1+0.5=1.5Ω

Totalreactanceofsecondarycircuit=0.8+0.6=1.4Ω

secondarycircuitphaseangleδ

forsecondarycircuit,cosδ=0.73andsinδ=0.68

Given,forbar-typeCT,primarynumberofturnsNP=1

SecondarynumberofturnsNS=300

turnsration=NS/NP=300

Withoutanyturnscompensation,nominalratioequalstheturnsratio,thusKn=n=300Given,losscomponentofcurrent=Ic=25A

Magnetisingcurrent

PrimarycurrentIp=Transformationratio×Secondarycurrent=R×Is

or,Ip=311.8×4=1247.2A

(b)Toachievezeroratioerror,wemusthavethetransformationratioandnominalratiotobeequal.

R=Kn

Thus,secondarynumberofturnsrequired=n×NP=288.2×1=288.2

reductioninsecondarywindingturns=300-288.2≈12

Example3.6

Abar-typeCTwithturnsratio1:199isratedas2000:10A,50 VA. The magnetising and core loss components ofprimarycurrentare15Aand10Arespectivelyunderratedcondition.Determine the ratio and phase angle errors forthe rated burden and rated secondary current at 0.8 p.f.lagging and 0.8 p.f. leading. Neglect impedance ofsecondarywinding.

SolutionGiven,forbar-typeCT.primarynumberofturnsNP=1

Turnsration=NS/NP=199

secondarynumberofturnsNS=199

NominalratioKn=2000/10=200

Given,losscomponentofcurrent=Ic=10A

MagnetisingcurrentIm=15A

PowerFactor=0.8lagging

Forlaggingp.f.,thesecondaryphaseangleδispositive.

Thus,cosδ=0.8andsinδ

PowerFactor=0.8leading

Forlaggingp.f.,thesecondaryphaseangleδisnegative.

Thus,cosδ=0.8andsinδ=-0.6

3.9 POTENTIALTRANSFORMERS(PT)

Measurement of voltage, power, etc., of high voltage lines requires the high level ofvoltage being stepped down before being applied to the measuring instrument. This isessential from the point of view of safety of operating personnel, reduction in size ofinstrument and saving in insulation cost.Potential transformersorPTs areused in suchcases tooperatevoltmeters,potentialcoilsofwattmeters, relaysandotherdevices tobeoperatedwithhigh-voltagelines.TheprimarywindingofthePTisconnectedacrossthehigh-voltage line whose voltage is to be measured and the measuring instruments areconnectedacross the secondaryof thePT.For all thesepurposes, it is essential that thesecondaryvoltagebeadefinitefractionoftheprimaryvoltage,andinsomeapplicationsthey need to be in the same phase as well. Uses of PT for such applications areschematicallyshowninFigure3.14.

Figure3.14UseofPTfor(a)voltage,and(b)powermeasurement

There is essentially no difference in theory between a PT used for measurementpurposesandapowertransformerforregularuse.ThemaindifferencesbetweenaPTandapowertransformerareactuallyspecialrequirementsforthemeasurementsystem.Thesearethefollowing:

1. Attenuation ratiomustbeaccuratelymaintained inaPTsince it isbeingused formeasurementpurposes.

2.VoltagedropsinthewindingsmustbeminimisedinaPTinordertoreduceeffectsofphaseshiftand ratioerror.Voltagedrops inwindingscanbe reducedbyproperdesigntominimiseleakagereactanceandusinglargecopperconductors.

3.LoadinginaPTisalwayssmall,onlyoftheorderoffewvolt-amperes.LoadingofaPTisactually limitedbyaccuracyconsiderations;whereas inapower transformer,loadlimitationisonaheatingbasis.

4. Overload capacity for PTs are designed to be up to 2-3 times their normal ratedvalues.Whereas,highcapacitypowertransformers,underspecialcircumstances,cantakeupoverloadsuptoonly20%abovetheirnormalrating.

3.10 THEORYOFPOTENTIALTRANSFORMERS

Figure 3.15 represent the equivalent circuit of a PT and Figure 3.16 plots the phasordiagramunderoperatingconditionofthePT.

Figure3.15EquivalentcircuitofaPT

VP = primarysupplyvoltageEP = primarywindinginducedvoltageVS = secondaryterminalvoltageES = secondarywindinginducedvoltageIP = primarycurrentIS = secondarycurrent10 = no-loadcurrentIC = corelosscomponentofcurrentIM = magnetisingcomponentofcurrentrP = resistanceofprimarywindingxP = reactanceofprimarywindingrS = resistanceofsecondarywindingxS = reactanceofsecondarywindingRC = imaginaryresistancerepresentingcorelossesXM = magnetisingreactance

rE = resistanceofexternalload(burden)includingresistanceofmeters,currentcoilsetc.

xE = reactanceofexternalload(burden)includingreactanceofmeters,currentcoils,etc.NP = primarywindingnumberofturnsNS = secondarywindingnumberofturns

n = turnsratio =NP/NS

φ = workingfluxofthePTθ = the‘phaseangle’ofthePT

δ = phaseanglebetweensecondarywindingterminalvoltageandsecondarywindingcurrent(i.e.,phaseangleofloadcircuit)

β = phaseanglebetweenprimaryloadcurrentandsecondaryterminalvoltagereversedα = phaseanglebetweenno-loadcurrentI0andfluxφ

Figure3.16PhasordiagramofaPT

Thefluxjisplottedalongthepositivex-axis.MagnetisingcomponentofcurrentIm isinphasewiththeflux.ThecorelosscomponentofcurrentIC,leadsbyIM90°.SummationofIcandImproducestheno-loadcurrentI0.

Theprimarywinding inducedvoltageEP is in the samephasewith the resistive coreloss component of current IC. As per transformer principles, the secondary windinginducedvoltageESwillbe180°outofphasewith theprimarywinding inducedvoltageEP. Secondary output terminal voltage VS is obtained by vectorically subtracting thesecondarywindingresistiveandreactivevoltagedropsISrSandISxSrespectivelyfromthesecondaryinducedvoltageES.

Secondary voltageswhen referred to primary side need to bemultiplied by the turnsration,whereas,whensecondarycurrentsaretobereferredtoprimaryside,theyneedtobedividedbyn.SecondarycurrentIS,whenreflectedbacktoprimary,canberepresentedby the 180° shifted phasor indicated by IS/n. Primary winding current Ip is the phasorsummation of this reflected secondary current (load component) IS/n and the no-loadcurrentI0.

Vectoricallyadding theprimarywinding resistiveand reactivevoltagedropswith theprimaryinducedvoltagewillgivetheprimarylinevoltageVP.

3.10.1VoltageTransformationRatioofPTRedrawingtheexpandedviewofthephasordiagramofFigure3.14,weobtainthephasor

diagramofFigure3.17.

Figure3.17ExpandedviewofasectionofFigure3.16

The phase-angle difference θ between the primary voltage VP and the reflectedsecondaryvoltagenVSiscalledphaseangleofthePT.Ideally,withoutanyno-loadcurrentandwithoutanyvoltagedropinwindingimpedances,thesetwophasorsmusthavebeeninthesamephase,i.e.,ideallyθ=0.

FromtheequivalentcircuitofthePTshowninFigure3.15andthephasordiagramofFigure3.16,wehave

FromthephasordiagraminFigure3.17,wehave:

In reality, thephase angle differenceθ is quite small, thus for the sake of simplicity,bothVPandVSreversedcanbeapproximatedtoperpendiculartothefluxj,andhence:

Inreality,onceagain,sinceθ isverysmall,sometimesevenlessthan1°,thenwecanapproximateas

cosθ=1,andVPcosθ=VP

SubstitutingtheabovevaluesinEq.(3.12)wehave,

Here,RP=equivalentresistanceofthePTreferredtoprimaryside

XP=equivalentreactanceofthePTreferredtoprimaryside

Thus,actualvoltagetransformationratio:

Equation(3.14)maybere-writtenas

Here,RS=equivalentresistanceofthePTreferredtosecondaryside

XS=equivalentreactanceofthePTreferredtosecondaryside

Thus,actualvoltagetransformationratiocanagainbewrittenas

FollowingEqs(3.16)and(3.18),theerrorinratio,i.e.,thedifferencebetweenactualtransformationratioandturnsratiocanbeexpressedineitherofthefollowingtwo

forms:

3.10.2PhaseAngleofPTFromthephasordiagramofFigure3.17,

To simplify the computations, here we can make the assumption that in thedenominator,thetermscontainingIpandISbeingmuchlesscomparedtothelargevoltage

nVS,thosetermscanbeneglected;thuswegetasimplifiedform:

FollowingEq.(3.12),weget

Since0issmall,wecanassumetan0=0;thus,

3.11ERRORSINTRODUCEDBYPOTENTIALTRANSFORMERS

3.11.1RatioErrorandPhase-AngleErrorItcanbeseenfromtheabovesectionthat,likecurrenttransformers,potentialtransformersalsointroduceerrorsinmeasurement.Thiserrormaybeintermsofmagnitudeorphase,in themeasuredvalueofvoltage.The ratioerror (differencebetweennominal ratioandactual transformation ratio) only is important whenmeasurements of voltage are to bemade;thephaseangleerrorisofimportanceonlywhilemeasurementofpower.

Inpresenceoftheseerrors,thevoltageappliedtotheprimarycircuitofthePTcannotbe obtained accurately by simply multiplying the voltage measured by the voltmeterconnectedacrossthesecondarybytheturnsrationofthePT.

These errors dependupon the resistance and reactanceof the transformerwinding aswellasonthevalueofno-loadcurrentofthetransformer.

3.11.2ReducingErrorsinPTAsdiscussedintheprevioussection,errorsareintroducedintheratioandphaseangleofaPTowing to thepresenceof theno-load componentof theprimary current andvoltagedrops across winding impedances. Improvement of accuracy, then, depends uponminimisingthesecomponentsornullifyinginsomewaytheireffectsinintroducingerrors.Thiscanbeachievedbyacombinationofthefollowingschemes:

1. Reducing the loss component and magnetising components, i.e., the no-loadcomponent of the primary current can be achieved by reducing the length ofmagnetic path in the core, using good quality core magnetic materials, designingwith appropriate value of flux densities in the core, and adopting precautionarymeasureswhileassemblingandinterleavingofcorelaminations.

2. Winding resistance can be reduced by using thick conductors and taking care toreducethelengthofmeanturnofthewindings.

3. Winding leakage fluxandhence leakage reactancecanbe reducedbykeeping theprimaryandsecondarywindingsascloseaspermissible from thepointofviewofinsulationrequirements.

4.Sufficientlyhighfluxdensitiesinthecorewillreducethecorecross-section,therebyreducing the lengthofwindingwoundover thecore.This, in turn,will reduce thewindingresistance.Anoptimisationinthecorefluxdensityvaluetobeusedneedstodone,sincetoohighafluxdensitywillincreasetheno-loadcurrent,whichisalsonotdesirable.

5.From(3.18)itisclearthatatnoload,theactualPTtransformationratioexceedstheturnsratiobyanamount(ICrP+IMXP)/VS.Withincreasedloading,thisdifferencegrowsduetofurthervoltagedropsinwindingresistanceandreactance.Iftheturnsratiocanbe setatavalue less than thenominal ratio, then thedifferencebetweennominal ratio and actual transformation ratio under operating condition can bebroughtdown.Thiscanbeachievedbyreducingthenumberofturnsintheprimarywindingorincreasingthenumberofturnsinthesecondarywinding.Thismakesitpossibletomaketheactualtransformationratiotobeequaltothenominalratio,atleastforaparticularvalueandtypeofburden.

3.12OPERATIONALCHARACTERISTICSOFPOTENTIALTRANSFORMERS

Characteristics of potential transformers under different operating conditions may beestimatedfromthephasordiagramasshowninFigure3.20andexpressionsforratioerror(3.19)andphase-angleerror(3.22).

3.12.1EffectofChangeinSecondaryBurden(VAorCurrent)

WithincreaseinPTsecondaryburden,thesecondarycurrentisincreased.Thisinturnwillincrease the primary current as well. Both primary and secondary voltage drops areincreased and hence, for a given value of the primary supply voltage VP, secondaryterminalvoltageVSisreducedwithincreaseofburden.Theeffectisthereforetoincreasetheactual transformationratioVP/VSwithresultingincreaseintheratioerrorasperEq.(3.19).This increase in ratio errorwith increasing secondaryburden is almost linear asshowninFigure3.18.

Figure3.18Effectsofsecondaryburdenvariationon(a)PTratioerror,and(b)PTphaseangleerror

Withregardtothephaseangle,withincreasingvoltagedropsduetoincreasedburden,thephasedifferencebetweenVPandVSreversedincreaseswithresultingincreaseinphaseangle error. Such a variation of phase-angle error with varying secondary burden in atypicalpotentialtransformerisshowninFigure3.18.

3.12.2EffectofChangeinPowerFactorofSecondaryBurdenAscanbeobservedfromthephasordiagramofpotentialtransformerinFigure3.18, forallinductiveburdens,thesecondarywindingcurrentISlagsbehindthesecondaryterminalvoltageVS, so that thephaseangledifferenceδ ispositive.At lowerpowerfactors, thisphase angle difference δ increases as IS moves further away fromVS. Thus, from thephasordiagram,itisapparentthatIpwillnowbecomeclosertoI0.Thiswill,inturn,moveVPandVSmoretowardstobeinphasewithEPandESrespectively.Itistobekeptinmindthatchange inpower factordoesnotaffect themagnitudesof resultantvoltagedrops inprimary and secondary windings substantially. Under these conditions, with primary

supplyvoltageVPbeingconsideredtoremainthesame,thereisareductionofEPrelativeto VP, and VS relative to ES. The actual transformation ratio VP /VS of the potentialtransformerwillthusincreasewithreductioninburdenpowerfactor.

Further,sinceVS isadvancedinphaseandVP is retardedinphase, thephaseangleofthe transformer (between VS andVP) is reduced with reduction in burden (inductive)powerfactor.

Figure 3.19 shows the variations of ratio and phase-angle errors in a typical currenttransformeratdifferentvaluesofthesecondaryburdenpowerfactor.

Figure3.19Effectsofsecondaryburdenpowerfactorvariationon(a)PTratioerror,and(b)PTphaseangleerror

3.13DESIGNANDCONSTRUCTIONALFEATURESOFPOTENTIALTRANSFORMERS

1.Core

ThecoreconstructionofaPTmaybeofshelltypeorcoretype.Core-typeconstructionisonly used for low voltage applications. Special care is taken during interleaving andassemblingofthecorelaminationssothatminimalairgapispresentinthestackjoints.

2.Winding

Theprimaryandsecondarywindingsaremadecoaxialtorestricttheleakagereactancetoaminimum.Insimplifyingassemblyandreducinginsulationrequirement,thelow-voltage

secondary winding is placed nearer to the core, with the high-voltage primary beingwoundoverthesecondary.Forlowervoltageratingthehigh-voltageprimarywindingcanbemadeofasinglecoil,butforhighervoltages,however,anumberofseparatecoilscanbeassembledtogethertoreduceinsulationcomplicacies.

3.Insulation

Cottontapeandvarnishisthemostcommoninsulationappliedoverwindingsduringcoilconstruction.Atlowvoltages,PTsareusuallyfilledwithsolidcompounds,butathighervoltagesabove7-10kV,theyareoil-immersed.

4.Bushings

Oil-filledbushingsarenormallyusedforoil filledpotential transformersas this reducestheoverallheight.Somepotential transformers connectedbetween line andneutralof agrounded neutral system have only one bushing for the high voltage terminal. Somepotential transformerscanhave twobushingswhenneither sideof the line is atgroundpotential.Aviewofsuchatwo-bushingpotentialtransformerisshowninFigure3.20.

Figure3.20Cutawayviewoftwo-bushingtypepotentialtransformer(CourtesyofWestinghouseElectricCorp.)

5.CostandSize

Power transformers are designed keeping in view the efficiency, regulation and costconstraints.Thecostinsuchcasesisreducedbyusingsmallercoresandconductorsizes.Inpotential transformers, however, cost cannot be compromisedwith respect to desiredperformance and accuracy.Accuracy requirements in potential transformers in terms ofratioandphaseangleobviatetheuseofgoodqualityandamountofmagneticmaterialforthecoreandalsothickconductorsforthewinding.

6.OverloadCapacity

Potential transformers are normally designed for very low power ratings and relativelylarge weight/ power ratio as compared to a power transformer. Theoretically, this canenable a potential transformer to run on appreciable overloads without causing muchheating.Overloadcapacitiesofpotential transformersare,however, limitedbyaccuracy

requirements,ratherthanheating.

Example3.1 Apotentialtransformerwithnominalratio1100/110Vhasthefollowingparameters:

Primaryresistance=82Φsecondaryresistance=0.9Φ

Primaryreactance=76Φsecondaryreactance=0.72Φ

Noloadcurrent=0.02aat0.4powerfactor

Calculate(a)phaseangleerroratnoload

(b)burdeninVAatunitypowerfactoratwhichphaseangleerrorwillbezero

SolutionNoloadpowerfactor=cos(90°+α)=0.4α=23.6°andsina=0.4,cosa=0.917

IC=I0sina=0.02¥0.4=0.008A

IM=I0cosa=0.02¥0.0.917=0.0183A

Turnsration=1100/110=10

FromEq.(3.21),

(a)Atnoload,IS=0

(b)Atunitypowerfactor,δ=0;thuscosδ=1andsinδ=0

Forzerophase-angleerror,θ=0;

XP-Totalimpedancereferredtoprimary-xP+n×XS

or, xP-76+102×0.72-148Ω

Thus,or,

secondaryburden-VS×IX-110×0.06-6.6VA

A potential transformer rated at 6600/110 V has 24000

Example3.8

turns in the primary and 400 turns in the secondarywinding. With rated voltage applied to the primary andsecondary circuit opened, the primary winding draws acurrent of0.004 A, lagging the voltage by 75°. In anotheroperatingconditionwithacertainburdenconnectedtothesecondary, the primary draws 0.015 A at an angle 60°lagging with respect to the voltage. The followingparametersaregivenforthetransformer:

Primaryresistance=600Ω secondaryresistance=0.6Ω

Primaryreactance=1500Ω secondaryreactance=0.96Ω

Calculate(a)Secondaryloadcurrentandterminalvoltage,usingratedappliedvoltageasthereference

(b)Theloadburdeninthiscondition

(c)Actualtransformationratioandphaseangle

(d) Howmany turns shouldbechanged in theprimarywinding tomake theactualratioequaltothenominalratioundersuchoperatingcondition?

SolutionThecorrespondingphasordiagramisshowninthefigure.

Nominalratio=6600/110=60Turnsratio=24000/400=60Noloadcurrent=0.004A

Noloadpowerfactor=cos75°=0.26andsin75°=0.966Primarycurrent=0.015A

Primarypowerfactor=cos60°=0.5andsin60°=0.866

PrimaryvoltageVPistakenasreference

Thus,VP=6600+j0

Ip=0.015(0.5-j0.866)=0.0075-j0.013

I0=0.004(0.26-j0.966)=0.00104-j0.0039

AsseenfromFigure3.21,thephasor isthephasordifferenceofIpandIq.

Thus,

Thus,IS(reversed)=60×(0.00646-j0.0091)=0.388-j0.546

secondarycurrentphasorIS=-(0.388-j0.546)=-0.388+j0.546

(a)Secondarycurrentmagnitude PrimaryvoltageEP=VP-IP×ZP

or, EP=6600+j0-(0.0075-j0.013)(600+j1500)

or, EP=6576-j3.45

Secondaryinducedvoltage(reversed)

secondaryinducedvoltagephasor=ES=-(-109.6-j0.0575)

or, ES=-109.6+j0.575

secondaryterminalvoltageVs=Es-IsxZs

=-109.6+j0.0575-(-0.388+j0.546)(0.6+j0.96)

=-109.9+j0.76

magnitudeofsecondaryterminalvoltage

(b)Secondaryloadburden=VS×IS=109.9×0.67=73.63VA

(c)Actualtransformationratio

VS(reversed)--(-109.9+j0.76)-109.9-j0.76V

PhaseanglebywhichVS(reversed)lagsVP

(d)Inordertomakeactualratioequaltothenominalratio,theprimarynumberofturnsshouldbereducedto

3.14 DIFFERENCESBETWEENCTANDPT

Insummary,thefollowingdifferencesbetweenacurrenttransformer(CT)andapotentialtransformer(PT)canbetabulated:

EXERCISE

Objective-typeQuestions1.Thedisadvantagesofusingshuntsforhighcurrentmeasurementsare

(a)powerconsumptionbytheshuntsthemselvesishigh

(b)itisdifficulttoachievegoodaccuracywithshuntsathighcurrents

(c)themeteringcircuitisnotelectricallyisolatedfromthepowercircuit

(d)alloftheabove

2.Thedisadvantagesofusingmultiplierswithvoltmetersformeasuringhighvoltagesare

(a)powerconsumptionbymultipliersthemselvesishighathighvoltages

(b)multipliersathighvoltageneedtobeshieldedtopreventcapacitiveleakage

(c)themeteringcircuitisnotelectricallyisolatedfromthepowercircuit

(d)alloftheabove

3.Theadvantagesofinstrumenttransformersare

(a)thereadingsofinstrumentsusedalongwithinstrumenttransformersrarelydependontheimpedanceoftheinstrument

(b)duetoavailabilityofstandardisedinstrumenttransformersandassociatedinstruments,thereisreductionincostandeaseofreplacement

(c)themeteringcircuitiselectricallyisolatedfromthepowercircuit

(d)alloftheabove

4.Nominalratioofacurrenttransformeris

(a)ratioofprimarywindingcurrenttosecondarywindingcurrent

(b)ratioofratedprimarywindingcurrenttoratedsecondarywindingcurrent

(c)ratioofnumberofturnsintheprimarytonumberofturnsinthesecondary

(d)alloftheabove

5.BurdenofaCTisexpressedintermsof

(a)secondarywindingcurrent

(b)VAratingofthetransformer

(c)powerandpowerfactorofthesecondarywindingcircuit

(d)impedanceofsecondarywindingcircuit

6.RatioerrorinaCTisdueto

(a)secondarywindingimpedance(b)loadimpedance

(c)noloadcurrent(d)alloftheabove

7.Phase-angleerrorinaCTisdueto

(a)primarywindingimpedance

(b)primarycircuitphaseangle

(c)leakagefluxbetweenprimaryandsecondary

(d)alloftheabove

8.Errorsininstrumenttransformerscanbeaggravatedby

(a)leakageflux(b)coresaturation

(c)transientsinmainpowerline(d)alloftheabove

9.Phase-angleerrorinaCTcanbereducedby

(a)reducingnumberofsecondaryturns

(b)usingthinconductorsfortheprimarywinding

(c)usinggoodquality,lowlosssteelforcore

(d)alloftheabove

10.RatioerrorinaCTcanbereducedby

(a)usinggoodquality,lowlosssteelforcore

(b)placingprimaryandsecondarywindingsclosertoeachother

(c)usingthickconductorsforsecondarywinding

(d)alloftheabove

11.Fluxdensityininstrumenttransformersmustbedesignedtobe

(a)sufficientlylowtoreducecorelosses

(b)sufficientlyhightoreducecoresectionandhencereducelengthofwinding

(c)sufficientlylowtopreventcoresaturation

(d)properlyoptimizedtohaveabalanceamong(a)-(c)

12.CurrentintheprimarywindingofCTdependson

(a)burdeninthesecondarywindingofthetransformer

(b)loadconnectedtothesysteminwhichtheCTisbeingusedformeasurement

(c)bothburdenofthesecondaryandloadconnectedtothesystem

(d)noneoftheabove

13.TurnscompensationisusedinCTtoreduce

(a)phase-angleerror

(b)bothratioandphaseangleerror

(c)primarilyratioerror,reductioninphaseangleerrorisincidental

(d)noneoftheabove

14.SecondarywindingofCTshouldneverbeopencircuitedwithprimarystillenergisedbecausethatwill

(a)increasepowerlossinthesecondarywinding

(b)increaseterminalvoltageinthesecondarywinding

(c)increasetheleakagefluxmanifolds

(d)alloftheabove

15.OpencircuitingthesecondarywindingofCTwithprimarystillenergisedwillresultin

(a)unrestrictedprimaryfluxtogeneratehighvoltagesacrosssecondaryterminals

(b)possibleinsulationdamageduetohighvoltagebeinggenerated

(c)injurytocarelessoperator

(d)alloftheabove

16.Ashort-circuitinglinkisprovidedonthesecondarysideofaCTto

(a)allowhighcurrenttoflowintheprimarywhenthesecondarywindingoftheCTisshortcircuitedwiththelink

(b)allowadjustmentstobemadeinthesecondaryside,likereplacingtheammeter,withtheprimaryenergizedbuttheshortcircuitinglinkinuse

(c)enableprimarycurrenttodropdowntozerowhenthesecondaryisopencircuitedwiththeshortcircuitinglinkinuse

(d)alloftheabove

17.Clamp-ontypeandsplit-coretypeCTsareusedbecause

(a)theiraccuracyishigh

(b)itispossibletoinserttheCTinthecircuitwithoutbreakingthemainline

(c)theyarecheaper

(d)alloftheabove

18.TransformationratioofaPTisdefinedas

(a)ratioofprimarywindingvoltagetosecondarywindingvoltage

(b)ratioofratedprimarywindingvoltagetoratedsecondarywindingvoltage

(c)ratioofprimarynumberofturnstosecondarynumberofturns

(d)alloftheabove

19.WhenthesecondarywindingofaPTissuddenlyopencircuitedwiththeprimarywindingstillopencircuitedthen

(a)largevoltageswillbeproducedacrossthesecondaryterminalsthatmaybedangerousfortheoperatingpersonnel

(b)largevoltagesthusproducedmaydamagetheinsulation

(c)theprimarywindingdrawsonlyno-loadcurrent

(d)noneoftheabove

20.ThesizeofaPTascomparedtoapowertransformerofsameVA

(a)issmaller(b)isbigger

(c)isthesame(d)thereisnorelationassuch

Short-answerQuestions1. Discuss the advantages of instrument transformers as compared to shunts and multipliers for extension of

instrumentrange.

2.Describewithclearschematicdiagrams,howhighvoltageandcurrentsaremeasuredwiththehelpofinstrumenttransformers.

3.Drawandexplainthenatureofequivalentcircuittheandcorrespondingphasordiagramofacurrenttransformer.

4.Discussthemajorsourcesoferrorinacurrenttransformer.

5.Describethedesignandconstructionalfeaturesofacurrenttransformerforreducingratioerrorandphase-angleerror.

6.Explainwiththehelpofasuitableexample,themethodofturnscompensationinaCTtoreduceratioerror.

7.WhyshouldthesecondarywindingofaCTneverbeopencircuitedwithitsprimarystillenergised?

8.ExplainhowthecoreofaCTmaygetpermanentmagnetisationinducedinit.Whatarethebadeffectsofsuchpermanentmagnetisation?Whatarethewaystode-magnetisethecoreinsuchsituations?

9.Drawandexplaintheconstructionalfeaturesofwound-type,bartype,clamptypeandbushingtypeCTs.

10. Drawtheequivalentcircuitandphasordiagramofapotential transformerbeingusedformeasurementofhighvoltages.

11.Whatarethedifferencesbetweenapotentialtransformerandaregularpowertransformer?

12.DescribethemethodsemployedforreducingratioerrorandphaseangleerrorinPTs.

Long-answerQuestions1. Drawandexplain thenatureof equivalent circuit andcorrespondingphasordiagramof a current transformer.

Deriveexpressionsforthecorrespondingratioerrorandphaseangleerror.

2.(a)Whatarethesourcesoferrorinacurrenttransformer?

(b)Aring-coretypeCTwithnominalratio1000/5andabarprimaryhasasecondarywindingresistanceof0.8Ωandnegligiblereactance.Thenoloadcurrentis4Aatapowerfactorof0.35whenfullloadsecondarycurrentisflowinginaburdenif1.5Ωno-inductiveresistance.Calculatetheratioerrorandphase-angleerroratfullload.Alsocalculatethefluxinthecoreat50Hz.

3.(a)Describethedesignandconstructionalfeaturesofacurrenttransformerforreducingratioerrorandphase-angleerror.

(b)A1000/10A,50Hzsingle-turnprimarytypeCThasasecondaryburdencomprisingofapureresistanceof1.0Ω.Calculatefluxinthecore,ratioerrorandphase-angleerroratfullload.Neglectleakagereactanceandassumetheironlossinthecoretobe5Ωatfullload.Themagnetisingampere-turnsis180.

4.(a)WhythesecondarywindingofaCTshouldneverbeopencircuitedwithitsprimarystillenergised?

(b)Abar-typeCThas300turnsinthesecondarywinding.Theimpedanceofthesecondarycircuitis(1.5+j2)Ω.With5Aflowinginthesecondary,themagnetisingmmfis1000AandtheironlossisDetermineratioandphase-angleerrors.

5.(a)ExplainthemethodofturnscompensationinaCTtoreduceratioerror.

(b)Abar-typeCThas400turnsinthesecondarywinding.Anammeterconnectedtothesecondaryhasresistanceof1.5Ωandreactanceof1.0Ω,andthesecondarywindingimpedance is(0.6+ j0.8)Ω.Themagnetisingmmfrequirement for thecore is80Aand tosupply the iron loss thecurrent required is30A. (i)Find theprimarywindingcurrentandalsodeterminetheratioerrorwhentheammeterinthesecondarywindingshows4 A. (ii) How many turns should be reduced in the secondary to bring down ratio error to zero at thiscondition?

6. Drawandexplainthenatureofequivalentcircuitandcorrespondingphasordiagramofapotentialtransformer.Deriveexpressionsforthecorrespondingratioerrorandphase-angleerror.

7.(a)Whatarethedifferencesbetweenapotentialtransformerandaregularpowertransformer?

(b)Apotentialtransformerwithnominalratio1000/100Vhasthefollowingparameters:

Primaryresistance=96Ω secondaryresistance=0.8Ω

Primaryreactance=80Ω secondaryreactance=0.65Ω

Noloadcurrent=0.03aat0.35powerfactorCalculate

(i) phaseangleerroratnoload(ii) burdeninVAatunitypowerfactoratwhichphaseangleerrorwillbezero.

(a)DescribethemethodsemployedforreducingratioerrorandphaseangleerrorinPTs?

(b)Apotentialtransformerratedat6000/100Vhas24000turnsintheprimaryand400turnsinthesecondarywinding.Withratedvoltageappliedtotheprimaryandsecondarycircuitopened,theprimarywindingdrawsacurrentof0.005Alaggingthevoltageby700.Inanotheroperatingconditionwithacertainburdenconnectedtothesecondary,theprimarydraws0.012Aatanangle540laggingwithrespecttothevoltage.Thefollowingparametersaregivenforthetransformer:

Primaryresistance=600Ω secondaryresistance=0.6Ω

Pimaryreactance=1500Ω secondaryreactance=0.96Ω

Calculate

(i) Secondaryloadcurrentandterminalvoltage,usingratedappliedvoltageasthereference

(ii) Theloadburdeninthiscondition(iii) Actualtransformationratioandphaseangle(iv) Howmany turns should be changed in the primarywinding tomake the

actualratioequaltothenominalratioundersuchoperatingcondition?

4.1 INTRODUCTION

Resistorsareusedinmanyplacesinelectricalcircuitstoperformavarietyofusefultasks.Propertiesofresistancesplayanimportantroleindeterminingperformancespecificationsforvariouscircuit elements includingcoils,windings, insulations, etc. It is important inmanycasestohavereasonablyaccurateinformationofthemagnitudeofresistancepresentinthecircuitforanalysingitsbehaviour.Measurementofresistanceisthusoneoftheverybasic requirements inmanyworkingcircuits,machines, transformers,andmeters.Apartfrom these applications, resistors are used as standards for the measurement of otherunknownresistancesandforthedeterminationofunknowninductanceandcapacitance.

Fromthepointofviewofmeasurement,resistancescanbeclassifiedasfollows:

1.LowResistances

Allresistancesoftheorderlessthan1Ωmaybeclassifiedaslowresistances.Inpractice,such resistances can be found in the copper winding in armatures, ammeter shunts,contacts,switches,etc.

2.MediumResistances

Resistancesintherange1Ωto100kΩmaybeclassifiedasmediumresistances.Mostoftheelectricalapparatusused inpractice,electroniccircuits,carbonresistanceandmetal-filmresistorsarefoundtohaveresistancevalueslyinginthisrange.

3.HighResistances

Resistanceshigherthan100kΩareclassifiedashighresistances.Insulationresistancesinelectricalequipmentareexpectedtohaveresistancesabovethisrange.

The above classifications are, however, not rigid, but only form a guideline for themethodofmeasurementtobeadopted,whichmaybedifferentfordifferentcases.

4.2 MEASUREMENTOFMEDIUMRESISTANCES

The different methods for measurement of medium range resistances are (i) ohmmetermethod, (ii) voltmeter–ammetermethod, (iii) substitutionmethod, and (iv)Wheatstone-bridgemethod.

4.2.1OhmmeterMethodforMeasuringResistanceOhmmeters are convenient direct reading devices for measurement of approximateresistance of circuit components without concerning too much about accuracy. Thisinstrumentis,however,verypopularinthesensethatitcangivequickanddirectreadingsforresistancevalueswithoutanypreciseadjustmentsrequirementsfromtheoperator.Itisalsousefulinmeasurementlaboratoriesasanadjuncttoaprecisionbridge.Valueoftheunknownresistancetobemeasuredisfirstobtainedbytheohmmeter,andthiscansavelotoftimeinbridgebalancingforobtainingthefinalprecisionvalueusingthebridge.

Series-typeOhmmeter

Figure4.1showstheelementsofasimplesingle-rangeseries-typeohmmeter.

Figure4.1Single-rangeseriesohmmeter

The series-type ohmmeter consists basically of a sensitive dc measuring PMMCammeterconnectedinparallelwithavariableshuntR2.Thisparallelcircuitisconnectedin series with a current limiting resistance R1 and a battery of emf E. The entirearrangementisconnectedtoapairofterminals(A–B)towhichtheunknownresistanceRxtobemeasuredisconnected.

Beforeactual readingsare taken, the terminalsA–Bmust be shorted together.At thispositionwithRx=0,maximumcurrentflowsthroughthemeter.TheshuntresistanceR2isadjusted so that themeter deflects corresponding to its rightmost full scale deflection(FSD)position.TheFSDpositionofthepointerismarked‘zero-resistance’,i.e.,0Ωonthescale.Ontheotherhand,whentheterminalsA–Barekeptopen(Rx→∞),nocurrentflowsthroughthemeterandthepointercorrespondstotheleftmostzerocurrentpositiononthescale.Thispositionofthepointerismarkedas‘∞Ω’onthescale.Thus,themeterwillreadinfiniteresistanceatzerocurrentpositionandzeroresistanceatfull-scalecurrentposition.Seriesohmmeters thushave ‘0’markat the extreme right and ‘∞’markat theextremeleftofscale(oppositetothoseforammetersandvoltmeters).

Themaindifficultyisthefactthatohmmetersareusuallypoweredbybatteries,andthe

battery voltage gradually changeswith use and age. The shunt resistanceR2 is used insuchcasestocounteractthiseffectandensureproperzerosettingatalltimes.

Forzerosetting,Rx=0,whereRm=internalresistanceofthebasicPMMCmetercoil

ThecurrentI2canbeadjustedbyvaryingR2sothatthemetercurrentImcanbeheldatitscalibratedvaluewhenthemaincurrentI1changesduetodropinthebatteryemfE.

IfR2werenotpresent,thenitwouldalsohavebeenpossibletobringthepointertofullscalebyadjustmentoftheseriesresistanceR1,Butthiswouldhavechangedthecalibrationallalongthescaleandcauselargeerror..

(i)DesignofR1andR2Theextremescalemarkings,i.e.,0and∞,inanohmmeterdonotdependonthecircuitconstants.However,distributionsofthescalemarkingsbetweenthesetwoextremesareaffectedbytheconstantsofthecircuit.Itisthusessentialtodesignforpropervaluesofthecircuitconstants,namely,R1andR2 inparticular tohavepropercalibrationofthescale.ThefollowingparametersneedtobeknownfordeterminationofR1andR2.

•MetercurrentImatfullscaledeflection(=IFSD.)

•Metercoilresistance,Rm•Ohmmeterbatteryvoltage,E

•Valueoftheunknownresistanceathalf-scaledeflection,(Rh),i.e.,thevalueofRxwhenthepointerisatthemiddleofscale

WithterminalsA–Bshorted,whenRx=0

Meter carries maximum current, and current flowing out of the battery is given as

whereRi=internalresistanceoftheohmmeter

Athalf-scaledeflection,

Forfull-scaledeflection,

Thus,

Again,since ,puttingthevalueofR2from(4.1),weget

(ii) .ShapeofScale inSeriesOhmmetersElectricalequivalentcircuitofa series-typeohmmeterisshowninFigure4.2.

Figure4.2Electricalequivalentcircuitofaseries-typeohmmeter

Internalresistanceoftheohmmeter

WiththeterminalsA–BshortcircuitedRx=0;thus,from(4.3)wehave

From(4.3)and(4.4),themetercanberelatedtotheFSDas

Thus,

FromEq.(4.5),itcanbeobservedthatthemetercurrentImisnotrelatedlinearlywiththeresistanceRxtobemeasured.Thescale(angleofdeflection)inseriesohmmeterif

thusnon-linearandcramped.

The above relation (4.5) also indicates the fact that the meter current and hencegraduationsofthescalegetchangedfromtheinitialcalibratedvalueseachtimetheshuntresistance R2 is adjusted. A superior design is found in some ohmmeters where anadjustable soft-iron shunt is placed across the pole pieces of themeter, as indicated inFigure4.3.

Figure4.3Seriesohmmeterwithsoft-ironmagneticshunt

The soft-iron magnetic shunt, when suitably positioned with the help of screwadjustment,modifies the air gap fluxofmainmagnet, andhence controls sensitivity ofmovement. The pointer can thus be set at proper full scale marking in compensationagainst changes is battery emf, without any change in the electrical circuit. The scalecalibrationsthusdonotgetdisturbedwhenthemagneticshuntisadjusted.

1.Multi-rangeSeriesOhmmeter

For most practical purposes, it is necessary that a single ohmmeter be used formeasurement of a wide range of resistance values. Using a single scale for suchmeasurementswill lead to inconvenience inmeter readingsandassociated inaccuracies.Multi-range ohmmeters, as shown schematically in Figure 4.4, can be used for suchmeasurements.TheadditionalshuntresistancesR3,R4…,R7areusedtoadjustthemetercurrenttocorrespondto0toFSDscaleeachtimetherangeoftheunknownresistanceRxis changed. Inapracticalmulti-rangeohmmeter, these shunt resistancesarechangedbyrotatingtherangesettingdialoftheohmmeter.Thephotographofsuchalaboratorygradeanalogmulti-rangeohmmeterisprovidedinFigure4.5.

Figure4.4Multi-rangeseries-typeohmmeter

Figure4.5Photographofmulti-rangeohmmeter(Courtesy,SUNWA)

2.Shunt-typeOhmmeter

Figure4.6showstheschematicdiagramofasimpleshunt-typeohmmeter.

Theshunt-typeohmmeterconsistsofabatteryinserieswithanadjustableresistanceR1andasensitivedcmeasuringPMMCammeter.TheunknownresistanceRxtobemeasuredisconnectedacrossterminalsA–Bandparallelwiththemeter.

Figure4.6Shunt-typeohmmeter

When the terminalsA–Bare shorted (Rx=0), themeter current is zero, sinceall thecurrent in thecircuitpasses through theshortcircuitedpathA–B, rather than themeter.This positionof the pointer ismarked ‘zero-resistance’, i.e., ‘0Ω’ on the scale.On theother hand,whenRx is removed, i.e., the terminalsA–B open circuited (Rx→∞), entirecurrent flows through the meter. Selecting proper value of R1, this maximum currentpositionof thepointer canbemade to read full scaleof themeter.Thispositionof the

pointerismarkedas‘∞Ω’onthescale.Shunttypeohmmeters,accordingly,has‘0Ω’attheleftmostpositioncorrespondingtozerocurrent,and‘∞Ω’attherightmostendofthescalecorrespondingtoFSDcurrent.

Whennotundermeasurement,i.e.,nothingisconnectedacrosstheterminalsA–B(Rx→∞)thebatteryalwaysdrivesFSDcurrentthroughthemeter.Itisthusessentialtodisconnectthebatteryfromrestofthecircuitwhenthemeterisidle.AswitchS,asshowninFigure4.6,isthusneededtopreventthebatteryfromdrainingoutwhentheinstrumentisnotinuse.

ShapeofScaleinShuntOhmmetersInternalresistanceoftheohmmeter

WithterminalsA–Bopen,thefull-scalecurrentthroughthemeteris

WithRxconnectedbetweenterminalsA-B,thecurrentoutofthebatteryis

Thus,metercurrent

FromEqs(4.6)and(4.7),themetercanberelatedtotheFSDas

FromEq(4.8),itcanbeobservedthatthemetercurrentImincreasesalmostlinearlywiththeresistanceRxtobemeasuredforsmallervaluesofRxwhenRx<<R;.Thescale(angleofdeflection)inshunttypeohmmetersisthusalmostlinearinthelowerrange,butprogressivelybecomesmorecrampedathighervaluesofRx.Shunt-typeohmmetersarethusparticularlysuitableformeasurementoflowresistanceswhenthemeterscaleisnearlyuniform.

Designasingle-rangeseries-typeohmmeterusingaPMMCammeterthathasinternalresistanceof50Ωandrequiresacurrentof1mAforfull-scaledeflection.

Example4.1The internal battery has a voltage of 3V. It is desired toreadhalf scaleata resistancevalueof2000Ω.Calculate(a)thevaluesofshuntresistanceandcurrentlimitingseriesresistance,and(b)rangeofvaluesoftheshuntresistancetoaccommodatebatteryvoltagevariation in therange2.7 to3.1V.

SolutionSchematicdiagramoftheseriesohmmeterwiththegivenvaluesisshowninthefollowingfigure

Given,Rm=meterinternalresistance=50Ω

IFSD=meterfullscaledeflectioncurrent=1mA

Rh=half-scaledeflectionresistance=2000W

E=batteryvoltage=3V

(a)WithterminalsA–Bshorted,whenRx=0

Meter carries maximum current, and current flowing out of the battery is given as

whereE=batteryvoltage=3V,and

Ri=internalresistanceoftheohmmeter

Athalf-scaledeflection,Rx=Rh,andbatterycurrent

Forfull-scaledeflection,

(b)ForabatteryvoltageofE=2.7V,batterycurrentathalfscaleis

Forfull-scaledeflection,

Im=IFSD=1mAandI1=2Ih=1.35mA

Also,ImRm=I2R2andI1-Im=(1.35-1)mA=0.35mA

ForabatteryvoltageofE=3.1V,batterycurrentathalfscaleis

Forfull-scaledeflection,

Im=IFSD=1mAandI1=2Ih=1.55mA

Also,ImRm=I2R2andI1-Im=(1.55-1)mA=0.55mA

rangeofR2toaccommodatethegivenchangeinbatteryvoltageis142.86Ω>R2>90.9Ω.

Example4.2

A shunt-type ohmmeter uses a 2 mA basic d’Arsonvalmovementwithaninternalresistanceof25Ω.Thebatteryemfis1.5V.Calculate(a)valueoftheresistorinserieswiththebatteryto adjust the FSD, and (b) at what point (.percentage) offull-scalewill100Ωbemarkedonthescale?

SolutionSchematicdiagramofashunttype-ohmmeterundertheconditionasstatedinExample4.2isshownbelow:

AtFSDwhenterminalsA–Bisopened,meterFSDcurrentis

WhenRx=100Ω,batteryoutputcurrentwillbe

metercurrentis

Thus,percentageoffullscaleatwhichthemeterwouldread100Ωis

4.2.2Voltmeter–AmmeterMethodforMeasuringResistanceThevoltmeter–ammetermethodisadirectapplicationofohm’slawinwhichtheunknownresistanceisestimatedbymeasurementofcurrent(I) flowing through itand thevoltagedrop(V)acrossit.Thenmeasuredvalueoftheresistanceis

Thismethodisverysimpleandpopularsincetheinstrumentsrequiredformeasurementareusuallyeasilyavailableinthelaboratory.

Two types of connections are employed for voltmeter–ammetermethod as shown inFigure4.7.

Figure4.7Measurementofresistancebyvoltmeter–ammetermethod

Rx=truevalueofunknownresistance

Rm=measuredvalueofunknownresistance

Ra=internalresistanceofammeter

RV=internalresistanceofvoltmeter

It is desired that in both the cases shown in Figure 4.7, themeasured resistanceRmwouldbeequaltothetruevalueRxoftheunknownresistance.Thisisonlypossible,aswewillsee,iftheammeterresistanceiszeroandthevoltmeterresistanceisinfinite.

CaseA

In this circuit, the ammeter is connected directly with the unknown resistance, but thevoltmeter is connected across the series combination of ammeter and the resistanceRx.Theammetermeasuresthetruevalueofcurrentthroughtheresistancebutthevoltmeterdoesnotmeasurethetruevalueofvoltageacrosstheresistance.ThevoltmetermeasuresthesumofvoltagedropsacrosstheammeterandtheunknownresistanceRx.

Let,voltmeterreading=V

And,ammeterreading=I

measuredvalueofresistance

However, V=Va+Vror, V=I×Ra+I×Rx=I×(Ra+Rx)

Thus,

ThemeasuredvalueRmoftheunknownresistanceisthushigherthanthetruevalueR,bythequantityRa,internalresistanceoftheammeter.Itisalsoclearfromtheabovethattruevalueisequaltothemeasuredvalueonlyiftheammeterresistanceiszero.

Errorinmeasurementis

Equation (4.10) denotes the fact that error inmeasurement using connectionmethod

showninCaseAwillbenegligibleonlyiftheratio .Inotherwords,iftheresistance

undermeasurementismuchhigherascomparedtotheammeterresistance(RxRa.), thentheconnectionmethodshowninCaseAcanbeemployedwithoutinvolvingmucherror.

Therefore,circuitshowninCaseAshouldbeusedformeasurementofhighresistancevalues.

CaseB

Inthiscircuit,thevoltmeterisconnecteddirectlyacrosstheunknownresistance,buttheammeter is connected in series with the parallel combination of voltmeter and theresistance Rx. The voltmeter thus measures the true value of voltage drop across theresistance but the ammeter does not measure the true value of current through theresistance.TheammetermeasuresthesummationofcurrentflowingthroughthevoltmeterandtheunknownresistanceRx.

Let,voltmeterreading=V

And,ammeterreading=I

Thus, V=IR×RX=IV×RVHowever, I=IV+IRmeasuredvalueofresistance

ThemeasuredvalueRmoftheunknownresistanceisthuslowerthanthetruevalueRxbyaquantityrelatedtointernalresistanceofthevoltmeter.ItisalsoclearfromEq.(4.11)thattruevalueisequaltothemeasuredvalueonlyifthequantity ,i.e.,ifvoltmeterresistanceisinfinite.Inotherwords,ifthevoltmeterresistanceismuchhigherascomparedtotheresistanceundermeasurement(RV>>RA)thentheconnectionmethodshowninCaseBcanbeemplotedwithoutinvolvingmucherror.

Therefore,circuitshowninCaseBshouldbeusedformeasurementoflowresistancevalues.

Example4.3

Avoltmeterof600Ωresistanceandamilliammeterof0.8Ωresistanceareusedtomeasuretwounknownresistancesbyvoltmeter–ammetermethod.Ifthevoltmeterreads40Vandmilliammeterreads120mAin both the cases, calculate the percentage error in thevalues ofmeasured resistances if (a) in the first case, the

voltmeterisputacrosstheresistanceandthemilliammeterconnected in serieswith the supply, and (b) in the secondcase, the voltmeter is connected in the supply side andmilliammeter connected directly in series with theresistance.

SolutionTheconnectionsareshowninthefollowingfigure.VoltmeterreadingV=40V

AmmeterreadingI=120mA

measuredresistancefromvoltmeterandI

ammeterreadingsisgivenby

TheammeterreadsthecurrentflowingIRthroughtheresistanceRxandalsothecurrentIVthroughthevoltmeterresistanceRV.

Thus, I=IV+IRNow, the voltmeter and the resistance Rx being in parallel, the voltmeter reading is

givenby

V=IR×RX=IV×RV

Currentthroughvoltmeter

truecurrentthroughtresistanceIR=I-IV=120-66.67=55.33mA

truevalueofresistance

Thus,percentageerror

Theconnectionsareshowninthefollowingfigure.

VoltmeterreadingV=40V

AmmeterreadingI=120mA

measuredresistancefromvoltmeterandammeterreadingsisgivenby

VoltmeterreadsthevoltagedropVracrosstheresistanceRxandalsothevoltagedropVaacrosstheammeterresistanceRa.

Thus, V=Va+VrVoltagedropacrossammeter

Va=I×Ra=120×10-3×0.8=0.096V

truevoltagedropacrosstheresistance

Vr=V-Va=40–0.096×39.904V

truevalueofresistance

Percentageerrorinmeasurementis

4.2.3SubstitutionMethodforMeasuringResistanceTheconnectiondiagramforthesubstitutionmethodisshowninFigure4.8.

In this method the unknown resistance Rx is measured with respect to the standardvariable resistance S.The circuit also contains a steady voltage sourceV, a regulatingresistancerandanammeter.AswitchistheretoconnectRxandSinthecircuitalternately.

Tostartwith, theswitchisconnectedinposition1,sothattheunknownresistanceRxgetsincludedinthecircuit.Atthiscondition,theregulatingresistancerisadjustedsothattheammeterpointercomestoaspecifiedlocationonthescale.Next,theswitchisthrowntoposition2,sothatthestandardresistanceScomesintocircuitinplaceofRx.Settingsintheregulatingresistancearenotchanged.ThestandardvariableresistanceSisvariedtillammeter pointer reaches the same location on scale as was withRx. The value of thestandardresistanceSatthispositionisnotedfromitsdial.Assumingthatthebatteryemfhasnotchangedandalsosincethevalueofr iskeptsameinboththecases, thecurrenthasbeenkeptat thesamevaluewhilesubstitutingone resistancewithanotherone.Thetwo resistances thus,must be equal.Hence, value of the unknown resistanceRx canbe

estimatedfromdialsettingsofthestandardresistanceS.

Figure4.8Substitutionmethod

Accuracyofthismethoddependsonwhetherthebatteryemfremainsconstantbetweenthetwomeasurements.Also,otherresistancesinthecircuitexceptingRandSshouldalsonotchangeduring thecourseofmeasurement.Readingsmustbe takenfairlyquicklysothat temperature effects do not change circuit resistances appreciably. Measurementaccuracy also depends on sensitivity of the ammeter and also on the accuracy of thestandardresistanceS.

4.2.4WheatstoneBridgeforMeasuringResistanceTheWheatstonebridgeis themostcommonlyusedcircuitformeasurementofmedium-rangeresistances.TheWheatstonebridgeconsistsoffourresistancearms,togetherwithabattery(voltagesource)andagalvanometer(nulldetector).ThecircuitisshowninFigure4.9.

Figure4.9Wheatstonebridgeformeasurementofresistance

Inthebridgecircuit,R3andR4aretwofixedknownresistances,R2isaknownvariableresistanceandRXistheunknownresistancetobemeasured.Underoperatingconditions,

current ID through the galvanometerwill depend on the difference in potential betweennodesBandC.AbridgebalanceconditionisachievedbyvaryingtheresistanceR2andcheckingwhether thegalvanometerpointer isrestingat itszeroposition.Atbalance,nocurrentflowsthroughthegalvanometer.Thismeansthatatbalance,potentialsatnodesBandCareequal.Inotherwords,atbalancethefollowingconditionsaresatisfied:1.Thedetectorcurrentiszero,i.e.,1D=0andthusIt=I3andI2=I42.PotentialsatnodeBandCaresame,i.e.,VB=VC,orinotherwords,voltagedropin

thearmABequalsthevoltagedropacrossthearmAC,i.e.,VAB=VACandvoltagedropinthearmBDequalsthevoltagedropacrossthearmCD,i.e.,VBD=VCD

FromtherelationVAB=VACwehaveI1×Rx=I2×R2(4.12)

Atbalanced‘null’position,sincethegalvanometercarriesnocurrent,itasifactsasifopencircuited,thus

Thus, measurement of the unknown resistance is made in terms of three knownresistances.ThearmsBDandCDcontainingthefixedresistancesR3andR4arecalledtheratio arms. The arm AC containing the known variable resistance R2 is called thestandardarm.TherangeoftheresistancevaluethatcanbemeasuredbythebridgecanbeincreasedsimplybyincreasingtheratioR3/R4.

ErrorsinaWheatstoneBridge

AWheatstonebridgeisafairlyconvenientandaccuratemethodformeasuringresistance.However,itisnotfreefromerrorsaslistedbelow:

1.Discrepanciesbetweenthetrueandmarkedvaluesofresistancesofthethreeknownarmscanintroduceerrorsinmeasurement.

2. Inaccuracyof thebalancepointdue to insufficient sensitivityof thegalvanometermayresultinfalsenullpoints.

3. Bridge resistances may change due to self-heating (I2R) resulting in error inmeasurementcalculations.

4. Thermal emfs generated in the bridge circuit or in the galvanometer in theconnectionpointsmayleadtoerrorinmeasurement.

5. Errorsmaycreep intomeasurementdue to resistancesof leads andcontacts.Thiseffectishowever,negligibleunlesstheunknownresistanceisofverylowvalue.

6.Theremayalsobepersonalerrorsinfindingthepropernullpoint,takingreadings,orduringcalculations.

Errors due to inaccuracies in values of standard resistors and insufficient sensitivity ofgalvanometercanbeeliminatedbyusinggoodqualityresistorsandgalvanometer.

Temperaturedependent changeof resistancedue to self-heating canbeminimisedbyperformingthemeasurementwithinasshorttimeaspossible.

Thermal emfs in the bridge arms may cause serious trouble, particularly whilemeasuringlowresistances.Thermalemfingalvanometercircuitmaybeseriousinsomecases,socaremustbetakentominimisethoseeffectsforprecisionmeasurements.Somesensitive galvanometers employ all-copper systems (i.e., copper coils aswell as coppersuspensions),sothatthereisnojunctionofdissimilarmetalstoproducethermalemf.Theeffectofthermalemfcanbebalancedoutinpracticebyaddingareversingswitchinthecircuit between the battery and the bridge, then making the bridge balance for eachpolarityandaveragingthetworesults.

Example4.4

FourarmsofaWheatstonebridgeareasfollows:AB=100Ω,BC=10Ω,CD=4Ω,DA=50Ω.Agalvanometerwithinternalresistanceof20ΩisconnectedbetweenBD,whilea battery of 10-V dc is connected between AC. Find thecurrent through the galvanometer. Find the value of theresistance to be put on the armDA so that the bridge isbalanced.

SolutionConfigurationof thebridgewith thevaluesgiven in theexample isasshownbelow:

To find out current through the galvanometer, it is required to find out TheveninequivalentvoltageacrossnodesBDandalsotheTheveninequivalentresistancebetweenterminalsBD.

To find out Thevenin’s equivalent voltage across BD, the galvanometer is opencircuited,andthecircuitthenlookslikethefiguregivenbelow.

Atthiscondition,voltagedropacrossthearmBCisgivenby

VoltagedropacrossthearmDCisgivenby:

Hence, voltage difference between the nodes B and D, or the Thevenin equivalentvoltagebetweennodesBandDis

VTH=VBD=VB–VD=VBC–VDC=0.91-0.74=0.17V

ToobtaintheTheveninequivalentresistancebetweennodesBandD,the10Vsourceneedtobeshorted,andthecircuitlookslikethefiguregivenbelow.

TheTheveninequivalentresistancebetweenthenodesBandDisthus

Hence,currentthroughgalvanometeris

Inordertobalancethebridge,thereshouldbenocurrentthroughthegalvanometer,orinotherwords,nodesBandDmustbeatthesamepotential.

Balanceequationisthus

Example4.5

ThefourarmsofaWheatstonebridgeareasfollows:AB=100 Ω, BC = 1000 Ω, CD = 4000 Ω, DA = 400 Ω. Agalvanometer with internal resistance of 100 Ω andsensitivity of 10mm/μA is connectedbetweenAC,whileabattery of 4V dc is connected betweenBD.Calculate thecurrent through the galvanometer and its deflection if theresistanceofarmDAischangedfrom400Ωto401Ω.

SolutionConfigurationof thebridgewith thevaluesgiven in theexample isasshownbelow:

To find out current through the galvanometer, it is required to find out theTheveninequivalentvoltageacrossnodesACandalsotheTheveninequivalentresistancebetweenterminalsAC.

TofindoutTheveninequivalentvoltageacrossAC,thegalvanometerisopencircuited.Atthiscondition,voltagedropacrossthearmABisgivenby

VoltagedropacrossthearmCBisgivenby

Hence,voltagedifferencebetweenthenodesAandC,ortheTheveninequivalentvoltagebetweennodesAandCis

VTH=VAC=VA–VC=VAB–VCB=0.798–0.8=–0.002V

ToobtaintheTheveninequivalentresistancebetweennodesAandC,the10Vsourceneedtobeshorted.Underthiscondition,theTheveninequivalentresistancebetweenthenodesAandCisthus

Hence,currentthroughthegalvanometeris

Deflectionofthegalvanometer

=Sensitivity×Current=10mm/µA=2.04µA=20.4mm

4.3 MEASUREMENTOFLOWRESISTANCES

The methods used for measurement of medium resistances are not suitable formeasurement of low resistances. This is due to the fact that resistances of leads andcontacts, though small, are appreciable in comparison to the low resistances undermeasurement.Forexample,acontactresistanceof0.001Ωcausesanegligibleerrorwhena medium resistance of value say, 100 Ω is being measured, but the same contactresistancewouldcauseanerrorof10%whilemeasuringalowresistanceofvalue0.01Ω.Hencespecialtypeofconstructionandtechniquesneedtobeusedformeasurementoflowresistances to avoid errors due to leads and contacts. The different methods used formeasurement of low range resistances are (i) voltmeter–ammetermethod, (iii)Kelvin’sdouble-bridgemethod,and(iv)potentiometermethod.

4.3.1Voltmeter–AmmeterMethodforMeasuringLowResistance

In principle, the voltmeter–ammetermethod formeasurement of low resistance is verysimilar to theoneused formeasurementofmediumresistances,asdescribed inSection4.2.2.Thismethod,duetoitssimplicity,isverycommonlyusedformeasurementoflowresistanceswhenaccuracyoftheorderof1%issufficient.Theresistanceelements,tobeusedforsuchmeasurements,however,needtoofspecialconstruction.LowresistancesareconstructedwithfourterminalsasshowninFigure4.10.

Figure4.10Voltmeter–ammetermethodformeasuring

Onepairof terminalsCC’,called thecurrent terminals, isused to leadcurrent toandfrom the resistor.The voltage drop across the resistance ismeasured between the otherpair of terminals PP’, called the potential terminals. The voltage indicated by thevoltmeteristhussimplythevoltagedropoftheresistoracrossthepotentialterminalsPP’and does not include any contact resistance drop that may be present at the currentterminalsCC’.

Contactdropat thepotential terminalsPP’are,however, less itself,since thecurrentspassing through these contacts are extremely small (even zero under ‘null’ balancecondition)owing tohigh resistance involved in thepotential circuit. In addition to that,sincethepotentialcircuithasahighresistancevoltmeterinit,anycontactresistancedropin the potential terminals PP’ will be negligible with respect to the high resistancesinvolvedinthepotentialcircuit.

ValueoftheunknownresistanceRXinthiscaseisgivenby

Precise measurement in this method requires that the voltmeter resistance to beappreciably high, otherwise the voltmeter currentwill be an appreciable fraction of thecurrent actually flowing through the ammeter, anda serious errormaybe introduced inthisaccount.

4.3.2Kelvin’sDouble-BridgeMethodforMeasuringLowResistance

Kelvin’sdouble-bridgemethod isoneof thebestavailablemethods formeasurementoflowresistances.ItisactuallyamodificationoftheWheatstonebridgeinwhichtheerrorsduetocontactsandleadresistancescanbeeliminated.TheconnectionsofthebridgeareshowninFigure4.11.

Figure4.11Kelvin’sdoublebridge

Kelvin’sdoublebridgeincorporatestheideaofasecondsetofratioarms,namely,pandq,andhencethename‘doublebridge’.

Xistheunknownlowresistancetobemeasured,andSisaknownvaluestandardlowresistance. ‘r’ is a very low resistance connecting lead used connect the unknownresistanceXtothestandardresistanceS.AllotherresistancesP,Q,p,andqareofmediumrange.BalanceinthebridgeisachievedbyadjustingS.

Underbalancedcondition,potentialsatthenodesaandbmustbeequalinorderthatthegalvanometerG gives “null” deflection. Since at balance, no current flows through thegalvanometer,itcanbeconsideredtobeopencircuitedandthecircuitcanberepresentedasshowninFigure4.12.

Figure4.12Kelvin’sdouble-bridgeunderbalancedcondition

Sinceunderbalancedcondition,potentialsatthenodesaandbareequal,thewemusthave

thebalanceequationVcb=Vcdacannowbere-writtenas

ThesecondquantityoftheEq.(4.18), ,canbemadeverysmallbymakingthe

ratioP/Qascloseaspossibletop/q.Inthatcase,thereisnoeffectoftheconnectingleadresistance‘r’on theexpressionfor theunknownresistance.Thus, theexpressionfor theunknownresistanceXcannowbesimplywrittenas

However,inpractice,itisneverpossibletomaketheratiop/qexactlyequaltoP/Q.Thus,thereisalwaysasmallerror.

andhence,theresistancevaluebecomes

Itisthusalwaysbettertokeepthevalueof‘r’assmallaspossible,sothattheproductΔ×risextremelysmallandthereforetheerrorpartcanbeneglected,andwecanassume,underbalancedcondition,

Inorder to take intoaccount theeffectsof thermoelectricemf, twomeasurementsarenormallydonewiththebatteryconnectionsreversed.Thefinalvalueofresistanceistakenastheaverageofthesetworeadings.

A 4-terminal resistor was measured with the help of aKelvin’sdoublebridgehavingthefollowingcomponents:Standardresistor=98.02nW,innerratioarms=98.022Ω

Example4.6 and 202W, outer ratio arms = 98.025 Ω and 201.96W,resistance of the link connecting the standard resistanceandtheunknownresistance=600nW.Calculatethevalueoftheunknownresistance.

SolutionFromEq.(4.18),valueoftheunknownresistanceis

4.3.3PotentiometerMethodforMeasuringLowResistanceThe circuit for measurement of low value resistance with a potentiometer is shown inFigure4.13.

Figure4.13Measurementoflowresistanceusingpotentiometer

TheunknownresistanceX is connected in serieswitha standardknown resistanceS.Currentthroughtheammeterinthecircuitiscontrolledbyarheostat.Atwo-poledoublethrowswitchisused.Whentheswitchis intheposition1-1’, theunknownresistanceXgets connected to the potentiometer, whereas when the switch is at position 2-2’, thestandardresistanceSgetsconnectedtothepotentiometer.

Potentiometersarebelievedtogivereasonablyaccuratevaluesofpotentials.

Thus,with the switch in position 1-1’, the potentiometer reading is the voltage dropacrosstheunknownresistance,givenby

Withoutchanginganyofthecircuitparameters,nowiftheswitchisthrowntoposition2-2’,potentiometernowreadsthevoltagedropacrossthestandardresistance,givenby

FromEqs(4.21)and(4.22),weget

Knowledge of accurate value of the standard resistance S can thus give reasonablyaccuratevaluesoftheunknownresistanceX.

Accuracyofthismethodhowever,dependsontheassumptionthatthevalueofcurrent

remainsabsolutelyconstantduringthetwosetsofmeasurements.Therefore,anextremelystabiliseddcpowersupplyisrequiredinthismethod.ValueofthestandardresistorSshouldbeofthesameorderastheunknownresistance

X.Theammeterinsertedinthecircuithasnootherfunctionratherthansimplyindicatingwhetherthereisanycurrentisflowinginthecircuitisnot.Exactvalueofthecurrentisnotrequiredforfinalcalculations.Itishowever,desiredthatthecurrentflowingthroughthecircuitbesoadjustedthatthevoltagedropacrosseachresistorisoftheorderof1Vtobesuitableforaccuratemeasurementbycommerciallyavailablepotentiometers.

4.4 MEASUREMENTOFHIGHRESISTANCES

Highresistancesof theorderofseveralhundredsand thousandsofmeghoms(MW)areoftenencounteredinelectricalequipmentsintheformofinsulationresistanceofmachinesand cables, leakage resistance of capacitors, volume and surface resistivity of differentinsulationmaterialsandstructures.

4.4.1DifficultiesinMeasurementofHighResistance1.Sincetheresistanceundermeasurementhasveryhighvalue,verysmallcurrentsare

encountered in themeasurementcircuit.Adequateprecautionsandcareneed tobetakentomeasuresuchlowvaluecurrents.

2. Surface leakage is the main difficulty encountered while measurement of highresistances.Theresistivityoftheresistanceundermeasurementmaybehighenoughtoimpedeflowofcurrentthroughit,butduetomoisture,dust,etc.,thesurfaceoftheresistormayprovidealowerresistancepathforthecurrenttopassbetweenthetwomeasuring electrodes. In other words, there may thus be a leakage through thesurface. Leakage paths not only pollute the test results, but also are generallyvariablefromdaytoday,dependingontemperatureandhumidityconditions.TheeffectofleakagepathsonmeasurementscanbeeliminatedbytheuseofguardcircuitsasdescribedbyFigure4.14.Figure4.14(a) showsahigh resistanceRX beingmounted on a piece of insulationblock.Abatteryalongwithavoltmeterandamicro-ammeterareusedtomeasuretheresistancebyvoltmeter–ammetermethod.The resistanceRX undermeasurement isfittedontheinsulatingblockatthetwobindingpostsAandB.IXistheactualcurrentflowingthroughthehighresistanceandIListhesurfaceleakagecurrentflowingoverthe body of the insulating block. Themicro-ammeter, in this case, thus reads theactual current through the resistor, and also the leakage current (I = IX + IL.).Measuredvalueoftheresistance,thuscomputedfromtheratioE/I,willnotbethetrue value of RX, but will involve some error. To avoid this error, a guardarrangementhasbeenaddedinFigure4.14(b).Theguardarrangement,atoneendisconnected to the battery side of themicro-ammeter, and the other end iswrappedover the insulating body and surrounds the resistance terminal A. The surfaceleakagecurrentnow,flowsthroughthisguardandbypassesthemicro-ammeter.The

micro-ammeter thus reads the true of current IX through the resistance RX. Thisarrangement thus allows correct determination of the resistance value from thereadingsofvoltmeterandmicro-ammeter.

Figure4.14Guardcircuitformeasurementofhighresistance:(a)Circuitwithoutguard(b)Circuitwithguard

3.Duetoelectrostaticeffects,straychargesmaybeinducedinthemeasuringcircuit.Flow of these stray charges can constitute a current that can be comparable inmagnitudewiththelowvaluecurrentundermeasurementinhighresistancecircuits.This may thus, cause errors in measurement. External alternating electromagneticfieldscanalsoaffectthemeasurementconsiderably.Therefore,themeasuringcircuitneeds to be carefully screened to protect it against such external electrostatic orelectromagneticeffects.

4.Whilemeasuringinsulationresistance,thetestobjectoftenhasconsiderableamountof capacitance as well. On switching on the dc power supply, a large chargingcurrentmay flow initially through the circuit,which gradually decays down. Thisinitial transient current may introduce errors in measurement unless considerabletime is provided between application of the voltage supply and reading themeasurement,sothatthechargingcurrentgetssufficienttimetodiedown.

5. High resistancemeasurement results are also affected by changes in temperature,humidityandappliedvoltageinaccuracies.

6. Reasonablyhighvoltagesareusedformeasurementofhighresistancesinordertoraisethecurrenttosubstantialvaluesinordertobemeasured,whichareotherwiseextremelylow.So,theassociatedsensitivegalvanometersandmicro-ammetersneedtobeadequatelyprotectedagainstsuchhighvoltages.

Taking these factors into account, the most well-known methods of high resistancemeasurements are (i) direct deflection method, (ii) loss of charge method, and (iii)megohmmeterormeggar.

4.4.2DirectDeflectionMethodforHighResistanceMeasurement

The direct deflection method for measuring high resistances is based on the circuitdescribed in Figure 4.14, which in effect is the voltmeter–ammeter method. Formeasurement of high resistances, a sensitive galvanometer is used instead of a micro-ammeterasshowninFigure4.14.Aschematicdiagramfordescribingthedirectdeflection

method formeasurement of insulation resistance of ametal sheathed cable is given inFigure4.15.

Figure4.15Measurementofcableinsulationresistance

The test specimen, cable in this case, is connected across a high voltage stable dcsource;oneendofthesourcebeingconnectedtotheinnerconductorofthecable,andtheotherend,totheoutermetalsheathofthecable.ThegalvanometerG,connectedinseriesasshowninFigure4.15,isintendedtomeasurethecurrentIXflowingthroughthevolumeoftheinsulationbetweenthecentralconductor

and the outer metal sheath. Any leakage current IL flowing over the surface of theinsulating material is bypassed through a guard wire wound on the insulation, andthereforedoesnotflowthroughthegalvanometer.

AmoredetailedschemeformeasurementofinsulationresistanceofaspecimensheetofsolidinsulationisshowninFigure4.16.

Figure4.16Measurementofhighresistancebydirectdeflectionmethod

Ametaldiskcoveringalmosttheentiresurfaceisusedaselectrodeononesideoftheinsulationsheetundermeasurement.Ontheothersideoftheinsulatingsheet,thesecondelectrode is made of a smaller size disk. A guard ring is placed around the secondelectrodewithasmallspacinginbetweenthem.Thisguardingarrangementbypassesanysurfaceleakagecurrentontheinsulatororanyotherpartsofthecircuitfromenteringtheactualmeasuringcircuit.Thegalvanometer thusreadsspecifically thevolumeresistanceoftheinsulationspecimen,independentofanysurfaceleakage.

AcalibratedAyrton shunt isusually includedalongwith thegalvanometer toprovidevariousscalerangesandalsotoprotectit.

The galvanometer scale is graduated directly in terms of resistance.After one set ofmeasurement is over, the galvanometer is calibratedwith the help of a high value (≈ 1MΩ)calibratingresistorandtheshunts.

Incasetheinsulationundermeasurementhashighinherentcapacitancevalues(likeinacable), there will be an initial inrush of high capacitive charging current when the dcsourceisfirstswitchedon.Thischargingcurrentwill,however,decaydowntoasteadydcvaluewith time.Toprotect thegalvanometer fromsuch initial rushofhighcurrent, theAyrtonshuntconnectedacrossthegalvanometershouldbeplacedatthehighestresistanceposition (lowermostpoint inFigure4.16).Thus, initially thegalvanometer is bypassedfromthehighchargingcurrent.

After the test is complete, it is required that the test specimen should be discharged,especially if it is of capacitive in nature.The ‘test-short’ switch is placed in the ‘short’positionsothatanychargeremainingintheinsulationspecimenisdischargedthroughtheshortcircuitedpath.

The change-over switch across the battery enables tests at different polarities. Theswitchacrossthegalvanometerenablesreversalofthegalvanometerconnections.

A special technique, Price’s guard-wire method is employed for measurement ofinsulation resistance of cables which do not have metal sheath outside. The schematicdiagramofsuchameasurementsystemisprovidedinFigure4.17.

Figure4.17MeasurementofhighresistancebyPrice’sguard-wiremethod

Theunsheathedcable,exceptatthetwoendswhereconnectionsaremade,isimmersedinwaterinatank.Fortestingofthecableinsulation,thecablecoreconductoractsasoneelectrodeandintheabsenceofthemetalsheathoutside,thewaterandthetankactastheotherelectrodeformeasurement.Thecableisimmersedinslightlysalinewaterforaboutadayandatnearlyconstantambienttemperature.

ThetwoendsofthecablesaretrimmedasshowninFigure4.17,thusexposingthecore

conductor aswell as someportionof the insulation.Thecoreconductors areconnectedtogether to form one electrode of the measuring system. A guard circuit is formed bytwistingabarewirearoundtheexposedportionoftheinsulationatthetwostrippedendsofthecable.Thisguardwireisconnectedtothenegativeterminalofthesupplybattery.The positive terminal of the battery is connected to the metal tank. This enables anysurfaceleakagecurrenttobypassthegalvanometerandpassdirectlytothebattery.Thus,thegalvanometerwillreadonlytruevalueof thecurrentflowingthroughvolumeoftheinsulation,andnottheadditionalsurfaceleakagecurrent.

TheD’Arsonvalgalvanometertobeusedisnormallyofveryhighresistanceandverysensitive to record the normally extremely low insulation currents.AnAyrtonuniversalshuntisusuallyincludedalongwiththegalvanometertoprovidevariousscalerangesandalsotoprotectit.Thegalvanometerscaleisgraduateddirectlyintermsofresistance.Afteronesetofmeasurement isover, thegalvanometer iscalibratedwith thehelpof thehighvalue(≈1MΩ)calibratingresistorRandtheshunt.TheresistanceRandtheshuntalsoserve the purpose of protecting the galvanometer from accidental short circuit currentsurges. The 4-terminal commutator C, as shown in Figure 4.17 is used for reversal ofgalvanometerconnections.

Since the cable will invariably have high capacitance value, there will be an initialinrushofhighcapacitivechargingcurrentwhen thedc source is first switchedon.Thischargingcurrentwill,however,decaydowntoasteadydcvaluewithtime.Toprotectthegalvanometerfromsuchinitialrushofhighcurrent,theswitchS2isplacedonpositionaso that initially the galvanometer is bypassed from the high charging current.Once thecapacitor charging period is over and the current settles down, the switch S2 is pushedovertopositionbtobringthegalvanometerbackinthemeasurementcircuit.ThecontactsaandbaresufficientlycloseenoughtopreventthecircuitfrombreakingwhiletheswitchS2ismovedover.

Afterthetestiscomplete,itisrequiredthatthetestspecimenshouldbedischarged.TheswitchS1isusedforthispurpose,sothatanychargeremainingintheinsulationspecimenisdischargedthroughitself.

4.4.3LossofChargeMethodforHighResistanceMeasurementIn thismethod, the resistance to bemeasured is connected directly across a dc voltagesource inparallelwith a capacitor.Thecapacitor is chargedup to a certainvoltageandthen discharged through the resistance to bemeasured. The terminal voltage across theresistance-capacitance parallel combination is recorded for a pre-defined period of timewithahelpofahigh-resistancevoltmeter(electrostaticvoltmeterordigitalelectrometers).Value of the unknown resistance is calculated from the discharge time constant of thecircuit.OperationofthelossofchargemethodcanbedescribedbytheschematiccircuitdiagramofFigure4.18.

Figure4.18Lossofchargemethodformeasurementofhighresistance

In Figure 4.18, the unknown resistance R to be measured is connected across thecapacitorCandtheirparallelcombinationisconnectedtothedcvoltagesource.

LetthecapacitorisinitiallychargeduptoavoltageofVwhiletheswitchiskeptON.OncetheswitchisturnedOFF,thecapacitorstartstodischargethroughtheresistanceR.

Duringthedischargeprocess,thevoltagevacrossthecapacitoratanyinstantoftimetisgivenby

Thus,theinsulationresistancecanbecalculatedas

WithknownvalueofCandrecordedvaluesoft,Vandv,theunknownresistanceRcanbeestimatedusing(4.24).

ThepatternofvariationofvoltagevwithtimeisshowninFigure4.19.

Figure4.19Capacitordischargepattern

Great care must be taken to record the voltages V and v and also the time t veryprecisely,otherwiselargeerrorsmaycreepintothecalculationresults.

Thismethod, though simple in principle, require careful choice of the capacitor.ThecapacitorCitselfmusthavesufficientlyhighvalueofitsownleakageresistance,atleastin the same range as the unknown resistance undermeasurement.The resistance of thevoltmeteralsoneedstobeveryhightohavemoreaccurateresults.

4.4.4Megohmmeter,orMeggar,forHighResistance

MeasurementOneofthemostpopularportabletypeinsulationresistancemeasuringinstrumentsisthemegohmmeterorinshort,meggar.Themeggarisusedverycommonlyformeasurementofinsulationresistanceofelectricalmachines,insulators,bushings,etc.InternaldiagramofameggarisshowninFigure4.20.

The traditional analog deflecting-type meggar is essentially a permanent magnetcrossed-coilshunttypeohmmeter.

Theinstrumenthasasmallpermanentmagnetdcgeneratordeveloping500Vdc(someothermodelsalsohave100V,250V,1000or2500Vgenerators).Thegeneratorishanddriven, through gear arrangements, and through a centrifugally controlled clutch switchwhich slips at a predefined speed so that a constant voltage can be developed. Somemeggarsalsohaverectifiedacaspowersupply.

Figure4.20Meggarforhighresistancemeasurement

Themovingsysteminsuch instrumentsconsistsof twocoils, thecontrolcoilCCandthedeflectingcoilCD.Boththecoilsaremountedrigidlyonashaftthatcarriesthepointeras well. The two coilsmove in the air gap of a permanentmagnet. The two coils arearrangedwithsuchnumbersofturns,radiiofaction,andconnectedacrossthegeneratorwith such polarities that, for external magnetic fields of uniform intensity, the torqueproducedbytheindividualcoilsareinoppositionthusgivinganastaticcombination.ThedeflectingcoilisconnectedinserieswiththeunknownresistanceRXundermeasurement,afixedresistorRDandthenthegenerator.Thecurrentcoilorthecompensatingcoil,alongwith thefixedresistanceRC isconnecteddirectlyacross thegenerator.Foranyvalueoftheunknown,thecoilsandthepointertakeupafinalsteadypositionsuchthatthetorquesof the two coils are equal and balanced against each other. For example, when theresistanceRXundermeasurementisremoved,i.e.,thetestterminalsareopen-circuited,nocurrentflowsthroughthedeflectingcoilCD,butmaximumcurrentwillflowthroughthecontrolcoilCC.ThecontrolcoilCCthussetsitselfperpendiculartothemagneticaxiswiththepointerindicating‘∞Ω’asmarkedinthescaleshowninFigure4.20.AsthevalueofRXisbroughtdownfromopencircuitcondition,moreandmorecurrentflowsthroughthe

deflecting coil CD, and the pointer moves away from the ‘∞ Ω’ mark clockwise(accordingtoFigure4.20)on thescale,andultimatelyreaches the‘0Ω’markwhenthetwotestterminalsareshortcircuited.

Thesurfaceleakageproblemistakencareofbytheguard-wirearrangement.Theguardring (GR in Figure 4.20) and the guard wire diverts the surface leakage current fromreachingthemainmovingsystemandinterferingwithitsperformance.

PhotographsofsomecommerciallyavailablemeggarsareshowninFigure4.21.

Figure4.21Commercialmeggars:(a)Analogtype(Courtesy,WACO)(b)Digitaltype(Courtesy,Yokogawa)

Example4.7

Acableistestedforinsulationresistancebylossofchargemethod.Anelectrostaticvoltmeterisconnectedbetweenthecable conductor and earth. This combination is found toforma capacitance of 800 pF between the conductor andearth.Itisobservedthatafterchargingthecablewith500V or sufficiently long time, when the voltage supply iswithdrawn, the voltage drops down to 160V in 1minute.Calculatetheinsulationresistanceofthecable.

SolutionThearrangementcanbeschematicallyshownbythefollowingfigure.

Whilethecableischargedwith500Vforalongperiodoftime,itisexpectedthatthecapacitance of the system is charged up to a steady voltage of 500 V before it isdischarged.

Thus,thecapacitordischargesfrom500Vto160Vin1minute.

Duringthedischargeprocess,thevoltagevacrossthecapacitoratanyinstantoftimetisgivenby

whereVistheinitialvoltageinthecapacitorC,connectedacrosstheunknownresistanceR.

Thus,theinsulationresistanceis

4.5 LOCALISATIONOFCABLEFAULTS

Underground cables during their operation can experience various fault conditions.Whereas routine standard tests are there to identify and locate faults in high-voltagecables,specialprocedures,aswillbedescribedinthissectionarerequiredforlocalisationofcablefaultsinlowdistributionvoltagelevelcables.Determinationofexactlocationoffaultsectionsinundergrounddistributioncablesisextremelyimportantfromthepointofviewofquickrestorationofservicewithoutlossoftimeforrepair.

The faults thataremost likely tooccurareground faultswhere cable insulationmaybreakdowncausingacurrenttoflowfromthecoreofthecabletotheoutermetalsheathortotheearth;ortheremaybeshort-circuitfaultswhereainsulationfailurebetweentwocables,orbetweentwocoresofamulti-corecableresultsinflowofcurrentbetweenthem.

Loop tests are popularly used in localisation of the aforesaid types of faults in lowvoltagecables.Thesetestscanbecarriedouttolocaliseagroundfaultorashort-circuitfault,providedthatanunfaultycablerunsalongwiththefaultycable.Suchtestshavetheadvantage that fault resistancedoesnotaffect themeasurementsensitivity, that the faultresistanceisnottoohigh.LooptestsworkonthesimpleprinciplesofaWheatstonebridgeformeasurementofunknownresistances.

4.5.1MurrayLoopTestConnectionsfor this testareshowninFigure4.22.Figure4.22(a)shows theconnection

diagramforlocalisationofgroundfaultsandFigure4.22(b)relatestolocalisationofshortcircuitfaults.ThegeneralconfigurationofaWheatstonebridgeisgiveninFigure4.23forreadyreference.

Figure4.22Murraylooptestfor(a)earthfault,and(b)short-circuitfaultlocalosationincables

TheloopcircuitsformedbythecableconductorsformaWheatstonebridgecircuitwiththe two externally controllable resistorsP andQ and the cable resistance X andR asshown in Figure 4.22. The galvanometerG is used for balance detection. The ridge isbalancedbyadjustmentofPandQtillthegalvanometerindicateszerodeflection.

Figure4.23WheatstonebridgeconfigurationrelatingtoFigure4.22

Underbalancedcondition,

Here,(R+X)isthetotalloopresistanceformedbythegoodcableandthefaultycable.When the cables have the same cross section and same resistivity, their resistances areproportionaltotheirlengths.

IfLXrepresentsthedistanceofthefaultpointfromthetestend,andListhetotallengthofeachcableundertest,thenwecanwrite

1.TheresistanceXisproportionaltothelengthLX2.Theresistance(R+X)isproportionaltothetotallength2L

Equation(4.25)cannowbeexpressedintermsofthelengthsas

Thus,positionofthefaultcaneasilybelocatedwhenthetotallengthofthecablesareknown.

4.5.2VarleyLoopTestInthistest,thetotalloopresistanceinvolvingthecablesisdeterminedexperimentallytoestimatethefaultlocation,ratherthanrelyingupontheinformationoflengthofcablesandtheir resistances per unit length. Connections diagrams for Varley loop test to detectground fault location and short-circuit fault location in low voltage cables is shown inFigure4.24(a)andFigure4.24(b)respectively.

Figure4.24Varleylooptestfor(a)earthfault,and(b)short-circuitfaultlocalisationincables

The single pole double throw switch Sw is first connected to terminal ‘a’ and theresistanceSisvariedtoobtainbridgebalance.

Let,atthiscondition,thevalueofresistanceS=S1whenthebridgeisbalanced.Thus,fromWheatstonebridgeprinciples,atbalanceconditionwiththeswitchatpositiona,wecanwrite

Thetotalloopresistance(R+X)canthusbeexperimentallydeterminedusing(4.27)byreading the values ofP,Q and S1 under bridge balanced condition with the switch atpositiona.

Now,theswitchSwischangedovertoterminalbandthebridgeisbalancedagainbyvarying S. Let, at this condition, the value of resistance S = S2 when the bridge isbalanced.Thus,onceagain,fromWheatstonebridgeprinciples,atbalanceconditionwiththeswitchatpositionb,wecanwrite

Thus,Xcanbecalculatedfrom(4.28)fromknownvaluesofP,Q,andS2andthevalueoftotalloopresistance(R+X)obtainedfrom(4.27).

IfLXrepresentsthedistanceofthefaultpointfromthetestend,andListhetotallengthofeachcableundertest,thenwecanwrite:

1.theresistanceXisproportionaltothelengthLX2.theresistance(R+X)isproportionaltothetotallength2LThenwecanwrite

Thus,thepositionofthefaultcaneasilybelocatedwhenthetotallengthofthecablesareknown.

BothMurray and Varley loop tests are valid only when the cable cross sections areuniform throughout the loopandalsobetween thehealthyand faultycables.Correctionfactorsneedalso tobe included to takecareof temperaturevariationeffects.Toomanycablejointswithinlengthofthecablesmayalsointroduceerrorsinmeasurement.

Example4.8

In a test for fault to earth byMurray loop test, the faultycablehasalengthof5.2km.The faulty cable is loopedwitha sound (healthy) cableofthesamelengthandcrosssection.Resistancesof theratioarmofthemeasuringbridgecircuitare100Ωand41.2Ωatbalance.Calculatethedistanceofthefaultpointfromthetestingterminal.

Solution If X is the resistance of the cable from test end to the fault point, R is theresistanceofcableloopfromthefaultpointbackovertotheotherendofthetestpoint,andPandQaretheresistanceoftheratioarm,thenwecanwrite

IfLXbethedistanceofthefaultpointfromthetestendandLbethelengthofeachcable.Ifresistivityof thecablecorematerialr isandeachof themhascross-sectionalareaA,thenwecanwrite

Thus,thefaulthasoccurredatadistanceof3.03kmfromthetestend.

Example4.9

VarleyLoop test isbeingused to locateshortcircuit fault.The faulty and sound cables are identicalwith resistancesof0.5Ωperkm.Theratioarmsaresetat15Ωand40Ω.Valuesof thevariable resistanceconnectedwith the faultycableare20Ωand10Ωatthetwopositionsoftheselectorswitch. Determine the length of each cable and faultdistancefromtestend.

SolutionLetS1betheresistanceofthevariableresistanceatloopresistancemeasuringposition of the selector switch and S2 be the resistance of the variable resistor at faultlocationmeasuringpositionoftheselectorswitch.

Hence,atthefirstpositionoftheswitchwecanwrite:

whereXistheresistanceofthecablefromtestendtothefaultpoint,Ristheresistanceofcableloopfromthefaultpointbackovertotheotherendofthetestpoint,andPandQaretheresistanceoftheratioarm

Thus,totalresistanceoftheloopisgivenas

Thus,resistanceofeachcable=7.5/2=3.75Wlengthofeachcable=3.75/0.5=7.5kmAtthesecondpositionoftheswitch,wehave

.distanceofthefaultpointfromtestend=2.73/0.5=5.45km

EXERCISE

Objective-typeQuestions1.Inaseries-typeohmmeter

(a)zeromarkingisontheleft-handside

(b)zeromarkingisatthecentre

(c)zeromarkingisontheright-handside

(d)zeromarkingmaybeeitheronleftorright-handside

2.Inseriestypeohmmeters,zeroadjustmentshouldbedoneby

(a)changingtheshuntresistanceacrossthemetermovement

(b)changingtheseriesresistance

(c)changingtheseriesandtheshuntresistance

(d)changingthebatteryvoltage

3.Screwadjustmentsarepreferredovershuntresistanceadjustmentsforzerocalibrationinohmmetersbecause

(a)theformermethodislesscostly

(b)theformermethoddoesnotdisturbthescalecalibration

(c)theformermethoddoesnotdisturbthemetermagneticfield

(d)alloftheabove

4.Theshapeofscaleinananalogseries-typeohmmeteris

(a)linearlyspaced(b)crampednearthestart

(c)crampedneartheend(d)directlyproportionaltotheresistance

5.Shunt-typeohmmetershaveontheirscale

(a)zeroohmmarkingontherightcorrespondingtozerocurrent

(b)zeroohmmarkingontherightcorrespondingtofullscalecurrent

(c)infiniteohmmarkingontherightcorrespondingtozerocurrent

(d)infiniteohmmarkingontherightcorrespondingtofullscalecurrent

6.Shunt-typeohmmetershaveaswitchalongwiththebatteryto

(a)disconnectthebatterywhennotinuse

(b)preventmeterfromgettingdamagedwhenmeasuringverylowresistances

(c)compensateforthermo-emfeffectsbyreversingbatterypolarity

(d)alloftheabove

7.Theshapeofscaleinananalogshunt-typeohmmeteris

(a)linearlyspacedatlowerscales(b)crampednearthestart

(c)linearlyspacedathigherscales(d)uniformallthroughoutthescale

8.Highresistancesusingthevoltmeter–ammetermethodshouldbemeasuredwith

(a)voltmeterconnectedtothesourceside

(b)ammeterconnectedtothesourceside

(c)anyofthetwoconnections

(d)readingsaretobetakenbyinterchangingammeterandvoltmeterpositions

9.Lowresistancesusingthevoltmeter–ammetermethodshouldbemeasuredwith

(a)voltmeterconnectedtothesourceside

(b)ammeterconnectedtothesourceside

(c)anyofthetwoconnections

(d)readingsaretobetakenbyinterchangingammeterandvoltmeterpositions

10.Accuracyofthesubstitutionmethodformeasurementofunknownresistancedependson

(a)accuracyoftheammeter

(b)accuracyofthestandardresistancetowhichtheunknowniscompared

(c)accuracyintakingthereadings

(d)alloftheabove

11.ThenulldetectorusedinaWheatstonebridgeisbasicallya

(a)sensitivevoltmeter(b)sensitiveammeter

(c)maybeanyoftheabove(d)noneof(a)or(b)

12.Wheatstonebridgeisnotpreferredforprecisionmeasurementsbecauseoferrorsdueto

(a)resistanceofconnectingleads(b)resistanceofcontacts

(c)thermo-electricemf(d)alloftheabove

13.Errorduetothermo-electricemfeffectsinaWheatstonebridgecanbeeliminatedby

(a)takingthereadingsasquicklyaspossible

(b)byavoidingjunctionswithdissimilarmetals

(c)byusingareversingswitchtochangebatterypolarity

(d)alloftheabove

14.Lowresistancesaremeasuredwithfourterminalsto

(a)eliminateeffectsofleads

(b)enabletheresistancevaluetobeindependentofthenatureofcontactatthecurrentterminals

(c)tofacilitateconnectionstocurrentandpotentialcoilsofthemeters

(d)alloftheabove

15.Kelvin’sdoublebridgeiscalled‘double’because

(a)ithasdoubletheaccuracyofaWheatstonebridge

(b)itsmaximumscalerangeisdoublethatofaWheatstonebridge

(c)itcanmeasuretwounknownresistancessimultaneously,i.e.,doublethecapacityofaWheatstonebridge

(d)ithastwoadditionalratioarms,i.e.,doublethenumberofratioarmsascomparedtoaWheatstonebridge

16.TwosetsofreadingsaretakeninaKelvin’sdoublebridgewiththebatterypolarityreversedinorderto

(a)eliminatetheerrorduetocontactresistance

(b)eliminatetheerrorduetothermo-electriceffect

(c)eliminatetheerrorduetochangeinbatteryvoltage

(d)alloftheabove

17.Potentiometers,whenusedformeasurementofunknownresistances,givemoreaccurateresultsascomparedtothevoltmeter–ammetermethodbecause

(a)thereisnoerrorduetothermo-electriceffectinpotentiometers

(b)theaccuracyofvoltagemeasurementishigherinpotentiometers

(c)personnelerrorswhilereadingapotentiometeriscomparativelyless

(d)alloftheabove

18. ‘Null detection method’ is more accurate than ‘deflection method’ for measurement of unknown resistancesbecause

(a)theformerdoesnotincludeerrorsduetononlinearscaleofthemeters

(b)theformerdoesnotincludeerrorsduetochangeinbatteryvoltage

(c)theformerdoestodependonmetersensitivityatbalancedcondition

(d)alloftheabove

19.Guardterminalsarerecommendedforhighresistancemeasurementsto

(a)bypasstheleakagecurrent

(b)guardtheresistancefromeffectsofstrayelectro-magneticfields

(c)guardtheresistancefromeffectsofstrayelectro-staticfields

(d)noneoftheabove

20.Whenmeasuringcableinsulationusingadcsource,thegalvanometerusedisinitiallyshortcircuitedto

(a)dischargethestoredchargeinthecable

(b)bypassthehighinitialchargingcurrent

(c)preventthegalvanometerfromgettingdamagedduetolowresistanceofthecable

(d)alloftheabove

21.Thelossofchargemethodisusedformeasurementof

(a)highvaluecapacitances

(b)dissipationfactorofcapacitances

(c)lowvalueresistances

(d)highvalueresistances

22.Ameggarisusedformeasurementof

(a)lowvalueresistances

(b)mediumvalueresistances

(c)highvalue,particularlyinsulationresistances

(d)alloftheabove

23.Controllingtorqueinameggarisprovidedby

(a)controlsprings

(b)balanceweights

(c)controlcoil

(d)anyoneoftheabove

24.TheadvantageofVarleylooptestoverMurraylooptestforcablefaultlocalisationis

(a)theformercanbeusedforlocalisingfaultsevenwithoutknowledgeofcableresistance

(b)theformercanbeusedforlocalisingbothearthfaultandshortcircuitfaults

(c)theformercanexperimentallydeterminethetotalloopresistance

(d)alloftheabove

25.Possiblesourcesoferrorinusinglooptestforcablefaultlocalisationare

(a)unevencableresistance/km

(b)temperaturevariations

(c)unknowncablejointresistances

(d)alloftheabove

Short-answerQuestions1. Describetheoperationofaseries-typeohmmeterwiththehelpofaschematicdiagram.Commentonthescale

markingsandzeroadjustmentproceduresinsuchaninstrument.

2. Derive an expression for the meter current as a function of the full-scale deflection value in a series typeohmmetertodeterminetheshapeofscale.

3. Describetheoperationofashunt-typeohmmeterwiththehelpofaschematicdiagram.Commentonthescalemarkingsandzeroadjustmentproceduresinsuchaninstrument.

4. Derive an expression for the meter current as a function of the full-scale deflection value in a shunt typeohmmetertodeterminetheshapeofscale.

5. List the sourcesoferrors inaWheatstonebridge thatmayaffect itsprecisionwhilemeasuringmediumrangeresistances.Explainhowtheseeffectsareeliminated/minimised?

6. What are the different problems encountered while measuring low resistances. Explain how a 4-terminalconfigurationcanminimisetheseerrorswhilemeasuringlowresistancesusingavoltmeter–ammetermethod.

7.Describehowlowresistancescanbemeasuredwiththehelpofapotentiometer.

8.Describewithsuitableschematicdiagram,howahighresistancecanbeeffectivelymeasuredusingPrice’sguardwiremethod.

9. Explaintheprinciplesofthelossofchargemethodformeasurementofhighresistances.Alsocommentonthecompensationsrequiredtobemadeinthecalculationstotakecareofcircuitcomponentnonidealities.

10.Drawandexplaintheoperationofameggarusedforhighresistancemeasurement.

11.Describewithsuitableschematicdiagram,theMurrayLooptestforlocalisingearthfaultinlowvoltagecables.

12.Describewithsuitableschematicdiagram,theVarleylooptestforlocalisingearthfaultinlowvoltagecables.

Long-answerQuestions1.(a)Discusswithsuitablediagrams,thedifferentwaysofzeroadjustmentinaseries-typeohmmeter.

(b)Designasinglerangeseries-typeohmmeterusingaPMMCammeterthathasinternalresistanceof60Ωandrequiresacurrentof1.2mAforfullscaledeflection.Theinternalbatteryhasavoltageof5V.Itisdesiredtoreadhalfscaleataresistancevalueof3000Ω.Calculate(a)thevaluesofshuntresistanceandcurrentlimitingseriesresistance,and(b)rangeofvaluesoftheshuntresistancetoaccommodatebatteryvoltagevariationintherange4.7to5.2V.

2. (a) Describetheoperationofashunt-typeohmmeterwiththehelpofaschematicdiagram.Commentsonthescalemarkingsandzeroadjustmentproceduresinsuchaninstrument?

(b) Ashunt-typeohmmeterusesa2mAbasicd’Arsonvalmovementwithan internal resistanceof50Ω.Thebatteryemfis3V.Calculate(a)valueoftheresistorinserieswiththebatterytoadjusttheFSD,and(b)atwhatpoint(percentage)offullscalewill200Ωbemarkedonthescale?

3.(a)Describeinbrief,theuseofvoltmeter–ammetermethodformeasurementofunknownresistance.

(b)Avoltmeterof500Ωresistanceandamilliammeterof0.5Ωresistanceareusedtomeasuretwounknownresistancesbyvoltmeter–ammetermethod.Ifthevoltmeterreads50Vandmilliammeterreads50mAinboththe cases, calculate the percentage error in the values of measured resistances if (i) in the first case, thevoltmeterisputacrosstheresistanceandthemilliammeterconnectedinserieswiththesupply,and(ii)inthesecondcase,thevoltmeterisconnectedinthesupply,sideandmilliammeterconnecteddirectlyinserieswiththeresistance.

4.(a)DrawthecircuitofaWheatstonebridgeformeasurementofunknownresistancesandderivetheconditionforbalance.

(b) Four armsof aWheatstonebridgeare as follows:AB=150W,BC=15W,CD=6W,DA=60Ω.Agalvanometer with internal resistance of 25 Ω is connected between BD, while a battery of 20 V dc isconnectedbetweenAC.Findthecurrentthroughthegalvanometer.FindthevalueoftheresistancetobeputonthearmDAsothatthebridgeisbalanced.

5.(a)ExplaintheprincipleofworkingofaKelvin’sdoublebridgeformeasurementofunknownlowresistances.Explainhowtheeffectsofcontactresistanceandresistanceofleadsareeliminated.

(b) A 4-terminal resistor was measured with the help of a Kelvin’s double bridge having the followingcomponents:Standard resistor=100.02 |iW, inner ratio arms=100.022Ωand199W,outer ratio arms=100.025Ωand200.46W,resistanceofthelinkconnectingthestandardresistanceandtheunknownresistance=300mW.Calculatevalueoftheunknownresistance.

6. Discuss thedifficulties involved formeasurementofhigh resistances.Explain thepurposeofguardingahighresistancemeasurementcircuits.

7.(a)Deriveanexpressionfortheunknownresistancemeasuredusingthelossofchargemethod.

(b)Acableistestedforinsulationresistancebylossofchargemethod.Anelectrostaticvoltmeterisconnectedbetweenthecableconductorandearth.Thiscombinationisfoundtoformacapacitanceof600pFbetweentheconductorandearth.It isobservedthatafterchargingthecablewith1000Vforsufficiently longtime,whenthevoltagesupplyiswithdrawn,thevoltagedropsdownto480Vin1minute.Calculatetheinsulationresistanceofthecable.

8. (a) Describewith suitable schematicdiagrams, theMurray loop test for localizationof earth fault and shortcircuitfaultinlowvoltagecables.

(b) na test for fault toearthbyMurray loop test, thefaultycablehasa lengthof6.8km.Thefaultycable isloopedwithasound(healthy)cableofthesamelengthandcrosssection.Resistancesoftheratioarmofthemeasuringbridgecircuitare200Ωand444Ωatbalance.Calculatethedistanceofthefaultpointfromthetestingterminal.

9.(a)Describewithsuitableschematicdiagrams,theVarleylooptestforlocalisationofearthfaultandshort-circuitfaultinlowvoltagecables.

(b) Varley loop test is beingused to locate short circuit fault.The faulty and sound cables are identicalwithresistances of 0.4 Ω per km. The ratio arms are set at 20 Ω and 50Ω. Values of the variable resistanceconnectedwiththefaultycableare30Ωand15Ωatthetwopositionsoftheselectorswitch.Determinethelengthofeachcableandfaultdistancefromtestend.

5.1 INTRODUCTION

Apotentiometer is an instrumentwhich isused formeasurementofpotentialdifferenceacross a known resistance or between two terminals of a circuit or network of knowncharacteristics. A potentiometer is also used for comparing the emf of two cells. Apotentiometerisextensivelyusedinmeasurementswheretheprecisionrequiredishigherthanthatcanbeobtainedbyordinarydeflectinginstruments,orwhereit isrequiredthatnocurrentbedrawnfromthesourceundertest,orwherethecurrentmustbelimitedtoasmallvalue.

Sinceapotentiometermeasuresvoltagebycomparingitwithastandardcell,itcanbealsoused tomeasure thecurrentsimplybymeasuring thevoltagedropproducedby theunknown current passing through a known standard resistance. By the potentiometer,powercanalsobecalculatedandifthetimeisalsomeasured,energycanbedeterminedbysimplymultiplyingthepowerandtimeofmeasurement.Thuspotentiometerisoneofthemostfundamentalinstrumentsofelectricalmeasurement.

Someimportantcharacteristicsofpotentiometerarethefollowing:

•Apotentiometermeasurestheunknownvoltagebycomparingitwithaknownvoltagesourceratherthanbytheactualdeflectionofthepointer.Thisensuresahighdegreeofaccuracy.

•Asapotentiometermeasuresusingnullorbalancecondition,hencenopowerisrequiredforthemeasurement.

•Determinationofvoltageusingpotentiometerisquiteindependentofthesourceresistance.

5.2 ABASICdcPOTENTIOMETER

ThecircuitdiagramofabasicdcpotentiometerisshowninFigure5.1.

Operation

First,theswitchSisputinthe‘operate’positionandthegalvanometerkeyKkeptopen,the battery supplies the working current through the rheostat and the slide wire. Theworkingcurrentthroughtheslidewiremaybevariedbychangingtherheostatsetting.Themethodofmeasuringtheunknownvoltage,E1,dependsuponthefindingapositionforthesliding contact such that the galvanometer shows zero deflection, i.e., indicates null

condition,when thegalvanometerkeyK is closed.Zerogalvanometerdeflectionmeansthat theunknownvoltageE1 is equal to thevoltagedropE2, acrosspositiona–c of theslidewire.Thus,determinationofthevaluesofunknownvoltagenowbecomesamatterofevaluatingthevoltagedropE2alongtheportiona–coftheslidewire.

When the switch S is placed at ‘ calibrate’ position, a standard or reference cell isconnectedtothecircuit.Thisreferencecellisusedtostandardizethepotentiometer.Theslidewirehasauniformcross-sectionandhenceuniformresistancealongitsentirelength.A calibrated scale in cm and fractions of cm, is placed along the slidewire so that theslidingFigure5.1Abasic potentiometer circuitcontact canbeplaced accurately at anydesired position along the slide wire. Since the resistance of the slide wire is knownaccurately,thevoltagedropalongtheslidewirecanbecontrolledbyadjustingthevaluesof working current. The process of adjusting the working current so as to match thevoltagedropacrossaportionofslidingwireagainstastandardreferencesourceisknownas‘standardisation’.

Figure5.1Abasicpotentiometercircuit

5.3 CROMPTON’SdcPOTENTIOMETER

Thegeneral arrangement of a laboratory-typeCrompton’s dc potentiometer is shown inFigure5.2.Itconsistsofadialswitchwhichhasfifteen(ormore)steps.Eachsteephas10Ωresistance.So thedial switchhas total150Ω resistance.Theworkingcurrentof thispotentiometeris10mAandthereforeeachstepofdialswitchcorrespondsto0.1volt.Sotherangeofthedialswitchis1.5volt.

Thedialswitchisconnectedinserieswithacircularslidewire.Thecircularslidewirehas10Ωresistance.Sotherangeofthatslidewireis0.1volt.Theslidewirecalibratedwith 200 scale divisions and since the total resistance of slide wire corresponds to avoltagedropof0.1volt,eachdivisionoftheslidewirecorrespondsto volt.It

isquitecomfortabletointerpolatereadingsupto ofascaledivisionandthereforewith

thisCrompton’spotentiometeritispossibletoestimatethereadingupto0.0001volt.

ProcedureforMeasurementofUnknownemf

•Atfirst,thecombinationofthedialswitchandtheslidewireissettothestandardcellvoltage.Letthestandardsellvoltagebe1.0175volts,thenthedialresistorisputin1.0voltandtheslidewireat0.0175voltssetting.

•Theswitch‘S’isthrowntothecalibratepositionandthegalvanometerswitch‘K’ispresseduntiltherheostatisadjustedforzerodeflectiononthegalvanometer.The10kWprotectiveresistanceiskeptinthecircuitintheinitialstagessoastoprotectthegalvanometerfromoverload.

•Afterthenulldeflectiononthegalvanometerisapproachedtheprotectiveresistanceisshortedsoastoincreasethesensitivityofthegalvanometer.Finaladjustmentismadeforthezerodeflectionwiththehelpoftherheostat.Thiscompletesthestandardisationprocessofthepotentiometer.

•Aftercompletionofthestandardisation,theswitch‘S’isthrowntotheoperatepositiontherebyconnectingtheunknownemfintothepotentiometercircuit.Withtheprotectiveresistanceinthecircuit,thepotentiometerisbalancedbymeansofthemaindialandtheslidewireadjustment.

•Assoonasthebalancedisapproached,theprotectiveresistanceisshortedandfinaladjustmentsaremadetoobtaintruebalance.

•Afterthefinaltruebalanceisobtained,thevalueoftheunknownemfisreadoffdirectlyfromthesettingofthedialswitchandtheslidewire.

•Thestandardisationofthepotentiometerischeckedagainbyreturningtheswitch‘S’tothecalibrateposition.Thedialsettingiskeptexactlythesameasintheoriginalstandardisationprocess.Ifthenewreadingdoesnotagreewiththeoldone,asecondmeasurementofunknownemfmustbemade.Thestandardisationagainshouldbemadeafterthemeasurement.

Figure5.2GeneralarrangementofCrompton’sdcpotentiometer

A basic slide-wire potentiometer has a working battery

Example5.1

voltage of 3.0 volts with negligible resistance. Theresistanceof the slide-wire is 400Ωand its length is 200cm. A 200-cm scale is placed along the slide wire. Theslide-wire has 1 mm scale divisions and it is possible toreadupto1/5ofadivision.Theinstrumentisstandardisedwith1.018voltstandardcellwithwithslidingcontactatthe101.8cmmarkonscale.

Calculate

(a)Workingcurrent

(b)Resistanceofseriesrheostat

(c)Measurementrange

(d)Resolutionoftheinstrument

Solution

(a)Workingcurrent,ImBecausetheinstrumentisstandardisedwithanemfof1.018voltswithslidingcontactat101.8cm,itisobviousthatalength101.8cmrepresentsavoltageof1.018volts.

(b)Resistanceofseriesrheostat,RhTotalresistanceofbatterycircuit=Resistanceofrheostat(Rh)+Resistanceofslidewire.

Rh=Totalresistance–Resistanceofslidewire

(c)Measurementrange

Themeasurementrangeisthetotalvoltageacrosstheslidewire.

rangeofvoltage=0.005×400=2.0volt.

(d)Resolutionoftheinstrument

Alengthof200cmrepresents2.0voltandtherefore1mmrepresentsavoltageofê2ê1

Sinceitispossibletoread ofImV,therefore,resolutionoftheinstrumentis ×1=

0.2mV

A single-range laboratory-type potentiometer has an 18-step dial switch where each step represents 0.1 volt. The

Example5.2

dial resistors are 10 Ω each. The slide wire of thepotentiometeriscircularandhas11turnsandaresistanceof 1 Ω per turn. The slide wire has 100 divisions andinterpolation can be done to one forth of a division. Theworkingbatteryhasavoltageof6.0volt.Calculate(a)themeasuringrangeofthepotentiometer,(b)theresolution,(c)workingcurrent,and(d)settingoftherheostat.

SolutionDialresistor=10Weach

Eachstep=0.1v

(a)Themeasuringrangeofthepotentiometer

Totalresistanceofmeasuringcircuit,

Rm=Resistanceofdial+resistanceofslidewire

or, Rm=18×10+11=191

voltagerangeofthetotalinstrument

=Rm×workingcurrent

=191×10mA

=1.91V

(b)Theresolution

Theslidewirehasaresistanceof11Ωandthereforevoltagedropacrossslidewire

=11×10mA=0.11volt

Theslidewirehas11turns,andthereforevoltagedropacrosseachturn

Eachturnisdividedinto100divisionsandthereforeeachdivisionrepresentsavoltagedropof .

Sinceeachturncanbeinterpolatedtoofadivision,

Resolutionofinstrument=×00001=0000025volt=25mV

(c)Workingcurrent,ImAspreviouslymentioned,workingcurrent=1mA.

(d)Settingofrheostat

Totalresistanceacrossbatterycircuit

Totalresistanceofpotentiometercircuitis191Ω

resistanceofseriesrheostat,Rh=600-191=409W.

5.4 APPLICATIONSOFdcPOTENTIOMETERS

Practicalusesofdcpotentiometersare

•Measurementofcurrent

•Measurementofhighvoltage

•Measurementofresistance

•Measurementofpower

•Calibrationofvoltmeter

•Calibrationofammeter

•Calibrationofwattmeter

5.4.1MeasurementofCurrentbyPotentiometerThe circuit arrangement for measurement of current by a potentiometer is shown in

Figure5.3.Theunknowncurrent I,whosevalue is tobemeasured, ispassed throughastandardresistorRasshown.Thestandardresistorshouldbeofsuchavaluethatvoltagedropacrossitcausedbyflowofcurrenttobemeasured,maynotexceedtherangeofthepotentiometer.VoltagedropacrossthestandardresistorinvoltsdividedbythevalueofRinohmsgivesthevalueofunknowncurrentinamperes.

Figure5.3Measurementofcurrentwithpotentiometer

Example5.3

Asimpleslidewirepotentiometer isused formeasurementofcurrent inacircuit.Thevoltagedropacrossastandardresistorof0.1Ωisbalancedat75cm.findthemagnitudeofthecurrentifthestandardcellemfof1.45voltisbalancedat50cm.

SolutionForthesameworkingcurrent,if50cmcorrespondsto1.45volt.Then75cmoftheslidewirecorrespondsto

So, across the resistance 0.1 ? the voltage drop is 2.175 volt. Then the value of thecurrentis

5.4.2MeasurementofHighVoltagebyPotentiometerSpecial arrangementsmust bemade tomeasure very high voltage by the potentiometer(sayahundredsofvolts)asthishighvoltageisbeyondtherangeofnormalpotentiometer.Thevoltageabovethedirectrangeofpotentiometer(generally1.8volt)canbemeasuredby using a volt–ratio box in conjunction with the potentiometer. The volt–ratio boxconsistsofasimpleresistancepotentialdividerwithvarioustappingontheinputside.Thearrangement is shown in Figure5.4. Each input terminal ismarkedwith themaximumvoltage which can be applied and with the corresponding multiplying factor for thepotentialscale.

High emf to bemeasured is applied the suitable input terminal of volt–ratio box andleadstothepotentiometeraretakenfromtwotappingpointsintendedforthispurpose.

Thepotentialdifferenceacrossthesetwopointsismeasuredbythepotentiometer.Ifthevoltagemeasuredby thepotentiometer isvandk be themultiplying factorof thevolt–ratiobox,thenthehighvoltagetobemeasuredisV=kvvolt.

Figure5.4Measurementofhighvoltagebypotentiometerinconjunctionwithvolt–ratiobox

5.4.3MeasurementofResistancebyPotentiometerTheconnectiondiagramformeasuringunknownresistancewiththehelpofpotentiometerisshowninFigure5.5.TheunknownresistanceR,isconnectedinserieswiththeknownstandard resistor S. The rheostat connected in the circuit controls the current flowingthrough the circuit.Anammeter is also connected in the circuit to indicatewhether thevalueoftheworkingcurrentiswithinthelimitofthepotentiometerornot.Otherwise,theexactvalueoftheworkingcurrentneednotbeknown.

Whenthetwo–poledoublethrowswitchisputinposition1,theunknownresistanceisconnectedtothepotentiometer.LetthereadingofthepotentiometerinthatpositionisVR.Then

Now the switch is thrown to position 2, this connects the standard resistor S to thepotentiometer.IfthereadingofthepotentiometeristhatpositionisVSthen,

Figure5.5Measurementofresistancebypotentiometer

ThevalueofRcanbecalculatedaccuratelysincethevalueofthestandardresistorSisknown.Thismethodofmeasurementofresistanceisusedforlowvalueoftheresistor.

5.4.4MeasurementofPowerbyPotentiometerInmeasurementofpowerbypotentiometerthemeasurementsaremadeoneacrossthe

standardresistorSconnectedinserieswiththeloadandanotheracrossthevolt–ratioboxoutputterminals.ThearrangementisshowninFigure5.6.

TheloadcurrentwhichisexactlyequaltothecurrentthroughthestandardresistorS,asit is connected in series with the load, is calculated from the voltage drop across thestandardresistordividedbythevalueofthestandardresistorS.

Loadcurrent

whereVS=voltagedropacrossstandardresistorSasmeasuredbythepotentiometer.

Voltagedropacrosstheloadisfoundbytheoutputterminalofthevolt–ratiobox.IfVRisthevoltagedropacrosstheoutputterminalofthevolt–ratioboxandVL isthevoltagedropacrossloadthen,

VL=k×VRwherekisthemultiplyingfactorofthevolt–ratiobox.

Thenthepowerconsumed,

Figure5.6Measurementofpowerbypotentiometer

5.4.5CalibrationofVoltmeterbyPotentiometerIncaseofcalibrationofvoltmeter,themainrequirementisthatasuitablestabledcvoltagesupplyisavailable,otherwiseanychangeinthesupplyvoltagewillcauseachangeinthecalibrationprocessofthevoltmeter.

Figure5.7Calibrationofvoltmeterbypotentiometer

Thearrangement for calibratingavoltmeterbypotentiometer is shown inFigure5.7.Thepotentialdividernetworkconsistsoftworheostats.Oneforcoarseandtheotherforfinecontrolofcalibratingvoltage.Withthehelpofthesecontrols,itispossibletoadjustthe supply voltage so that the pointer coincides exactly with a major division of thevoltmeter.

The voltage across the voltmeter is steeped down to a value suitable for thepotentiometerwiththehelpofthevolt–ratiobox.Inordertogetaccuratemeasurements,itisnecessarytomeasurevoltagesnearthemaximumrangeofthepotentiometer,asfaraspossible.

The potentiometer measures the true value of the voltage. If the reading of thepotentiometerdoesnotmatchwith thevoltmeter reading,apositiveornegativeerror isindicated.Acalibrationcurvemaybedrawnwith thehelpof thepotentiometer and thevoltmeterreading.

5.4.6CalibrationofAmmeterbyPotentiometerFigure 5.8 shows the circuit arrangement for calibration of an ammeter using

potentiometer.

Figure5.8sCalibrationofammeterbypotentiometer

A standard resistor S of high current carrying capacity is placed in series with theammeter under test. The voltage drop across S measured with the help of thepotentiometerandthenthecurrentthroughSandhencetheammetercanbecomputedbydividingthevoltagedropbythevalueofthestandardresistor.

Current, isthevoltagedropacrossthestandardresistorS.

Now,comparethereadingoftheammeterwiththecurrentfoundbycalculation.Iftheydo notmatch, a positive or negative errorwill be induced.A calibration curvemay bedrawnbetweentheammeterreadingandthetruevalueofthecurrentasindicatedbythepotentiometerreading.

As theresistanceof thestandardresistorS isexactlyknown, thecurrent throughS isexactlycalculated.Thismethodofcalibrationofammeterisveryaccurate.

5.4.7CalibrationofWattmeterbyPotentiometerInthiscalibrationprocess,thecurrentcoilofthewattmeterissuppliedfromlowvoltagesupplyandpotentialcoilfromthenormalsupplythroughpotentialdivider.ThevoltageVacross the potential coil of thewattmeter under calibration ismeasured directly by thepotentiometer.Thecurrentthroughthecurrentcoilismeasuredbymeasuringthevoltagedrop across a standard resistor connected in serieswith the current coil divided by thevalueofthestandardresistor.

ThetruepoweristhenVI,whereVisthevoltageacrossthepotentialcoilandI is thecurrentthroughthecurrentcoilofthewattmeter.Thewattmeterreadingmaybecomparedwiththisvalue,andacalibrationcurvemaybedrawn.

ThearrangementforcalibratingawattmeterisshowninFigure5.9.

Figure5.9Calibrationofwattmeterbydcpotentiometer

Example5.4The emf of a standard cell used for standardisation is1.0186 volt. If the balanced is achieved at a length of 55cm,determine

(a)Theemfofthecellwhichbalancesat70cm

(b) The current flowing through a standard resistance of 2 Ω if the potentialdifferenceacrossitbalancesat60cm

(c) The voltage of a supply main which is reduced by a volt–ratio box to onehundredthandbalanceisobtainedat85cm

(d)Thepercentageerrorinavoltmeterreading1.40voltwhenbalanceisobtainedat80cm

(e)Thepercentageerrorinammeterreading0.35amperewhenbalanceisobtainedat 45 cmwith the potential difference across a 2.5Ω resistor in the ammetercircuit

SolutionEmfofthestandardcell=1.0186voltsThevoltagedroppercmlengthofpotentiometerwire,

(a)Theemfofacellbalancedat70cm,

=v·l=0.01852×70=1.2964volt

(b)Thepotentialdifferencewhichisbalancedat60cm

=v·l=0.01852×60=1.1112volt

Magnitudeofthestandardresistor,S=2W

Therefore,currentflowingthrough2ΩresistanceV

(c)Thepotentialdifferencewhichbalancesat85cm,

V=v·l=0.01852×85=1.5742volt

voltageofsupplymain=V×ratioofvolt–ratiobox

1.5742×100=157.42volt

(d)Thepotentialdifferencewhichbalancesat80cm,

V=v·l=0.01852×80=1.4816volt

Voltmeterreading=1.40volt

percentageerrorinvoltmeterreading

(e)Thepotentialdifferencewhichbalancesat45cm,

V=v·l=0.01852×45=0.8334volt

Currentflowingthrough2.5ΩresistanceV0.8334

percentageerrorinammeterreading

Example5.5

The following readings were obtained during themeasurementofalowresistanceusingapotentiometer:Voltagedropacrossa0.1Ωstandardresistance=1.0437VVoltagedropacrossthelowresistanceundertest=0.4205VCalculate the value of unknown resistance, current andpowerlostinit.

SolutionGiven:S=0.1Ω;VS=1.0437V;VR=0.4205V

Resistanceofunknownresistor,

Powerloss,PI2R=(10.437)2×0.04=4.357Wa

Example5.6

A Crompton’s potentiometer consists of a resistance dialhaving15stepsof10Ωeachandaseriesconnectedslidewire of 10 Ω which is divided into 100 divisions. If theworking current of the potentiometer is 10mA and eachdivisionof slidewirecanbe readaccuratelyupto thofits span, calculate the resolution of the potentiometer involts.

SolutionTotalresistanceofthepotentiometer,

R=Resistanceofthedial+Resistanceoftheslidewire

=15×10+10=160W

Workingcurrent,I=10mA=0.01A

Voltage range of the potentiometer = Working current × Total resistance of thepotentiometer

=0.01×160=1.6

Voltagedropacrossslidewire=Workingcurrent×Slidewireresistance

=0.01×10=0.1V

Sinceslidewirehas100divisions,therefore,eachdivisionrepresents or0.001volt

Aseachdivisionofslidewirecanbereadaccuratelyupto potentiometerofitsspan,therefore,resolutionofthepotentiometer

5.5 POTENTIOMETERS

Anacpotentiometer issameasdcpotentiometerbyprinciple.Only themaindifferencebetween the ac and dc potentiometer is that, in case of dc potentiometer, only themagnitude of the unknown emf is compared with the standard cell emf, but in acpotentiometer,themagnitudeaswellasphaseangleoftheunknownvoltageiscomparedtoachievebalance.

This condition of ac potentiometer needs modification of the potentiometer asconstructedfordcoperation.

The following points need to be considered for the satisfactory operation of the acpotentiometer:

1.Toavoiderrorinreading,theslidewireandtheresistancecoilofanacpotentiometershouldbenon-inductive.

2.Thereadingisaffectedbystrayorexternalmagneticfield,sointhetimeofmeasurementtheymustbeeliminatedormeasuredandcorrespondingcorrectionfactorshouldbeintroduced.

3.Thesourcesofacsupplyshouldbefreefromharmonics,becauseinpresenceofharmonicsthebalancemaynotbeachieved.

4.Theacsourceshouldbeassinusoidalaspossible.

5.Thepotentiometercircuitshouldbesuppliedfromthesamesourceasthevoltageorcurrentbeingmeasured.

5.6 CLASSIFICATIONOFACPOTENTIOMETERS

Therearetwogeneraltypesofacpotentiometers:

1.PolarPotentiometer

As the name indicates, in these potentiometers, the unknown emf ismeasured in polarform,i.e.,intermsofitsmagnitudeandrelativephase.Themagnitudeisindicatedbyonescale and the phase with respect to some reference axis is indicated by another scale.Thereisprovisionforreadingphaseanglesupto360°.

ThevoltageisreadintheformV–θ.

Example:Drysdalepolarpotentiometer

2.CoordinatePotentiometer

Here, the unknown emf is measured in Cartesian form. Two components along andperpendiculartosomestandardaxisaremeasuredandindicateddirectlybytwodifferentscalesknownasinphase(V1)andquadrature(V2)scales(Figure5.10).Provisionismadeinthisinstrumenttoreadbothpositiveandnegativevaluesofvoltagessothatallanglesupto360°arecovered.

Example:Gall–TinsleyandCampbell–Larsentypepotentiometer

Figure5.10Polarandcoordinaterepresentationofunknownemf

5.6.1DrysdalePolarPotentiometerThedifferentcomponentsofaDrysdalepolarpotentiometerisshowninFigure5.11.

Figure5.11Drysdalepolarpotentiometer

TheslidewireS1–S2issuppliedfromaphaseshiftingcircuitforacmeasurement.Thephase shifting circuit is so arranged that the magnitude of the voltage supplied by itremains constant while its phase can be varied through 360°. Consequently, slide wirecurrentcanbemaintainedconstantinmagnitudebutvariedinphase.

The phase shifting circuit consists of two stator coils connected in parallel suppliedfrom the same source; their currents aremade to differ by 90° by using very accuratephase shifting technique. The two windings produce rotating flux which induces asecondaryemfintherotorwindingwhichisofconstantmagnitudebutthephaseofwhichcanbevariedbyrotatingtherotorinanyposition.Thephaseoftherotoremfisreadfromthecirculardialattachedinthepotentiometer.

Beforetheacmeasurement,thepotentiometerisfirstcalibratedbyusingdcsupplyforslidewireandstandardcellfortestterminalsT1andT2.Theunknownalternatingvoltagetobemeasuredisappliedacrosstestterminalsandthebalanceisachievedbyvaryingtheslidewirecontactandthepositionoftherotor.Theammeterconnectedintheslidewirecircuitgives themagnitudeof theunknownemfand thecirculardial in therotorcircuitgivesthephaseangleofit.

5.6.2GallCoordinatePotentiometerThe Gall coordinate potentiometer consists of two separate potentiometer circuit in asinglecase.Oneofthemiscalledthe‘in-phase’potentiometerandtheotheroneiscalledthe quadrature potentiometer. The slide-wire circuits of these two potentiometers aresuppliedwith twocurrentshavingaphasedifferenceof90°.Thevalueof theunknownvoltageisobtainedbybalancingthevoltagesof in-phaseandquadraturepotentiometersslide wire simultaneously. If the measured values of in-phase and quadraturepotentiometerslide-wiresareV1andV2respectivelythenthemagnitudeoftheunknownvoltageis V=V12+V22andthephaseangleoftheunknownvoltageisgivenbyq=tan .

Figure5.12showstheschematicdiagramofaGallcoordinate-typepotentiometer.W–Xand Y–Z are the sliding contacts of the in-phase and quadrature potentiometerrespectively.R andR' are two rheostats to control the two slide-wire currents. The in-phasepotentiometerslide-wireissuppliedfromasingle-phasesupplyandthequadraturepotentiometer slide-wire is supplied from a phase-splitting device to create a phasedifference of 90° between the two slide-wire currents. T1 and T2 are two step-downtransformers having an output voltage of 6 volts. These transformers also isolate thepotentiometer from the high-voltage supply. R and C are the variable resistance andcapacitanceforphase-splittingpurpose.VGisavibrationgalvanometerwhichistunedtothesupplyfrequencyandKisthegalvanometerkey.Aisadynamometerammeterwhichisused todisplay thecurrent inboth theslide-wiresso that theycanbemaintainedatastandardvalueof50mA.SW1andSW2are twosign-changingswitcheswhichmay benecessary to reverse the direction of unknown emf applied to the slidewires.SW3 is aselectorswitchanditisusedtoapplytheunknownvoltagetothepotentiometer.

OperationBeforeusing thepotentiometer for acmeasurements, the current in the in-

phase potentiometer slide wire is first standardised using a standard dc cell of knownvalue.ThevibrationgalvanometerVG is replaced by aD’Arsonval galvanometer.Nowthein-phaseslidewirecurrentisadjustedtothestandardvalueof50mAbyvaryingtherheostatR.Thissettingisleftunchangedforaccalibration;thedcsupplyisreplacedbyacandtheD’Arsonvalgalvanometerbythevibrationgalvanometer.Themagnitudeofthecurrentinthequadraturepotentiometerslidewiremustbeequal

tothein-phasepotentiometerslidewirecurrentandthetwocurrentsshouldbeexactlyinquadrature.TheswitchSW3isplacedtotestposition(asshowninFigure5.12)sothattheemfinducedinthesecondarywindingofmutualinductanceMisimpressedacrossthein-phasepotentiometerwire through the vibration galvanometer. Since the induced emf inthesecondaryofmutualinductanceMwillbeequalto2pfMivoltinmagnitude;wherefisthesupplyfrequencyandwilllag90°behindthecurrentinthequadratureslide-wirei,sothevalueofemfcalculatedfromtherelatione'=2pfMiforacurrenti=50mAissetonin-phasepotentiometerslidewireandR'areadjustedtillexactbalancepointisobtained.Atbalanceposition,thecurrentinthepotentiometerwireswillbeexactlyequalto50mAinmagnitudeandexactlyinquadraturewitheachother.ThepolaritydifferencebetweenthetwocircuitsiscorrectedbychangingswitchesSW1andSW2.

Figure5.12Gallcoordinatepotentiometer

Lastly,theunknownvoltageisappliedtothepotentiometerbymeansoftheswitchSW3andbalance isobtainedonboth thepotentiometer slide-wirebyadjusting theslide-wiresetting.Thereadingofslide-wireWXgivesthein-phasecomponent(V1)andslidewireYZgivesquadraturecomponent(V2)oftheunknownvoltage.

ADVANTAGESANDDISADVANTAGESOFac

5.7 POTENTIOMETERS

Advantages

1.Anacpotentiometerisaveryversatileinstrument.Byusingshuntandvolt–ratiobox,itcanmeasurewiderangeofvoltage,currentandresistances.

2.Asitisabletomeasurephaseaswellasmagnitudeoftwosignals,itisusedtomeasurepower,inductanceandphaseangleofacoil,etc.

3. Theprincipleofacpotentiometer is also incorporated incertain special application likeArnoldcircuit for themeasurementofCT(CurrentTransformer)errors.

Disadvantages

1.Asmalldifferenceinreadingofthedynamometerinstrumenteitherindcoraccalibrationbringsonerrorinthealternatingcurrenttobesetatstandardvalue.

2.ThenormalvalueofthemutualinductanceMisaffectedduetotheintroductionofmutualinductancesofvariouspotentiometerpartsandsoaslightdifferenceisobservedinthemagnitudeofthecurrentofquadraturewirewithcomparedtothatinthein–phasepotentiometerwire.

3. Inaccuracy in themeasuredvalueof frequencywillalso result in thequadraturepotentiometerwirecurrent todifferfromthatofin–phasepotentiometerwire.

4. The presence of mutual inductances in the various parts of the potentiometer and the inter capacitance, thepotentialgradientofthewiresisaffected.

5. Since the standardisation is done on the basis of rms value and balance is obtained dependent upon thefundamentalfrequencyonly,therefore,thepresenceofharmonicsintheinputsignalintroducesoperatingproblemandthevibrationgalvanometertunedtothefundamentalfrequencymaynotshowfullnullpositionatall.

5.8 APPLICATIONSOFacPOTENTIOMETER

Themajorapplicationsoftheacpotentiometersare1.Measurementofself-inductance

2.Calibrationofvoltmeter

3.Calibrationofammeter

4.Calibrationofwattmeter

5.8.1MeasurementofSelf–inductanceThecircuitdiagramformeasurementofself inductanceofacoilbyacpotentiometer isshowninFigure5.13(a).Astandardnon-inductiveresistorisconnectedinserieswiththecoil under test and two potential differencesV1 andV2 aremeasured inmagnitude andphasebythepotentiometer.

ThevectordiagramisshowninFigure5.13(b).Refertothisfigure.

VoltagedropacrossstandardresistorRS,V2=IRSwhere,I=currentflowingthroughthecircuit,and

RS=resistanceofthestandardnon-inductiveresistor

Figure5.13Measurementofself-inductancebyacpotentiometer

Voltagedropacrossinductivecoil=V1Phaseanglebetweenvoltageacrossandcurrentthroughthecoil=θ

Voltagedropduetoresistanceofcoil,IR=V1cosθ

5.8.2CalibrationofAmmeterThemethodofcalibrationofanacammeterissimilartodcpotentiometermethodfordcammeter(refertoSection5.4.6)i.e.,acammeterundercalibrationisconnectedinserieswith a non inductive variable resistance for varying the current, and a non-inductivestandard resistor and voltage drop across standard resistor is measured on acpotentiometer.However, the standardisingof the acpotentiometer involves theuseof asuitabletransferinstrument.

5.8.3CalibrationofVoltmeterThemethodofcalibrationofanacvoltmeterbyusingacpotentiometerissimilartothatadoptedforcalibrationofdcvoltmeterbyusingdcpotentiometer(referSection5.4.5).

5.8.4CalibrationofWattmeterThecircuitdiagramforcalibrationofwattmeterbyacpotentiometer isshowninFigure5.14.Thecalibrationprocessissamethatadoptedincaseofcalibrationofwattmeterbydcpotentiometer(referSection5.4.7).

Thecurrentcoilof thewattmeter is supplied througha stepdown transformerand thepotentialcoilfromthesecondaryofavariabletransformerwhoseprimaryissuppliedfromtherotorofaphaseshiftingtransformer.

ThevoltageVacross thepotentialcoilof thewattmeterand thecurrent I through thecurrentcoilofwattmeteraremeasuredbythepotentiometer,introducingavolt–ratioboxandastandardresistorasshowninFigure5.14.

Figure5.14Calibrationofwattmeterbyacpotentiometer

The power factor cos q is varied by rotating the phase shift rotor, the phase anglebetweenvoltageandcurrent,Fbeinggivenbythereadingonthedialofthephaseshifter.ThepoweristhenVIcosFandthewattmeterreadingmaybecomparedwiththisreading.Acalibrationcurvemaybedrawnifnecessary.AsmallmutualinductanceMisincludedtoensureaccuracyofmeasurementofzeropowerfactor.

Example5.7

Thefollowingreadingswereobtainedduringmeasurementofinductanceofacoilonanacpotentiometer:Voltagedropacross0.1Ωstandardresistorconnectedinserieswiththecoil= 0.613 -12°6'Voltage across the test coil through a100:1 volt–ratio box = 0.781 -50°48'Frequency 50 Hz.Determinethevalueoftheinductanceofthecoil.

Solution

Currentthroughthecoil

Voltageacrossthecoil

impedanceofthecoil

Resistanceofthecoil

Reactanceofthecoil

The power factor cos q is varied by rotating the phase shift rotor, the phase anglebetweenvoltageandcurrent,Fbeinggivenbythereadingonthedialofthephaseshifter.ThepoweristhenVIcosFandthewattmeterreadingmaybecomparedwiththisreading.

Acalibrationcurvemaybedrawnifnecessary.AsmallmutualinductanceMisincludedtoensureaccuracyofmeasurementofzeropowerfactor.

Example5.7

The following results were obtained for determination ofimpedance of a coil by using a coordinate typepotentiometer: Voltage across the 1.0 Ωresistor in serieswith the coil=+0.2404V in phasedial and0.0935VonquadraturedialVoltageacross10:1potentialdividerusedwiththecoil=+0.3409Voninphasedialand+0.2343VonquadraturedialCalculate the resistanceand reactanceofthecoil.

Solution

Currentthroughthecoil

Example5.9

The following results were obtained during themeasurement of power by a polar potentiometer:Voltageacross0.2Ωstandardresistorinserieswiththeload=1.52-35°Voltageacross200:1potentialdivideracrosstheline=1.43 -53°Calculate the current, voltage, power and powerfactoroftheload.

Solution

(a)Currentthroughtheload,

MagnitudeofthecurrentI=7.6A

(b)VoltageacrosstheloadV=200×(1.43<53°)=286<53°V

MagnitudeofthevoltageV=286V

(c)Phaseangleoftheload=53°<35°=18°

powerfactoroftheloadcosφ=cos18°=0.951(lagging)

(d)Powerconsumedbytheload,P=Icosφ=286××0.951

EXERCISE

Objective-typeQuestions1.Thetransferinstrumentwhichisusedforstandardisationofapolar-typeacpotentiometeris

(a)anelectrostaticinstrument

(b)adynamometerinstrument

(c)amovingcoilinstrument

(d)athermalinstrument

2.Adcpotentiometerisdesignedtomeasureuptoabout2voltswithaslidewireof800mm.Astandardcellofemf1.18voltobtainsbalanceat600mm.atestcellisseentoobtainedbalanceat680mm.Theemfofthetestcellis

(a)1.50volts

(b)1.00volts

(c)1.34volts

(d)1.70volts

3.Formeasuringanacvoltagebyanacpotentiometer,itisdesirablethatthesupplyforthepotentiometeristakenfrom

(a)abattery

(b)thesamesourceastheunknownvoltage

(c)asourceotherthanthesourceofunknownvoltage

(d)anyoftheabove

4.Thecalibrationofavoltmetercanbecarriedoutbyusing

(a)anammeter

(b)afunctiongenerator

(c)afrequencymeter

(d)apotentiometer

5.Aslidewirepotentiometerhas10wiresof1meach.Withthehelpofastandardvoltagesourceof1.018voltitisstandardisebykeepingthejockeyat101.8cm.Iftheresistanceofthepotentiometerwireis1000Ωthenthevalueoftheworkingcurrentis

(a)1mA

(b)0.5mA

(c)0.1A

(d)10mA

6.Inthepotentiometercircuit,thevalueoftheunknownvoltageEunderbalanceconditionwillbe

(a)3V

(b)200mV

(c)2.8V

(d)3.2V

7.Thepotentiometerisstandardisedformakingit

(a)precise

(b)accurate

(c)accurateandprecise

(d)accurateanddirectreading

8. Consider the following statements.A dc potentiometer is the bestmeans available for themeasurement of dcvoltagebecause

1.Theprecisioninmeasurementisindependentofthetypeofdetectorused

2.Itisbasedonnullbalancetechnique

3.Itispossibletostandardizebeforeameasurementisundertaken

4.ItispossibletomeasuredcvoltagesranginginvaluefrommVtohundredsofvoltsOfthesestatements,

(a)2and3arecorrect

(b)1and4arecorrect

(c)2and4arecorrect

(d)3and4arecorrect

9.Inadcpotentiometermeasurements,asecondreadingisoftentakenafterreversingthepolaritiesofdcsupplyandtheunknownvoltage,andtheaverageofthetworeadingsistaken.Thisiswithaviewtoeliminatetheeffectsof

(a)ripplesinthedcsupply

(b)straymagneticfield

(c)straythermalemfs

(d)erroneousstandardisation

Short-answerQuestions1.Explainwhyapotentiometerdoesnotloadthevoltagesourcewhosevoltageisbeingmeasured.

2.Describetheprocedureofstandardisationofadcpotentiometer.

3.Whatisavoltratiobox?Explainitsprinciplewithasuitableblockdiagram.

4.Explainthereasonswhydcpotentiometerscannotbeusedforacmeasurementdirectly.

5.Explaintheprocedureformeasurementofself-reactanceofacoilwiththehelpofacpotentiometer.

6.Whatisthedifferencebetweenaslide-wirepotentiometeranddirectreadingpotentiometer?

7.Howcanadcpotentiometerbeusedforcalibrationofvoltmeter?

8.Explainwithsuitablediagramhowadcpotentiometercanbeusedforcalibrationofanammeter.

9.Explainwithasuitablediagramhowadcpotentiometercanbeusedforcalibrationofwattmeter.

10.Whatarethedifferentformsofacpotentiometersandbringoutthedifferencesbetweenthem.

Long-answerQuestions1.(a)ExplaintheworkingprincipleofaCromptondcpotentiometerwithasuitablediagram.

(b)Theemfofastandardcellismeasuredwithapotentiometerwhichgivesareadingof1.01892volts.Whena1MΩresistorisconnectedacrossthestandardcellterminals,thepotentiometerreadingdropsto1.01874volts.Calculatetheinternalresistanceofthecell.

[Ans:176.6Ω]

2.(a)Namethedifferenttypesofdcpotentiometersandexplainoneofthem.

(b)Aslidewirepotentiometerisusedtomeasurethevoltagebetweenthetwopointsofacertaindccircuit.Thepotentiometerreadingis1.0volt.Acrossthesametwopointswhena10000Ω/Vvoltmeterisconnected,thereadingonthevoltmeteris0.5voltofits5–voltrange.Calculatetheinputresistancebetweentwopoints.

[Ans:50000Ω]

3. (a) Writedowntheprocedureofstandardisationofadcpotentiometer.Howcan itbeusedforcalibrationofammetersandvoltmeters?

(b)Aslidewirepotentiometerhasabatteryof4voltsandnegligibleinternalresistance.Theresistanceofslidewire is 100 Ω and its length is 200 cm. A standard cell of 1.018 volts is used for standardising thepotentiometerandtherheostatisadjustedsothatbalanceisobtainedwhentheslidingcontactisat101.8cm.

(i) Findtheworkingcurrentoftheslidewireandtherheostatsetting. [Ans:20mA,100

Ω]

(ii) If theslidewirehasdivisionsmarkedinmmandeachdivisioncanbeinterpolatedtoonefifth,calculatetheresolutionofthepotentiometer.

[Ans:0.2mV]

4.(a)Whataretheproblemsassociatedwithacpotentiometers?Describetheworkingofanyoneacpotentiometer.

(b)Powerisbeingmeasuredwithanacpotentiometer.Thevoltageacrossa0.1Ωstandardresistanceconnectedin serieswith the load is (0.35 – j0.10) volt. The voltage across 300:1 potential divider connected to thesupplyis(0.8+j0.15)volt.Determinethepowerconsumedbytheloadandthepowerfactor.

[Ans:801W,0.8945]

5.(a)Describetheconstructionandworkingofanaccoordinate–typepotentiometer.

(b)Measurementsforthedeterminationoftheimpedanceofacoilaremadeonacoordinatetypepotentiometer.Theresultare:Voltageacross1Ωstandardresistanceinserieswiththecoil=+0.952Voninphasedialand–0.340V on quadrature dial; voltage across 10:1 potential divider connected to the terminals of the coil =+1.35Voninphasedialand+1.28Vonquadraturedial.

Calculatetheresistanceandreactanceofthecoil.

[Ans:R=8.32Ω,×=16.41Ω]

6.Describebrieflytheapplicationsofacpotentiometers.

7.Writeshortnotesonthefollowing(anythree):

(a)Simpledcpotentiometeranditsuses

(b)Calibrationoflowrangeammeter

(c)Measurementofhighvoltagebydcpotentiometer

(d)Polarpotentiometer

(e)Coordinate–typepotentiometer

(f)Comparisonbetweenacanddcpotentiometer

6.1 INTRODUCTION

Alternating current bridges are most popular, convenient and accurate instruments formeasurementofunknowninductance,capacitanceandsomeotherrelatedquantities.Initssimplest form, ac bridges can be thought of to be derived from the conventional dcWheatstonebridge.Anacbridge, in itsbasicform,consistsoffourarms,analternatingpowersupply,andabalancedetector.

6.2 SOURCESANDDETECTORSINacBRIDGES

For measurements at low frequencies, bridge power supply can be obtained from thepowerlineitself.Higherfrequencyrequirementsforpowersuppliesarenormallymetbyelectronic oscillators. Electronic oscillators have highly stable, accurate yet adjustablefrequencies.Theiroutputwaveformsareveryclosetosinusoidalandoutputpowerlevelsufficientformostbridgemeasurements.

When working at a single frequency, a tuned detector is preferred, since it givesmaximum sensitivity at the selected frequency and discrimination against harmonicfrequencies.Vibrationgalvanometers aremostcommonlyusedas tuneddetectors in thepowerfrequencyandlowaudio-frequencyranges.Thoughvibrationgalvanometerscanbedesigned towork as detectors over the frequency rangeof 5Hz to 1000Hz, theyhavehighestsensitivitywhenoperatedforfrequenciesbelow200Hz.

Headphonesoraudioamplifiersarepopularlyusedasbalancedetectorsinacbridgesatfrequenciesof250Hzandabove,upto3to4kHz.

Transistor amplifier with frequency tuning facilities can be very effectively used asbalancedetectorswithacbridges.Withproper tuning, thesecanbeused tooperateataselective band of frequencies with high sensitivity. Such detectors can be designed tooperateoverafrequencyrangeof10Hzto100kHz.

6.3GENERALBALANCEEQUATIONFORFOUR-ARMBRIDGE

An ac bridge in its general form is shown in Figure 6.1, with the four arms beingrepresentedbyfourunspecifiedimpedancesZ1,Z2,Z3andZ4.

Figure6.1General4-armbridgeconfiguration

Balanceinthebridgeissecuredbyadjustingoneormoreofthebridgearms.Balanceisindicated by zero response of the detector. At balance, no current flows through thedetector, i.e., there is no potential difference across the detector, or in otherwords, thepotentialsatpointsBandCarethesame.ThiswillbeachievedifthevoltagedropfromAtoBequalsthevoltagedropfromAtoC,bothinmagnitudeandphase.

Thus,wecanwriteintermsofcomplexquantities:

Alsoatbalance,sincenocurrentflowsthroughthedetector,

CombiningEqs(6.2)and(6.3)intoEq.(6.1),wehave

Whenusingadmittancesinplaceofimpedances,Eq.(6.4)canbere-orientedas

Equations(6.4)and(6.6)representthebasicbalanceequationsofanacbridge.Whereas(6.4)isconvenientforuseinbridgeconfigurationshavingserieselements,(6.6)ismore

usefulwhenbridgeconfigurationshaveparallelelements.

Equation (6.4) indicates that under balanced condition, the product of impedances ofonepairofoppositearmsmustbeequaltotheproductofimpedancesoftheotherpairofoppositearms,withtheimpedancesexpressedascomplexnumbers.Thiswillmean,bothmagnitudeandphaseanglesofthecomplexnumbersmustbetakenintoaccount.

Re-writing the expressions in polar form, impedances can be expressed aswhere Z represents the magnitude and θ represents the phase angle of the compleximpedance.

Ifsimilarformsarewrittenforallimpedancesandsubstitutedin(6.4),weobtain:

Thus,forbalancewehave,

Equation(6.7)showsthattworequirementsmustbemetforsatisfyingbalanceconditioninabridge.

Thefirstconditionisthatthemagnitudeoftheimpedancesmustmeettherelationship;

Thesecondconditionisthatthephaseanglesoftheimpedancesmustmeettherelationship;

Example6.1 In the AC bridge circuit shown in Figure 6.1, the supplyvoltage is 20 V at 500 Hz. Arm AB is 0.25 mμ purecapacitance;armBDis400ΩpureresistanceandarmAChasa120Ωresistanceinparallelwitha0.15mμcapacitor.Find resistanceand inductanceor capacitanceof thearmCDconsideringitasaseriescircuit.

SolutionImpedanceofthearmABis

ImpedanceofarmBDisZ3=400Ω

Sinceitispurelyresistive,incomplexnotation,

ImpedanceofarmACcontaining120Ωresistanceinparallelwitha0.15µFcapacitoris

6.4 MEASUREMENTOFSELF-INDUCTANCE

6.4.1Maxwell’sInductanceBridgeThisbridgeisusedtomeasurethevalueofanunknowninductancebycomparingitwithavariable standard self-inductance. The bridge configuration and phasor diagram underbalancedconditionareshowninFigure6.2.

The unknown inductor L1 of resistance R1 in the branch AB is compared with thestandardknowninductorL2of resistanceR2onarmAC.The inductorL2 isof thesameorder as the unknown inductor L1. The resistances R1,R2, etc., include, of course theresistancesofcontactsandleadsinvariousarms.BranchBDandCDcontainknownno-inductiveresistorsR3andR4respectively.

ThebridgeisbalancedbyvaryingL2andoneoftheresistorsR3orR4.Alternatively,R3andR4canbekeptconstant,andtheresistanceofoneoftheothertwoarmscanbevariedbyconnectinganadditionalresistor.

Underbalancedcondition,nocurrentflowsthroughthedetector.Undersuchcondition,currentsinthearmsABandBDareequal(I1).Similarly,currentsinthearmsACandCDareequal(I2).Underbalancedcondition,sincenodesBandDareat thesamepotential,voltagedropsacrossarmBDandCDareequal(V3=V4);similarly,voltagedropacrossarmsABandACareequal(V1=V2).

Figure6.2Maxwell’sinductancebridgeunderbalancedcondition:(a)Configuration(b)Phasordiagram

As shown in the phasor diagram of Figure 6.2 (b),V3 andV4 being equal, they areoverlapping.ArmsBDandCDbeingpurelyresistive,currentsthroughthesearmswillbein the same phase with the voltage drops across these two respective branches. Thus,currentsI1andI2willbecollinearwiththephasorsV3andV4.ThesamecurrentI1flowsthroughbranchAB aswell, thus thevoltagedrop I1R1 remains in the samephase as I1.Voltage dropwI1L1 in the inductorL1 will be 90° out of phase with I1R1 as shown inFigure6.2(b).PhasorsummationofthesetwovoltagedropsI1R1andwI1L1willgivethevoltagedropV1 across the armAB. At balance condition, since voltage across the twobranchesABandACareequal,thusthetwovoltagedropsV1andV2areequalandareinthe same phase. Finally, phasor summation ofV1 andV3 (orV2 andV4) results in thesupplyvoltageV.

Unknownquantitiescanhencebecalculatedas

CaremustbetakenthattheinductorsL1andL2mustbeplacedatadistancefromeach

othertoavoideffectsofmutualinductance.

Thefinalexpression(6.10)showsthatvaluesofL1andR1donotdependonthesupplyfrequency.Thus,thisbridgeconfigurationisimmunetofrequencyvariationsandevenharmonicdistortionsinthepowersupply.

6.4.2Maxwell’sInductance–CapacitanceBridgeIn this bridge, the unknown inductance is measured by comparison with a standardvariablecapacitance.Itismucheasiertoobtainstandardvaluesofvariablecapacitorswithacceptable degree of accuracy. This is however, not the casewith finding accurate andstable standard value variable inductor as is required in the basic Maxwell’s bridgedescribedinSection6.4.1.

ConfigurationofaMaxwell’sinductance–capacitancebridgeandtheassociatedphasordiagramatbalancedstateareshowninFigure6.3.

Figure6.3Maxwell’sinductance–capacitancebridgeunderbalancedcondition:(a)Configuration(b)Phasordiagram

TheunknowninductorL1ofeffectiveresistanceR1inthebranchABiscomparedwiththestandardknownvariablecapacitorC4onarmCD.TheotherresistancesR2,R3,andR4areknownasnon–inductiveresistors.

ThebridgeispreferablybalancedbyvaryingC4andR4,givingindependentadjustmentsettings.

Underbalancedcondition,nocurrentflowsthroughthedetector.Undersuchcondition,currentsinthearmsABandBDareequal(I1).Similarly,currentsinthearmsACandCDareequal(I2).Underbalancedcondition,sincenodesBandDareat thesamepotential,voltagedropsacrossarmBDandCDareequal(V3=V4);similarly,voltagedropsacrossarmsABandACareequal(V1=V2).

As shown in the phasor diagram of Figure 6.3 (b),V3 andV4 being equal, they areoverlappingboth inmagnitudeandphase.ThearmBDbeingpurelyresistive,currentI1

throughthisarmwillbeinthesamephasewiththevoltagedropV3across it.Similarly,thevoltagedropV4acrossthearmCD,current IR through theresistanceR4 in thesamebranch,andtheresultingresistivevoltagedropIRR4areallinthesamephase[horizontallineinFigure6.3(b)].TheresistivecurrentIRwhenaddedwiththequadraturecapacitivecurrent IC, results in themain current I2 flowing in the armCD. This current I2 whileflowingthroughtheresistanceR2inthearmAC,producesavoltagedropV2=I2R2,thatisinsamephaseasI2.Underbalancedcondition,voltagedropsacrossarmsABandACareequal,i.e.,V1=V2.ThisvoltagedropacrossthearmABisactuallythephasorsummationofvoltagedropI1R1acrosstheresistanceR1andthequadraturevoltagedropwI1L1acrosstheunknowninductorL1.Finally,phasorsummationofV1andV3(orV2andV4)resultsinthesupplyvoltageV.

Equatingrealandimaginaryparts,wehave

Thus,theunknownquantitiesare

Onceagain,thefinalexpression(6.11)showsthatvaluesofL1andR1donotdependonthesupplyfrequency.Thus,thisbridgeconfigurationisimmunetofrequencyvariationsandevenharmonicdistortionsinthepowersupply.

It is interesting tonote thatboth in theMaxwell’s InductanceBridgeandInductance-CapacitanceBridge,theunknownInductorL1wasalwaysassociatedwitharesistanceR1.Thisseriesresistancehasbeenincludedtorepresentlossesthattakeplaceinaninductorcoil. An ideal inductor will be lossless irrespective of the amount of current flowingthroughit.However,anyrealinductorwillhavesomenon-zeroresistanceassociatedwithit due to resistance of the metal wire used to form the inductor winding. This seriesresistancecausesheatgenerationduetopowerloss.Insuchcases, theQualityFactorortheQ-Factor of such a lossy inductor is used to indicate how closely the real inductorcomestobehaveasanidealinductor.TheQ-factorofaninductorisdefinedastheratioofitsinductivereactancetoitsresistanceatagivenfrequency.Q-factorisameasureoftheefficiencyof the inductor.Thehigher thevalueofQ-factor, thecloser itapproaches thebehaviorofanideal,losslessinductor.AnidealinductorwouldhaveaninfiniteQatallfrequencies.

TheQ-factor of an inductor is given by the formula , whereR is its internalresistanceR(seriesresistance)andwLisitsinductivereactanceatthefrequencyω.

Q-factorofan inductorcanbe increasedbyeither increasing its inductancevalue(byusing a good ferromagnetic core) or by reducing itswinding resistance (by using goodqualityconductormaterial,inspecialcasesmaybesuperconductorsaswell).

In the Maxwell’s Inductance-Capacitance Bridge, Q-factor of the inductor undermeasurementcanbefoundatbalanceconditiontobe or,

Theaboverelation(6.12)fortheinductorQfactorindicatethatthisbridgeisnotsuitableformeasurementofinductorvalueswithhighQfactors,sinceinthatcase,therequiredvalueofR4forachievingbalancebecomesimpracticablyhigh.

AdvantagesofMaxwell’sBridge1.Thebalanceequations(6.11)areindependentofeachother,thusthetwovariablesC4andR4canbevariedindependently.

2.Finalbalanceequationsareindependentoffrequency.

3. The unknown quantities can be denoted by simple expressions involving knownquantities.

4.Balanceequationisindependentoflossesassociatedwiththeinductor.

5.Awiderangeofinductanceatpowerandaudiofrequenciescanbemeasured.

DisadvantagesofMaxwell’sBridge1. Thebridge,for itsoperation,requiresastandardvariablecapacitor,whichcanbe

veryexpensiveifhighaccuraciesareaskedfor.Insuchacase,fixedvaluecapacitorsareusedandbalanceisachievedbyvaryingR4andR2.

2.ThisbridgeislimitedtomeasurementoflowQinductors(1<Q<10).

3.Maxwell’sbridgeisalsounsuitedforcoilswithverylowvalueofQ(e.g.,Q<1).Such lowQ inductorscanbe found in inductive resistorsandRFcoils.Maxwell’sbridge findsdifficult and laborious toobtainbalancewhilemeasuring such lowQinductors.

6.4.3Hay’sBridgeHay’s bridge is a modification of Maxwell’s bridge. This method of measurement isparticularlysuitedforhighQinductors.

ConfigurationofHay’sbridgeandtheassociatedphasordiagramunderbalancedstateareshowninFigure6.4.

TheunknowninductorL1ofeffectiveresistanceR1inthebranchABiscomparedwith

thestandardknownvariablecapacitorC4onarmCD.ThisbridgeusesaresistanceR4 inserieswiththestandardcapacitorC4(unlikeinMaxwell’sbridewhereR4wasinparallelwithC4).TheotherresistancesR2andR3areknownno-inductiveresistors.

ThebridgeisbalancedbyvaryingC4andR4.

Underbalancedcondition,sincenocurrentflowsthroughthedetector,nodesBandDare at the same potential, voltage drops across arm BD andCD are equal (V3 = V4);similarly,voltagedropsacrossarmsABandACareequal(V1=V2).

Figure6.4Hay’sbridgeunderbalancedcondition:(a)Configuration,(b)Phasordiagram

As shown in the phasor diagram of Figure 6.4 (b),V3 andV4 being equal, they areoverlappingbothinmagnitudeandphaseandaredrawonalongthehorizontalaxis.ThearmBDbeingpurelyresistive,currentI1throughthisarmwillbeinthesamephasewiththe voltage drop V3 = I1R3 across it. The same current I1, while passing through theresistanceR1inthearmAB,producesavoltagedropI1R1thatisonceagain,inthesamephase as I 1. Total voltage dropV 1 across the armAB is obtained by adding the twoquadraturephasorsI1R1andwI1L1representingresistiveandinductivevoltagedropsinthesamebranchAB.Sinceunderbalancecondition,voltagedropsacrossarmsABandAC are equal, i.e., (V 1 =V 2), the two voltagesV 1 andV 2 are overlapping both inmagnitude andphase.ThebranchAC beingpurely resistive, thebranch current I 2 andbranchvoltageV2willbeinthesamephaseasshowninthephasordiagramofFigure6.4(b).ThesamecurrentI2flowsthroughthearmCDandproducesavoltagedropI2R4acrosstheresistanceR4.ThisresistivevoltagedropI2R4,obviouslyisinthesamephaseasI2.ThecapacitivevoltagedropI2/wC4inthecapacitanceC4presentinthesamearmACwillhowever,lagthecurrentI2by90°.PhasorsummationofthesetwoseriesvoltagedropsacrossR4andC4willgivethetotalvoltagedropV4acrossthearmCD.Finally,phasorsummationofV1andV3(orV2andV4)resultsinthesupplyvoltageV.

Equatingrealandimaginaryparts,wehave

SolvingEqs(6.13)and(6.14)wehavetheunknownquantitiesas

and

Qfactoroftheinductorinthiscasecanbecalculatedatbalanceconditionas

Hay’sbridgeismoresuitableformeasurementofunknowninductorshavingQfactormorethan10.Inthosecases,bridgebalancecanbeattainedbyvaryingR2only,withoutlosingmuchaccuracy.

From(6.15)and(6.17),theunknowninductancevaluecanbewrittenasForinductorswith

Q>10,thequantity(1/Q)2willbelessthan1/100,andthuscanbeneglectedfromthedenominatorof(6.18).Insuchacase,theinductorvaluecanbesimplifiedtoL1=R2R3C4,whichessentiallyisthesameasobtainedinMaxwell’sbridge.

6.4.4Anderson’sBridgeThis method is a modification of Maxwell’s inductance–capacitance bridge, in whichvalueoftheunknowninductorisexpressedintermsofastandardknowncapacitor.Thismethodisapplicableforprecisemeasurementofinductancesoverawiderangeofvalues.

Figure6.5 showsAnderson’s bridge configuration and correspondingphasor diagramunderbalancedcondition.

TheunknowninductorL1ofeffectiveresistanceR1inthebranchABiscomparedwiththestandardknowncapacitorConarmED.Thebridgeisbalancedbyvaryingr.

Underbalancedcondition,sincenocurrentflowsthroughthedetector,nodesBandEareatthesamepotential.

Figure6.5Anderson’sbridgeunderbalancedcondition:(a)Configuration(b)Phasordiagram

As shown in the phasor diagramofFigure6.5 (b), I1 andV3 = I1R3 are in the samephasealongthehorizontalaxis.Sinceunderbalancecondition,voltagedropsacrossarmsBDandEDareequal,V3=I1R3=IC/wCandallthethreephasorsareinthesamephase.ThesamecurrentI1,whenflowingthroughthearmABproducesavoltagedropI1(R1+r1)which isonceagain, inphasewith I1.Sinceunderbalancedcondition,nocurrent flowsthrough thedetector, the same current IC flows through the resistance r in armCE andthenthroughthecapacitorCinthearmED.PhasorsummationofthevoltagedropsICrinarmtheCEandIC/wCinthearmEDwillbeequaltothevoltagedropV4acrossthearmCD.V4beingthevoltagedropintheresistanceR4onthearmCD, thecurrentI4andV4willbe in the samephase.Ascanbe seen from theAnderson’sbridgecircuit, andalsoplottedinthephasordiagram,phasorsummationofthecurrentsI4inthearmCDandthecurrent IC in thearmCEwillgive rise to thecurrent I2 in thearmAC. This current I2,whilepassingthroughtheresistanceR2willgiverisetoavoltagedropV2= I2R2acrossthearmACthatisinphasewiththecurrentI2.Since,underbalance,potentialsatnodesBandEarethesame,voltagedropsbetweennodesA-BandbetweenA-C-Ewillbeequal.Thus,phasorsummationofthevoltagedropV2=I2R2inthearmACICr inarmtheCEwillbuilduptothevoltageV1acrossthearmAB.ThevoltageV1canalsobeobtainedbyadding the resistivevoltagedrop I1(R1 + r1)with thequadrature inductivevoltagedropwI1L1inthearmAB.Finally,phasorsummationofV1andV3(orV2andV4)resultsinthesupplyvoltageV.

Atbalance,I2=IC+I4

PuttingthevalueofICfromEq.(6.19)inEq.(6.20),wehave:Ir(+R+jwL)=IR+jwIRCr

Then,puttingthevalueofICfromEq.(6.19)inEq.(6.21),wehave:Ê1ˆ

FromEqs(6.22)and(6.23),weobtain:

Equatingrealandimaginaryparts,weget

TheadvantageofAnderson’sbridgeoverMaxwell’sbrideisthatinthiscaseafixedvaluecapacitorisusedtherebygreatlyreducingthecost.Thishowever,isattheexpenseofconnectioncomplexitiesandbalanceequationsbecomingtedious.

6.4.5Owen’sBridgeThis bridge is used for measurement of unknown inductance in terms of known valuecapacitance.

Figure6.6 shows theOwen’sbridgeconfigurationandcorrespondingphasordiagramunderbalancedcondition.

TheunknowninductorL1ofeffectiveresistanceR1inthebranchABiscomparedwiththestandardknowncapacitorC2onarmAC.ThebridgeisbalancedbyvaryingR2andC2independently.

Underbalancedcondition,sincenocurrentflowsthroughthedetector,nodesBandCareatthesamepotential,i.e.,V1=V2andV3=V4.

AsshowninthephasordiagramofFigure6.5(b),I1,V3=I1R3andV4=I2/wC4areallinthesamephasealongthehorizontalaxis.TheresistivevoltagedropI1R1inthearmABisalsointhesamephase

Figure6.6Owen’sbridgeunderbalancedcondition:(a)Configuration(b)Phasordiagram

with I1. The inductive voltage dropwI1L1 when added in quadraturewith the resistivevoltage drop I1R1 gives the total voltage drop V1 across the arm AB. Under balancecondition, voltage drops across arms AB andAC being equal, the voltages V1 and V2coincidewitheachotherasshowninthephasordiagramofFigure6.6(b).ThevoltageV2is once again summation of twomutually quadrature voltage drops I2R2 (resistive) andI2/wC2 (capacitive) in the armAC. It is to be noted here that the current I2 leads thevoltageV4by90°duetopresenceofthecapacitorC4.ThismakesI2andhenceI2R2tobevertical,asshowninthephasordiagram.Finally,phasorsummationofV1andV3(orV2andV4)resultsinthesupplyvoltageV.

Simplifying and separating real and imaginary parts, the unknown quantities can befoundoutas

and

ItisthuspossibletohavetwoindependentvariablesC2andR2forobtainingbalanceinOwen’sbridge.Thebalanceequationsarealsoquitesimple.Thishowever,doescomewithadditionalcostforthevariablecapacitor

Example6.2 A Maxwell’s inductance–capacitance bridge is used tomeasure a unknown inductive impedance. The bridgeconstantsatbridgebalanceare:Pureresistancearms=2.5

kΩand50kΩ.Inbetweenthesetworesistors,thethirdarmhasacapacitorofvalue0.012μFinserieswitharesistorofvalue 235 kΩ. Find the series equivalent of the unknownimpedance.

SolutionReferringtothediagramofaMaxwell’sinductance–capacitancebridge:

Usingthebalanceequation,

Example6.3 Thefourarmsofabridgeareconnectedasfollows:

ArmAB:AchokecoilL1withanequivalentseriesresistancer1ArmBC:AnoninductiveresistanceR3ArmCD:AmicacapacitorC4inseriesanoninductiveresistanceR4ArmDA:AnoninductiveresistanceR2

Whenthebridgeissuppliedfromasourceof450HzisgivenbetweenterminalsAandCandthedetectorisconnectedbetweennodesBandD,balanceisobtainedthefollowingconditions:R2=2400Ω,R3=600Ω,C4=0.3μFandR4=55.4Ω.Seriesresistanceofthecapacitoris0.5Ω.Calculatetheresistanceandinductanceofthechokecoil.

SolutionThebridgeconfigurationisshownbelow:

Giventhatatbalance,

and

6.5 MEASUREMENTOFCAPACITANCE

Bridgesareusedtomakeprecisemeasurementsofunknowncapacitancesandassociatedlossesintermsofsomeknownexternalcapacitancesandresistances.Anidealcapacitorisformed by placing a piece of dielectric material between two conducting plates orelectrodes.Inpracticalcases,thisdielectricmaterialwillhavesomepowerlossesinitdueto dielectric’s conduction electrons and also due to dipole relaxation phenomena.Thus,whereasanidealcapacitorwillnothaveanylosses,arealcapacitorwillhavesomelossesassociatedwithitsoperation.Thepotentialenergyacrossacapacitoristhusdissipatedinall real capacitors as heat loss inside its dielectric material. This loss is equivalently

representedbyaseriesresistance,calledtheequivalentseriesresistance(ESR).Inagoodcapacitor,theESRisverysmall,whereasinapoorcapacitortheESRislarge.CrealCidealESR

A real, lossy capacitor can thus be equivalently represented by an ideal loss lesscapacitor in series CR with its equivalent series resistance (ESR) shown Figure 6.7Equivalentseriesresistance(ESR)inFigure6.7.

Figure6.7Equivalentseriesresistance(ESR)

ThequantifyingparametersoftenusedtodescribeperformanceofacapacitorareESR,itsdissipationfactor(DF),QualityFactor(Q-factor)andLossTangent (tand).Notonlythat these parameters describe operation of the capacitor in radio frequency (RF)applications,butESRandDFarealsoparticularly important forcapacitorsoperating inpowersupplieswherealargedissipationfactorwillresultinlargeamountofpowerbeingwasted in thecapacitor.CapacitorswithhighvaluesofESRwillneed todissipate largeamount of heat. Proper circuit design needs to be practiced so as to take care of suchpossibilitiesofheatgeneration.

Dissipationfactorduetothenon-idealcapacitorisdefinedastheratiooftheresistivepowerlossintheESRtothereactivepoweroscillatinginthecapacitor,or

Whenrepresentingtheelectricalcircuitparametersasphasors,acapacitor’sdissipationfactorisequaltothetangentoftheanglebetweenthecapacitor’simpedancephasorandthenegativereactiveaxis,asshownintheimpedancetrianglediagramofFigure6.8ThisgivesrisetotheparameterknownasthelosstangentdwhereFigure.6.8Impedance

Figure.6.8Impedancetrianglediagram

LosstangentofarealcapacitorcanalsobedefinedinthevoltagetrianglediagramofFigure 6.9 as the ratio of voltage drop across the ESR to the voltage drop across thecapacitoronly, i.e. tangentof theanglebetween thecapacitorvoltageonlyand the totalvoltagedropacrossthecombinationofcapacitorandESR.

Figure.6.9Voltagetrianglediagram

Though the expressions for dissipation factor (DF) and loss tangent (tan δ) are thesame, normally the dissipation factor is used at lower frequencies, whereas the losstangentismoreapplicableforhighfrequencyapplications.Agoodcapacitorwillnormallyhavelowvaluesofdissipationfactor(DF)andlosstangent(tanδ).

In addition to ESR, DF and loss tangent, the other parameter used to quantifyperformance of a real capacitor is its Quality Factor or Q-Factor. Essentially for acapacitoritistheratiooftheenergystoredtothatdissipatedpercycle.

It can thus be deduced that the Q can be expressed as the ratio of the capacitivereactancetotheESRatthefrequencyofinterest.

Ahighqualitycapacitor(highQ-factor)willthushavelowvaluesofdissipationfactor(DF)andlosstangent(tanδ),i.e.lesslosses.

ThemostcommonlyusedbridgesforcapacitancemeasurementareDeSauty’sbridgeandScheringBridge.

6.5.1DeSauty’sBridgeThisisthesimplestmethodoffindingoutthevalueofaunknowncapacitorintermsofaknownstandardcapacitor.ConfigurationandphasordiagramofaDeSauty’sbridgeunderbalancedconditionisshowninFigure6.10.

Figure6.10DeSauty’sbridgeunderbalancedcondition:(a)Configuration(b)Phasordiagram

The unknown capacitorC1 in the branch AB is compared with the standard knownstandard capacitorC2 on armAC. The bridge can be balanced by varying either of thenon-inductiveresistorsR3orR4.

Underbalancedcondition,sincenocurrentflowsthroughthedetector,nodesBandCareatthesamepotential,i.e.,V1=V2andV3=V4.

AsshowninthephasordiagramofFigure6.7(b),V3=I1R3andV4=I2R4beingequalbothinmagnitudeandphase,theyoverlap.CurrentI1inthearmBDandI2inthearmCDarealsointhesamephasewithI1R3andI2R4alongthehorizontalline.CapacitivevoltagedropV1 = I1/wC1 in the armAB lags behind I1 by 90°. Similarly, the other capacitivevoltagedropV2=I2/wC2inthearmAClagsbehindI2by90°.Underbalancedcondition,thesetwovoltagedropsV1andV2beingequalinmagnitudeandphase,theyoverlapeachotheralongtheverticalaxisasshowninFigure6.7(b).Finally,phasorsummationofV1andV3(orV2andV4)resultsinthesupplyvoltageV.

TheadvantageofDeSauty’sbridgeisitssimplicity.However,thisadvantagemaybenullifiedbyimpuritiescreepinginthemeasurementifthecapacitorsarenotfreefromdielectriclosses.Thismethodisthusbestsuitedforloss-lessaircapacitors.

In order to make measurement in capacitors having inherent dielectric losses, themodifiedDeSauty’sbridgeassuggestedbyGrover,canbeused.Thisbridgeisalsocalledthe series resistance-capacitance bridge. Configuration of such a bridge and itscorrespondingphasordiagramunderbalancedconditionisshowninFigure6.11.

Figure6.11ModifiedDeSauty’sbridgeunderbalancedcondition:(a)Configuration,and(b)Phasordiagram

TheunknowncapacitorC1withinternalresistancer1representinglossesinthebranchAB is comparedwith the standard known standard capacitorC2 alongwith its internalresistancer2onarmAC.ResistorsR1andR2 areconnectedexternally inserieswithC1

andC2 respectively.The bridge can be balanced by varying either of the non-inductiveresistorsR3orR4.

Underbalancedcondition,sincenocurrentflowsthroughthedetector,nodesBandCareatthesamepotential,i.e.,V1=V2andV3=V4.

AsshowninthephasordiagramofFigure6.11(b),V3=I1R3andV4=I2R4beingequalbothinmagnitudeandphase,theyoverlap.CurrentI1inthearmBDandI2inthearmCDarealsointhesamephasewithI1R3andI2R4alongthehorizontalline.Theotherresistivedrops, namely, I1R1 in the arm AB and I2R2 in the arm AC are also along the samehorizontalline.Finally,resistivedropsinsidethecapacitors,namely,I1r1andI2r2areonceagain,inthesamephase,alongthehorizontalline.CapacitivevoltagedropsI1/wC1 lagsbehindI1r1by90°.Similarly,theothercapacitivevoltagedropI2/wC2lagsbehindI2r2by90°. Phasor summation of the resistive drop I1r1 and the quadrature capacitive drop I1/wC1producesthetotalvoltagedropVC1acrosstheseriescombinationofcapacitorC1andits internal resistance r1. Similarly, phasor summation of the resistive drop I2r2 and thequadrature capacitive drop I2/wC2 produces the total voltage dropVC2 across the seriescombinationofcapacitorC2anditsinternalresistancer2.d1andd2representlossanglesforcapacitorsC1andC2 respectively.PhasorsummationofI1R1andVC1gives the totalvoltagedropV1acrossthebranchAB.Similarly,phasorsummationofI2R2andVC2givesthetotalvoltagedropV2acrossthebranchAC.Finally,phasorsummationofV1andV3(orV2andV4)resultsinthesupplyvoltageV.

Equatingrealandimaginaryparts,wehave

ThemodifiedDeSauty’sbridgecanalsobeusedtoestimatedissipationfactorfortheunknowncapacitorasdescribedbelow:

Dissipationfactorforthecapacitorsaredefinedas

FromEq.(6.29),wehave

UsingEq.(6.31),wegetor,D-D=w(CR-CR)

SubstitutingthevalueofC1fromEq.(6.30),wehave

Thus,dissipation factor foronecapacitorcanbeestimated ifdissipation factorof theothercapacitorisknown.

6.5.2ScheringBridgeSchering bridges are most popularly used these days in industries for measurement ofcapacitance,dissipationfactor,andlossangles.Figure6.12illustratestheconfigurationofaScheringbridgeandcorrespondingphasordiagramunderbalancedcondition.

Figure6.12Scheringbridgeunderbalancedcondition:(a)Configuration(b)Phasordiagram

The unknown capacitor C1 along with its internal resistance r1 (representing loss)placedonthearmABiscomparedwiththestandardloss-lesscapacitorC2placedonthearmAC.ThiscapacitorC2 iseitheranairoragascapacitortomakeit lossfree.R3isanon-inductive resistance placed on arm BD. The bridge is balanced by varying thecapacitorC4andthenon-inductiveresistorR4parallelwithC4,placedonarmCD.

Underbalancedcondition,sincenocurrentflowsthroughthedetector,nodesBandCareatthesamepotential,i.e.,V1=V2andV3=V4.

AsshowninthephasordiagramofFigure6.12(b),V3=I1R3andV4=IRR4beingequal

both in magnitude and phase, they overlap. Current I1 in the arm BD and IR flowingthroughR4arealso in thesamephasewithI1R3and IRR4along thehorizontal line.Theotherresistivedropnamely,I1R1inthearmABisalsoalongthesamehorizontalline.TheresistivecurrentIRthroughR4andthequadraturecapacitivecurrentICthroughC4willaddup to the total current I2 in thebranchCD (and also inACunder balanced condition).AcrossthearmAB,theresistivedropI1r1andthequadraturecapacitivedropI1/wC1willadduptothetotalvoltagedropV1acrossthearm.Atbalance,voltagedropV1acrossarmABwillbesameasthevoltagedropV2=I2/wC2acrossthearmAC.Itcanbeconfirmedfrom the phasor diagram in Figure 6.12(b) that the current I2 has quadrature phaserelationship with the capacitive voltage drop I2/wC2 in the arm AC. Finally, phasorsummationofV1andV3(orV2andV4)resultsinthesupplyvoltageV.

Equatingrealandimaginaryparts,wehavetheunknownquantities:

and

DissipationFactor

Thus,usingScheringbridge,dissipationfactorcanbeobtained in termsof thebridgeparametersatbalancecondition.

6.6 MEASUREMENTOFFREQUENCY

6.6.1Wien’sBridgeWien’sbridgeisprimarilyusedfordeterminationofanunknownfrequency.However,itcan be used for various other applications including capacitance measurement, inharmonicdistortionanalysers,where it isusedasnotchfilter,andalso inaudioandHF

oscillators.

Configuration of a Wien’s bridge for determination of unknown frequency andcorrespondingphasordiagramunderbalancedconditionisshowninFigure6.13.

Figure6.13Wien’sbridgeunderbalancedcondition:(a)Configuration(b)Phasordiagram

Underbalancedcondition,sincenocurrentflowsthroughthedetector,nodesBandCareatthesamepotential,i.e.,V1=V2andV3=V4.

As shown in the phasor diagramof Figure6.13 (b),V3 = I1R3 andV4 = I2R4 beingequalbothinmagnitudeandphase,theyoverlap.CurrentI1inthearmBDandI2flowingthroughR4arealsointhesamephasewithI1R3andI2R4along thehorizontal line.Theotherresistivedrop,namely,I2R2inthearmACisalsoalongthesamehorizontalline.TheresistivevoltagedropIRR2acrossR2andthequadraturecapacitivedropI2/wC2acrossC2willadduptothetotalvoltagedropV2inthearmAC.Underbalancedcondition,voltagedropsacrossarmsABandACareequal,thusV1=V2bothinmagnitudeandphase.ThevoltageV1willbeinthesamephaseasthevoltagedropIRR1acrosstheresistanceR1 inthesamearmAB.TheresistivecurrentIRwillthusbeinthesamephaseasthevoltageV1=IRR1.PhasoradditionoftheresistivecurrentIRandthequadraturecapacitivecurrentIC,whichflowsthroughtheparallelR1C1branch,willadduptothetotalcurrentI1inthearmAB.Finally,phasorsummationofV1andV3(orV2andV4)resultsinthesupplyvoltageV.

Equatingrealandimaginaryparts,weget

C2R1R4=C2R2R3+C1R1R3

and

Inmostbridges,theparametersaresochosenthat,

R1=R2=RandC1=C2=C

Then,fromEq.(6.37),weget

SlidersfortheresistorsR1andR2aremechanicallycoupledtosatisfythecriteriaR1=R2.

Wien’sbridgeisfrequencysensitive.Thus,unlessthesupplyvoltageispurelysinusoidal,achievingbalancemaybetroublesome,sinceharmonicsmaydisturbbalancecondition.Useoffilterswiththenulldetectorinsuchcasesmaysolvetheproblem.

Example6.4 Thefourarmsofabridgeareconnectedasfollows:

ArmAB:AcapacitorC1withanequivalentseriesresistancer1ArmBC:AnoninductiveresistanceR3ArmCD:AnoninductiveresistanceR4ArmDA:AcapacitorC2withanequivalent series resistance r2 in serieswith a

resistanceR2A supply of 500Hz is given between terminals A andC and the detector is connectedbetweennodesBandD.Atbalance,R2=5Ω,R3=1000Ω,R4=3000Ω,C2=0.3μFandr2 = 0.25Ω. Calculate the values of C1 and r1, and also dissipation factor of thecapacitor.

SolutionTheconfigurationcanbeshownas

Example6.5 Thefourarmsofabridgesuppliedfromasinusoidalsourceareconfiguredasfollows:

ArmAB:Aresistanceof100Ωinparallelwithacapacitanceof0.5μF

ArmBC:A200Ωnoninductiveresistance

ArmCD:A800Ωnoninductiveresistance

ArmDA:AresistanceRxinserieswitha1μFcapacitance

DeterminethevalueofRxandthefrequencyatwhichthebridgewillbalance.

SupplyisgivenbetweenterminalsAandCandthedetectorisconnectedbetweennodesBandD.

SolutionTheconfigurationcanbeshownas

The configuration shows that it is a Wien’s bridge. Thus, following Eq. (6.36), thebalanceequationcanbewrittenas

ThefrequencyatwhichbridgeisbalancedisgivenbyEq.(6.37):

6.7 WAGNEREARTHINGDEVICE

A serious problem encountered in sensitive ac bridge circuits is that due to straycapacitances.Straycapacitancesmaybeformedinanacbridgebetweenvariousjunctionpointswithin the bridge configuration and nearest ground (earthed) object. These straycapacitors affect bridge balance in severe ways since these capacitors carry leakagecurrentwhenthebridgeisoperatedwithac,especiallyathighfrequencies.FormationofsuchstraycapacitorsinasimpleacbridgecircuitisschematicallyshowninFigure6.14.

Figure6.14Formationofstraycapacitorsinanacbridge

Onepossiblewayofreducingthiseffectistokeepthedetectoratgroundpotential,sothere will be no ac voltage between it and the ground, and thus no current through Figure 6.14

Formation of stray capacitors in an ac bridge the stray capacitances can leak out.However,directlyconnectingthenulldetectortogroundisnotanoption,sinceitwouldcreate a direct current path for other stray currents. Instead, a special voltage-dividercircuit,calledaWagnergroundorWagnerearth,maybeusedtomaintainthenulldetectoratgroundpotentialwithouthavingtomakeadirectconnectionbetweenthedetectorandground.

TheWagner earth circuit is nothingmore than a voltage divider as shown in Figure6.15.Therearetwoadditional(auxiliary)armsZAandZBinthebridgeconfigurationwithagroundconnectionat their junctionE.TheswitchS isused toconnectoneendof thedetector alternately to the ground point e and the bridge connection point d. The twoimpedancesZA andZBmust bemadeof such components (R,L, orC) so that they arecapableof formingabalancedbridgewith theexistingbridearmpairsZ1–Z2 orZ3–Z4.StraycapacitancesformedbetweenbridgejunctionsandtheearthingpointEareshownasC1,C2,C3andC4.

Figure6.15Wagnerearthingdevice

The bridge is first balanced with the arms Z1–Z2 and Z3–Z4 with the switch at thepositiond. The switch is next thrown to position e and balance is once again attainedbetween armsZ1–Z2 andZ5–Z6. The process is repeated till both bridge configurationsbecomebalanced.Atthispoint,potentialatthepointsb,d,eare thesameandareallatearthpotential.Thus,theWagnerearthingdividerforcesthenulldetectortobeatgroundpotential, without a direct connection between the detector and ground. Under theseconditions, no current can flow through the stray capacitors C2 and C3 since theirterminalsarebothatearthpotential.TheothertwostraycapacitorsC1andC4becomepartof(shuntto)theWagnerarmsZAandZB,andthusgeteliminatedfromtheoriginalbridgenetwork.

The Wagner earthing method gives satisfactory results from the point of view ofeliminating stray capacitance charging effects in ac bridges, but the entire balancingprocessistimeconsumingattimes.

EXERCISE

Objective-typeQuestions1. Abridgecircuitworksatafrequencyof2kHz.Whichof thefollowingcanbeusedasnulldetector insucha

bridge?

(a)Vibrationgalvanometersandtunableamplifiers

(b)Headphonesandtunableamplifiers

(c)Vibrationgalvanometersandheadphones

(d)Alloftheabove

2.Underbalancedconditionofabridgeformeasuringunknownimpedance,ifthedetectorissuddenlytakenout

(a)measuredvalueoftheimpedancewillbelower

(b)measuredvalueoftheimpedancewillbehigher

(c)measuredvalueoftheimpedancewillnotchange

(d)theimpedancecannotbemeasured

3.HarmonicdistortionsinpowersupplydoesnotaffecttheperformanceofMaxwell’sbridgesince

(a)filtersareusedtoremoveharmonics

(b)finalexpressionforunknowninductancecontainonlyfundamentalfrequency

(c)mechanicalresonancefrequencyofnulldetectorsarebeyondtherangeofharmonicfrequencies

(d)finalexpressionforunknowninductanceisindependentoffrequency

4.Maxwell’sbridgecanbeusedformeasurementofinductancewith

(a)highQfactors

(b)verylowQfactors

(c)mediumQfactors

(d)widerangeofQfactorvariations

5.TheadvantageofHay’sbridgeoverMaxwell’sinductance–capacitancebridgeisthat

(a)itsfinalbalanceequationsareindependentoffrequency

(b)itreducescostbynotmakingcapacitororinductorasthevariableparameters

(c)itcanbeusedmeasuringlowQinductors

(d)itcanbeusedmeasuringhighQinductors

6.TheadvantageofAnderson’sbridgeoverMaxwell’sbridgeisthat

(a)itsfinalbalanceequationsareindependentofinductorlosses

(b)itreducescostbynotmakingcapacitororinductorasthevariableparameters

(c)numberofbridgecomponentsrequiredareless

(d)attainingbalanceconditioniseasierandlesstimeconsuming

7.ThemainadvantageofOwen’sbridgeformeasurementofunknowninductanceisthat

(a)ithastwoindependentelementsRandCforachievingbalance

(b)itcanbeusedformeasurementofveryhighQcoils

(c)itisveryinexpensive

(d)itcanbeusedformeasurementofunknowncapacitanceaswell

8.DeSauty’sbridgeisusedformeasurementof

(a)highQinductances

(b)lowQinductances

(c)losslesscapacitors

(d)capacitorswithdielectriclosses

9.Scheringbridgecanbeusedformeasurementof

(a)capacitanceanddissipationfactor

(b)dissipationfactoronly

(c)inductancewithinherentloss

(d)capacitorbutnotdissipationfactor

10.Frequencycanbemeasuredusing

(a)Anderson’sbridge

(b)Maxwell’sbridge

(c)DeSauty’sbridge

(d)Wien’sbridge

Short-answerQuestions1.Derivethegeneralequationsforbalanceinacbridges.Showthatbothmagnitudeandphaseconditionsneedtobe

satisfiedforbalancinganacbridge.

2. Derive the expression for balance inMaxwell’s inductance bridge.Draw the phasor diagram under balancedcondition.

3.ShowthatthefinalbalanceexpressionsareindependentofsupplyfrequencyinaMaxwell’sbridge.Whatistheadvantageinhavingbalanceequationsindependentoffrequency?

4.DiscusstheadvantagesanddisadvantagesofMaxwell’sbridgeformeasurementofunknowninductance.

5. ExplainwhyMaxwell’s inductance–capacitancebridgeissuitableformeasurementof inductorshavingqualityfactorintherange1to10.

6.Explainwiththehelpofphasordiagram,howunknowninductancecanbemeasuredusingOwen’sbridge.

7. Explain howWien’s bridge can be used formeasurement of unknown frequencies.Derive the expression forfrequencyintermsofbridgeparameters.

Long-answerQuestions1. (a) Explainwith thehelpof a phasor diagram,howunknown inductance canbemeasuredusingMaxwell’s

inductance–capacitancebridge.

(b)Thefollowingdatarelatetoabasicacbridge:

2.DescribetheworkingofHay’sbridgeformeasurementofinductance.Derivetheequationsforbalanceanddrawthe phasor diagram under balanced condition. Explain how this bridge is suitable formeasurement of highQchokes?

3. Derive equations for balance for anAnderson’s bridge.Draw its phasor diagramunder balance.What are itsadvantagesanddisadvantages?

4. Describe howunknowncapacitors canbemeasuredusingDeSauty’s bridge.What are the limitations of thisbridgeandhowtheycanbeovercomebyusingamodifiedDeSauty’sbridge?Drawrelevantphasordiagrams

5.DescribetheworkingofaScheringbridgeformeasurementofcapacitanceanddissipationfactor.Deriverelevantequationsanddrawphasordiagramunderbalancedcondition.

6.InanAnderson’sbridgeformeasurementofinductance,thearmABconsistsofanunknownimpedancewithLandR, thearmBC contains a variable resistor, fixed resistances of 500Ω each in armsCD andDA, a knownvariableresistanceinthearmDE,andacapacitoroffixedcapacitance2μFinthearmCE.Theacsupplyof200Hz isconnectedacrossAandC, and thedetector is connectedbetweenBandE. If balance is obtainedwith aresistance of 300 Ω in the armDE and a resistance of 600 Ω in the arm BC, calculate values of unknownimpedanceLandR.Derivetherelevantequationsforbalanceanddrawthephasordiagram.

7.ThefourarmsofaMaxwell’sinductance–capacitancebridgeatbalanceareArmAB:AchokecoilL1withanequivalentseriesresistanceR1ArmBC:Anon-inductiveresistanceof800ΩArmCD:Amicacapacitorof0.3μFinparallelwithanoninductive resistanceof800ΩArmDA :Anon-inductive resistance800ΩSupply isgivenbetweenterminalsAandCandthedetectorisconnectedbetweennodesBandD.Derivetheequationsforbalance

of thebridgeandhencedeterminevaluesofL1andR1.Draw thephasordiagramof thebridgeunderbalancedcondition.

8.ThefourarmsofaHay’sbridgeusedformeasurementofunknowninductanceisconfiguredasfollows:ArmAB:AchokecoilofunknownimpedanceArmBC:Anon-inductiveresistanceof1200ΩArmCD:Anon-inductiveresistanceof900Ωinserieswithastandardcapacitorof0.4μFArmDA:Anoninductiveresistance18000ΩIfasupplyof300Vat50HzisgivenbetweenterminalsAandCandthedetectorisconnectedbetweennodesBandD,determinetheinductanceandinherentresistanceoftheunknownchokecoil.Derivetheconditionsforbalanceanddrawthephasordiagramunderbalancedcondition.

9. AcapacitorbusingformsthearmABofaScheringbridgeandastandardcapacitorof400μFcapacitanceandnegligible loss, form thearmAD.ArmBC consists of a non-inductive resistance of 200Ω.When the detectorconnectedbetweennodesBandDshowsnodeflection,thearmCDhasaresistanceof82.4Ωinparallelwithacapacitanceof0.124μF.Thesupplyfrequencyis50Hz.Calculatethecapacitanceanddielectriclossangleofthecapacitor.Derivetheequationsforbalanceanddrawtherelevantphasordiagramatbalancedstate.

10.(a)Anacbridgeisconfiguredasfollows:

ArmAB:Aresistanceof600Ωinparallelwithacapacitanceof0.3μF

ArmBC:Anunknownnon-inductiveresistance

ArmCD:Anoninductiveresistanceof1000Ω

ArmDA:Aresistanceof400Ωinserieswithacapacitanceof0.1μF

IfasupplyisgivenbetweenterminalsAandCandthedetectorisconnectedbetweennodesBandD,findtheresistancerequiredinthearmBCandalsothesupplyfrequencyforthebridgetobebalanced.

(b)ExplainhowWien’sbridgecanbeusedformeasurementofunknownfrequency.Drawthephasordiagramunderbalancedconditionandderivetheexpressionforbalance.

7.1 INTRODUCTION

Measurement of electric power is as essential in industry as in commercial or evendomestic applications. Prior estimation and subsequent measurements of instantaneousand peak power demands of any installation are mandatory for design, operation andmaintenanceoftheelectricpowersupplynetworkfeedingit.Whereasanunder-estimationofpowerdemandmayleadtoblowingoutofpowersupplysideaccessories,ontheotherhand, over-estimation can end up with over-design and additional cost of installation.Knowledgeabout accurateestimation, calculationandmeasurementof electricpower isthus of primary concern for designers of new installations. In this chapter, the mostpopularpowermeasurementmethodsandinstrumentsindcandaccircuitsareillustrated.

7.2 POWERMEASUREMENTINdcCIRCUITS

Electricpower(P)consumedbya load(R)suppliedfromadcpowersupply(VS) is theproductofthevoltageacrosstheload(VR)andthecurrentflowingthroughtheload(IR):

Thus,powermeasurementinadccircuitcanbecarriedoutusingavoltmeter(V)andanammeter(A)usinganyoneofthearrangementsshowninFigure7.1.

Figure7.1Twoarrangementsforpowermeasurementindccircuits

OnethingshouldbekeptinmindwhileusinganyofthetwomeasuringarrangementsshowninFigure7.1;thatboththevoltmeterandtheammeterrequirespowerfortheirownoperations. In the arrangementofFigure7.1(a), the voltmeter is connected between theloadand theammeter.Theammeter thus, in thiscasemeasures thecurrent flowing intothevoltmeter,inadditiontothecurrentflowingintotheload.

Thus,Powerindicated=Powerconsumed+Powerlossinvoltmeter

InthearrangementofFigure7.1(b),thevoltmetermeasuresthevoltagedropacrosstheammeterinadditiontothatdroppingacrosstheload.

Thus,Powerindicated=Powerconsumed+PowerlossinAmmeter

Thus,botharrangements indicate theadditionalpowerabsorbedbytheinstruments inaddition to indicating the true power consumed by the load only. The correspondingmeasurementerrorsaregenerallyreferredtoasinsertionerrors.

Ideally,intheory,ifweconsidervoltmeterstohaveinfiniteinternalimpedanceandammeterstohavezerointernalimpedance,thenfrom(7.3)and(7.5)onecanobservethatthepowerconsumedbytherespectiveinstrumentsgodowntozero.Thus,inidealcases,boththetwoarrangementscangivecorrectindicationofthepowerconsumedbytheload.Underpracticalconditions,thevalueofpowerlossininstrumentsisquitesmall,ifnottotallyzero,ascomparedwiththeloadpower,andtherefore,theerrorintroducedonthisaccountissmall.

Example7.1 Two incandescent lampswith80Ωand120Ωresistancesare connected in series with a 200 V dc source. Find theerrors inmeasurementofpower in the80Ω lampusingavoltmeter with internal resistance of 100 kΩ and anammeterwith internal resistance of 0.1mΩ,when (a) thevoltmeterisconnectednearertothelampthantheammeter,and(b)whentheammeterisconnectednearertothelampthanthevoltmeter

SolutionAssumingboththeinstrumentstobeideal,i.e.,thevoltmeterwithinfiniteinternalimpedance and ammeter with zero internal impedance, the current through the seriescircuitshouldbe

=200/(80+120)=1A

Figure7.2ActualconnectionsforExample7.1(a)

Hence,truepowerconsumedbythe80Ωlampwouldhavebeen

=12X80=80Ω

However, considering the internal resistance of the ammeter and voltmeter, theequivalentcircuitwilllooklikeFigure7.3.

Figure7.3EquivalentcircuitforExample7.1(a)

Supplycurrent(ammeterreading)

Figure7.4ActualconnectionforExample7.1(b)

Figure7.5EquivalentcircuitforExample7.1(a)

Supplycurrent

Thus,wecanhavethefollowinganalysis:

Power in dc circuits can also be measured by wattmeter. Wattmeter can give directindication of power and there is no need tomultiply two readings as in the casewhenammeterandvoltmeterisused.

The type of wattmeter most commonly used for such power measurement is thedynamometer. It is built by (1) two fixed coils, connected in series and positionedcoaxiallywithspacebetweenthem,and(2)amovingcoil,placedbetweenthefixedcoilsandfittedwithapointer.Suchaconstructionforadynamometer-typewattmeterisshowninFigure7.6.

It can be shown that the torque produced in the dynamometer is proportional to theproductofthecurrentflowingthroughthefixedcoilstimesthatthroughthemovingcoil.

The fixed coils, generally referred to as current coils, carry the load current while themovingcoil,generallyreferredtoasvoltagecoil,carriesacurrentthatisproportional,viathemultiplierresistorRV,tothevoltageacrosstheloadresistorR.Asaconsequence,thedeflectionofthemovingcoilisproportionaltothepowerconsumedbytheload.

AtypicalconnectionofsuchawattmeterforpowermeasurementindccircuitisshowninFigure7.7.

Figure7.6Basicconstrucionofdynamometer-typewattmeter

Insuchaconnectionofthewattmeter,theinsertionerror,asintheperviouscasewithammeter and voltmeter, still exists. Relative β positioning of the current coil and thevoltage coil with respect to load, introduce similarVS errors inmeasurement of actualpower. In particular, by connecting the voltage coil betweenA andC (Figure 7.7), thecurrentcoilscarrythesurpluscurrentflowingthroughthevoltagecoil.Ontheotherhand,by connecting themoving coil betweenB andC, this current error canbe avoided, butnowthevoltagecoilmeasuresthesurplusvoltagedropacrossthecurrentcoils.

Figure7.7Connectionofdynamometer-typewattmeterforpowermeasurementindccircuit

7.3 POWERMEASUREMENTINacCIRCUITS

Inalternatingcurrentcircuits,theinstantaneouspowervariescontinuouslyasthevoltageandcurrentvarieswhilegoingthroughacycle.Insuchacase,thepoweratanyinstantisgivenby

where, p(t), v(t), and i(t) are values of instantaneous power, voltage, and current

respectively.

Thus, if both voltage and current can be assumed to be sinusoidal, with the currentlaggingthevoltagebyphase-angleφ,then

where,VmandImarepeakvaluesofvoltageandcurrentrespectively,andwistheangularfrequency.

Theinstantaneouspowerpisthereforegivenby

Averagevalueofpoweroveracompletecycleinsuchacasewillbe

where,VandIarermsvaluesofvoltageandcurrentrespectivelyandcosjispowerfactoroftheload.

Involvement of the power-factor term cos j in the expression for power in ac circuitindicatesthatacpowercannotbemeasuredsimplybyconnectingapairofammeterandvoltmeter.Awattmeter,within-builtfacilityfortakingintoaccountthepowerfactor,canonlybeusedformeasurementofpowerinaccircuits.

Figure7.8 plots thewaveformsof instantaneous powerp(t), voltagev(t), and currenti(t).

Figure7.8Plotofthewaveformsofinstantaneouspowervoltageandcurrentinaccircuit

Readers may find interesting to note in Figure 7.8 that though voltage and currentwaveformshavezeroaveragevalueoveracompletecycle, the instantaneouspowerhasoffsetabovezerohavingnon-zeroaveragevalue.

7.4 ELECTRODYNAMOMETER-TYPEWATTMETER

An electrodynamometer-type wattmeter is similar in design and construction with theanalogelectrodynamometer-typeammeterandvoltmeterdescribedinChapter2.

7.4.1ConstructionofElectrodynamometer-typeWattmeterSchematicdiagramdisplayingthebasicconstructionalfeaturesofaelectrodynamometer-typewattmeterisshowninFigure7.9.

Figure7.9Schematicofelectrodynamometer-typewattmeter

InternalviewofsuchanarrangementisshowninthephotographofFigure7.10.

Figure7.10nternalphotographofelectrodynamometer-typewattmeter:(1)Fixed(current)coil(2)Moving(potential)coil

1.FixedCoilSystemSuchaninstrumenthastwocoilsconnectedindifferentwaystothesamecircuitofwhichpoweristobemeasured.Thefixedcoilsorthefieldcoilsareconnectedinserieswiththeloadsoastocarrythesamecurrentastheload.Thefixedcoilsarehence,termedastheCurrentCoils(CC)ofthewattmeter.Themainmagneticfieldisproducedbythesefixedcoils.Thiscoil isdivided in twosections soas toprovidemoreuniformmagnetic fieldnearthecentreandtoallowplacementoftheinstrumentmovingshaft.

Fixed coils are usually wound with thick wires for carrying the main load currentthroughthem.Windingsofthefixedcoilisnormallymadeofstrandedconductorsrunningtogether but, insulated from each other. All the strands are brought out to an externalcommutating terminator so that a number of current ranges of the instrument may beobtainedbygroupingthemallinseries,allinparallel,orinaseries–parallelcombination.Such strandingof the fixedcoils also reducesEddy-current loss in the conductors.Stillhighercurrentorvoltageranges,however,canbeaccommodatedonlythroughtheuseofinstrumenttransformers.

Fixedcoilsaremountedrigidlywiththecoilsupportingstructurestopreventanysmallmovement whatsoever and resulting field distortions. Mounting supports are made ofceramic,andnotmetal,soasnottodisturbthemagneticfielddistribution.

2.MovingCoilSystemThemoving coil that is connected across the load carries a current proportional to thevoltage.Sincethemovingcoilcarriesacurrentproportionaltothevoltage,itiscalledthevoltagecoilorthepressurecoilorsimplyPCofthewattmeter.Themovingcoilisentirelyembracedbythepairoffixedcoils.Ahighvaluenon-inductiveresistance isconnectedinserieswiththevoltagecoiltorestrictthecurrentthroughittoasmallvalue,andalsotoensurethatvoltagecoilcurrentremainsasfaraspossibleinphasewiththeloadvoltage.

Themovingcoil,madeoffinewires,iswoundeitherasaself-sustainingair-coredcoil,orelsewoundonanonmetallicformer.Ametallicformer,otherwisewouldinduceEddy-currentsinthemunderinfluenceofthealternatingfield.

3.MovementandRestoringSystem

Themoving,orvoltagecoilalongwiththepointerismountedonanaluminumspindleincase jewelbearingsareused to support the spindle.Forhigher sensitivity requirements,themoving coilmaybe suspended froma torsionheadby ametallic suspensionwhichserves as a lead to the coil. Inother constructions, the coilmaybe suspendedbya silkfibretogetherwithaspiralspringwhichgivestherequiredtorsion.Thephosphor-bronzesprings are also used to lead current into and out of themoving coil. In any case, thetorsion head with suspension, or the spring, also serves the purpose of providing therestoringtorquetobringthepointerbacktoitsinitialpositiononcemeasurementisover.

Themoving,orvoltagecoilcurrentmustbelimitedtomuchlowvalueskeepinginmindthedesignrequirementsofthemovementsystem.Currentisleadtoandoutofthemovingcoilthroughtwospiralsprings.Currentvalueinthemovingcoilisthustobelimitedtovaluesthatcanbesafelycarriedbythespringswithoutappreciableheatingbeingcaused.

4.DampingSystemDampinginsuchinstrumentsmaybeprovidedbysmallaluminumvanesattachedatthebottom of the spindle. These vanes are made to move inside enclosed air chambers,therebycreatingthedampingtorque.Inothercases,themovingcoilitselfcanbestitchedonathinsheetofmica,whichactsasthedampingvanewhilemovements.Eddy-currentdamping,however,cannotbeusedwiththeseinstruments.Thisisduetothefactthatanymetallic element to be used for Eddy-current damping will interfere and distort theotherwise weak operating magnetic field. Moreover, introduction of any externalpermanent magnet for the purpose of Eddy-current damping will severely hamper theoperatingmagneticfield.

5.ShieldingSystemThe operating field produced by the fixed coils, is comparatively lower inelectrodynamometer-typeinstrumentsascomparedtoother typeof instruments.Insomecases, even the earth’s magnetic field can pollute themeasurement readings. It is thusessential to shield the electrodynamometer-type instruments from effects of externalmagnetic fields. Enclosures of such instruments are thus made of alloys with highpermeabilitytorestrictpenetrationofexternalstraymagneticfieldsintotheinstrument.

7.4.2OperationofElectrodynamometer-typeWattmeterTheschematicoperationalcircuitofanelectrodynamometer-typewattmeterbeingusedformeasurementofpowerinacircuitisshowninFigure7.11.

Figure7.11Operationalcircuitofelectrodynamometer-typewattmeter

V =voltagetobemeasured(rms)

I =currenttobemeasured(rms)

iP =voltage(pressure)coilinstantaneouscurrent

iC =currentcoilinstantaneouscurrent

RV =externalresistanceconnectedwithpressurecoil

RP =resistanceofpressurecoilcircuit(PCresistance+RV)

M =mutualinductancebetweencurrentcoilandpressurecoil

θ =angleofdeflectionofthemovingsystem

ω =angularfrequencyofsupplyinradianspersecond

φ =phase-anglelagofcurrentIwithrespecttovoltageV

As described in Chapter 2, the instantaneous torque of the electrodynamometerwattmetershowninFigure7.11isgivenby

Instantaneousvalueofvoltageacrossthepressure-coilcircuitis

Ifthepressurecoilresistancecanbeassumedtobeveryhigh,thewholepressurecoilcanbeassumedtobebehavinglikearesistanceonly.Thecurrent iP inthepressurecoilthus,canbeassumedtoinphasewiththevoltagevP,anditsinstantaneousvalueis

whereIP=V/RPisthermsvalueofcurrentinpressurecoil.

Assumingthatthepressure-coilresistanceissufficientlyhightopreventbranchingoutofanyportionofthesupplycurrenttowardsthepressurecoil,thecurrentcoilcurrentcanbewrittenas

Thus,instantaneoustorquefrom(7.9)canbewrittenas

Presence of the term containing 2wt, indicates the instantaneous torque as shown in(7.10)variesattwicethefrequencyofvoltageandcurrent.

Averagedeflectingtorqueoveracompletecycleis

With a spring constantK, the controlling torque provided by the spring for a finalsteady-statedeflectionofθisgivenby

TC=Kθ

Under steady-state condition, the average deflecting torque will be balanced by thecontrollingtorqueprovidedbythespring.Thus,atbalancedconditionTC=Td

where,PisthepowertobemeasuredandK1=1/KRPisaconstant.

Steady-state deflection θ is thus found to be an indication of the power P to bemeasured.

7.4.3ShapeofscaleinElectrodynamometer-typeWattmeterSteady-statedeflectionθcanbemadeproportionaltothepowerPtobemeasured,i.e.,thedeflection will vary linearly with variation in power if the rate of change of mutualinductance is constant over the range of deflection. In other words, the scale ofmeasurementwillbeuniformifthemutualinductancebetweenthefixedandmovingcoilsvaries linearly with angle of deflection. Such a variation in mutual inductance can beachievedby careful designof the instrument.Figure7.12 shows the expected nature of

variationofmutual inductancebetween fixedandmovingcoilswith respect toangleofdeflection.

Figure7.12Variationofmutualinductancewithdeflection

By a suitable design, themutual inductance between fixed andmoving coils can bemade tovary linearlywithdeflectionangleovera rangeof40° to50°oneither sideofzeromutualinductanceposition,asshowninFigure7.12. If thepositionofzeromutualinductance can be kept at themid-scale, then the scale can be graduated to be uniformover80°to100°,whichcoversalmostentirerangeofthescale.

7.4.4ErrorsinElectrodynamometer-typeWattmeter1.ErrorduetoPressure-CoilInductanceIt was assumed during the discussions so far that the pressure coil circuit is purelyresistive. In reality, however, the pressure coil will have certain inductance along withresistance.Thiswillintroduceerrorsinmeasurementunlessnecessarycompensationsaretakencareof.Tohaveanestimateofsucherror,letusconsiderthefollowing:

V =voltageappliedtothepressurecoilcircuit(rms)

I =currentinthecurrentcoilcircuit(rms)

IP =currentinthevoltage(pressure)coilcircuit(rms)

rP =resistanceofpressurecoilonly

L =inductanceofpressurecoil

RV =externalresistanceconnectedwithpressurecoil

RP =resistanceofpressurecoilcircuit(PCresistance+RV)

ZP =impedanceofpressurecoilcircuit

M =mutualinductancebetweencurrentcoilandpressurecoil

ω =angularfrequencyofsupplyinradianpersecond

φ =phase-anglelagofcurrentIwithrespecttovoltageV

Due to inherent inductanceof thepressure coil circuit, the current andvoltage in thepressurecoilwillnolongerbeinphase,ratherthecurrentthroughthepressurecoilwilllagthevoltageacrossitbyacertainanglegivenby

AscanbeseenfromFigure7.13,currentthroughthepressurecoillagsvoltageacrossitbyaphase-anglewhichislessthanthatbetweenthecurrentcoilcurrentandthepressurecoilvoltage.

Figure7.13Wattmeterphasordiagramwithpressurecoilinductance

Insuchacase,phase-angledifferencebetweenthewithpressurecoil inductancepressurecoilcurrentandcurrentcoilcurrentis

Followingfrom(7.11),thewattmeterdeflectionwillbe

RelatingtoRP=ZPcosαinthepressurecoilcircuit,thewattmeterdeflectioncanbere-writtenasVIdM

Intheabsenceofinductance,ZP=RPandα=0;wattmeterinthatcasewillreadtruepower,givenby,

Takingtheratiooftruepowerindicationtoactualwattmeterreading,weget

TruepowerindicationcanthusbeobtainedfromtheactualwattmeterreadingusingthecorrectionfactorCFas

Truepowerindication=CFXActualwattmeterreading

Thus,forlaggingpowerfactorloads,s

Theaboverelations,alongwithFigure7.13indicatethatunderlaggingpowerfactorloads,unlessspecialprecautionsaretaken,actualwattmeterreadingwilltendtodisplayhighervaluesascomparedtotruepowerconsumed.

For leading power factor loads, however, the wattmeter phasor diagram will be asshowninFigure7.14.

Figure7.14Wattmeterphasordiagramwithpressurecoilinductanceduringleadingload

Forleadingpowerfactorloads,s

Theaboverelations,alongwithFigure7.13indicatethatunderleadingpowerfactorloads,unlessspecialprecautionsaretaken,actualwattmeterreadingwilltendtodisplayhighervaluesascomparedtotruepowerconsumed.

2.CompensationforPressureCoilInductanceAwattmetercanbecompensatedforpressurecoilinductancebyconnectingapresetvalueofcapacitanceacrossacertainportionoftheexternalresistanceconnectedinserieswiththepressurecoil,asshowninFigure7.15.

Figure7.15Compensationforpressurecoilinductance

Thetotalimpedanceofthecircuitinsuchacasecanbewrittenas

To make the entire circuit behave as purely resistive, if we can design the circuitparametersinsuchacasethatforpowerfrequencies

w2C2r2<<1

Thenwecanre-writethetotalimpedanceofthepressurecoilas

ZP=(rp+RV–r)+jwL+r–jwCr2=rP+RV+jw(L–Cr2)

Ifbyproperdesign,wecanmakeL=Cr2

Then,impedance=rp+RV=RPThuserrorintroducedduepressurecoilinductancecanbesubstantiallyeliminated.

3.ErrorduetoPressureCoilCapacitanceThe voltage, or pressure coil circuit may have inherent capacitance in addition toinductance.Thiscapacitanceeffectismainlyduetointer-turncapacitanceofthewindingand external series resistance. The effect of stray capacitance of the pressure coil isoppositetothatduetoinductance.Therefore,thewattmeterreadslowonlaggingpowerfactors andhighon leadingpower factors of the load.Actual readingof thewattmeter,thus,onceagainneeds tobecorrectedby thecorrespondingcorrection factors toobtainthe true reading. The effect of capacitance (aswell as inductance) varieswith variablefrequencyofthesupply.

4.ErrorduetoConnectionTherearetwoalternatemethodsofconnectionofwattmetertothecircuitformeasurementofpower.TheseareshowninFigure7.16.Ineitheroftheseconnectionmodes,errorsareintroducedinmeasurementduepowerlossesinpressurecoilandcurrentcoil.

Figure7.16Wattmeterconnections

In the connectionofFigure7.16(a), the pressure coil is connected across the supply,thuspressurecoilmeasures thevoltageacross the load,plus thevoltagedropacross thecurrentcoil.Wattmeterreadinginthiscasewillthusincludepowerlossincurrentcoilaswell,alongwithpowerconsumedbytheload.

Wattmeterreading=Powerconsumedbyload+PowerlossinCC

In the connection of Figure7.16(b), the current coil is connected to the supply side;therefore,itcarriesloadcurrentplusthepressurecoilcurrent.Hence,wattmeterreadinginthiscaseincludes,alongwithpowerconsumedbytheload,powerlossinthepressurecoilaswell.

Wattmeterreading=Powerconsumedbyload+PowerlossinPC

Inthecasewhenloadcurrentissmall,powerlossinthecurrentcoilissmallandhencetheconnectionofFigure7.16(a)willintroducecomparativelylesserrorinmeasurement.Ontheotherhand,whenloadcurrentislarge,currentbranchingthroughthepressurecoilisrelativelysmallanderrorinmeasurementwillbelessifconnectionofFigure7.16(b)isused.

ErrorsduetobranchingoutofcurrentthroughthepressurecoilcanbeminimisedbytheuseofcompensatingcoilasschematicallyshowninFigure7.17.

Figure7.17Schematicconnectiondiagramofcompensatedwattmeter

Inthecompensatedconnection,thecurrentcoilconsistsoftwowindings,eachwindinghavingthesamenumberofturns.Thetwowindingsaremadeasfaraspossibleidenticalandcoincident.Oneofthetwowindings(CC)ismadeofheavywirethatcarriestheloadcurrentplusthecurrentforthepressurecoil.Theotherwinding(compensatingcoil–CoC)which is connected in serieswith the pressure coil, uses thinwire and carries only thecurrent to the pressure coil. This current in the compensating coil is, however, in adirectionoppositetothecurrentinmaincurrentcoil,creatingafluxthatopposesthemainflux.Theresultantmagneticfieldis thusduetothecurrentcoilonly,effectsofpressurecoil current on the current coil fluxmutually nullifying each other. Thus, error due topressure coil current flowing in the current coil in cancelled out and the wattmeterindicatescorrectpower.

5.Eddy-currentErrorsUnlessadequateprecautionsareadopted,Eddy-currentsmaybeinducedinmetallicpartsoftheinstrumentandevenwithinthethicknessoftheconductorsbyalternatingmagneticfield of the current coil. TheseEddy-currents produce spuriousmagnetic fields of theirownanddistortthemagnitudeandphaseofthemaincurrentcoilmagneticfield,therebyintroducingerrorinmeasurementofpower.

ErrorcausedbyEddy-currentsisnoteasytoestimate,andmaybecomeobjectionableifmetalpartsarenotcarefullyavoidedfromnearthecurrentcoil.Infact,solidmetalincoilsupportsandstructuralpartshouldbekepttoaminimumasfaraspracticable.Anymetalthat is used is kept away and is selected to have high resistivity so as to reduceEddy-currentsinducedinit.StrandedconductorsarerecommendedforthecurrentcoiltorestrictgenerationofEddy-currentwithinthethicknessoftheconductor.

6.StrayMagneticFieldErrorsTheoperatingfieldinelectrodynamometer-typeinstrumentsbeingweak,specialcaremustbe taken to protect these instruments from external magnetic fields. Hence, theseinstruments should be shielded against effects of straymagnetic fields. Laminated ironshields are used in portable laboratory instruments,while steel casings are provided asshields in switchboard mounted wattmeter. Precision wattmeters, however, are notprovidedwithmetalsshields,forthatwillintroduceerrorsduetoEddy-current,andalsosome dc error due to permanent magnetization of the metal shield under influence ofexternal magnetic field. Such wattmeters are manufactured to have astatic system asshowninFigure

Figure7.18Astaticsystemsforelectrodynamometerwattmeter

Astaticelectrodynamometerinstrumentsareconstructedwithtwosimilarsetsoffixedandmovingcoilsmountedonthesameshaft.Thepairoffixedcoilsissoconnectedthattheir magnetic fields are in opposition. Similarly, the pair of moving coils is alsoconnected to producemagnetic fields in opposite directions. Thismakes the deflectingtorqueactingonthetwomovingcoilstobeinthesamedirection.Deflectionofthepointeristhusduetoadditiveactionofthetwomovingcoils.However,sincethetwofieldsinthetwo pairs of fixed andmoving coils are in opposition, any external uniform field willaffectthetwosetsofpairsdifferently.Theexternalfieldwillreducethefieldinonecoilandwillenhancethefieldintheothercoilbyidenticalamount.Therefore,thedeflectingtorqueproducedbyonecoilisincreasedandthatbytheothercoilisreducedbyan]equalamount.Thismakesthenettorqueonaccountoftheexternalmagneticfieldtozero.

7.ErrorCausedbyVibrationoftheMovingSystemTheinstantaneoustorqueonthemovingsystemvariescyclicallyattwicethefrequencyofthevoltageandcurrent(7.10).Ifanypartofthemovingsystem,suchasthespringorthepointerhasnaturalfrequencyclosetothatoftorquepulsation,thenaccidentalresonancemay take place. In such a case, the moving system may vibrate with considerableamplitude.Thesevibrationsmayposeproblemswhilenoting thepointerpositionon thescale.Theseerrorsduetovibrationsmaybeavoidedbydesigningthemovingelementstohave natural frequencies much further away from twice the frequency of the supplyvoltage.

8.TemperatureErrorsTemperature changesmay affect accuracy ofwattmeter by altering the coil resistances.Temperaturemychangeduetochangeinroomtemperatureorevenduetoheatingeffectsinconductorswithflowofcurrent.Changeintemperaturealsoaffectsthespringstiffness,

thereby introducingerror in thedeflectionprocess.High-precision instrumentsare fittedwithtemperaturecompensatingresistorsthattendtoneutralisetheeffectsoftemperaturevariation.

Example7.2 An electrodynamometer-type wattmeter has a current coilwith a resistance of 0.1 Ω and a pressure coil withresistanceof6.5kΩ.Calculatethepercentageerrorswhilethemeter is connectedas (i) current coil to the load side,and(ii)pressurecoiltotheloadside.Theloadisspecifiedas(a)12Aat250Vwithunitypowerfactor,and(b)12Aat25Vwith0.4laggingpowerfactor.

Solution

(a)Loadspecifiedas12Aat250Vwithunitypowerfactor

(i)Currentcoil(CC)onloadside

Truepower=VIcosj

=250X12X1

=3000Ω

PowerlostinCC=I2XrC(whererCistheresistanceofCC)

=122X0.1

=14.4Ω

Thewattmeterwillthusreadtotalpower=3000+14.4=3014.4Ω

Hence,errorinmeasurement

(ii)Pressurecoil(CC)onloadside

Truepower=VIcosj

=250X12X1

=3000Ω

PowerlostinPC=V2/RP(whereRPistheresistanceofPC)

=2502/6500

=9.6W

Thewattmeterwillthusreadtotalpower=3000+9.6=3009.6Ω

Hence,errorinmeasurement

(b)Loadspecifiedas12Aat250Vwith0.4powerfactor

(i)Currentcoil(CC)onloadside

Truepower=VIcosj

=250X12X0.4

=1200Ω

PowerlostinCC=I2XrC(whererCistheresistanceofCC)

=122X0.1

=14.4W

Thewattmeterwillthusreadtotalpower=1200+14.4=1214.4Ω

Hence,errorinmeasurement

(ii)Pressurecoil(CC)onloadside

Truepower=1200Ω

PowerlostinPC=V2/RP(whereRPistheresistanceofPC)

=2502/6500

=9.6W

Thewattmeterwillthusreadtotalpower=1200+9.6=1209.6Ω

Hence,errorinmeasurement

An electrodynamometer-type wattmeter is used for power

Example7.3 measurementofaloadat100Vand9Aatapowerfactorof0.1lagging.Thepressurecoilcircuithasaresistanceof3000Ωandinductanceof30mH.Calculatethepercentageerror in wattmeter reading when the pressure coil isconnected(a)ontheloadside,and(b)onthesupplyside.The current coil has a resistance of 0.1Ω and negligibleinductance.Assume50Hzsupplyfrequency.

Solution

(a)Loadspecifiedas9Aat100Vwith0.1powerfactor:

Truepower=VIcosφ

=100X9X0.1

=90W

Phase-angleφ=cos−1(0.1)=1.471rad

Given,resistanceofpressurecoilcircuit=3000Ω

andreactanceofpressurecoilcircuit=2pX50X30X10-3=9.42Ω

∴phase-angleofthepressurecoilcircuit

(i)Pressurecoilconnectedontheloadside

Following the expression (7.15) for actual power indication of the wattmeter in thepresenceofpressurecoilinductance,theactualwattmeterreadingisgivenby

(ii)Currentcoilconnectedontheloadside

Truepowerremains=90W

TheCCgets in serieswith the load, andpower loss inCCgets included in the totalpower.

Totalpower=90+I2XrC=90+92X0.1=98.1W

LoadimpedanceZ=V/I=100/9=11.1Ω

LoadresistanceRL=ZXcosφ=11.1X0.1=1.11Ω

LoadreactanceXL=ZXsinφ=11.1X0.995=11.05Ω

TotalloadresistanceincludingCCresistance

RL¢=1.11+0.1=11.21Ω

SinceCChasnoinductance,totalloadreactanceincludingCCreactance=XL¢=11.05+0=11.05Ω

TotalloadpowerfactorincludingCC

Largererrorincase(ii)ascomparedtocase(i)confirmsthefactthatlowpowerfactorpowermeasurementsshouldnothavetheCCofwattmeterconnectedtotheloadside.

7.5 INDUCTION-TYPEWATTMETER

Induction-typewattmetersworkinsimilarprinciplesasforinductiontypeammetersandvoltmeters previously discussed in Chapter 2. Induction-type wattmeters, however,followingtheverybasicprinciplesofmutualinduction,canonlybeusedformeasurementofacpower,incontrasttoelectrodynamometertypewattmetersthatcanbeusedforpowermeasurements in both ac anddc circuits. Induction typewattmeters, in contradiction toelectrodynamometer-type wattmeters, can be used only with circuits having relativelysteadyvaluesoffrequencyandvoltage.

7.5.1ConstructionofInduction-typeWattmeterSchematic diagram displaying the basic constructional features of an induction-typewattmeterisshowninFigure7.19.

Figure7.19Constructionaldetailsofinduction-typewattmeter

Induction-type wattmeters have two laminated iron-core electromagnets. One of theelectromagnetsisexcitedbytheloadcurrent,andtheotherbyacurrentproportionaltothevoltageofthecircuitinwhichthepoweristobemeasured.TheuppermagnetinFigure7.19,whichisconnectedacrossthevoltagetobemeasured,isnamedastheshuntmagnet,whereastheotherelectromagnetconnectedinserieswiththeloadtocarryloadcurrentiscalled the seriesmagnet.A thin aluminumdisc,mounted in the space between the twomagnets is acted upon by a combined effect of fluxes coming out of these twoelectromagnets. In ac circuits, interaction of these changing fluxes will induce Eddy-currentwithinthealuminumdisc.

Thetwovoltagecoils,connectedinseries,arewoundinsuchawaythatbothofthemsendfluxthroughthecentrallimb.Coppershadingbandsfittedonthecentrallimboftheshuntmagnetmakesthefluxcomingoutofthemagnetlagbehindtheappliedvoltageby90°.

Theseriesmagnethousestwosmallcurrentcoilsinseries.Thesearewoundinawaythatthefluxestheycreatewithinthecoreofthemagnetareinthesamedirection.

7.5.2OperationofInduction-typeWattmeterA simplified phasor diagram for describing the theory of operation of induction-typewattmeterisshowninFigure7.20.

Figure7.20Phasordiagramforinduction-typewattmeter

V = voltagetobemeasured

I = currenttobemeasured

φ = phase-anglelagofcurrentIwithrespecttovoltageV

φsh = fluxoftheshuntmagnet

φse = fluxoftheseriesmagnet

Esh = eddyemfinducedinthediscbythefluxjshofshuntmagnet

Ish = eddy-current fl owing in the disc due to and in phase with Esh (neglectinginductanceoftheEddy-currentpath)

Ese = eddyemfinducedinthediscbythefluxjseofseriesmagnet

Ise = eddy-current fl owing in the disc due to and in phase with Ese (neglectinginductanceoftheEddy-currentpath)

Z = impedanceoftheEddy-currentpath

ω = angularfrequencyofsupplyinradianspersecond

Td = averagetorqueactingonthedisc

Theshuntmagnetfluxφshismadetolagbehindtheappliedvoltage(V)by90°.Thisisachievedbytheuseofcoppershadingrings.Ontheotherhand,theseriesmagnetfluxφseisinthesamephaseastheloadcurrent(I)throughit.

Continuingfromtheoriesofinduction-typeinstrumentsinChapter2,theinstantaneoustorqueactingonthealuminumdiscisproportionalto(φsh·ise-φse·ish).

Let,instantaneousvaluetheappliedvoltageis

v=Vmsinwt

Then,theinstantaneouscurrentisgivenby

i=Imsin(wt-j)

Theshuntmagnetfluxgeneratedis

wherek¢isaconstantandtheminus(-)signindicatingthefactthefluxφsh lagsbehindthevoltageby90°.

Theseriesmagnetfluxgeneratedis

wherekisanotherconstant.

Theeddyemfinducedinthediscduetotheshuntmagnetfluxis

Theresultanteddy-currentflowinginthediscis

whereαisthephase-angleoftheeddypathimpedance(Z).

Similarly,theeddyemfinducedinthediscduetotheseriesmagnetfluxis

TheresultantEddy-currentflowinginthediscis

ZTheinstantaneousdeflectingtorque(T)actingonthedisccannowbecalculatedas

Theaveragetorqueactingonthediscisthus

where,VandIarermsvaluesofvoltageandcurrent.Averagetorqueontheinstrumentisthusfoundtobeproportionaltothepowerinthecircuit.

7.5.3DifferencesBetweenDynamometerWattmeterandInduction-typeWattmeters

Though both electrodynamometer and induction type wattmeters can be used formeasurementofpower,followingarethedifferencesbetweenthetwo.

7.6 POWERMEASUREMENTINPOLYPHASESYSTEMS

Blondel’sTheoremThetheoremstatesthat‘inann-phasenetwork,thetotalpowercanbeobtainedbytakingsummationofthenwattmeterssoconnectedthatcurrentelementsofthewattmetersareeachinoneofthenlinesandthecorrespondingvoltageelementisconnectedbetweenthatlineandacommonpoint’.

Consider the case of measuring power usingthree wattmeters in a 3-phase, 3-wiresystemasshown

Figure7.21Powermeasurementina3-phase3-wiresystem

Currentcoilsofthethreewattmeters,W1,W2andW3areconnectedtothethreelinesR,Y,andB.PotentialcoilsofthethreewattmetersareconnectedtothecommonpointC.ThepotentialatthepointCmaybedifferentfromtheneutralpoint(N)potentialofload.

Powerconsumedbytheload

ReadingofwattmeterW1,P1=VRCXIRReadingofwattmeterW2,P2=VYCXIYReadingofwattmeterW3,P3=VBCXIBNow,ifthevoltagedifferencebetweenthenodesCandNistakenasVCN=VC−VN,

thenwecanhave

VRN=VR−VN=VR−VC+VC−VN=VRC+VCNVYN=VY−VN=VY−VC+VC−VN=VYC+VCNVBN=VB−VN=VB−VC+VC−VN=VBC+VCN

Sumofthethreewattmeterreadingscannowbecombinedas

P1+P2+P3=(VRN−VCN)XIR+(VYN−VCN)XIY+(VBN−VCN)XIB=VRNXIR+VYNXIY+VBNXIB−VCN(IR+IY+IB)

ApplyingKirchhoff’scurrentlawatnodeN,(IR+IY+IB)=0

Thus,sumofwattmeterreadings,

ComparingwithEq.(7.22),itisobservedthatsumofthethreeindividualwattmeterreadingsindicatethetotalpowerconsumedbytheload.

7.7 POWERMEASUREMENTINTHREE-PHASESYSTEMS

7.7.1Three-WattmeterMethod1.Three-PhaseThree-WireSystemsMeasurement of power in a 3-phase 3-wire system using three wattmeters has alreadybeendescribedinSection7.6.1.

2.Three-PhaseFour-WireSystemsWattmeterconnectionsformeasurementofpowerina3-phase4-wiresystemareshowninFigure7.22.

Figure7.22Powermeasurementin3-phase4-wiresystem

Inthiscase,thecommonpointofthethreepressurecoilscoincideswiththeneutralNofthesystem.Voltageacrosseachpotentialcoilisthus,effectivelytheper-phasevoltagesofthe corresponding phases. Current through current coils of the three wattmeters arenothingbutthephasecurrentsofthecorrespondingphases.

Sumofthethreewattmeterreadingsinsuchacasewillbe

P1+P2+P3=VRNXIR+VYNXIY+VBNXIBThisisexactlythesameasthepowerconsumedbytheload.

Hence,summationofthethreewattmeterreadingsdisplaythetotalpowerconsumedbytheload.

7.7.2Two-WattmeterMethodThisisthemostcommonmethodofmeasuringthree-phasepower.Itisparticularlyusefulwhentheloadisunbalanced.

1.Star-ConnectedSystemThe connections formeasurement of power in the case of a star-connected three-phaseloadareshown

Figure7.23Two-wattmetermethodforstar-connectedload

Thecurrent coilsof thewattmeters are connected in linesRandB, and their voltagecoilsareconnectedbetweenlinesRandY,andBandYrespectively.

Powerconsumedbytheload

ReadingofwattmeterW1,P1=VRYXIR=(VRN−VYN)XIRReadingofwattmeterW2,P2=VBYXIB=(VBN−VYN)XIBSummationofthetwowattmeterreadings:

=P1+P2=(VRN−VYN)XIR+(VBN−VYN)XIB

FromKirchhoff’slaw,summationofcurrentsatnodeNmustbezero,i.e.,

IR+IY+IB=0

or IR+IB=−IYThus,fromEq.(7.25),wecanre-write,

Itcanthus,beconcludedthatsumofthetwowattmeterreadingsisequaltothetotalpowerconsumedbytheload.Thisisirrespectiveoffactwhethertheloadisbalancedornot.

2.Delta-ConnectedSystemTwowattmeterscanalsobeusedformeasurementoftotalpowerinathree-phasedelta-connectedsystem.Theconnectionsinthecaseofadelta-connectedthree-phaseloadareshowninFigure7.24.

Figure7.24Two-wattmetermethodfordelta-connectedload

Thecurrent coilsof thewattmeters are connected in linesRandB, and their voltagecoilsareconnectedbetweenlinesRandY,andBandYrespectively.

Powerconsumedbytheload

ReadingofwattmeterW1,P1=−VYRX(iR−iY)

ReadingofwattmeterW2,P2=VBYX(iB−iR)

Summationofthetwo-wattmeterreadings:

=P1+P2=−VYRX(iR−iY)+VBYX(iB−iR)

FromKirchhoff’svoltagelaw,summationofvoltagedropsacrossaclosedloopiszero,i.e.,

VYR+VBY+VRB=0

or VYR+VBY=−VRBThus,fromEq.(7.28)wecanre-write,

Therefore,sumofthetwowattmeterreadingsisequaltothetotalpowerconsumedbytheload.Thisisonceagain,irrespectiveoffactwhethertheloadisbalancedornot.

3.EffectofPowerFactoronWattmeterReadingsPhasordiagramforthestar-connectedloadofFigure7.23withabalancedloadisshowninFigure7.25.

Figure7.25Phasordiagramforbalancedthree-phasestar-connectedload

Let,VRN,VBN,andVYNarephasevoltagesandIR,IB,andIYarephasecurrentsfor thebalancedthreephasestar-connectedsystemunderstudy.

Forabalancedsystem,phasevoltages,VRN=VBN=VYN=V(say)

And,phasecurrents,IR=IB=IY=I(say)

Forastar-connectedsystem,

LinevoltagesVRY=VYB=VBR=√3V

LinecurrentsIR=IB=IY=I

Powerfactor=cosϕ,whereϕistheanglebywhicheachofthephasecurrentslagthecorrespondingphasevoltages.

Current through theCCofwattmeterW1 is IR and voltage across its potential coil isVRY.ThecurrentIRleadsthevoltagebyVRYanangle(30°−ϕ),asshowninFigure7.25.

∴readingofwattmeterW1is,

Current through theCCofwattmeterW2 is IB and voltage across its potential coil isVBY.ThecurrentIBlagsthevoltagebyVBYanangle(30°+ϕ),asshowninFigure7.25.

∴readingofwattmeterW2is,

Sumofthesetwo-wattmeterreadings:

This is the total power consumed by the load, adding together the three individualphases.

Thus,atanypowerfactor, thetotalpowerconsumedbytheloadwillbe, inanycase,summationofthetwowattmeterreadings.

Thereiswaytofindoutvalueoftheloadpowerfactor,ifunknown,byafewstepsofmanipulation.

UsingEq.(7.30)andEq.(7.31),differenceofthetwowattmeterreadings:

TakingtheratioEq.(7.33)toEq.(7.32),onecanhave,

4.UnityPowerFactor

Thus,atunitypowerfactor,readingsofthetwowattmetersareequal;eachwattmeterreadshalfthetotalpower.

5.0.5PowerFactor

Thus, summationof the twowattmeter readings which is same asthe22totalpower.

Therefore,at0.5powerfactor,oneofthewattmetersreadszero,andtheotherreadstotalpower.

6.ZeroPowerFactor

Thus,summationoftwo-wattmeterreadings whichissameasthetotalpower.

Therefore,atzeropowerfactor,readingsofthetwowattmetersareequalbutofoppositesign.

Itshouldbenotedfromtheabovediscussionsthat,atpowerfactorsbelow0.5,oneofthewattmeterswouldtendtogivenegativereadings.Figure7.26plotsthenatureofvariationsinthetwowattmeterreadingswithchangingpowerfactor.However,inmanycases,meterscalesarenotmarkedonthenegativeside,andhencenegativereadingscannotberecorded.Insuchacase,eitherthecurrentorthepressurecoilneedstobereversed;suchthatthemeterreadsalongpositivescale.Thispositivereading,however,shouldbetakenwithanegativesignforcalculationoftotalpower.

Figure7.26Variationoftwowattmeterreadings(P1andP2)incomparisontothetotalpower(P)withrespecttochangingpowerfactor;loadisassumedtobe5Aat100V

Example7.4 Two wattmeters are connected to measure the powerconsumed by a 3-phase balanced load. One of thewattmetersread1500Ωand theother700Ω.Findpowerfactoroftheload,when(a)boththereadingsarepositive,and (b) when the reading of the second wattmeter isobtainedafterreversingitscurrentcoilconnection.

Solution

Example7.5 Two wattmeters are connected to measure the powerconsumed by a 3-phase loadwith power factor 0.4. Totalpower consumed by the load, as indicated by the twowattmeters is 30 kW. Find the individual wattmeterreadings.

Solution IfP1 andP2 are the two individual wattmeter readings then according to theproblem,P1+P2=30kW

Solving(i)and(ii),wegetP1=34.85kWandP2=–4.85kW

7.8 REACTIVEPOWERMEASUREMENTS

IfVandIarethermsvaluesofthevoltageandcurrentinasingle-phasecircuitandΦisthephase-angledifferencebetweenthem,thentheactivepowerinthecircuitis,VIcosΦ.The active power is obtained by multiplying the voltage by the component of currentwhichisinsamephasewiththevoltage(i.e.,IcosΦ).Thecomponentofcurrentwhichis90°outofphasewiththevoltage(i.e.,IsinΦ)iscalledthereactivecomponentofcurrentand the productVI sinΦ is called the reactive power.Measurement of reactive power,alongwithactivepowerissometimesimportant,sincethephase-angleΦofthecircuitcanbeobtainedfromtheratio(reactivepower)/(activepower).

Thesamewattmeterthatisusedformeasurementofactivepowercanalsobeusedfor

measurement of reactive powerwith slightmodifications in the connections.ObservingthefactthatsinΦ=cos(90°–Φ),thewattmetermaybesoconnectedthatthecurrentcoilcarriestheloadcurrentandthevoltagecoilshouldhaveavoltagethatis90°outofphasewiththeactualvoltageofthecircuit.Underthesecircumstances,thewattmeterwillread

VIcos(90°Φ),orVIsinΦ

For single-phase measurements, the pressure coil circuit may be made to behave aslarge inductive by inclusion of external inductors in series with it. This will cause thepressurecoilcurrenttolagbehindthevoltageby90°,andthusthewattmeterwillread

VIcos(90°-Φ)=VIsinΦ=Reactivepower

Formeasurementofreactivepowerinacircuitwithabalanced3-phaseload,asinglewattmeter may be used with suitable connections as shown in Figure 7.27, thecorrespondingphasordiagramisdrawninFigure7.28.

Figure7.27Connectiondiagramforreactivepowermeasurement

ThephasorIBrepresentsthecurrentflowingthroughtheCCofthewattmeter.ThevoltageappliedacrossthevoltagecoilisthevoltagedifferencebetweenthelinesRandY,i.e.,thedifference between the phasors VRN and VYN, i.e., the phasor VRY. The phase-anglebetweenVRYand−VYNis30°,forthebalancedsystem,andthatbetween−VYNandVBNis60°. Thus, the total phase-angle difference betweenVRY andVBN is 90°, and the anglebetweenVRYandIBis(90°+Φ).Thewattmeterwillread

where,VistheperphasermsvoltageandIisthelinecurrentofthesystem.

Thetotalreactivepowerofthecircuitisthus:

Figure7.28Phasordiagramforreactivepowermeasurement

7.9POWERMEASUREMENTWITHINSTRUMENTTRANSFORMERS

Powermeasurements inhigh-voltage,high-currentcircuitscanbeeffectivelydonebytheuseofPotentialTransformers(PT)andCurrentTransformers(CT)inconjunctionwithconventionalwattmeters.Byusinganumberofcurrenttransformersofdifferentratioforthecurrentcoil,andanumberofpotential transformerswithdifferent turnsratiofor thevoltage coil, the same wattmeter can be utilised for power measurements over a widerange.

Primary winding of the CT is connected in series with the load and the secondarywindingisconnectedwiththewattmetercurrentcoil,oftenwithanammeterinbetween.

Primarywinding of the PT is connected across themain power supply lines, and itssecondarywindingisconnectedinparallelwiththewattmetervoltagecoil.

TheconnectionsofawattmeterwhensousedareshowninFigure7.29,anammeterandavoltmeterisalsoconnectedinthecircuit.

Figure7.29Powermeasurementusinginstrumenttransformers

PT and CT are, however, unless carefully designed and compensated, have inherentratio andphase-angle errors.Ratio errors aremore severe for ammeters andvoltmeters,wherephase-angleerrorshavemorepronouncedeffectsonpowermeasurements.Unlessproperlycompensatedfor,thesecanleadtosubstantialerrorsinpowermeasurements.

Error introduced in power measurement due to ratio errors in PT and CT can beexplained with the help of phasor diagrams of current and voltage in load and also inwattmeter coils, as shown in Figure 7.30. Figure 7.30(a) refers to a load with laggingpowerfactor,andFigure7.30(b)toaloadwithleadingpowerfactor.

Figure7.30Phasordiagramshowingphase-angleerrorduringpowermeasurementusinginstrumenttransformersfor(a)laggingload,and(b)leadingload

V = voltageacrosstheload

I = loadcurrent

Φ = loadphase-anglebetweenVandI

VP = voltageacrosssecondarywiningofPTVoltageacrossPCofWattmeter

IP = currentthroughthePC

β = phase-anglelagbetweencurrentIPandvoltageVPduetoinductanceofthePC

IC = secondarycurrentofCTCurrentthroughCCofwattmeter

α = phase-angledifferencethecurrentsinCCandPCofwattmeter

δ = phase-angleerrorofPT,i.e.,thedeviationfromsecondarybeingexactly180°outofphasewithRespecttoprimary

θ = phase-angleerrorofCT,i.e.,thedeviationfromsecondarybeingexactly180°outofphasewithrespecttoprimary

ThePhasorshownwithdottedlinesareimagesofVandIwith180°phaseshift.

1.LaggingPowerFactorIn general, phase-angle (θ ) of CT is positive, whereas phase-angle of PT (δ) may bepositiveornegative.

Thus,phase-angleoftheloadisΦ=θ+α+β±δ

2.LeadingPowerFactorPhase-angleoftheloadisΦ=α−θ−β±δ

3.CorrectionFactorsFor the time being, neglecting the ratio error, the correction factor that need to beincorporatedforlaggingpowerfactorloadis

Forleadingpowerfactor,thecorrectionfactoris

Considering ratio errors forbothPTandCT, the correspondingcorrection factors forratioerrorsalsoneedtobeincorporated.

Generalexpressionforthepowertobemeasuredcannowbewrittenas

Power=KxActualPTratioxActualCTratioxWattmeterreading

Example7.6 A110V,5Awattmeter indicates450Ω,whenusedalongwithaPTwithnominalratio110:1andaCTwithnominalratio 25:1 respectively. Resistance and inductance of thewattmeter pressure coil circuit is 250 Ω and 7 mH

respectively. The ratio errors and phase-angles of PT andCTare+0.6%,-60’,and-0.3%and+75’respectively.Whatisthetruevalueofpowerbeingmeasured?Theloadphase-angleis35°lagging,andthesupplyfrequencyis50Hz.

SolutionResistanceofpressurecoilcircuit=250Ω

Reactanceofpressurecoilcircuit

=2pX50X70X10-3=2.2Ω

∴phase-angleofpressurecoil

Given,

Phase-angleofCT=θ=+75′

Phase-angleofPT=δ=-60′

Phase-angleofload=Φ=35°

∴phase-anglebetweenwattmeterpressurecoilcurrentIPandcurrentcoilcurrentICis

α=Φ−θ−β−δ=35°−75′−60′−30′

or,α=32°15′

Correctionfactorforphase-angleerror,

ForPTorCT,thepercentageratioerrorisgivenby

whereKn=NominalratioandKa=Actualratio

Hence,truepowerofloadP=1.495X25.08X109.34X450X10-3

=1844.8kW

EXERCISE

Objective-typeQuestions1.Powerconsumedbyasimpledccircuitcanbemeasuredwiththehelpofasingleammeterif

(a)theloadresistanceisknown

(b)thesupplyvoltageisknown

(c)bothof(a)and(b)known

(d)cannotbemeasured

2.Powerindicatedwhilemeasuringpowerinadccircuitusinganammeterandavoltmeter,whenthevoltmeterisconnectedtotheloadside,is

(a)truepowerconsumedbytheload

(b)powerconsumedbytheloadpluspowerlostinammeter

(c)powerconsumedbytheloadpluspowerlostinvoltmeter

(d)powerconsumedbyloadpluspowerlostinbothammeterandvoltmeter

3.Inammeter–voltmetermethodformeasurementofpowerindccircuits,truepowerwillbeobtainedwithammeterconnectedtotheloadsidewhen

(a)voltmeterhaszerointernalimpedance

(b)ammeterhaszerointernalimpedance

(c)ammeterhasinfiniteinternalimpedance

(d)voltmeterhasinfiniteinternalimpedance

4.Electrodynamometer-typewattmetershaveaconstructionwhere

(a)currentcoilisfixed

(b)voltagecoilisfixed

(c)bothvoltageandcurrentcoilsaremovable

(d)bothvoltageandcurrentcoilsarefixed

5.Inelectrodynamometer-typewattmeters,currentcoilismadeoftwosections

(a)toreducepowerloss

(b)toproduceuniformmagneticfield

(c)topreventEddy-currentloss

(d)toreduceerrorsduetostraymagneticfield

6.Inelectrodynamometer-typewattmeters,currentcoilscarryingheavycurrentsaremadeofstrandedwire

(a)toreduceironloss

(b)toreduceEddy-currentlossinconductor

(c)toreducehysteresisloss

(d)alloftheabove

7. In electrodynamometer-typewattmeters, a high value noninductive resistance is connected in series with thepressurecoil

(a)topreventoverheatingofthespringleadingcurrentinthepressurecoil

(b)torestrictthecurrentinthepressurecoil

(c)toimprovepowerfactorofthepressurecoil

(d)alloftheabove

8.Inelectrodynamometer-typewattmeters,bothcurrentcoilandpressurecoilarepreferablyair-cored

(a)toreduceeffectsofstraymagneticfield

(b)toreduceEddy-currentlossesunderACoperation

(c)toincreasethedeflectingtorque

(d)alloftheabove

9.Inelectrodynamometer-typewattmeters,pressurecoilinductanceproduceerrorwhichis

(a)constantirrespectiveofloadpowerfactor

(b)higheratlowpowerfactorsofload

(c)loweratlowpowerfactorsofload

(d)sameatlaggingandleadingpowerfactorsofload

10.Whenmeasuringpowerinacircuitwithlowcurrent,thewattmetercurrentcoilshouldbeconnected

(a)totheloadside

(b)tothesourceside

(c)anywhere,eitherloadsideorsourceside,doesnotmatter

(d)inserieswiththeloadalongwithCTforcurrentamplification

11.Whenmeasuringpowerinacircuitwithhighcurrent

(a)currentcoilshouldbeconnectedtotheloadside

(b)pressurecoilshouldbeconnectedtotheloadside

(c)pressurecoilshouldbeconnectedtothesourceside

(d)theplacementofpressureandcurrentcoilsareimmaterial

12.Ininduction-typewattmeters,

(a)voltagecoilisthemovingcoil

(b)currentcoilisthemovingcoil

(c)botharemoving

(d)nonearemoving

13.Threewattmetersareusedtomeasurepowerina3-phasebalancedstarconnectedload.

(a)Thereadingwillbehigherwhentheneutralpointisusedasthecommonpointforwattmeterpressurecoils.

(b)Thereadingwillbelowerwhentheneutralpointisusedasthecommonpointforwattmeterpressurecoils.

(c)Wattmeterreadingwillremainunchangedirrespectivewhethertheneutralisusedformeasurementornot.

(d)Thethree-wattmetermethodcannotbeusedinsystemswith4wires.

14.Twowattmeterscanbeusedtomeasurepowerina

(a)three-phasefour-wirebalancedload

(b)three-phasefour-wireunbalancedload

(c)three-phasethree-wireunbalancedload

(d)alloftheabove

15. In 2-wattmeter method for measurement of power in a star-connected 3 phase load, magnitude of the twowattmeterreadingswillbeequal

(a)atzeropowerfactor

(b)atunitypowerfactor

(c)at0.5powerfactor

(d)readingsofthetwowattmeterswillneverbeequal

Short-answerQuestions1. Draw and label the different internal parts of an electrodynamometer-type wattmeter. What are the special

constructionalfeaturesofthefixedandthemovingcoilsinsuchaninstrument?

2. Discuss about the special shielding requirements and measures taken for shielding internal parts of anelectrodynamometer-typewattmeteragainstexternalstraymagneticfields.

3.Drawandexplaintheoperationofacompensatedwattmeterusedtoreduceerrorsduetoconnectionofpressurecoilnearertotheloadsideaspertinenttoelectrodynamometer-typewattmeters.

4.Drawandexplaintheconstructionalfeaturesofaninduction-typewattmeterusedformeasurementofpower.

5.Drawtheschematicandderivehowthree-phasepowerconsumedbyadelta-connectedloadcanbemeasuredbytwowattmeters.

6.Explainhowpowerfactorofanunknownthree-phaseloadcanbeestimatedbyusingtwowattmeters.

7. Twowattmetersareconnectedtomeasurethepowerconsumedbya3-phaseloadwithapowerfactorof0.35.Totalpowerconsumedbytheload,asindicatedbythetwowattmeters,is70kW.Findtheindividualwattmeterreadings.

8.Withthehelpofsuitablediagramsandsketches,explainhowasinglewattmetercanbeusedformeasurementofreactivepowerina3-phasebalancedsystem.

9.Deriveanexpressionforthecorrectionfactornecessarytobeincorporatedinwattmeterreadingstorectifyphase-angleerrorininstrumenttransformerswhileusedformeasurementofpower.

Long-answerQuestions1.Describetheconstructionaldetailsofanelectrodynamometer-typewattmeter.Commentupontheshapeofscale

whenspringcontrolisused.

2.Derivetheexpressionfortorquewhenanelectrodynamometer-typewattmeterisusedformeasurementofpowerinaccircuits.Whyshouldthepressure-coilcircuitbemadehighlyresistive?

3.Listthedifferentsourcesoferrorinelectrodynamometer-typewattmeters.Brieflydiscusstheerrorduetopressurecoilinductance.Howisthiserrorcompensated?

4.(a)Discussthespecialfeaturesofdampingsystemsinelectrodynamometer-typewattmeters.

(b)Anelectrodynamometer-typewattmeterisusedforpowermeasurementofaloadat200Vand9Aatapowerfactorof0.3lagging.Thepressure-coilcircuithasaresistanceof4000andinductanceof40mH.Calculatethepercentageerrorinthewattmeterreadingwhenthepressurecoilisconnected(a)ontheloadside,and(b)onthesupplyside.Thecurrentcoilhasaresistanceof0.2andnegligibleinductance.Assume50Hzsupplyfrequency.

5.A250V,10Aelectrodynamometerwattmeterhasresistanceofcurrentcoilandpotentialcoilof0.5and12.5krespectively.Findthepercentageerrorduetothetwopossibleconnections:(a)pressurecoilonloadside,and(b)currentcoilonloadsidewithunitypowerfactorloadsat250Vwithcurrents(i)4A,and(ii)8A.Neglecterrorduetopressurecoilinductance.

6.Discussinbrieftheconstructionaldetailsofaninduction-typewattmeter.Showhowthedeflectingtorqueinsuchininstrumentcanbemadeproportionaltothepowerinaccircuits.

7.(a)Drawtheschematicandderivehowthree-phasepowerconsumedbyastar-connectedloadcanbemeasuredbytwowattmeters.

(b) Twowattmeters are connected tomeasure the power consumed by a 3-phase balanced load. One of thewattmetersreads1500Ωandtheother,700Ω.Calculatepowerandpowerfactoroftheload,when(a)boththe readings are positive, and (b)when the reading of the secondwattmeter is obtained after reversing itscurrentcoilconnection.

8.A110V,5Arangewattmeterisusedalongwithinstrumenttransformerstomeasurepowerconsumedbyaloadat6KVtaking100Aat0.5laggingpowerfactor.Theinstrumenttransformershavethefollowingspecifications:

PT:Nominalratio=80:1;Ratioerror=+1.5%;Phaseerror=–2°

CT:Nominalratio=20:1;Ratioerror=–1.0%;Phaseerror=+1°

Assumingwattmeterreadscorrectly,findtheerrorintheindicatedpowerduetoinstrument-transformererrors.

8.1 INTRODUCTION

Energyisthetotalpowerconsumedoveratimeinterval,thatisEnergy=Power×Time.Generally, the process of measurement of energy is same as that for measurement ofpowerexcept for the fact that the instrumentused shouldnotmerelymeasurepowerorrate of consumptionof energy, butmust also take into account the time interval duringwhichthepowerisbeingsupplied.

TheunitofenergycanbeexpressedintermsofJouleorWatt-secondorWatt-hourasperconvenience.Alargerunitthatismostcommonlyusediskilowatt-hour(kWh),whichis defined as the energy consumed when power is delivered at an average rate of 1kilowatt for one hour. In commercial metering, this amount of 1 kilowatt-hour (kWh)energyisspecifiedas1unitofenergy.

Energy meters used for measurement of energy have moving systems that revolvecontinuously,unlikeinindicatinginstrumentswhereitdeflectsonlythroughafractionofa revolution. In energy meters, the speed of revolution is proportional to the powerconsumed.Thus, total number of revolutionsmadeby themetermoving systemover agiven interval of time is proportional to the energy consumed. In this context, a termcalledmeterconstant,definedasthenumberofrevolutionsmadeperkWh,isused.Valueofthemeterconstantisusuallymarkedonthemeterenclosure.

8.2 SINGLE-PHASEINDUCTION-TYPEENERGYMETER

Induction-typeinstrumentsaremostcommonlyusedasenergymetersformeasurementofenergy in domestic and industrial ac circuits. Induction-typemeters have lower frictionand higher torque/weight ratio; they are inexpensive, yet reasonably accurate and canretaintheiraccuracyoverconsiderablerangeofloadsandtemperature.

8.2.1BasicTheoryofInduction-typeMetersIn all induction-type instruments, two time-varying fluxes are created in the windingsprovidedonthestaticpartoftheinstrument.Thesefluxesaremadetolinkwithametaldiscordrumandproduceemftherein.Theseemfs in turn,circulateeddycurrentonthebodyofthemetaldisc.Interactionofthesefluxesandeddycurrentsproducetorquesthatmakethediscordrumtorotate.SchematicdiagramsrepresentingfrontandtopviewsofsuchaninstrumentisshowninFigure8.1.

A thin aluminumdisc free to rotate about its central axis is fittedwith a spindle andplaced below the two poles φ1 and φ2. Fluxes φ1 and φ2 coming out of the two

electromagnetsφ1 andφ2 link with the aluminum disc placed below. These fluxes arealternating in nature, and hence they induce emfs in the aluminumdisc.These inducedemfswillinturnproduceeddycurrentsi1andi2onthedisc,asshowninFigure8.1.Therearetwosetsoffluxesφ1andφ2,andtwosetsofcurrentsi1andi2.Currenti1interactswithfluxφ2 to produce a forceF1 and hence a torqueTd1 on the disc. Similarly, current i2interactswith fluxφ1 to produce a forceF2 and hence a torqueTd2 on the disc. TotaltorqueisresultantofthetorquesTd1andTd2.

Figure8.1Workingprincipleofinduction-typeinstrument:(a)Frontview(b)Topview

Letφ1andφ2aretheinstantaneousvaluesoftwofluxeshavingaphasedifferenceofαbetweenthem.Therefore,wecanwrite

where,φ1mandφ2marepeakvaluesoffluxesφ1andφ2respectively.

Thefluxφ1willproduceanalternatingemfisthedisc,givenby

Similarly,thealternatingemfproducedinthediscduetothefluxφ2isgivenby

If, is considered to the impedance of the aluminumdiscwith power factorβ then

eddycurrentinducedinthediscduetotheemfe1canbeexpressedas

Similarly,eddycurrentinducedinthediscduetotheemfe2isgivenby

Instantaneoustorquedevelopedinproportionaltotheproductofinstantaneouscurrentand instantaneous flux are those that interact with each other to produce the torque inquestion.

instantaneoustorqueTd1producedduetointeractionofthecurrent i1andfluxφ2 isgivenby

Similarly,instantaneoustorqueTd2producedduetointeractionofthecurrenti2andfluxφ1isgivenby

Totaldeflectingtorquecanthusbecalculatedas

ThefollowingtwoobservationscanbemadefromEq.(8.1):

1.Thetorqueisdirectlyproportional to thepowerfactorof thealuminumdisc(cosβ).Thus,toincreasethedeflectingtorque,thepathofeddycurrentinthediscmustbeasresistiveaspossible,sothatvalueofcosβisashighaspossible.

2. The torque is directly proportional to sin α. Therefore, to have large deflecting

torque, the angle α between the two fluxes should preferably be as nearly aspossiblecloseto90°.

8.2.2ConstructionalDetailsofInduction-TypeEnergyMeterConstructional details of an induction-type single-phase energymeter are schematicallyshowninFigure8.2(a).ThephotographofsuchanarrangementisshowninFigure8.2(b).

Figure8.2(a)Constructionaldetailsofinduction-typesingle-phaseenergymeter(b)Photographofinduction-typesingle-phaseenergymeter(Courtesy,CreativeCommonsAttributionShareAlike2.5)

1.Volatagecoil–manyturnsoffinewireencasedinplastic,connectedinparallelwithload.

2.Currentcoil–fewturnsofthickwire,connectedinserieswithload

3.Stator–concentratesandconfinesmagneticfield.

4.Aluminumrotordisc.

5.Rotorbrakemagnets

6.Spindlewithwormgear.

7.Displaydials

Asinglephaseenergymeterhasfouressentialparts:

(i)Operatingsystem

(ii)Movingsystem

(iii)Brakingsystem

(iv)Registeringsystem

1.OperatingSystemTheoperatingsystemconsistsof twoelectromagnets.Thecoresof theseelectromagnetsare made of silicon steel laminations. The coils of one of these electromagnets (seriesmagnet) are connected in serieswith the load, and is called the current coil. The otherelectromagnet (shuntmagnet) iswoundwith a coil that is connected across the supply,called thepressure coil.Thepressure coil, thus, carries a current that is proportional tosupplyvoltage.

Shadingbandsmadeofcopperareprovidedon thecentral limbof the shuntmagnet.Shadingbands,aswillbedescribedlater,areusedtobringthefluxi—BearingproducedbyashuntmagnetexactlyinquadraturePivotwiththeappliedvoltage.

Figure8.3Pivotandjewelbearing

2.MovingSystemThemovingsystemconsistsofa lightaluminumdiscmountedonaspindle.Thediscisplacedinthespacebetweentheseriesandshuntmagnets.Thediscissopositionedthatitintersects the flux produced by both themagnets. The deflecting torque on the disc isproducedbyinteractionbetweenthesefluxesandtheeddycurrenttheyinduceinthedisc.Inenergymeters,thereisnocontrolspringassuch,sothatthereiscontinuousrotationofthedisc.

Thespindleissupportedbyasteelpivotsupportedbyjewelbearingsatthetwoends,asshown in Figure 8.3. A unique design for suspension of the rotating disc is used in‘floating-shaft’energymeters. In suchaconstruction, the rotatingshafthasonesmallpiece of permanentmagnet at each end. The uppermagnet is attracted by amagnetplaced in theupperbearing,whereas the lowermagnet isattractedbyanothermagnetplacedinthelowerbearing.Themovingsystemthusfloatswithouttouchingeitherofthe bearing surfaces. In this way, friction while movement of the disc is drasticallyreduced.

3.BrakingSystemThe braking system consists of a braking devicewhich is usually a permanentmagnetpositionedneartheedgeofthealuminumdisc.ThearrangementisshowninFigure8.4.

Theemfinducedinthealuminumdiscduetorelativemotionbetweentherotatingdiscand the fixed permanentmagnet (brakemagnet) induces eddy current in the disc. Thiseddycurrent,whileinteractingwiththebrakemagnetflux,producesaretardingorbrakingtorque.Thisbrakingtorqueisproportionaltospeedoftherotatingdisc.Whenthebrakingtorquebecomesequaltotheoperatingtorque,thediscrotatesatasteadyspeed.

Figure8.4Brakemagnettoprovideeddycurrentbrakingininduction-typesingle-phaseenergymeter:(a)Schematicdiagram(b)Actualpicture(1)Aluminumrotatingdisc(2)Brakemagnet

The position of the permanentmagnetwith respect to the rotating disc is adjustable.Therefore,braking torquecanbeadjustedbyshifting thepermanentmagnet todifferentradialpositionswithrespecttothedisc.

Itispertinenttomentionherethattheseriesmagnetalsoactsasabrakingmagnet,sinceitopposesthemaintorqueproducingfluxgeneratedbytheshuntmagnet.

4.RegisteringSystemThe function of a registering or counting system is to continuously record a numericalvalue that isproportional to thenumberof revolutionsmadeby the rotatingsystem.Bysuitablecombinationofatrainofreductiongears,rotationofthemainaluminumdisccanbetransmittedtodifferentpointerstoregistermeterreadingsondifferentdials.Finally,thekWhreadingcanbeobtainedbymultiplyingthenumberofrevolutionsaspointedoutby

thedialswiththemeterconstant.Thephotographofsuchadial-typeregisteringsystemisshowninFigure8.5.

Figure8.5Photographofdial-typesinglephaseenergymeter

8.2.3OperationofInduction-TypeEnergyMeterAsper construction, the pressure coilwinding ismade highly inductive by providing alargenumberofturns.Theairgapsinashuntmagnetcircuitarealsomadesmalltoreducethereluctanceofshuntfluxpaths.Thus,assupplyvoltageisappliedacrossthepressurecoil,thecurrentIPthroughthepressurecoilisproportionaltothesupplyvoltageandlagsbehind itbyanangle that isonlya fewdegrees less than90°. Ideally, thisangleof lagshouldhavebeen90°butforthesmallunavoidableresistancepresentinthewindingitselfandtheassociatedironlossesinthemagneticcircuit.

Figure8.6 shows thepathofdifferent fluxeswhile themeter isunderoperation.ThecorrespondingphasordiagramisshowninFigure8.7.

Figure8.6Fluxpathsininduction-typesingle-phaseenergymeter

Figure8.7Phasordiagramofsingle-phaseinduction-typeenergymeter

Let,

V =supplyvoltageI =loadcurrentθ =phaseangleofloadβ =phaseangleofaluminumdiscα =phaseanglebetweenshuntmagnetandseriesmagnetfluxesδ =phaseanglebetweensupplyvoltageandpressurecoilflux

The current IP produces a fluxφpt that is in same phase as IP. This flux ismade todivideitselfintwoparts,φgandφp.Themajorportionoftotalpressurecoilflux,i.e.,φgpassesthroughthesidegapsasshowninFigure8.6,asreluctanceofthesepathsarelowdueverysmallairgaps.Remainingportionoftheflux,i.e.,φppassesthroughthediscandis responsible forproductionof thedriving torque.Due to larger reluctanceof thepath,thisfluxφpisrelativelyweaker.

ThefluxφpisproportionaltothecurrentIPandisinthesamephase,asshowninthephasordiagramofFigure8.7.ThefluxφpisthusproportionaltothesupplyvoltageVandlags it by an angle δ which is only a few degrees less than 90°. The flux φp beingalternatinginnature,inducesandeddyemfEep inthedisc,whichinturnproduceseddycurrentI.Dependingontheimpedanceangleβofthealuminumdisc,eddycurrentIwilllagbehindtheeddyemfEepbyanangleβ.

TheloadcurrentIflowsthroughtheseriesmagnetcurrentcoilandproducesafluxφs.ThisfluxisproportionaltotheloadcurrentIandisinphasewithit.Thisflux,inthesameway,inducesandeddyemfEes in thedisc,whichinturnproduceseddycurrentIes.TheeddycurrentIeslagsbehindtheeddyemfEesbythesameangleβ.

Now,theeddycurrentIesinteractswithfluxφptoproduceatorqueandtheeddycurrentIep interactswith fluxφs to produce another torque. These two torques are in opposite

directionasshowninFigure8.1,andtheresultanttorqueisthedifferenceofthesetwo.

Following(8.1), the resultantdeflecting torqueon thediscdue tocombinedactionoftwofluxesφpandφsisgivenas

where,Zistheimpedanceofthealuminumdiscandωistheangularfrequencyofsupplyvoltage.

Thedrivingtorquecanbere-writtenfollowingthephasordiagraminFigure8.7as

Sincewehave,jp Vandφs I,

IfNisthespeedofrotationofthedisc,thenbrakingtorqueTb=K4N

At steady running condition of the disc, the driving torque must equal the brakingtorque,

Ifwecanmakeδ=90°

Thus,inorderthatthespeedofrotationcanbemadetobeproportionatetothepowerconsumed, the angle differenceδ between the supply voltageV and the pressure coilfluxφpmustbemade90°

Totalnumberofrevolutionswithinatimeintervaldtis

If,ε=90°,totalnumberofrevolutions

Thus,totalnumberofrevolutionsisproportionaltotheenergyconsumed.

8.3ERRORSININDUCTION-TYPEENERGYMETERSANDTHEIRCOMPENSATION

8.3.1Phase-angleErrorIt is clear from (8.7) that the meter will indicate true energy only if the phase anglebetweenthepressurecoilfluxφpandthesupplyvoltageV is90°.This requires that thepressurecoilwindingshouldbedesignedashighly inductiveand its resistanceand ironlossesshouldbemademinimum.But,eventhenthephaseangleisnotexactly90°,ratherafewdegreeslessthan90°.Suitableadjustmentscanbeimplementedsuchthattheshuntmagnet flux linking with the disc can be made to lag the supply voltage by an angleexactlyequalto90°.

1.ShadingCoilwithAdjustableResistanceFigure8.8showsthearrangementwhereanadditionalcoil(shadingcoil)withadjustableresistance isplacedon thecentral limbof theshuntmagnetclose to thedisc.Mainfluxcreatedbytheshuntmagnetinducesanemfinthisshadingcoil.Thisemfcreatesitsownflux.Thesetwofluxesresultinamodifiedfluxtopassthroughtheairgaptolinkthediscandthusproducethedrivingtorque.Withproperadjustmentoftheshadingcoilresistance,theresultantfluxcanbemadetolagthesupplyvoltageexactlybyanangleof90°.

Operation of the shading coil can be explainedwith the help of the phasor diagramshowninFigure8.9.Thepressurecoil,whenexcitedfromthesupplyvoltageV,carriesacurrentIPandproducesanmmfATptwhichinturnproducesthetotalfluxφpt.Thefluxφptlags the supplyvoltageV by an angleφwhich is slightly less than 90°.The current IPproducesafluxφptthatisinsamephaseasIP.Thefluxφptgetsdividedintwoparts,φandφp. The portion of flux φ passes through the side gaps as shown in Figure 8.8, andremainingportionof the flux, i.e.,φp passes through thedisc andalso the shadingcoil.Duetolinkagewiththetimevaryingflux,anemfEsc is inducedintheshadingcoil thatlags behind its originating fluxφp by 90° (i.e.ESC is 180°) lagging behind the supplyvoltageV.ThisemfcirculatesandeddycurrentIscthroughtheshadingcoilitself.IsclagsbehindtheemfEscbyanangleλthatdependsontheimpedanceoftheshadingcoil.Theshading coil current Isc produces anmmfATsc which is in phasewith Isc. The flux φppassingthroughtothediscwillthusbeduetotheresultantmmfATpwhichissummationoftheoriginalmmfATptandthemmfATscduetotheshadingcoil.ThisfluxφpwillbeinphasewiththemmfATp.AsseeninthephasordiagramofFigure8.9,thefluxφpcanbemade to lag the supplyvoltageV by exactly90° if themmfATp or inotherwords, theshading coil phase angle λ can be adjusted properly. The shading coil phase angle caneasilybeadjustedbyvaryingtheexternalresistanceconnectedtotheshadingcoil.

Figure8.8ShadingcoilforlagadjustmentV

Figure8.9Phasordiagramshowingoperationofshadingcoilforlagadjustment

2.CopperShadingBandsA similar result of lag adjustment can be obtained by the use of copper shading bandsplacedonthecentrallimboftheshuntmagnet.SuchanarrangementisshowninFigure8.10.Followingthesamearguments,theresultantfluxφpcrossingovertothedisccanbemade to lag the supply voltage V by exactly 90° by proper adjustment of the mmfproducedbythecoppershadingbands.Adjustmentsinthiscasecanbedonebymovingtheshadingbandsalongtheaxisofthelimb.Asthebandsaremovedupwardsalongthelimb,theyembracemoreflux.Thisresultsinincreasedvaluesofinducedemf,increasedvaluesof inducededdycurrentandhence increasedvaluesof themmfproducedby the

bands. Similarly, as the bands are moved downwards, mmf produced by the bands isreduced.Thischangesthephaseangledifferencebetweenφpandφpt,ascanbeobservedfromthephasordiagramofFigure8.9.Thus,carefuladjustmentsof thecopper shadingbandspositioncanmakethephasedifferencebetweenthesupplyvoltageVandresultantshuntmagnetfluxφptobeexactly90°.

Figure8.10Coppershadingbandsforlagadjustment

8.3.2ErrorduetoFrictionatLightLoadsFrictioninbearingscanposeseriouserrorsinmeasurementofenergyintheformofthatitwill impede proper movement of the rotating disc. This problem is particularlyobjectionableatlowloads,whenthedrivingtorqueitselfisverylow;therefore,unwantedfriction torque can even stop the disc from rotating. To avoid this, it is necessary toprovideanadditionaltorquethatisessentiallyindependentoftheload,tobeappliedinthedirectionofthedrivingtorque,i.e.,oppositetothefrictionaltorquetocompensateforthefrictional retarding torque. This is achieved bymeans of a small vane or shading loopplacedintheairgapbetweenthecentrallimboftheshuntmagnetandthealuminumdisc,and slightly off-centre from the central limb, as shown in Figure 8.11. Interactionsbetweenfluxeswhicharelinkedandnotlinkedbytheshadingorcompensatingvaneandthecurrentstheyinduceinthediscresultinasmalldrivingtorquethatcancompensateforthefrictionalretardingtorque.Thevalueofthissmalladditionaltorquecanbeadjustedbylateralmovementofthevaneinandoutofitspositionintheairgap.

Figure8.11Shadingvaneforfrictioncompensation

8.3.3CreepingErrorIn somemeters, a slowbut continuous rotation of the disc can be observed evenwhenthere isnocurrent flowing through thecurrentcoil, andonlypressurecoil is energised.Thisiscalledcreeping.Theprimaryreasonforcreepingisduetoover-compensationforfriction. Though the main driving torque is absent at no-load, the additional torqueprovidedby the frictioncompensatingvanewillmake thedisccontinue to rotate.Othercauses of creeping may be excessive voltage across the potential coil resulting inproduction of excessive torque by the friction compensating device, or vibrations, andstraymagneticfields.

Creeping can be avoided by drilling two holes on the aluminum disc placed ondiametrically opposite locations. Drilling such holes will distort the eddy current pathsalongthediscandthediscwill tendtostopwiththeholescomingunderneaththeshuntmagnetpoles.Thedisccanthuscreeponlytillamaximumofhalftherotationtilloneoftheholescomesbelowtheshuntmagnetpole.Thiseffectishowever,tooinsignificanttohamperdiscmovementduringnormalrunningoperationsunderload.

Creepingcanalsobeavoidedbyattachingatinypieceofirontotheedgeofthedisc.Thebrakemagnetinsuchacasecanlocktheironpiecetoitselfandpreventcreepingofthe disc. Once again, this action is too insignificant to hamper disc movement duringnormalrunningoperationsunderload.ThearrangementisschematicallyshowninFigure8.12.

Figure8.12Softironpieceattheendofthedisctopreventcreeping

8.3.4ErrorduetoChangeinTemperatureErrorsintroducedbyvariationoftemperatureininduction-typeenergymetersareusuallysmall since thevarious effects tend toneutralise eachother.An increase in temperatureincreasesthepressurecoilresistance,therebyreducingpressurecoilcurrentandreducingpressurecoil flux.Thiswill tend to reduce thedriving torque.But the fluxof thebrakemagnetalsoreducesduetoincreaseintemperature,therebyreducingthebrakingtorque.Again,anincreaseintemperatureincreasestheresistancetoeddycurrentpathinthedisc,which reduces both driving torque and braking torque.The various effects thus tend toneutraliseeachother.

The effects of increasing temperature, however, in general cause themeter to rotatefasterandhence recordhighervalues.Temperatureeffects thusneed tobecompensatedforbyusingtemperatureshuntsinthebrakemagnet.

8.3.5ErrorduetoOverloadAt a constant voltage, the deflecting torque becomes simply proportional to the seriesmagnetfluxandhenceproportional to theloadcurrent.This isduetothefact thatfromEq.(8.2),atconstantvoltageastheshuntmagnetfluxφpisconstant,thedrivingtorqueTdφs I.

Ontheotherhand,asthediscrotatescontinuouslyinthefieldoftheseriesmagnet,anemfisinduceddynamicallyinthediscduetoitslinkagewiththeseriesmagnetfluxφs.This emf induces eddy currents in the disc that interactwith the seriesmagnet flux tocreate a retarding or braking torque that opposesmotion of the disc. This self brakingtorque is proportional to the square of the series magnet flux or is proportional to thesquareoftheloadcurrent;i.e.,Tb φ2s I2.

Athigherloads,thusthebrakingtorqueoverpowersthedeflectingtorqueandthemetertendstorotateatslowerspeed,andconsequentlyreadslowerthanactual.

Toavoidsucherrors,andtominimisetheself-brakingaction,thefullloadspeedofthedisc is set at lowervalues.Thecurrent coil fluxφs ismade smaller as compared to thepressurecoilfluxφp.Thus,thedynamicallyinducedemfthatcausesthebrakingtorqueisrestricted as compared to the driving torque.Magnetic shunts are also sometimes usedwithseriesmagnetstocompensateforoverloaderrorsathighcurrentvalues.

8.3.6ErrorduetoVoltageVariationsVoltage variations can cause errors in induction-type energymetersmainly due to tworeasons:

1. At toohighvoltages, the relationshipbetween thesupplyvoltageV and the shuntmagnetfluxφpnolongerremainlinearduetosaturationofironparts,and

2. For sudden fluctuations in supply voltage, the shunt magnet flux φp produces adynamically inducedemf in thediscwhich in turn results in a self-braking torqueandthediscrotationishampered.

Compensationforvoltagevariationisprovidedbyusingasuitablemagneticshuntthatdiverts a major portion of the flux through the disc when the voltage rises, therebyincreasingthedrivingtorquetoovercometheself-brakingtorque.Suchcompensationcanbe achievedby increasing the reluctanceof the side limbsof the shuntmagnet.This isdonebyprovidingholesinthesidelimbsasshowninFigure8.13.

Figure8.13Holesprovidedonsidelimbstocompensateforerrorsduetosuddenvoltagevariations

8.4 TESTINGOFENERGYMETERS

Energymetersaretestedatthefollowingconditions:

1.At5%ofratedcurrentatunitypowerfactor

2.At100%or125%ofratedcurrentwithunitypowerfactor

3.Atoneintermediateloadwithunitypowerfactor

4.Atratedcurrentand0.5laggingpowerfactor

5.CreeptestWithpressurecoilsuppliedwith110%ofratedvoltageandcurrentcoilopencircuited,themeterdiscshouldnotrotatebymorethanonerevolution,i.e.,itshouldnotcreep

6.StartingtestAt0.5%ofratedcurrentandfull ratedvoltage, themeterdiscshouldstartrotating

8.4.1PhantomLoadingWhen the current rating of the meter under test is high, a test with actual loadingarrangements would involve considerable wastage of energy and also it is difficult toarrangeforsuchlargeloadsunderlaboratorytestconditions.Insuchcases,toavoidthis,‘phantom’or‘fictitious’loadingarrangementsaredonefortestingofenergymeters.

Phantom loading consists of supplying the shuntmagnet pressure coil circuit from arated voltage source. The series magnet current coil is supplied from a separate lowvoltage supply source. It is possible to circulate rated current through the current coilcircuitwiththelowvoltagesourcesinceimpedanceofthiscircuitisverylow.Theenergyindicated by the meter under phantom loading condition is the same as the energy

indication aswouldhavebeenwith a real load.With this arrangement, the total energyconsumed for the test is comparatively smaller.The total energy required for the test isthatduetothesmallpressurecoilcurrentatratedvoltageandsmallcurrentcoilvoltageatratedcurrent.

Example8.1 Themeter constant of a 220V, 5 A energymeter is 2000revolutions per kWh. The meter is tested at half load atratedvoltageandunitypowerfactor.Themeterisfoundtomake34revolutionsin116s.Determinethemetererrorathalfload.

SolutionActualenergyconsumedathalfloadduring166s:

Energyasrecordedbythemeter

Example8.2 A230V,5Aenergymeteron full loadunitypower factortest makes 60 revolutions in 360 seconds. If the designedspeed of the disc is 520 revolutions per kWh, find thepercentageerror.

SolutionActualenergyconsumedatfullloadduring360s:

Energyasrecordedbythemeter

Example8.3 Anenergymeter is designed tohave80 revolutionsof thediscperunitofenergyconsumed.Calculatethenumberofrevolutions made by the disc when measuring the energyconsumedbyaloadcarrying30Aat230Vand0.6powerfactor.Findthepercentageerrorifthemeteractuallymakes330revolutions.

SolutionActualenergyconsumedbytheloadinonehour:

Themetermakes80revolutionsperunitofenergyconsumed,i.e.,perkWh.

Thusnumberofrevolutionsmadebythemetertorecord4.14kWhis

Incasethemetermakes330revolutions,thenerrorisgivenas

Example8.4 A230V, single-phasewatt hourmeter records a constantloadof10Afor4hoursatunitypowerfactor.Ifthemeterdiscmakes2760revolutionsduringthisperiod,whatisthemeter constant in termsof revolutionsperunit?Calculatetheloadpowerfactorifthenumberofrevolutionsmadebythemeteris1104whenrecording5Aat230Vfor6hours.

SolutionActualenergyconsumedbytheloadin4hours:

Withthisvalueofmeterconstant,with1104revolutions,themeterrecordsanenergy=1104/3003.68kWh

Thus,energyconsumed

Hence,powerfactorofloadiscosϕ=0.533

Example8.5 A220V,10Adcenergymeter is tested for itsnameplateratings. Resistance of the pressure coil circuit is 8000 Ωandthatofcurrentcoilitselfis0.12Ω.Calculatetheenergyconsumedwhentestingforaperiodof1hourwith(a)Directloadingarrangement(b)Phantomloadingwiththecurrentcoilcircuitexcitedbyaseparate9Vbattery

Solution Test arrangements with direct and phantom loading arrangements areschematicallyshowninthefigure.

(a)Withdirectloading

Powerconsumedinthepressurecoilcircuit

Powerconsumedinthecurrentcoil(series)circuit=220×10=2200W

totalpowerconsumedwithdirectmeasurement=2206.05W

totalenergyconsumedduring1hourwithdirectmeasurement

(b)Withphantomloading

Powerconsumedinthepressurecoilcircuit

Powerconsumedinthecurrentcoil(series)circuit=9×10=90W

totalpowerconsumedwithdirectmeasurement=96.05W

totalenergyconsumedduring1hourwithdirectmeasurement

Thus,energyconsumedisconsiderablylessinphantomloadingascomparedtodirectloadingforenergymetertesting.

EXERCISE

EXERCISE

Objective-typeQuestions1.Energymetersdonothaveacontrolspringto

(a)avoidunnecessaryfrictionlosses

(b)enablecontinuousrotationofthedisc

(c)avoiddampingduringmovement

(d)alloftheabove

2.Ininduction-typeenergymeters,thespeedofrotationofthediscisproportionaltothe

(a)energyconsumption

(b)powerconsumption

(c)derivativeofpowerconsumption

(d)noneoftheabove

3.Theadvantagesofinduction-typeenergymetersare

(a)lowtorque/weightratio

(b)lowfriction

(c)highandsustainedaccuracy

(d)alloftheabove

4.Induction-typeenergymetershavealuminumdiscastherotatingpartsothat

(a)fluxcanpassthroughtherotatingpart

(b)eddycurrentcanbeinducedintherotatingpart

(c)creepingerrorcanbeavoided

(d)alloftheabove

5.Ininduction-typeenergymeters

(a)pressurecoilisthemovingpart

(b)currentcoilisthemovingpart

(c)bothcurrentandpressurecoilsaremoving

(d)bothcurrentandpressurecoilsarestationary

6.Ininduction-typeenergymeters,highdrivingtorquecanbeobtainedby

(a)makingthediscpurelyresistive

(b)makingthephasedifferencebetweenthetwooperatingfluxesaslargeaspossible

(c)makingthediscimpedanceaslowaspossible

(d)alloftheabove

7.Brakingtorqueprovidedbythepermanentmagnetinaninduction-typeenergymeterisproportionalto

(a)speedoftherotatingdisc

(b)squareofthefluxofthepermanentmagnet

(c)distanceofthepermanentmagnetwithrespecttocentreofthedisc

(d)alloftheabove

8.Brakingtorqueprovidedbythepermanentmagnetinaninduction-typeenergymetercanbechangedby

(a)providingametalshuntandshiftingitsposition

(b)movingthepositionofthepermanentmagnetwithrespecttothedisc

(c)both(a)and(b)

(d)noneoftheabove

9.Insingle-phaseinduction-typeenergymeters,maximumtorqueisproducedwhentheshuntmagnetflux

(a)leadsthesupplyvoltageby90°

(b)lagsthesupplyvoltageby90°

(c)lagsthesupplyvoltageby45°

(d)isinphasewiththesupplyvoltage

10.Insingle-phaseinduction-typeenergymeters,lagadjustmentsaredoneby

(a)permanentmagnetplacedontheedgeofthedisc

(b)holesprovidedonthesidelimbsofthepressurecoil

(c)coppershadingbandsplacedonthecentrallimbofthepressurecoil

(d)metalshuntsplacedontheseriesmagnets

11.Insingle-phaseinduction-typeenergymeters,lagadjustmentscanbedoneby

(a)shiftingthecoppershadingbandalongtheaxisofthecentrallimb

(b)varyingtheexternalresistanceconnectedtotheshadingcoilplacedonthecentrallimb

(c)eitherof(a)or(b)asthecasemaybe

(d)noneoftheabove

12.Insingle-phaseinduction-typeenergymeters,frictioncompensationcanbedoneby

(a)placingshadingbandsinthegapbetweencentrallimbandthedisc

(b)drillingdiametricallyoppositeholesonthedisc

(c)providingholesonthesidelimbs

(d)alloftheabove

13.Creepinginasingle-phaseenergymetermaybedueto

(a)vibration

(b)overcompensationoffriction

(c)overvoltages

(d)alloftheabove

14.Creepinginasingle-phaseenergymetercanbeavoidedby

(a)usinggoodqualitybearings

(b)increasingstrengthofthebrakemagnet

(c)placingsmallsoftironpieceonedgeoftherotatingdisc

(d)alloftheabove

15.Increaseinoperatingtemperatureinaninduction-typeenergymeterwill

(a)reducepressurecoilflux

(b)reducebrakingtorque

(c)reducedrivingtorque

(d)alloftheabove

16.Overloaderrorsininduction-typeenergymeterscanbereducedby

(a)designingthemetertorunatlowerratedspeeds

(b)designingthecurrentcoilfluxtohavelowerratedvaluesascomparedtopressurecoilflux

(c)providingmagneticshuntsalongwithseriesmagnetsthatsaturateathigherloads

(d)alloftheabove

17.Overvoltagesmayhamperrotationofthediscininduction-typeenergymeterssince

(a)thepressurecoilfluxnolongerremainsinquadraturewiththecurrentcoilflux

(b)dynamicallyinducedemfinthediscfromthepressurecoilfluxproducesaself-brakingtorque

(c)effectofthebrakemagnetisenhanced

(d)alloftheabove

18.Ifaninduction-typeenergymeterrunsfast,itcanbesloweddownby

(a)movingupthecoppershadingbandsplacedonthecentrallimb

(b)adjustingthemagneticshuntplacedontheseriesmagnets

(c)movingthepermanentbrakemagnetawayfromcentreofthedisc

(d)bringingthepermanentbrakemagnetclosertocentreofthedisc

19.Phantomloadingfortestingofenergymetersisused

(a)formetershavinglowcurrentratings

(b)toisolatecurrentandpotentialcircuits

(c)totestmetershavingalargecurrentratingforwhichloadsmaynotbeavailableinthelaboratory

(d)alloftheabove

20.Insingle-phaseinduction-typeenergymeters,directionofrotationofthedisccanbereversedby

(a)reversingsupplyterminals

(b)reversingloadterminals

(c)openingthemeterandreversingeitherthepotentialcoilterminalsorthecurrentcoilterminals

(d)openingthemeterandreversingboththepotentialcoilterminalsandthecurrentcoilterminals

Short-answerQuestions1.Drawaschematicdiagramshowingconstructiondetailsofaninduction-typeenergymeterandlabelitsdifferent

parts.Commentonthedifferentmaterialsusedforthedifferentinternalcomponents.

2.Whybrakingtorqueisnecessaryininductiontypeenergymeters?Drawandexplainhowbrakingarrangementisdonesuchinstruments.

3.Whyisitnecessarytohavelagadjustmentdevicesininductiontypeenergymeters?Drawandexplaininbrief,operationofsucharrangementsinasingle-phaseenergymeter.

4.Whatistheeffectoffrictionininduction-typeenergymeters?Howisitovercomeinpractice?

5. What is creeping error in an energymeter?What are its possible causes?How can it be compensated in aninductiontypeenergymeter?

6.Explaintheeffectsofover-loadininductiontypeenergymeters.Howcanthiseffectbeavoided?

7. Why can sudden voltage variations cause errors in induction type energymeter readings?Discuss how theseerrorscanbeminimized.

8.Listthetestsnormallycarriedoutonsinglephaseenergymeters?Whyphantomloadingarrangementisdonefortestinghighcapacityenergymeters?

Long-answerQuestions1.Deriveanexpressionforthedrivingtorqueinasinglephaseinductiontypemeter.Showthatthedrivingtorqueis

maximumwhenthephaseanglebetweenthetwofluxesis900andtherotatingdiscispurelynon-inductive.

2. Draw the schematic diagram of the internal operating parts of a single phase induction type energy meter.Commentofthematerialsusedandoperationofthedifferentinternalparts.

3. Draw and describe the relevant phasor diagram and derive how the number of revolutions in a single phaseinductiontypeenergymeterisproportionaltotheenergyconsumed.

4.(a)Explainthesourcesoferrorinasinglephaseinductiontypeenergymeter.

(b)A220V,5Aenergymeteronfullloadunitypowerfactortestmakes60revolutionsin360seconds.Ifthedesignedspeedofthediscis550revolutionsperkWh,findthepercentageerror.

5.(a)Whatisphaseangleerrorinaninductiontypeenergymeter?Explainhowthiserrorisreducedinasinglephaseinductiontypeenergymeter.

(b)Anenergymeterisdesignedtohave60revolutionsofthediscperunitofenergyconsumed.Calculatethenumberofrevolutionsmadebythediscwhenmeasuringtheenergyconsumedbyaloadcarrying20Aat230Vand0.4powerfactor.Findthepercentageerrorifthemeteractuallymakes110revolutions.

6.(a)Whatistheeffectoffrictionininduction-typeenergymeters?Howisitovercome?Whatiscreepingerror?Howisitovercome?

(b)A230Vsingle-phasewatthourmeterrecordsaconstantloadof5Afor6hoursatunitypowerfactor.Ifthemeterdiscmakes2760revolutionsduringthisperiod,whatisthemeterconstantintermsofrevolutionsperunit?Calculatetheloadpowerfactorifthenumberofrevolutionsmadebythemeteris1712whenrecording4Aat230Vfor5hours.

7.(a)Whatarethetestsnormallycarriedoutonsingle-phaseenergymeters?Whyisphantomloadingarrangementisdonefortestinghighcapacityenergymeters?

(b) A230V,5Adcenergymeteris testedforitsnameplateratings.Resistanceofthepressurecoilcircuit is6000Ωandthatofcurrentcoilitselfis0.15Ω.Calculatetheenergyconsumedwhentestingforaperiodof2hourswith

(i) Directloadingarrangement

(ii) Phantomloadingwiththecurrentcoilcircuitexcitedbyaseparate6Vbattery

9.1 INTRODUCTION

TheCathodeRayOscilloscope(CRO)isaveryusefulandversatilelaboratoryinstrumentused for display, measurement and analysis of waveform and other phenomena inelectricalandelectroniccircuits.CROsare, in fact,veryfastX-Y plotters,displayinganinput signal versus another signal or versus time. The ‘stylus’ of this ‘plotter’ is aluminous spotwhichmoves over the display area in response to an input voltage. Theluminous spot is produced by a beam of electrons striking a fluorescent screen. Theextremelylowinertiaeffectsassociatedwithabeamofelectronsenablessuchabeamtobeusedfollowingthechangesininstantaneousvaluesofrapidlyvaryingvoltages.

The normal form of a CRO uses a horizontal input voltage which is an internallygenerated ramp voltage called ‘time base’. The horizontal voltagemoves the luminousspotperiodicallyinahorizontaldirectionfromlefttorightoverthedisplayareaorscreen.TheverticalinputtotheCROisthevoltageunderinvestigation.Theverticalinputvoltagemovestheluminousspotupanddowninaccordancewiththeinstantaneousvalueofthevoltage.Theluminousspotthustracesthewaveformoftheinputvoltagewithrespecttotime.Whentheinputvoltagerepeatsitselfatafastrate,thedisplayonthescreenappearsstationary on the screen. The CRO thus provides a means of visualising time-varyingvoltages. As such, the CRO has become a universal tool in all kinds of electrical andelectronicinvestigation.

9.2 BLOCKDIAGRAMOFACATHODERAYTUBE(CRT)

Themainpartof theCRO isCathodeRayTube (CRT). Itgenerates theelectronbeam,acceleratesthebeamtoahighvelocity,deflectsthebeamtocreatetheimageandcontainsa phosphor screen where the electron beam eventually becomes visible. The phosphorscreen is coated with ‘aquadag’ to collect the secondary emitted electrons. Foraccomplishingthesetasks,variouselectricalsignalsandvoltagesarerequired,whichareprovidedbythepowersupplycircuitoftheoscilloscope.Lowvoltagesupplyisrequiredfortheheateroftheelectrongunforgenerationofelectronbeamandhighvoltage,oftheorder of few thousand volts, is required for cathode ray tube to accelerate the beam.Normalvoltagesupply,saya fewhundredvolts, is requiredforothercontrolcircuitsoftheoscilloscope.

Horizontalandverticaldeflectingplatesarefittedbetweentheelectrongunandscreentodeflectthebeamaccordingtotheinputsignal.Theelectronbeamstrikesthescreenandcreatesavisiblespot.Thisspot isdeflectedonthescreeninthehorizontaldirection(X-

axis) with constant time dependent rate. This is accomplished by a time base circuitprovidedintheoscilloscope.Thesignaltobeviewedissuppliedtotheverticaldeflectionplates through the vertical amplifier, which raises the potential of the input signal to alevelthatwillprovideusabledeflectionoftheelectronbeam.Nowelectronbeamdeflectsin two directions, horizontal on X-axis and vertical on Y-axis. A triggering circuit isprovidedforsynchronisingtwotypesofdeflectionssothathorizontaldeflectionstartsatthesamepointoftheinputverticalsignaleachtimeitsweeps.Abasicblockdiagramofageneral-purposeoscilloscopeisshowninFigure9.1(a)andaschematicofinternalpartsofaCRTisshowninFigure9.1(b).

Figure9.1(a)Blockdiagramofageneral-purposeCRO

Figure9.1(b)CathodeRayTube(CRT)

9.3 ELECTROSTATICDEFLECTION

Figure9.2showsageneralarrangementforelectrostaticdeflection.Therearetwoparallelplateswithapotentialappliedbetween.Theseplatesproduceauniformelectrostaticfiledin theY direction.Thus any electron entering the fieldwill experience a force in theYdirectionandwillbeaccelerateinthatdirection.ThereisnoforceeitherinXdirectionorZdirectionandhencetherewillbenoaccelerationofelectronsinthesedirections.

Figure9.2Electrostaticdeflection

Let,Ea=voltageofpre-acceleratinganode;(volt)

e = chargeofanelectron;(Coulomb)m = massofelectron;(kg)θ = deflectionangleoftheelectronbeamvox = velocityofelectronwhenenteringthefieldofdeflectingplates;(m/s)Ed = potentialdifferencebetweendeflectingplates;(volt)d = distancebetweendeflectingplates;(m)ld = lengthofdeflectingplates;(m)L = distancebetweenscreenandthecentreofthedeflectingplates;(m)y = displacementoftheelectronbeamfromthehorizontalaxisattimet

andD=deflectionoftheelectronbeamonthescreeninYdirection;(m)

The loss of potential energy (PE ) when the electron moves from cathode toacceleratinganode;

Thegaininkineticenergy(KE)byanelectron

ThisisthevelocityoftheelectronintheXdirectionwhenitentersthedeflectingplates.ThevelocityintheXdirectionremainssamethroughoutthepassageofelectronsthroughthedeflectingplatesasthereisnoforceactinginthedirection.

SupposeayistheaccelerationoftheelectronintheYdirection,therefore,

Asthere isno initialvelocity in theYdirection[Eq. (9.8)], thedisplacementyatanyinstanttintheYdirectionis

AsthevelocityintheXdirectionisconstant,thedisplacementinXdirectionisgivenby

SubstitutingtheabovevalueoftinEq.(9.8),wehave

Thisistheequationofaparabola.

Puttingx=ldinEq.(9.12),wegetthevalueoftanθ.

After leaving thedeflectionplates, the electrons travel in a straight line.The straightlineoftravelofelectronistangenttotheparabolaatx=ldandthistangentintersectstheXaxisatpointO’.Thelocationofthispointisgivenby

Theapparentorigin is thus thecentreof thedeflectingplates, thedeflectionDon thescreenisgivenby

FromEq.(9.16)weconcludethefollowing:

For a given accelerating voltage Ea, and for particular dimensions of CRT, thedeflection of the electron beam is directly proportional to the deflecting voltage. ThismeansthattheCRTmaybeusedasalinearindicatingdevice.

ThediscussionsaboveassumethatEd isa fixeddcvoltage.Thedeflectionvoltage isusuallyatimevaryingquantityandtheimageonthescreenthusfollowsthevariationofthedeflectionsvoltageinalinearmanner.

Thedeflectionisindependentofthe(e/m)ratio.Inacathoderaytube,inadditiontotheelectronsmany typesof negative ions such as oxygen, carbon, chlorine etc arepresent.With electrostatic deflection system, because deflection is independent of e/m, the ions

travelwith the electrons and are not concentrated at onepoint.Hence cathode ray tubewithelectrostaticdeflectionsystemdoesnotproduceanionburn.

Thedeflectionsensitivity of aCRT is defined as thedeflectionof the screenper unitdeflectionvoltage.

ThedeflectionfactorofaCRTisdefinedasthereciprocalofsensitivity

ItisclearfromEq.(9.17),thatthesensitivitycanbeincreasedbydecreasingthevalueof accelerating voltageEa. but this has a disadvantage as the luminosity of the spot isdecreasedwithdecreaseinEa.On theotherhandahighvalueofEa,producedahighlyacceleratedbeamand thusproducesabright spot.However, ahighacceleratingvoltage(Ea) requires a high deflection potential (Ed) for a given deflection. Also, highlyacceleratedbeamismoredifficulttodeflectandissometimescalledhardbeam.

Example9.1 AnelectricallydeflectedCRThasa finalanodevoltageof2000Vandparalleldeflectingplates1.5cmlongand5mmapart. If the screen is 50 cm from the centre of deflectingplates,find(a)beamspeed,(b)thedeflectionsensitivityofthetube,and(c)thedeflectionfactorofthetube.

SolutionVelocityofthebeam

Deflectionsensitivity,

Example9.2 CalculatethemaximumvelocityofthebeamofelectronsinaCRT having a anode voltage of 800V.Assume that theelectrons to leave the anodewith zero velocity.Charge ofelectron = 1.6 × 10−19 C and mass of electron = 9.1 ×10−31kg.

SolutionVelocityofelectronis

Example9.3 ACRThasananodevoltageof2000Vand2cmlongand5mm apart parallel deflecting plates. The screen is 30 cmfromthecentreoftheplates.Findtheinputvoltagerequiredto deflect the beam through 3 cm. The input voltage isapplied to the deflecting plates through amplifiers havinganoverallgainof100.

Solution

9.4 TIMEBASEGENERATOR

Generally,oscilloscopesareusedtodisplayawaveformthatvariesasafunctionoftime.Forthewaveformtobeaccuratelyreproduced,thebeammusthaveaconstanthorizontalvelocity. Since the beam velocity is a function of the deflecting voltage, the deflectingvoltagemustincreaselinearlywithtime.Avoltagewiththischaracteristiciscalledarampvoltage.Ifthevoltagedecreasesrapidlytozerowiththewaveformrepeatedlyreproduced,asshowninFigure9.3,thepatternisgenerallycalledasawtoothwaveform.

During thesweep time,Ts, thebeammoves from left to rightacross theCRTscreen.Thebeamisdeflectedtotherightbytheincreasingamplitudeoftherampvoltageandthefact that the positive voltage attracts the negative electrons. During the retrace time orflybacktime,Tr,thebeamreturnsquicklytotheleftsideofthescreen.ThisactionwouldcausearetracelinetobeprintedontheCRTscreen.Toovercomethisproblemthecontrolgridisgenerally‘gatedoff’,whichblanksoutthebeamduringretracetimeandpreventsanundesirableretracepatternfromappearingonthescreen.

Figure9.3Typicalsawtoothwaveformappliedtothehorizontaldeflectionplates

Inlow-costoscilloscopesthetimebaseissaidtobefreerunning,althoughthetimebaseoscillatormay, in fact, be synchronised to the vertical amplifier signal.Unless the timebase is so synchronous, thewaveformmarches across the screen and remains unstable.

Synchronisationmeansthatthetimebasesignalsweepsacrossthescreeninatimethatisequaltoanintegernumberofverticalwaveformperiods.TheverticalwaveformwillthenappearlockedontheCRTscreen.

The vertical sector consists of a wideband preamplifier and power amplifiercombination thatdrivers theCRTverticaldeflectionplates.Thevertical amplifierhas ahigh gain, so large signals must be passed through an attenuator or, in low costoscilloscopes,averticalgaincontroller.

9.5VERTICALINPUTANDSWEEPGENERATORSIGNALSYNCHRONISATION

SeveralwaveformsthatareneededtobeobservedwiththehelpofCROwillbechangingat a rate much faster than the human eye can sense, perhaps many million times persecond.Toobservesuchrapidchanges,thebeammustretracethesamepatternrepeatedly.If the pattern is retraced in such a manner that the pattern always occupies the samelocationonthescreen,itwillappearasstationary.Thebeamwillretracethesamepatternatarapidrate.Iftheverticalinputsignalandthesweepgeneratorsignalaresynchronised,which means that the frequency of vertical input signal must be equal to or an exactmultipleof thesweepgeneratorsignal frequency,asshowninFigure9.4. If theverticalinputfrequencyisnotexactlyequaltooranexactmultipleofthesawtoothfrequency,thewaveformwillnotbesynchronisedandthedisplaymovesacrossthescreen.Ifthepatternmovestowardstheright,thefrequencyofthesawtoothwaveformistoohigh.Movementofthepatterntowardstheleftindicatesthatthefrequencyofthesawtoothistoolow.

Theverticalinputsignalandthesawtoothgeneratorsignalcanbesynchronizedintwodifferentways:

1.Freerunningsweep

2.Triggeredsweep

9.5.1FreeRunningSweepInlow-costoscilloscopes,thetimebaseissaidtobefreerunning.Intheseoscilloscopes,the sweep generator is continuously charging and discharging a capacitor. One rampvoltageisfollowedimmediatelybyanother;hence,thesawtoothpatternappears.Asweepgenerator working in this manner is said to be ‘free running’. In order to present astationarydisplayontheCRTscreen,thesweepgeneratorsignalmustbeforcedtoruninsynchronisationwith the vertical input signal. In basic or low-cost oscilloscopes this isaccomplishedbycarefullyadjustingthesweepfrequencytoavalueveryclosetotheexactfrequency of the vertical input signal or a submultiple of this frequency. When bothsignals are at same frequency, an internal synchronising pulse will lock the sweepgeneratorintotheverticalinputsignal.Thismethodofsynchronisationhassomeseriouslimitationswhenanattemptismadetoobservelowamplitudesignals,becauseitisverydifficulttoobservethataverylowamplitudesignalisstationaryormovableintheCRTscreen.However,themostseriouslimitationisprobablytheinabilityoftheinstrumentto

maintain synchronisationwhen the amplitude or frequency of the vertical signal is notconstant,suchasvariablefrequencyaudiosignalorvoice.

Figure9.4SynchronisedwaveformsandCRTdisplay

9.5.2TriggeredSweepIn free running sweep oscillators, it is not possible to observe the signals of variablefrequency. The limitation is overcome by incorporating a trigger circuit into theoscilloscopeasshowninFigure9.5.Thetriggercircuitmayreceiveaninputfromoneofthree sources depending on the setting of the trigger selecting switch. The input signalmaycomefromanexternalsourcewhenthetriggerselectorswitchissettoEXT,fromalow amplitude ac voltage at line frequencywhen the switch is set to line, or from theverticalamplifierwhentheswitchisset toINT.WhensetforInternalTriggering(INT),the trigger circuit receives its input from the vertical amplifier.When the vertical inputsignalthatisbeingamplifiedbytheverticalamplifiermatchesacertainlevel,thetriggercircuitprovidesapulsetothesweepgenerator,therebyensuringthatthesweepgeneratoroutputissynchronisedwiththesignalthattriggersit.

Figure9.5Blockdiagramofanoscilloscopewithtriggeredsweep.

Schmitt trigger or a voltage level detector circuit is frequently used in the ‘triggercircuit’blockofFigure9.5.Basically, theSchmitt triggercomparesan inputvoltage, in

thiscasefromtheverticalamplifier,withapre-setvoltage.

9.6MEASUREMENTOFELECTRICALQUANTITIESWITHCRO

TheCROisaveryversatileinstrumentinlaboratoryformeasurementofvoltage,current,frequency and phase angle of any electrical quantity. But beforewe go aheadwith thediscussion on measurement of electrical quantities with a CRO, we should understandsomebasicoscilloscopepatterns.

BasicOscilloscopePatternsAssumethatasinusoidalvoltageisappliedtothehorizontaldeflectingplateswithoutanyvoltagesignaltotheverticaldeflectingplates,asshowninFigure9.6.Onehorizontallinewillappearon the screenof theCRO.This linewouldbe in thecentralpositionon thescreenvertically.

Figure9.6Deflectionforasinusoidalvoltageappliedtothehorizontaldeflectionplates

Ifasinusoidalvoltagesignalisappliedtotheverticaldeflectingplateswithoutapplyingany voltage signal to the horizontal deflecting plates thenwe get a vertical line on thescreenofCRO,asshowninFigure9.7.Thislinewouldbeinthecentralpositiononthescreenhorizontally.

Now we would discuss what happens when both vertical and horizontal deflectionplatesaresuppliedwithsinusoidalvoltagesignalssimultaneously.Letusconsiderwhentwosinusoidalsignalsequalinmagnitudeandfrequencyandinphasewitheachotherareapplied to both of the horizontal and vertical deflection plates, as shown in Figure9.8.Herewegetastraightlineinclinedat45°tothepositiveX-axis.

Figure9.7Deflectionforasinusoidalvoltageappliedtotheverticaldeflectingplates

Figure9.8Deflectionforsinusoidalvoltagesignalsinphaseandequalinmagnitudeandfrequency,appliedtohorizontalandverticaldeflectionplates

Nowletusconsideracasewhentwosinusoidalvoltagesignalsappliedtothehorizontalandverticaldeflectionplatesareofequalmagnitudeandequalfrequencybutoppositeinphase,asshowninFigure9.9.Wegeta straight line inclinedat135° to thepositiveX-axis.

In the last case, if the two sinusoidal voltage signals, 90° out of phase and of equalmagnitudeandequalfrequency,areappliedtothehorizontalandverticaldeflectionplates,acirclewouldappearonthescreenasshowninFigure9.10.

Figure9.9Deflectionforsinusoidalvoltagesignalsequalinmagnitudeandfrequencybutoppositeinphase,appliedtohorizontalandverticaldeflectionplates

Figure9.10Deflectionforsinusoidalvoltagesignalsequalinmagnitudeandfrequencybut90°outofphase,appliedtohorizontalandverticaldeflectionplates

9.7 MEASUREMENTOFVOLTAGEANDCURRENT

Theexpressionforelectrostaticdeflectionis ,where

L = distancebetweenscreenandthecentreofthedeflectingplatesId = lengthofdeflectingplatesEd = potentialbetweendeflectingplatesd = distancebetweendeflectingplatesEa = voltageofpreacceleratinganode

Sodeflectionisproportionaltothedeflecting-platevoltage.Thus,thecathoderaytubewillmeasurevoltage.Itisusedtocalibratethetubeunderthegivenoperatingconditionsbyobservingthedeflectionproducedbyaknownvoltage.Directvoltagemaybeobtainedfrom the static deflection of the spot, alternating voltage from the length of the lineproducedwhenthevoltageisappliedtoY-plateswhilenovoltageisappliedtoX-plates.The length of the line corresponds to the peak to peak voltage. While dealing withsinusoidalvoltages,thermsvalueisgivenbydividingthepeaktopeakvoltageby

Formeasurementofcurrent,thecurrentundermeasurementispassedthroughaknownnoninductiveresistanceandthevoltagedropacrossitismeasuredbyCRO,asmentionedabove.Thecurrentcanbedeterminedsimplybydividing thevoltagedropmeasuredbythevalueofnon inductiveresistance.When thecurrent tobemeasured isofverysmallmagnitude, the voltage drop across noninductive resistance (small value) is usuallyamplifiedbyacalibratedamplifier.

9.8 MEASUREMENTOFFREQUENCY

It is interesting to consider the characteristicsofpatterns that appearon the screenof aCROwhensinusoidalvoltagesare simultaneouslyapplied to thehorizontal andverticalplates.ThesepatternsarecalledLissajouspatterns.

Lissajous patterns may be used for accurate measurement of frequency. The signal,whose frequency is to bemeasured, is applied to theY-plates.An accurately calibratedstandard variable frequency source is used to supply voltage to the X-plates, with theinternalsweepgeneratorswitchedoff.Thestandardfrequencyisadjusteduntilthepatternappears as a circle or an ellipse, indicating that both signals areof the same frequency.Whereitisnotpossibletoadjustthestandardsignalfrequencytotheexactfrequencyoftheunknownsignal,thestandardisadjustedtoamultipleorsubmultipleofthefrequencyoftheunknownsourcesothatthepatternappearsstationary.

Letusconsideranexample.SupposesinewavesareappliedtoXandYplatesasshowninFigure9.11.LetthefrequencyofwaveappliedtoYplatesistwicethatofthevoltageappliedtotheXplates.ThismeansthattheCRTspottravelstwocompletecyclesintheverticaldirectionagainstoneofthehorizontaldirection.

Thetwowavesstartatthesameinstant.ALissajouspatternmaybeconstructedintheusualwayanda8shapedpatternwithtwoloopsisobtained.Ifthetwowavesdonotstartat the same instantweget different pattern for the same frequency ratio.TheLissajouspatternfortheotherfrequencyratioscanbesimilarlydrawn.SomeofthesepatternsareshowninFigure9.12.

Figure9.11Lissajouspatternwithfrequencyratio2:1

Figure9.12Lissajouspatternswithdifferentfrequencyratio

Itcanbeshownthatforalltheabovecases,theratiosofthetwofrequenciesis

wherefy=FrequencyofsignalappliedtoYplates

fx=FrequencyofsignalappliedtoXplates

The above rule, however, does not hold for the Lissajous patternswith free ends asshown in Figure 9.13. The simple rule mentioned above needs the followingmodifications:

Two lines are drawn, one horizontal and the other vertical so that they do not passthrough any intersections of different parts of the Lissajous curve. The number ofintersections of the horizontal and the vertical lines with the Lissajous curve areindividuallycounted.Thefrequencyratioisgivenby

TheapplicationsoftheserulestoFigure9.13(a)givesafrequencyratio

Themodified rule is applicable in all caseswhether the Lissajous pattern is open orclosed.

Figure9.13Lissajouspatternwithhalftangencies

TheratiooffrequencieswhenopenendedLissajouspatternsareobtainedcanalsobefoundbytreatingtheopenendsashalftangenciesasshowninFigure9.13(b).

Thereare some restrictionson the frequencieswhichcanbeapplied to thedeflectionplates. One obviously, is that the CRO must have the bandwidth required for thesefrequencies. The other restriction is that the ratio of the two frequencies should not besuchastomakethepatterntoocomplicatedotherwisedeterminationoffrequencywouldbecomedifficult.Asarule,ratiosashighas10:1andaslowas10:9canbedeterminedcomfortably.

9.9 MEASUREMENTOFPHASEDIFFERENCE

Whentwosinusoidalvoltagesofequalfrequencywhichareinphasewitheachotherareappliedtothehorizontalandverticaldeflectingplates,thepatternappearingonthescreenisastraightlineasisclearfromFigure9.14.

Thuswhentwoequalvoltagesofequalfrequencybutwith90°phasedisplacementareappliedtoaCRO,thetraceonthescreenisacircle.ThisisshowninFigure9.15.

Figure9.14Lissajouspatternwithequalfrequencyvoltagesandzerophaseshift

Figure9.15Lissajouspatternwithequalvoltagesandaphaseshiftof90°

WhentwoequalvoltagesofequalfrequencybutwithaphaseshiftФ(notequalto0or90°)areappliedtoaCRO,weobtainanellipseasshowninFigure9.16.AnellipseisalsoobtainedwhenunequalvoltagesofsamefrequencyareappliedtotheCRO.

A number of conclusions can be drawn from the above discussions. When twosinusoidal voltages of same frequency are applied, a straight line resultswhen the twovoltagesareequalandareeitherinphasewitheachotheror180°outofphasewitheachother.Theangle formedwith thehorizontal is45°when themagnitudesofvoltagesareequal. An increase in the vertical deflecting voltage causes the line to have an anglegreaterthan45°withthehorizontal.

Figure9.16LissajouspatternwithtwoequalvoltagesofsamefrequencyandphaseshiftofФ

Two sinusoidalwaveforms of the same frequency produce a Lissajous patternwhichmaybeastraightline,acircleoranellipsedependinguponthephaseandthemagnitudeofthevoltages.

Figure9.17Lissajouspatternwithdifferentphaseshift

Acirclecanbeformedonlywhenthemagnitudeof thetwosignalsareequalandthephasedifferencebetweenthemiseither90°or270°.However,ifthetwovoltagesareoutofphaseanellipseisformed.

It is clear from Figure 9.17 that for equal voltages of same frequency, progressivevariationofphasevoltagecausesthepatterntovaryfromastraightdiagonallinetoellipseofdifferenteccentricitiesandthentoacircle,afterthatthroughanotherseriesofellipsesandfinallyadiagonalstraightlineagain.

Regardlessoftheamplitudesoftheappliedvoltagestheellipseprovidesasimplemeansoffindingphasedifferencebetweentwovoltages.ReferringtoFigure9.18,thesineofthephaseanglebetweenthevoltagesisgivenby

Forconvenience,thegainsoftheverticalandhorizontalamplifiersareadjustedsotheellipsefitsexactlyintoasquaremarkedbythelinesofthegraticule.

Ifthemajoraxisoftheellipseliesinthefirstandthirdquadrants(i.e.,positiveslope)asinFigure9.18(a), thephaseangle iseitherbetween0° to90°orbetween270° to360°.Whenthemajoraxisofellipseliesinsecondandfourthquadrants,i.e.,whenitsslopeisnegativeasinFigure9.18(b),thephaseangleiseitherbetween90°and180°orbetween180°and270°.

Figure9.18Determinationofangleofphaseshift

9.10 SAMPLINGOSCILLOSCOPE

Thisoscilloscopeisspeciallyusedforobservingveryhighrepetitiveelectricalsignalsbysampling the input waveform and reconstructing its shape from the sample. Such highfrequencysignalscannotbeviewedbyaconventionaloscilloscopebecauseitsfrequencyrange is limited by the gain bandwidth product of its vertical amplifier. The samplingfrequency may be as low as 1/100th of the input signal frequency, i.e., an ordinaryoscilloscope having a bandwidth of 10MHz can be used for observing input signal offrequency as high as 1000MHz.Asmany as 1000 samples are used to reconstruct theoriginalwaveform.

A block diagram of a sampling oscilloscope is given in Figure 9.19. The inputwaveform, whichmust be repetitive, as applied to the sampling gate. Sampling pulsesmomentarily bias the diodes of the balanced sampling gate in the forward direction,therebybrieflyconnectingthegateinputcapacitancetothetestpoint.Thesecapacitorsare

slightly charged toward the voltage level of the input circuit. The capacitor voltage isamplified by a vertical amplifier and applied to the vertical deflecting plates. Thesamplingmustbesynchronisedwiththeinputsignalfrequency.Thesignal isdelayedintheverticalamplifier,allowingthehorizontalsweeptobeinitiatedbytheinputsignal.

Figure9.19Blockdiagramofsamplingoscilloscope

Atthebeginningofeachsamplingcycle,thetriggerpulseactivatesanoscillatorandalinear ramp voltage is generated. The ramp voltage is applied to a voltage comparatorwhichcompares therampvoltage toastaircasegeneratoroutputvoltage.When the twovoltagesareequalinamplitude,thestaircasegeneratorisallowedtoadvanceonestepandsimultaneouslyasamplingpulseisappliedtothesamplinggate.Atthismoment,asampleoftheinputvoltageistaken,amplifiedandappliedtotheverticaldeflectingplates.

TheresolutionofthefinalimageonthescreenoftheCRTisdeterminedbythesizeofthe steps of the staircase generator. The smaller the size of these steps, the larger thenumberofsamplesandthehighertheresolutionoftheimage.

The sampling oscilloscope can be employed beyond 50 MHz into the UHF rangearound 500MHz and beyond up to 10GHz.However, sampling techniques cannot beusedforthedisplayoftransientswaveformsastheyarenotrepetitivesignals.

9.11 STORAGEOSCILLOSCOPE

Therearetwotypesofstorageoscilloscopes,namely,

1.Analogstorageoscilloscope

2.Digitalstorageoscilloscop

9.11.1AnalogStorageOscilloscopeStorage targets can be distinguished from standard phosphor targets by their ability toretainawaveformpatternforalongtime(10to15hoursafterthepatternisproducedonthe screen). In a conventional CRT, the persistence of the phosphor varies from a fewmilliseconds to several seconds as a result ofwhich,where persistence of the screen issmaller than the rate atwhich the signal sweeps across the screen, and the start of thedisplaywouldfadebeforetheendiswritten.

Ananalogstorageoscilloscopeusesthephenomenonofsecondaryelectronemissionto

build up and store electrostatic charges on the surface of an insulated target. Suchoscilloscopesarewidelyused(i)forreal-timeobservationofeventsthatoccuronlyonce,and(ii)fordisplayingthewaveformofaverylowfrequency(VLF)signal.

TheconstructionofaCRTusingvariablepersistencestoragetechnique,calledthehalf-toneormeshstorageCRTisshowninFigure9.20.WiththevariablepersistencetheslowswepttracecanbestoredondisplaycontinuouslybyadjustingthepersistenceoftheCRTscreentomatchthesweeptime.

Figure9.20Analogstorageoscilloscope

AmeshstorageCRT,illustratedinFigure9.20,containsastoragemesh,floodgunsandacollimator,inadditiontoalltheelementsofastandardCRT.Thestoragemeshthatisthestorage target behind the phosphor screen is a conductivemesh coveredwith dielectricmaterial consisting of a thin layer ofmaterial such asmagnesium fluoride.Thewritinggunisahigh-energyelectrongunsimilartotheconventionalgun,givinganarrowfocusedbeamwhichcanbedeflectedandusedtowritetheinformationtobestored.Thewritinggun etches a positively charged pattern on the storagemesh or target by knocking offsecondary emission electrons. This positively charged pattern remains exactly in thepositiononthestoragetargetwhereitisdeposited.Thisisduetotheexcellentinsulatingproperty of the magnesium fluoride coating on the storage target. The electron beam,which isdeflected in theconventionalmanner,both inhorizontal andverticaldirection,tracesoutthewavepatternonthestoragemesh.Inordertomakethepatternvisible,evenafterseveralhours,specialelectronguns,knownasthefloodgunsareswitchedon.

ThefloodgunsareofsimpleconstructionandareplacedinsidetheCRTinapositionbetween thedirectionplates and the storage target and they emit low-velocity electronscoveringalargeareatowardsthescreen.Theelectronpathsareadjustedbythecollimatorelectrodes consisting of a conductive coating on the inside surface of the CRT. Thecollimatorelectrodesarebiasedsoastodistributethefloodgunelectronsevenlyoverthetargetsurfaceandcausestheelectronstobeperpendiculartothestoragemesh.Mostofthefloodelectronsarestoppedandcollectedbythecollectormeshand,therefore,neverreachthe phosphor screen. Only electrons near the stored positive charge are pulled to thestoragetargetwithsufficientforcetohitthephosphorscreen.TheCRTdisplay,therefore,will be an exact replica of the pattern whichwas initially stored on the target and thedisplaywillremainvisibleaslongasthefloodgunoperates.Forerasingofthepatternonthestoragetarget,anegativechargeisappliedtoneutralisethestoredpositivecharge.

For achieving variable persistence, the erase voltage is applied in the form of pulsesinsteadof a steadydcvoltage; byvarying thewidthof thesepulses the rateof erase iscontrolled.

9.11.2DigitalStorageOscilloscopeThere are a number of distinct disadvantages of the analog storage oscilloscope. Thesedisadvantagesarelistedbelow:

1. There is a finite amount of time that the storage tube can preserve a storedwaveform.Eventually,thewaveformwillbelost.Thepowertothestoragetubemustbepresentaslongastheimageistobestored.

2. Thetraceofastoragetubeis,generally,notasfineasanormalcathoderaytube.Thus,thestoredtraceisnotascrispasaconventionaloscilloscopetrace.

3. Thewriting rateof the storage tube is less thanaconventionalcathode ray tube,whichlimitsthespeedofthestorageoscilloscope.

4. Thestoragecathoderay tube isconsiderablymoreexpensive thanaconventionaltubeandrequiresadditionalpowersupplies.

5. Only one image can be stored. If two traces are to be compared, theymust besuperimposedonthesamescreenanddisplayedtogether.

A superior method if trace storage is the digital storage oscilloscope (DSO). In thistechnique,thewaveformtobestoredisdigitised,storedinadigitalmemoryandretrievedfordisplayonthestorageoscilloscope.Thestoredwaveformiscontinuallydisplayedbyrepeatedly scanning the stored waveform and, therefore, a conventional CRT can beemployedforthedisplayandthussomeofthecostoftheadditionalcircuitryfordigitizingandstoringtheinputwaveformisoffset.Thestoreddisplaycanbedisplayedindefinitelyaslongasthepowerisappliedtothememory,whichcanbesuppliedwithasmallbattery.Thedigitisedwaveformcanbefurtheranalysedbyeither theoscilloscopeorbyloadingthecontentof thememoryintoacomputer.Someofthedigitalstorageoscilloscopeuse12-bit converter, giving 0.025% resolution and 0.1% accuracy on voltage and timereadings, which are better than the 2.5% of analog storage oscilloscopes. Split screencapabilities(simultaneouslydisplayingliveanalogtracesandreplayedstoredones)enableeasycomparisonofthetwosignals.Pre-triggercapabilityisalsoanimportantadvantage.Thedisplayofstoreddata ispossible inbothamplitudeversus time,andX-Ymodes. InadditiontothefastmemoryreadoutemployedforCRTdisplay,aslowreadoutispossiblefordevelopinghardcopywithexternalplotters.

Theonlydrawbackofdigitalstorageoscilloscopesislimitedbandwidthbythespeedoftheiranalog-to-digitalconverters(ADCs).However,20MHzdigitisingratesavailableonsome oscilloscopes yield a bandwidth of 5 MHz, which is adequate for most of theapplications.

Figure 9.21 gives the block diagram of a digital storage oscilloscope (DSO). It usesbothofdigital-to-AnalogandAnalog-to-Digital(DACsandADCs)fordigitising,storinganddisplayinganalogwaveforms.Theoveralloperationiscontrolledandsynchronisedbythe control circuits. Which usually have microprocessor executing a control programstoredinRead-OnlyMemory(ROM).Thedataacquisitionportionofthesystemcontains

a sample-and-hold (S/H) and a analog-to-digital converter that repetitively samples anddigitized the input signal at a rate determined by the sample clock, and transmits thedigitiseddatatomemoryforstorage.Thecontrolcircuitmakessurethatsuccessivedatapoints are stored in successivememory locationsbycontinuallyupdating thememory’saddresscounter.

Figure9.21BlockdiagramofDigitalStorageOscilloscope(DSO)

Whenmemoryisfull,thenextdatapointfromtheADCisstoredinthefirstmemorylocation writing over the old data, and so on for successive data points. This dataacquisition and the storage process continue until the control circuit receives a triggersignal from either the input waveform (internal trigger) or an external trigger source.Whenthetriggeringoccurs,thesystemstopsacquiringdatafurtherandentersthedisplaymodeofoperation,inwhichallorpartofthememorydataisrepetitivelydisplayedontheCathodeRayTube(CRT).

IndisplayoperationtwoDACsareemployedforprovidingtheverticalandhorizontaldeflecting voltages for the cathode ray tube. Data from memory produce the verticaldeflection of the electron beam, while the time base counter provides the horizontaldeflection in the form of a staircase sweep signal. The control circuits synchronize thedisplayoperationbyincrementingthememoryaddresscounterandthetimebasecounterat the same time so that eachhorizontal stepof theelectronbeam is accompaniedbyanew data value from the memory to the vertical DAC. The counters are continuouslyrecycledsothatthestoreddatapointsarerepetitivelyre-plottedonthescreenoftheCRT.The screendisplay consists of discrete dots representing thevariousdatapoints but thenumberofdotsisusuallysolarge(typically1000ormore)thattheytendtoblendtogetherandappeartobeacontinuouswaveform.

Thedisplayoperationistransmittedwhentheoperatorpressesafrontpanelbuttonthatcommendsthedigitalstorageoscilloscopetobeginanewdataacquisitioncycle.

9.12 MULTI-INPUTOSCILLOSCOPES

Modem oscilloscopes have the multi-input facility. They display the multi input

simultaneously. Two inputs is most generally used, although four and eight inputs areavailable for special applications. There are two primary types: single beam and dualbeam.Asinglebeamcanbeconvertedintoseveraltraces.Adualbeam,ontheotherhandmay also subsequently be converted into a further number of traces. Two inputoscilloscopesaredescribed in thischapter, although theprinciplesareapplicable toanynumberofinputs.

9.12.1DualTraceOscilloscopesTheblockdiagramof a dual trace oscilloscope is shown inFigure9.22. There are twoseparate vertical input channels, A and B, and these use separate attenuator andpreamplifierstages.Thereforetheamplitudeofeachinput,asviewedontheoscilloscope,can be individually controlled. After preamplification, the two channels meet at theelectronic switch. This has the ability to pass one channel at a time into the verticalamplifier,viathedelayline.

Figure9.22Blockdiagramofadualtraceoscilloscope

Therearetwocommonoperatingmodesfortheelectronicswitch,calledalternateandchop, and these are selected from the instrument’s front panel. The alternate mode isillustratedinFigure9.23.Inthisfigure,theelectronicswitchalternatesbetweenchannelsAandB,lettingeachthroughforonecycleofthehorizontalsweep.Thedisplayisblankedduringtheflybackandhold-offperiods,asintheconventionaloscilloscope.Providedthesweep speed ismuchgreater than the decay timeof theCRTphosphor, the screenwillshowastableofboth thewaveformatchannelsAandB.Thealternatemodecannotbeusedfordisplayingverylow-frequencysignals.

Figure9.23Waveformsforadualchanneloscilloscopeoperatinginalternatingmode:(a)HorizontalSweepvoltage(b)VoltagetochannelA(c)VoltagetochannelB,(d)Gridcontrolvoltage

Thechoppedoperatingmodeof theelectronicswitch isshowninFigure9.24. In thismodetheelectronicsswitchfreerunsatahighfrequencyoftheorderof100kHzto500kHz.TheresultisthatsmallsegmentsfromchannelsAandBareconnectedalternatelytotheverticalamplifier,anddisplayingon thescreen.Provided thechopping rate ismuchfaster than the horizontal sweep rate, the displaywill show a continuous line for eachchannel.Ifthesweeprateapproachesthechoppingratethentheindividualsegmentswillbevisible,andthealternatemodeshouldnowbeused.

The time base circuit shown in Figure 9.22 is similar to that of a single inputoscilloscope. Switch S2 allow the circuit to be triggered on either the A orB channelwaveforms,oronlinefrequency,oronanexternalsignal.Thehorizontalamplifiercanbefedfromthesweepgenerator,ortheBchannelviaswitchS1.ThisistheX-YmodeandtheoscilloscopeoperatesfromchannelAastheverticalsignalandchannelBasthehorizontalsignal,givingveryaccurateX-Ymeasurements.Severaloperatingmodescanbeselectedfromthefrontpanelfordisplay,suchaschannelAonly,channelBonly,channelsAandBastwotraces,andsignalsA+B,A−B,B−Aor−(A+B)asasingletrace.

Figure9.24Waveformsforadualchanneloscilloscopeoperatinginchoppedmode:(a)Horizontalsweepvoltage(b)VoltagetochannelA(c)VoltagetochannelB,(d)Gridcontrolvoltage

9.12.2DualBeamOscilloscopesThedual traceoscilloscopecannotcapture two fast transientevents, as it cannot switchquickly enough between traces. The dual beam oscilloscope has two separate electronbeams,andthereforetwocompletelyseparateverticalchannels,asinFigure9.23.Thetwochannels may have a common time base system, as in Figure 9.22, or they may haveindependent time base circuits, as in Figure 9.25. An independent time base allowsdifferent sweeps rates for the two channels but increases the size and weight of theoscilloscope.

TwomethodsareusedforgeneratingthetwoelectronbeamswithintheCRT.Thefirstmethodusedadoubleguntube.Thisallowsthebrightnessandfocusofeachbeamtobe

controlledseparatelybutitisbulkierthanasplitbeamtube.

Inthesecondmethod,knownassplitbeam,asingleelectrongunisused.AhorizontalsplitterplateisplacedbetweenthelastanodeandtheYdeflectionplates.Thisplateisheldat thesamepotentialas theanode,anditgoesalongthelengthof thetube,betweenthetwo vertical deflection plates. It therefore isolates the two channels. The split beamarrangement has half the brightness of a single beam,which has disadvantages at highfrequency operation. An alternative method of splitting the beam, which improves itsbrightness, is tohave twoapertures in the lastanode, insteadofone,so that twobeamsemergefromit.

Figure9.25Blockdiagramofadualbeamoscilloscopewithindependenttimebase

The disadvantage of the split beam construction is that the two displays may havenoticeablydifferentbrightness,ifoperatedatwidelyspacedsweepspeeds.Thebrightnessandfocuscontrolsalsoaffectthetwotracesatthesametime.

9.13 FREQUENCYLIMITATIONOFCRO

DeflectionofelectronbeamonthescreeninYdirectionisgivenby ,whereEdisthe potential between deflecting plates. In this derivation, the plate voltage is assumedconstant during the motion of the electrons through the deflecting field. If the voltageapplied to the vertical deflecting plates change during the transit time of the electronsthroughthehorizontalplates,thedeflectionsensitivitygetsdecreased.

wherel=lengthofdeflectingplates

Vox=velocityofelectronwhileenteringthefieldofdeflectingplates.

Thetransittimeimposealimitationoftheupperfrequencylimit.Anupperfrequencyisdefinedasthatfrequencyatwhichthetransittimeisequaltoonequarter oftheperiodofthevoltageappliedtoverticalplates.

Thefrequencyrangeoftheoscilloscopecanbeincreasedbysub-dividingthedeflectingplatesinanumberofsectionsinthepathofelectronbeam.Thevoltagebeingmeasuredisapplied to the vertical plates through an iterative network, whose propagation timecorrespondstothevelocityofelectron;therebythevoltageappliedtotheverticalplatesismadetosynchronisewiththevelocityofthebeam.TheuseofthistechniqueallowstheCROtobeuseduptofrequenciesof500MHzandabove.

EXERCISE

Objective-typeQuestions1.ThetimebasesignalinaCROis

(a)asinusoidalsignal

(b)asawtoothsignal

(c)asquarewavesignal

(d)atriangularwavesignal

2.InCRTaquadagcarries

(a)secondaryemissionelectrons

(b)sweepvoltage

(c)aqueoussolutionofgraphite

(d)noneofthese

3.InaCRO,thesawtoothvoltageisappliedatthe

(a)cathode

(b)acceleratinganode

(c)verticaldeflectingplates

(d)horizontaldeflectingplates

4.ThepurposeofthesynchronisingcontrolinaCROisto

(a)adjusttheamplitudeofdisplay

(b)controltheintensityofthespot

(c)focusthespotonthescreen

(d)lockthedisplayofsignal

5.Retraceperiodforanidealsawtoothwaveformis

(a)0second

(b)equaltotracingperiod

(c)infinite

(d)noneofthese

6.InaCRT,thehighestpositivepotentialisgivento

(a)cathode

(b)focusingelectrodes

(c)verticaldeflectingplates

(d)post-deflectionaccelerationanode

7.TheXandYinputsofaCROarerespectivelyVsinωtand−Vsinωt.TheresultingLissajouspatternwillbe

(a)astraightline

(b)acircle

(c)theshapeof8

(d)anellipse

8.Thepatternsusedtomeasurephaseandfrequencywithacathoderayoscilloscopearecalled

(a)Faraday’spattern

(b)Ohm’spatterns

(c)Lissajouspattern

(d)Phillipspattern

9. Thevoltage10 cosωtandV cos (ωt +α) are applied to theX andY plates of aCRO.TheLissajous figureobservedonthescreenisastraightlineof60°tothepositiveaxis.Then

(a)V=10,α=60°

(b)V=10,α=0°

(c)V=10 ,α=60°

(d)V=10 ,α=0°

10.Samplingoscilloscopesarespeciallydesignedtomeasure

(a)veryhighfrequency

(b)verylowfrequency

(c)microwavefrequency

(d)noneofthese

11.Whichofthefollowingstatementsisnotcorrectforastorage-typeoscilloscope?

(a)Secondaryemissionelectronsetchapositivelychargedpattern.

(b)Thefloodgunsusedfordisplay,emithighvelocityelectrons.

(c)Thefloodgunsareplacedbetweenthedeflectionplatesandstoragetarget.

(d)Thestoragetargetisaconductivemeshcoveredwithmagnesiumfluoride.

12.Inadigitaloscilloscope,theA/Dconvertersareusually

(a)ramptype

(b)flashtype

(c)integratingtype

(d)successiveapproximatetype

13.Adoublebeamoscilloscopehas

(a)twoscreens

(b)twoelectronguns

(c)twodifferentphosphorcoatings

(d)onewaveformdividedintotwoparts

14.TwoequalvoltagesofsamefrequencyappliedtotheXandYplatesofaCRO,produceacircleonthescreen.Thephasedifferencebetweenthetwovoltagesis

(a)150°

(b)90°

(c)60°

(d)30°

15.TheLissajouspatternonaCROscreenisshowninthegivenfigure: Thefrequency

ratiooftheverticalsignaltothehorizontaloneis

(a)3:2

(b)2:3

(c)5:1

(d)1:5

Short-answerQuestions1.WhatismeantbythedeflectionfactoranddeflectionsensitivityofaCRO?Whatisaquadag?

2.Discusstheadvantagesanddisadvantagesofanaloganddigitaltypeofoscilloscope.

3.ExplainthefunctioningofthetimebasegeneratorinaCROwithproperdiagram.

4.Describethephenomenonofsynchronisationofverticalinputsignaltoitssweepgenerator.

5.DiscussthetriggeredsweepinaCRO.

6.WhyisaCROconsideredoneofthemostimportanttoolsinthefieldofmodernelectronics?WhatistheheartofaCRO?

7.HowisthefrequencyofanacsignalmeasuredwiththehelpofCRO?

8.HowisthephasedifferencebetweentwosignalsmeasuredwiththehelpoftheCRO?

9.“ThefocusingsystemofaCROnamedasanelectrostaticlens.”Explain.

10.Whatarethedifferencesbetweendualtraceanddualbeamoscilloscopes?

Long-answerQuestions1.(a)DrawtheblockdiagramofaCROandexplainthedifferentcomponents.

(b)Thedeflectionsensitivityofanoscilloscopeis35V/cm.IfthedistancefromthedeflectionplatestotheCRTscreenis16cm,thelengthofthedeflectionplatesis2.5cmandthedistancebetweenthedeflectionplatesis1.2cm,whatistheaccelerationanodevoltage?

2. (a) Deriveanexpression for theverticaldeflectionon thescreenofacathoderay tube in termsof lengthofplates,separationdistance,acceleratingvoltageanddistanceofscreenfromtheorigin.

(b)InaCRT,thedistancebetweenthedeflectingplatesis1.0cm,thelengthofthedeflectingplatesis4.5cmandthedistanceofthescreenfromthecentreofthedeflectingplatesis33cm.Iftheacceleratingvoltagesupplyis300volt,calculatedeflectingsensitivityofthetube.

3. What areLissajouspatterns?From theLissajouspatterns,howcan the frequencyand thephasedifferencebemeasured?

4.Whataretheadvantagesofdualtraceoverdoublebeamformultitraceoscilloscopes?ExplaintheworkingofadualtraceCROwiththehelpoftheproperblockdiagram.

5.Explaintheworkingprincipleofasamplingoscilloscopewiththehelpofproperblockdiagram.Whatprecautionshouldbetakenwhenusingthesamplingoscilloscope?

6. Draw theblockdiagramof a storage-typeoscilloscopeandexplain theworkingof eachblock.Howdoes thedigitaloscilloscopedifferfromtheconventionalanalogstorageoscilloscope?

7.Writeshortnotesonthefollowing.

(a)Verticalamplifier

(b)Electromagneticfocusing

(c)Delayline

(d)FrequencyandphasemeasurementbyCRO

(e)Highfrequencyoscilloscope

(f)Freerunningsweep

(g)Oscilloscopelimitations

10.1 INTRODUCTION

Nowadayseveryoneisfamiliarwithanalogsignals.Theyareusedforthemovementofanelectromagneticmeter tomeasure voltage, current, resistance, power, etc.Although thebridgesandmultipliersuseelectricalcomponentsforthesemeasurements,theinstrumentsdescribedusenoamplifierstoincreasethesensitivityofthemeasurements.Theheartoftheseinstrumentswasthed’Arsonvalmeter,whichtypicallycannotbeconstructedwithafull-scale sensitivity of less than about 50 μA. Any measurement system using thed’Arsonvalmeter,without amplifiers,mustobtain at least50μA from the circuit undertest for a full-scale deflection. For themeasurement of currents of less than 50μA fullscale,anamplifiermustbeemployed.Theresistanceofasensitivemeter,suchasa50μAmeterforavolt-ohm-milliammeter,isoftheorderofafewhundredohmsandrepresentsa small but finite amount of power. As an example, 50 μA through a 200 Ω meterrepresents ½ microwatt. This represents the power required for a meter for full-scaledeflectionanddoesnotrepresentthepowerdissipatedintheseriesresistor,andthusthetotalpowerrequiredbytheexamplemeterwouldbegreaterthan½μWandwoulddependonthevoltagerange.Thisdoesnotsoundlikemuchpower,butmanyelectronicscircuitscannottoleratethismuchpowerbeingdrainedfromthem.Sotheelectronicsinstrumentsarerequiredformeasuringverysmallcurrentandvoltage.

Electronicinstruments,mainlyelectronicvoltmeters,usedeithertransistorsorvacuumtubes.ThelateroneiscalledtheVacuumTubeVoltmeter(VTVM)andtheformeroneiscalledtheTransistorisedVoltmeter(TVM).Inalmosteveryfieldofelectronics,VTVMshavebeenreplacedbyTVMsbecauseoftheirnumerousadvantages.InTVM,duetotheabsenceofaheatingelement,warm-uptimeisnotrequired.Itisportableduetothelightweightof the transistor.VTVMscannotmeasurecurrentdue to theveryhighresistancewhereasduetothelowresistanceoftheTVM,itcanmeasurethecurrentdirectlyfromthecircuit. VTVMs also cannotmeasure high-frequency signals. The only disadvantage ofTVMoverVTVMisthattheTVMhasverylowinputimpedance.ButusingFET(FieldEffect Transistor) in the input stage of the voltmeter overcomes this low-impedanceproblem,becauseanFEToffersinputimpedancealmostequaltoavacuumtube.

10.2MERITSANDDEMERITSOFDIGITALINSTRUMENTSOVERANALOGONES

Althoughelectronicsareusuallymorecostlythanelectricalinstrumentsbutarebecomingmoreandmorepopularbecauseoftheirvariousadvantagesoverconventionalones,some

ofthemainadvantagesarediscussedbelow:

1.Detection of Low Level Signals As indicated above analog instruments use PMMCmovement for indication. This movement cannot be constructed with a full scalesensitivityoflessthan50mA.AnymeasurementusingaPMMCmovementmustdrawacurrentof50mAfromthemeasuredquantityforitsoperationforfullscaledeflectionifconventionalvoltmetersareused.Thiswouldproducegreat loadingeffectsespeciallyinelectronicandcommunicationcircuits.Electronicvoltmeteravoids the loadingerrorsbysupplyingthepowerrequiredformeasurementbyusingexternalcircuitslikeamplifiers.Theamplifiersnotonlysupplypowerfortheoperationbutmakeitpossibleforlowlevelsignals,whichproduceacurrentlessthan50mAforfullscaledeflection,tobedetectedwhich otherwise cannot be detected in the absence of amplifiers. Let us examine theloadingeffect.Atypicalmeterhasaresistanceof200Wanditsoperatingcurrentatfullscaleis50mA.Thismeansthepowerconsumedisonly(50¥10–6)2¥200=0.5mW.Thisis extremely a low power for the power circuits but not for many electronic andcommunicationcircuits.Ifthispoweristakenfromthemeasurand,thesignalgetsgreatlydistortedincasepowerlevelthecircuitisverysmallandtooffsetthispowerissuppliedfromoutsidethroughuseofamplifiers.

Letushavealookatthevoltage.Ameterwith200Winternalresistanceandfullscalecurrentof50mAwillhavefullscalevoltagerangeof50¥10–6¥200=10mV.Nowincase of lower ranges of voltages have to be measured, the use of a voltage amplifierbecomesabsolutelynecessary.Thisisonlypossiblethroughuseofelectronicvoltmeterswhichallowtheuseofanamplifier.Therefore,itispossibletomeasurecurrentsbelow50mA,voltagesbelow10mVandkeepdrawnthepowerdrainagebelow0.5mWbyusingelectronic voltmeters through use of amplifiers which is otherwise not possible withconventional typesofmeterusingPMMCmovement.For thecaseofacmeasurements,the use of an amplifier for detection of low level signals is even more necessary forsensitivemeasurements.

2.High Input Impedance A conventional PMMC voltmeter is a rugged and an accurateinstrument,butitsuffersfromcertaindisadvantages.Theprincipleproblemisthatitlacksbothhighsensitivityandhighinputresistance.Ithasasensitivityof20kW/Vwitha0–0.5Vrangeandhasaninputresistanceofonly10kWatits0.5Vrangewiththeresultithasafullscalecurrentof50mAwhichloadsthemeasurandconsiderably.Inelectronicsandcommunicationcircuitseventhislowvalueofcurrentmaynotbetolerableonaccountof thefact that thesecircuitshavevery lowoperatingcurrents.Theelectronicvoltmeter(EVM),ontheotherhand,canhaveinputresistancesfrom10MWto100MWwiththeinputresistanceremainingconstantoverall rangesinsteadofbeingdifferentatdifferentranges,theEVMgivesforlessloadingeffects.

3.LowPowerConsumptionElectronicvoltmetersutilizetheamplifyingpropertiesofvacuumtubesandtransistorsandthereforethepowerrequiredforoperatingtheinstrumentcanbesupplied from an auxiliary source. Thus, while the circuit whose voltage is beingmeasuredcontrolsthesensingelementofthevoltmeter,thepowerdrawnfromthecircuitunder measurement is very small or even negligible. This can be interpreted as thevoltmeter circuit has very high input impedance.This feature of electronic voltmeter isindispensable for voltage measurement in many high impedance circuits such as

encounteredincommunicatingequipments.

4.High FrequencyRange Themost important feature of electronic voltmeters is that theirresponsecanbemadepracticallyindependentoffrequencywithinextremelywidelimits.Some electronic voltmeters permit the measurement of voltage from direct current tofrequency of the order of hundreds of MHz. the high frequency range may also beattributedtolowinputcapacitanceofmostelectronicsdevices.ThecapacitancemaybeoftheorderofafewpF.

5.Better Resolution Resolution (smallest reading perceivable) of analog instruments islimitedbyspaceonthescalemarkingsandalsobyabilityofthehumanoperatortoreadsuch small deviations in scalemarkings.Whereas in a digital instrument, themeasuredvalueisdisplayeddirectlyonaLEDorLCDpanelwhoseresolutionissolelydeterminedbyresolutionoftheanalogtodigitalconverter(ADC).Useof12bit(orhigher)ADCcanmakeadigitalinstrumenttoreadassmallas0.001Vin0–5Vrange.

6.StorageFacilityDigitalinstrumentshaveanadditionaloptionaladvantagethattheirreadingscanbestoredforfuturereference.SincethevaluedisplayedisobtainedthroughanADC,thedigitaldatacanbeeasilystoredinamicroprocessororPCmemory.Suchstoragefacilitycanonlybemadeavailableinanaloginstrumentsbytheuseofchartrecorderswherethepointerhasainksourcethatkeepsonmarkingthevaluesonarollofmovingpaper.

7.AccuracySincethereareveryfewmovingparts(orevennomovingparts)inthedigitalinstruments,ingeneraltheyareusuallymoreaccuratethantheanaloginstruments.Eventhe human error involved in reading these instruments is very less, which adds to theaccuracy of digital instruments. However, overall accuracy of a digital instrument willlargely depend on accuracies of the large number of individual electronic componentsusedforbuildingtheinstrument.

Inaddition,digitalinstrumentsaremoreuserfriendlyastheyareeasytoread,takesupsmallerspace,suitableformassproduction,andalsosometimeslesscostly.

DisadvantagesofDigitalInstruments1. Effectsonnoiseinmorepredominantondigitalinstrumentsthananaloginstruments.

Analoginstruments,duetoinertiaofitsmovingparts,normallyremaininsensitivetofastvaryingnoise,whiledigitalinstrumentscontinuetoshowerraticvariationsinpresenceofnoise.

2. Analoginstrumentshavehigheroverloadcapacitythandigitalinstruments.Thesensitiveelectroniccomponentsusedindigitalinstrumentsaremorepronetodamageincaseofevenmomentaryoverloads.

3. Digitalinstrumentscansometimeslooseitsreliabilityandtendtoindicateerraticvaluesduetofaultyelectroniccircuitcomponentsordamageddisplay.

4. Digitalinstrumentsandtheirinternalelectroniccomponentsareverymuchsensitivetoexternalatmosphericconditions.Incaseofhighhumidityandcorrosiveatmospheretheinternalpartsmaygetdamagedandindicatethefaultyvalues.

PERFORMANCECHARACTERISTICSOFDIGITAL

10.3 METERS

The performance characteristics of digital instruments are resolution, accuracy, linearerrors,monotonicity,settlingtimeandtemperaturesensitivity.

1.ResolutionItisthereciprocalofthenumberofdiscretestepsintheDigitaltoAnalog(D/A)converterinput. Resolution defines the smallest increment in voltage that can be discerned.Evidentlyresolutiondependsonthenumberofbits,i.e.,thesmallestincrementinoutputvoltageisdeterminedbytheLeastSignificantBit(LSB).Percentageresolutionis[1/(2n–1)]×100,whereNisthenumberofbits.

2.AccuracyItisameasureofthedifferencebetweenactualoutputandexpectedoutput.Itisexpressedasapercentageofthemaximumoutputvoltage.Ifthemaximumoutputvoltage(orfull-scaledeflection)is5voltandaccuracyis±0.1%,thenthemaximumerroris(0.1/100)×5=0.005voltor5mV. Ideally theaccuracyshouldbebetter than±½ofLSB. Ina8-bitconverter,LSBis1/255or0.39%offullscale.Theaccuracyshouldbebetterthan0.2%.

3.LinearErrorLinearitymeansthatequalincrementsindigitalinputofdigitalinstrumentsshouldresultinequalincrementinanalogoutputvoltage.Ifthevaluesofresistancesareveryaccurateandtheothercomponentsarealsoideal,therewouldbeperfectlylinearrelationbetweenoutputandinputandoutput–inputgraphwouldbeastraightline.Becauseofthefactthatresistances used in the circuit have some tolerance, a perfectly linear relation betweeninputandoutputisnotobtained.Aspecialcaseoflinearerrorisoffseterrorwhichistheoutputvoltagewhendigitalinputis0000.

4.MonotonicityADigitaltoAnalog(D/A)converterismonotonicifitdoesnottakeanyreversestepwhenitissequencedovertheentirerangeofinputbits.

5.SettlingTimeWhen the digital input signal changes, it is desirable that analog output signal shouldimmediatelyshowthenewoutputvalue.However, inactualpractice, theD/Aconvertertakessometimetosettleatthenewpositionoftheoutputvoltage.SettlingtimeisdefinedasthetimetakenbytheD/Aconvertertosettlewithin±½LSBofitsfinalvaluewhenachangeininputdigitalsignaloccurs.Thefinitetimetakentosettledowntonewvalueisduetothetransientsandoscillationsintheoutputvoltage.Figure

6.TemperatureSensitivityThe reference voltage supplied to the resistors of a D/A converter are all temperaturesensitive. Therefore, the analog output voltage depends, at least to some extent, on thetemperature.ThetemperaturesensitivityoftheoffsetvoltageandthebiascurrentofOP-AMP also affect the output voltage. The range of temperature sensitivity for a D/A

converterisfromabout±50to±1.5ppm/°C.

Figure10.1Settlingtimeofadigitalinstrument

10.4 DIGITALMULTIMETER

Adigitalmultimeterisanelectronicinstrumentwhichcanmeasureverypreciselythedcandacvoltage,current(dcandac),andresistance.Allquantitiesotherthandcvoltageisfirstconvertedintoanequivalentdcvoltagebysomedeviceandthenmeasuredwiththehelpofdigitalvoltmeter.

TheblockdiagramofadigitalmultimeterisshowninFigure10.2.Theproceduresofmeasurementofdifferentquantitiesaredescribedbelow.

Figure10.2Blockdiagramofadigitalmultimeter

For measurement of ac voltage, the input voltage, is fed through a calibrated,compensated attenuator, to a precision full-wave rectifier circuit followed by a ripplereduction filter. The resulting dc is fed to anAnalogDigital Converter (ADC) and thesubsequentdisplaysystem.Manymanufacturersprovidethesameattenuatorforbothacanddcmeasurements.

For current measurement, the drop across an internal calibrated shunt is measureddirectly by theADC in the ‘dc currentmode’, and after ac to dc conversion in the ‘accurrentmode’.Thisdrop isoften in the rangeof200mV (corresponding to full scale).

Due to the lack of precision in the ac–dc conversions, the accuracy in the ac range isgenerallyoftheorderof0.2to0.5%.Inaddition,themeasurementrangeisoftenlimitedto about 50 Hz at the lower frequency end due to the ripple in the rectified signalbecominganon-negligiblepercentageofthedisplayandhenceresultsinfluctuationofthedisplayednumber.At thehigher frequency end, deteriorationof theperformanceof theADCconverterlimitstheaccuracy.Inacmeasurementthereadingisoftenaverageorrmsvaluesoftheunknowncurrent.Sometimesformeasurementofcurrent,acurrent-tovoltageconvertermayalsobeused,asblockdiagraminFigure10.3.

Figure10.3Blockdiagramofacurrent-to-voltageconverter

Thecurrentundermeasurementisappliedtothesummingjunctionattheinputoftheop-amp.ThecurrentinthefeedbackresistorIRisequaltotheinputcurrentIINbecauseofveryhighinputimpedanceoftheop-amp.ThecurrentIRcausesavoltagedropacrossoneof the resistors, which is proportional to the input current IIN. Different resistors areemployedfordifferentranges.

For resistancemeasurement the digitalmultimeter operates bymeasuring the voltageacrosstheexternallyconnectedresistance,resultingfromacurrentforcedthroughitfromacalibratedinternalcurrentsource.Theaccuracyoftheresistancemeasurementisoftheorder of 0.1 to 0.5% depending on the accuracy and stability of the internal currentsources.Theaccuracymaybeproper in thehighestrangewhichisoftenabout10to20MΩ.Inthelowestrange,thefullscalemaybenearlyequalto>200Ωwitharesolutionofabout0.01Ωfora4½digitdigitalmultimeter. In this rangeof resistancemeasurement,theeffectoftheloadresistancewillhavetobecarefullyconsidered.

Table10.1Comparisonbetweenanaloganddigitalmultimeter

AnalogMultimeter DigitalMultimeter

Noexternalpowersupplyrequired. Anexternalpowersupplyisrequired.

Visualindicationofchangeinreadingisbetterobservable. Lessobservable.

Lesseffectofelectronicnoise. Moreaffectedbyelectronicnoise.

Lessisolationproblems. Moreisolationproblems.

Ithaslessaccuracy. Highlyaccurateinstrument.

Interfaceoftheoutputwithexternalequipmentisnotpossible.

Possibletoconnectanexternalinstrumentwiththeoutputreading.

Simpleinconstruction. Verycomplicatedinconstruction.

Biginsize. Smallinsize.

Lowcost. Morecostlierinstrument.

Theoutputisambiguousinmanytimes. Unambiguousreadingduetodigitalindication.

10.5 DIGITALFREQUENCYMETER

Afrequencycounterisadigitalinstrumentthatcanmeasureanddisplaythefrequencyofanyperiodicwaveform. It operateson theprincipleof gating theunknown input signalintothecounterforapredeterminedtime.Forexample,iftheunknowninputsignalweregatedintothecounterforexactly1second,thenumberofcountsallowedintothecounterwouldbepreciselythefrequencyoftheinputsignal.ThetermgatedcomesfromthefactthatanANDoranORgateisemployedforallowingtheunknowninputsignal intothecountertobeaccumulated.

Figure10.4Blockdiagramoffrequencycounter

Oneofthemoststraightforwardmethodsofconstructingafrequencycounterisshownin Figure 10.4 in simplified form. It consist of a counter with its associateddisplay/decoder circuitry, clock oscillator, a divider and an AND gate. The counter isusually made up of cascaded Binary Coded Decimal (BCD) counters and thedisplay/decoderunitconvertstheBCDoutputsintoadecimaldisplayforeasymonitoring.AGATEENABLEsignalofknowntimeperiodisgeneratedwithaclockoscillatorandadividercircuitandisappliedtoonelegofanANDgate.TheunknownsignalisappliedtotheotherlegoftheANDgateandactsastheclockforthecounter.Thecounteradvancesone count for each transition of the unknown signal, and at the end of the known timeinterval,thecontentsofthecounterwillbeequaltothenumberofperiodsoftheunknowninputsignalthathaveoccurredduringtimeinterval,t.Inotherwords,thecountercontentswillbeproportionaltothefrequencyoftheunknowninputsignal.Forinstanceifthegatesignalisofatimeofexactly1secondandtheunknowninputsignalisa600-Hzsquarewave, at the end of 1 second the counter will counts up to 600, which is exactly thefrequencyoftheunknowninputsignal.

ThewaveforminFigure10.5showsthataclearpulseisappliedtothecounteratt0 tosetthecounteratzero.Priortot1,theGATEENABLEsignalisLOW,andsotheoutputoftheANDgatewillbeLOWand thecounterwillnotbecounting.TheGATEENABLE

goesHIGHfromt1tot2andduringthistimeintervalt(=t2–t1),theunknowninputsignalpulseswillpass through theANDgateandwillbecountedby thecounter.After t2, theANDgateoutputwillbeagainLOWandthecounterwillstopcounting.Thus,thecounterwill have counted the number of pulses that occurred during the time interval, t of theGATEENABLESIGNAL,andtheresultingcontentsofthecounterareadirectmeasureofthefrequencyoftheinputsignal.

Figure10.5Differentwaveformsinafrequencycounter

Theaccuracyof themeasurementdependsalmost entirelyon the time intervalof theGATEENABLEsignal,whichneedstobecontrolledveryaccurately.Acommonlyusedmethod for obtaining very accurateGATEENABLE signal is shown in Figure10.6.Acrystal controlled oscillator is employed for generating a very accurate 100 kHzwaveform,whichisshapedintothesquarepulsesandfedtoaseriesofdecadecountersthatarebeingusedtosuccessivelydividethis100kHzfrequencyby10.Thefrequenciesattheoutputsofeachdecadecounterareasaccurateasthecrystalfrequency.

TheswitchisusedtoselectoneofthedecadecounteroutputfrequenciestobesuppliedtoasingleFlip-floptobedividedby2.Forinstanceinswitchposition1,the1Hzpulsesare supplied to flip-flopQ, which acts as a toggle flip-flop so that its outputwill be asquarewavewithaperiodifT=2sandaTpulseduration, 1s.Inposition2,thepulsedurationwouldbe0.1s,andsooninotherpositionsoftheselectswitch.

Figure10.6MethodofobtainingveryaccurateGATEENABLEsignal

DIGITALVOLTMETERS(DVMS)

10.6

The Digital Voltmeter (DVM) displays measurement of ac or dc voltages as discretenumbersinsteadofapointerdeflectiononacontinuousscaleasinanaloginstruments.Itisaversatileandaccurate instrument that isemployed inmany laboratorymeasurementapplications. Because of development and perfection of IC modules, their size, powerconsumptions and cost of the digital voltmeters has been drastically reduced and,therefore,DVMsarewidelyusedforallmeasurementpurposes.

TheblockdiagramofasimpledigitalvoltmeterisshowninFigure10.7.Theunknownsignal is fed to the pulse generator which generates a pulse whose width is directlyproportionaltotheinputunknownvoltage.

Figure10.7BlockdiagramofDVM

TheoutputofthepulsegeneratorisappliedtoonelegofanANDgate.TheinputsignaltotheotherlegoftheANDgateisatrainofpulses.TheoutputoftheANDgateis,thus,apositive trigger train of duration t second and the inverter converts it into a negativetriggertrain.Thecountercountsthenumberoftriggersintsecondswhichisproportionaltothevoltageundermeasurement.Thus,thecountercanbecalibratedtoindicatevoltageinvoltsdirectly.

Thus, the DVMs described above is an Analog to Digital Converter (ADC) whichconvertsananalogsignalintoatrainofpulses,thenumberofwhichisproportionaltotheinputvoltage.SoadigitalvoltmetercanbemadebyusinganyoneoftheanalogtodigitalconversionmethodsandcanberepresentedbyablockdiagramshowninFigure10.8.SotheDVMscanbeclassifiedonthebasisofADCsused.

Figure10.8RepresentationofDVMusingblocks

TheinputrangeoftheDVMmayvaryfrom±1.00000Vto±1000.00Vanditslimitingaccuracyisashighas±0.005percentofthereading.Itsresolutionmaybe1partin106,giving1μVreadingofthe1Vinputrange.Ithashighinputresistanceoftheorderof10MΩandinputcapacitanceoftheorderof40pF.

Digital voltmeters employing different analog to digital conversion methods aredescribedbelow:

10.6.1Ramp-TypeDVMTheoperationofaramp-typeDVMisbasedonthemeasurementofthetimethatalinear

rampvoltagetakestochangefromtheleveloftheinputvoltagetozerovoltageorvice-versa.Thistimeintervalismeasuredwithanelectronictimeintervalcounterandthecountisdisplayedasanumberofdigitsontheelectronicindicatingtubesofthevoltmeteroutputreadouts.Theoperatingprincipleandblockdiagramofa ramp-typeDVMaregiven inFigures

10.9(a)and10.9(b)respectively.

At the start ofmeasurement, a ramp voltage is initiated, this voltage can be positivegoingornegativegoing.InFigure10.9(a),negativegoingvoltagerampisillustrated.

The ramp voltage is continuously compared with the voltage under measurement(unknownvoltage).Attheinstantthevalueoframpvoltagebecomesequaltothevoltageundermeasurement,acoincidencecircuit,calledtheinputcomparator,generatesapulsewhichopensagate,asshowninFigure10.9(b).Therampvoltagecontinuestofalltillitreacheszerovalue(orgroundvalue).Atthisinstantanothercomparator,calledthegroundcomparator,generatesastoppulse.Theoutputpulsefromthisgroundcomparatorclosesthegate.Thetimedurationofthegateopeningisproportionaltothevalueofthedcinputvoltage.

The time elapsed between opening and closing the gate is t, as illustrated in Figure10.9(a).Duringthistimeintervalpulsesfromaclockpulseoscillatorpassthroughthegateandarecountedanddisplayed.Thedecimalnumberindicatedbythereadoutisameasureofthevalueoftheinputvoltage.

Thesampleratemultivibratordeterminestherateatwhichthemeasurementcyclesareinitiated.Thesampleratecircuitprovidesaninitiatingpulsefortherampgeneratortostartitsnextrampvoltage.Atthesametimearesetpulseisgenerated,whichresetsthecountertozerostate.

Figure10.9(a)Voltage-to-timeconversion(b)Blockdiagramofaramp-typeDVM

10.6.2Dual-SlopeIntegrating-TypeDVMTheblockdiagramofadual-slopeintegrating-typeDVMisgiveninFigure10.10(a).ThedualslopeADCconsistsoffiveblocksnamelyanOP-AMPemployedasanintegrator,alevelcomparator,abasicclockforgeneratingtimepulses,asetofdecimalcounterandablockoflogiccircuitry.

Forafixedtimeinterval(usually,thefullcountrangeofthecounter),theanaloginputvoltagetobemeasured,isappliedthroughtheswitchStotheintegratorwhichraisesthevoltage in the comparator to some negative value, as illustrated in Figure 10.10(b),obviouslyattheendoffixedtimeintervalthevoltagefromtheintegratorwillbegreaterinmagnitudeforlargerinputvoltage,i.e.,rateofincreaseofvoltageorslopeisproportionaltotheanaloginputvoltage.Attheendofthefixedcountinterval,thecountissetatzeroand the switch S is shifted to the reference voltage VREF of opposite polarity. Theintegrator output or input to the capacitor then starts increasing at a fixed rate, asillustratedin

Figure10.10(a)BlockdiagramofaDual-SlopeIntegrating-typeDVM(b)Principleofoperationofdual-slope-typeDVM

Figure10.10(b).Thecounteradvancesduring this time.The integratoroutputvoltageincreasesatafixedrateuntilitrisesabovethecomparatorreferencevoltage,atwhichthecontrol logic receives a signal (the comparator output) to stop the count. The pulsecountedbythecounterthushasadirectrelationwiththeinputvoltageVA.

Duringcharging,theoutputvoltageV0isgivenas

NowthecapacitorChasalreadyavoltageof (initialvoltage),

Duringdischarging,theoutputvoltageisgivenas

V0=Initialvoltageofthecapacitor

At t = T2 (the time measured by the counter), the output voltage of the integratorbecomeszero

Thus, the count shown by the counter (T2) is proportional to the input voltage to bemeasured,VA.Thedisplayunitdisplaysthemeasuredvoltage.

The averaging characteristics and cancellation of errors that usually limit theperformanceofaramp-typeDVMarethemainadvantagesofdualslopeintegratingtypeDVM.Theintegrationcharacteristicsprovidetheaveragevalueoftheinputsignalduringtheperiodoffirst integration.Consequently,disturbances,suchasspuriousnoisepulses,are minimised. Long-term drifts in the time constant as may result from temperaturevariations or aging, do not affect conversion accuracy. Also, long-term alternations inclockfrequencyhavenoeffect.

10.6.3Integrating-TypeDVM(VoltagetoFrequencyConversion)Suchadigitalvoltmetermakesuseofanintegrationtechniquewhichemploysavoltagetofrequency (V/f ) conversion. This voltmeter indicates the true average value of theunknownvoltageoverafixedmeasuringperiod.

An analog voltage can be converted into digital form by producing pulses whosefrequency is proportional to the analog input voltage. These pulses are counted by acounter for a fixed duration and the reading of the counter will be proportional to thefrequencyofthepulses,andhence,totheanalogvoltage.

AblockdiagramofavoltagetofrequencyADCisshowninFigure10.11.TheanaloginputvoltageVA isapplied toan integratorwhich in turnproducesarampsignalwhoseslope is proportional to the input voltage.When the output voltageV0 attains a certainvalue (a preset threshold level), a trigger pulse is produced and also a current pulse isgenerated which is used to discharge the integrator capacitor C. Now a new ramp isinitiated.Thetimebetweensuccessivethresholdlevelcrossingsisinverselyproportionaltotheslopeoftheramp.SincetherampslopeisproportionaltotheinputanalogvoltageVA, the frequency of the output pulses from the comparator is, therefore, directlyproportionaltotheinputanalogvoltage.Thisoutputfrequencymaybemeasuredwiththehelpofadigitalfrequencycounter.

Figure10.11Blockdiagramofanintegrating-typeDVM

Theabovemethodprovidesmeasurementof the trueaverageof the input signalovertherampduration,andsoprovideshighdiscriminationagainstnoisepresentattheinput.

However,thedigitisingratesareslowbecauseofhighintegrationdurations.TheaccuracyofthismethodiscomparablewiththeramptypeADC,andislimitedbythestabilityoftheintegratortimeconstant,andthestabilityandaccuracyofthecomparator.ThisDVMhasthedrawbackthatitneedsexcellentcharacteristicsinthelinearityofthe

ramp.Theacnoiseandsupplynoiseareaveragedout.

10.6.4ApplicationsofDVMsDVMs are often used in ‘data processing systems’ or ‘data logging systems’. In suchsystems, a number of analog input signals are scanned sequentially by an electronicsystem and then each signal is converted to an equivalent digital value by the A/DconverterintheDVM.

Thedigitalvalueis thentransmittedtoapointeralongwiththeinformationabouttheinputlinefromwhichthesignalhasbeenderived.Thewholedataisthenprintedout.

Inthisway,alargenumberofinputsignalscanbeautomaticallyscannedorprocessedandtheirvalueseitherprintedorlogged.

10.7 SIGNALGENERATORS

A signal generator is numerously known as test signal generator, tone generator,arbitrary waveform generator, frequency generator, digital pattern generator, functiongenerator, etc. It is an electronic device which produces repeating or non-repeatingelectronicsignals(eitheranalogorindigitalpatterns).Thesesignalsareutilisedintesting,designing, troubleshootingandrepairingelectronicdevices;apart fromtheirartisticusesaswell.Signalgeneratorsalsomodulatesinusoidaloutputsignalwithothersignals.Thisfeature is the main distinguisher between the signal generator and oscillator.When anunmodulatedsinusoidaloutputisgeneratedbythesignalgeneratorsthentheyaresaidtobeproducingCW(continuousheightwave)signal.Whentheyproducemodulatedoutputsignals then they can be in the form of square waves, externally applied sine waves,pulses, triangular waves, ormore complex signals, as well as internally generated sinewaves. Although Amplitude Modulation (AM) or Frequency Modulation (FM) can beused,yetamplitudemodulationisgenerallyemployed.InFigures10.12(a)and10.12(b),theprinciplesofamplitudemodulationandfrequencymodulationareshownrespectively.

Figure10.12(a)Amplitudemodulation(b)Frequencymodulation

For providing appropriate signals for calibration and testing, signal generators aremainlyemployed.Theyarealsousedfortroubleshootingoftheamplifiercircuitsusedinelectronic and communications circuit amplifiers. Signal generators also measure thefeaturesofantennasandtransmissionlines.

Figure 10.13 illustrates the block diagram of a signal generator. A Radio Frequency(RF) oscillatoris applied for producing a carrier waveform whose frequency can beattunedtypicallyfromabout100kHzto40MHz.Withthehelpofvernierdialsettingandrange selector switch, carrierwave frequencies can be varied and displayed. Frequencydividers are employed to determine the range.Anoscillators frequency stability is keptveryhighatallfrequencyranges.

Figure10.13BlockdiagramofanAMsignalgenerator

Thefollowingmeasuresaretakeninordertoattainstablefrequencyoutput.

1. Regulated power supply is employed to reduce the change in supply voltage as itchangesfrequencyofoutputvoltage.

2. Toseparatetheoscillatorcircuitfromoutputcircuit,bufferamplifiersareused.Thisis done so that any change in the circuit linked to the output does not affect theamplitudeandfrequencyoftheoscillator.

3. Temperaturecompensatingdevicesareused tostable the temperaturewhichcauseschangeinoscillatorfrequency.

4. InplaceofanLCoscillator,aquartzcrystaloscillatorisemployedtoachievehighQ-factor,forinstance,20000.

5. When an audio frequency modulating signal is generated in another very stableoscillator,itiscalledthemodulationoscillator.Forchangingtheamplitudeandthefrequencyoftheproducedsignal,provisionismadeinthemodulationoscillator.

6. Provision is also employed to get several types of waveforms such as the pulses,square, triangularoscillator.Themodulation frequencyand radio frequency signalsare applied to a broadband amplifier, called the output amplifier. Modulationpercentageisindicatedandadjustedbythemeter.

7. Acontroldevicecanadjustmodulationlevelupto95%.Theamplifieroutputisthensenttoanattenuatorandatlastthesignalreachestheoutputofthesignalgenerator.Anoutputmeterreadsordisplaysthefinaloutputsignal.

8. Animportantspecificationof thesignalgeneratorperformance isdependingby theaccuracytowhichthefrequencyoftheRFoscillatoristuned.Mostlaboratory-typesignalgeneratorsaregenerallycalibrated tobewithin0.5–1.0%of thedial setting.Formostmeasurements, this accuracy is sufficient. If greater accuracy is requiredthenacrystaloscillator(frequency

9. Depending upon the different purposes and applications, various types of signalgeneratorsareavailable,howevernodeviceissuitableforallpossibleapplications.Though traditional signal generators have embedded hardware units, with theadvancement of multimedia-computers, audio software, tone generators signalgeneratorshavebecomemoreuser-friendlyandversatile.

EXERCISE

Objective-typeQuestions1.Whichoneofthefollowingstatementsiscorrect?

Anelectronicvoltmeterismorereliableascomparedtomultimeterformeasuringvoltagesacrosslowimpedancebecause

(a)itssensitivityishigh

(b)itoffershighinputimpedance

(c)itdoesnotalterthemeasuredvoltage

(d)itssensitivityandinputimpedancearehighanddonotalterthemeasuredvalue

2.VTVMcanbeusedtomeasure

(a)dcvoltage

(b)acvoltageofhighfrequency

(c)dcvoltageandacvoltageuptotheorderof5MHzfrequency

(d)acvoltageoflowfrequency

3.Transistorvoltmeter

(acannotmeasureacvoltage

(b)cannotmeasurehighfrequencyvoltage

(c)cannotbedesignedtomeasureresistanceaswellasvoltage

(d)canmeasureacvoltage

4. An electronic voltmeter provides more accurate readings in high-resistance circuits as compared to anonelectronicvoltmeterbecauseofits

(a)lowmeterresistance

(b)highΩ/Vratings

(c)highV/Ωratings

(d)highresolution

5.TheinputimpedanceofaTVMascomparedtothatofaVTVMis

(a)low

(b)high

(c)same

(d)notcomparable

6.Thepowerconsumptionofadcvoltmeterusingadirectcoupledamplifierwhenmeasuringavoltageof0.5voltandhavinganinputimpedanceof10MΩis

(a)afewnanowatts

(b)afewmilliwatts

(c)afewmicrowatts

(d)afewwatts

7.FETsareusedintheamplifiertoget

(a)highoutputimpedance

(b)highinputimpedance

(c)lowoutputimpedance

(d)lowinputimpedance

8.Adirectvoltageisappliedtoapeakdiodevoltmeterwhosescaleiscalibratedtoreadrmsvoltageofasinewave.Ifthemeterreadingis36Vrms,thevalueoftheapplieddirectvoltageis

(a)51volts

(b)25volts

(c)36volts

(d)71volts

9.Amultimeterisusedforthemeasurementofthefollowing:

1.Bothacanddcvoltage

2.Bothacanddccurrent

3.Resistance

4.Frequency

5.Power

Selectthecorrectanswerusingthecodesgiven:

(a)1,2and4

(b)1,2and5

(c)1,3and5

(d)1,2and3

10.Modernelectronicmultimetersmeasureresistanceby

(a)usinganelectronicbridgecompensatorfornulling

(b)forcingaconstantcurrentandmeasuringthevoltageacrosstheunknownresistor

(c)usingabridgecircuit

(d)applyingaconstantvoltageandmeasuringthecurrentthroughtheunknownresistor

11.Ann-bitA/Dconverterisrequiredtoconvertananaloginputintherangeof0–5volttoanaccuracyof10mV.Thevalueofnshouldbe

(a)8

(b)9

(c)10

(d)16

12.Whichofthefollowingisnottrueforadigitalfrequencycounter?

(a)lesscostly

(b)highaccuracy

(c)acceptsinputsintheformoftrainofpulses

(d)widerangeoffrequencymeasurement

13.Theresolutionofa12-bitanalogtodigitalconverterinpercentis

(a)0.04882

(b)0.09760

(c)0.01220

(d)0.02441

14.ADVMmeasures

(a)peakvalue

(b)rmsvalue

(c)averagevalue

(d)peaktopeakvalue

15.Whichofthefollowingmeasurementscanbemadewiththehelpofafrequencycounter?

1.Fundamentalfrequencyofinputsignal

2.Frequencycomponentsoftheinputsignalatleastuptothirdharmonics

3.Timeintervalbetweentwopulses

4.Pulsewidth

Selectthecorrectanswerusingthecodesgivenbelow:(a)2and4

(b)1and2

(c)1,2and3

(d)1,3and4

16.AccuracyofDVMisspecifiedas

(a)percentageofthefullscalereading

(b)percentageoftheactualreading

(c)numberofleastsignificantdigit

(d)allofthese

Short-answerQuestions1.Whatarethemeritsofthedigitalsystemoveranalogsystem?

2.Brieflydescribetheperformancecharacteristicsofdigitalmeasurement.

3.Writedownthecomparisonbetweenanaloganddigitalmultimeters.

4.Whatisthebasicprincipleofdigitalfrequencymeter?

5.Howmanytypesofdigitalvoltmetersarethere?Explainanyoneofthembriefly.

6.Whataretheapplicationsofthedigitalvoltmeter?

7.Howdoesanelectronicvoltmeter(EVM)measureacsignal?

Long-answerQuestions1.(a)Whataretheadvantagesofdigitalsystemsoveranalog?

(b)Explainthefollowingtermsasappliedtodigitalmeasurement.

(i) Resolution(ii) Sensitivityofdigitalmeter(iii) Accuracyspecificationofdigitalmeters

2.(a)ExplaintheoperatingprincipleofaDVMusingasuitableblockdiagram.

(b)Withaneatsketch,describetheoperatingprincipleofdualslopintegratingtypeofDVM.

3.Explainwiththehelpofafunctionalblockdiagram,theprincipleofoperationofadigitalfrequencymeter.

4.Withthehelpofafunctionalblockdiagram,describetheprincipleofoperationofadigitalmultimeter.

5. What are the advantages of a digital voltmeter over analog type?What are its types?With a block diagram,explaintheworkingofanintegratingtype.Compareitsperformancewithothertypes.

11.1 INTRODUCTION

The physical quantity under measurement makes its first contact in the time ofmeasurementwith a sensor.A sensor is a device thatmeasures a physical quantity andconverts it into a signal which can be read by an observer or by an instrument. Forexample,amercury thermometerconverts themeasured temperature intoexpansionandcontraction of a liquid which can be read on a calibrated glass tube. A thermocoupleconvertstemperaturetoanoutputvoltagewhichcanbereadbyavoltmeter.Foraccuracy,allsensorsneedtobecalibratedagainstknownstandards.

Ineveryday life, sensorsareusedeverywhere suchas touchsensitivemobilephones,laptop’stouchpad,touchcontrollerlight,etc.Peopleusesomanyapplicationsofsensorsin their everyday lifestyle that even they are not aware about it. Examples of suchapplications are in the field of medicine, machines, cars, aerospace, robotics andmanufacturingplants.Thesensitivityofthesensorsisthechangeofsensor’soutputwhenthe measured quantity changes. For example, the output increases 1 volt when thetemperature in the thermocouple junction increases 1°C. The sensitivity of thethermocouple element is 1 volt/°C. Tomeasure very small charges, the sensors shouldhaveveryhighsensitivity.

A transducer is a device, usually electrical, electronic, electro-mechanical,electromagnetic, photonic, or photovoltaic that converts one type of energy or physicalattributetoanother(generallyelectricalormechanical)forvariousmeasurementpurposesincludingmeasurementorinformationtransfer(forexample,pressuresensors).

The term transducer is commonly used in two senses; the sensor, used to detect aparameterinoneformandreportitinanother(usuallyanelectricalordigitalsignal),andtheaudioloudspeaker,whichconvertselectricalvoltagevariationsrepresentingmusicorspeechtomechanicalconevibrationandhencevibratesairmoleculescreatingsound.

11.2 ELECTRICALTRANSDUCERS

Electricaltransducersaredefinedasthetransducerswhichconvertoneformofenergytoelectrical energy for measurement purposes. The quantities which cannot be measureddirectly, such as pressure, displacement, temperature, humidity, fluid flow, etc., arerequiredtobesensedandchangedintoelectricalsignalfirstforeasymeasurement.

Theadvantagesofelectricaltransducersarethefollowing:•Powerrequirementisverylowforcontrollingtheelectricalorelectronicsystem.

•Anamplifiermaybeusedforamplifyingtheelectricalsignalaccordingtotherequirement.

•Frictioneffectisminimised.

•Mass-inertiaeffectarealsominimised,becauseincaseofelectricalorelectronicssignalstheinertiaeffectisduetothemassoftheelectrons,whichcanbenegligible.

•Theoutputcanbeindicatedandrecordedremotelyfromthesensingelement.

BasicRequirementsofaTransducerThemainobjectiveofa transducer is to reactonlyfor themeasurementunderspecifiedlimitsforwhichitisdesigned.Itis,therefore,necessarytoknowtherelationshipbetweenthe input and output quantities and it should be fixed. A transducer should have thefollowingbasicrequirements:

1.LinearityIts input vs output characteristics should be linear and it should produce thesecharacteristicsinbalancedway.

2.RuggednessAtransducer shouldbecapableofwithstandingoverloadand somesafetyarrangementsmustbeprovidedwithitforoverloadprotection.

3.RepeatabilityThedeviceshouldreproducethesameoutputsignalwhenthesameinputsignalisappliedagain and again under unchanged environmental conditions, e.g., temperature, pressure,humidity,etc.

4.HighReliabilityandStabilityThe transducer should giveminimum error inmeasurement for temperature variations,vibrationsandothervariouschangesinsurroundings.

5.HighOutputSignalQualityThequalityofoutputsignalshouldbegood,i.e.,theratioofthesignaltothenoiseshouldbehighandtheamplitudeoftheoutputsignalshouldbeenough.

6.NoHysteresisItshouldnotgiveanyhysteresisduringmeasurementwhileinputsignalisvariedfromitslowvaluetohighvalueandviceversa.

7.ResidualReformationThereshouldnotbeanydeformationonremovalofinputsignalafterlongperiodofuse.

11.3LINEARVARIABLEDIFFERENTIALTRANSFORMER(LVDT)

Themostwidely used inductive transducer to translate the linearmotion into electricalsignalsistheLinearVariableDifferentialTransformer(LVDT).Thebasicconstructionof

LVDTisshowninFigure11.1.Thetransformerconsistsofasingleprimarywinding‘P’and two secondary windings S1 and S2 wound on a cylindrical former. A sinusoidalvoltage of amplitude 3 to 15Volt and frequency 50 to 20000Hz is used to excite theprimary.The two secondaries have equal numberof turns and are identicallyplacedoneithersideoftheprimarywinding.

Figure11.1LinearVariableDifferentialTransformer(LVDT)

Theprimarywindingisconnectedtoanalternatingcurrentsource.Amovablesoft-ironcore isplaced inside theformer.Thedisplacement tobemeasured isapplied to thearmattachedtothesoftironcore.Inpracticethecoreismadeofhighpermeability,nickeliron.This is slotted longitudinally to reduceeddycurrent losses.Theassembly isplaced inastainless steel housing to provide electrostatic and electromagnetic shielding. Thefrequencyofacsignalappliedtoprimarywindingmaybebetween50Hzto20kHz.

Since the primarywinding is excitedby an alternating current source, it produces analternatingmagneticfieldwhichinturninducesalternatingvoltagesinthetwosecondarywindings.

TheoutputvoltageofsecondaryS1isES1andthatofsecondaryS2 isES2. Inorder toconverttheoutputsfromS1andS2intoasinglevoltagesignal,thetwosecondaryS1andS2areconnectedinseriesoppositionasshowninFigure11.2.DifferentialoutputvoltageE0=ES1−ES2

Figure11.2ConnectionofLVDTcircuit

11.3.1OperationWhenthecoreisatitsnormal(NULL)position,thefluxlinkingwithboththesecondarywindingsisequalandhenceequalemfsareinducedinthem.Thus,atnullposition:ES1=ES2.Thus,theoutputvoltageE0iszeroatnullposition.

Nowifthecoreismovedtotheleftofthenullposition,morefluxlinkswithS1andlesswithwindingS2.Accordingly,outputvoltagesES1isgreaterthanES2.Themagnitudeofoutputvoltageisthus,E0=ES1−ES2andsayitisinphasewithprimaryvoltage.

Similarly,whenthecoreismovedtotherightofthenullpositionES2willbemorethanES1.ThustheoutputvoltageisE0=ES1−ES2and180°outofphasewithprimaryvoltage.

The amount of voltage change in either secondary winding is proportional to theamount of movement of the core. Hence, we have an indication of amount of linearmotion.Bynoticingwhetheroutputvoltageis increasedordecreased,wecandeterminethedirectionofmotion.

11.3.2AdvantagesandDisadvantagesofLVDTAdvantages

•Linearityisgoodupto5mmofdisplacement.

•Outputisratherhigh.Therefore,immediateamplificationisnotnecessary.

•Outputvoltageissteplessandhencetheresolutionisverygood.

•Sensitivityishigh(about40V/mm).

•Itdoesnotloadthemeasurandmechanically.

•Itconsumeslowpowerandlowhysteresislossalso.

Disadvantages•LVDThaslargethreshold.

•Itisaffectedbystrayelectromagneticfields.Hencepropershieldingofthedeviceisnecessary.

•Theacinputsgeneratenoise.

•Itssensitivityislowerathighertemperature.

•Beingafirst-orderinstrument,itsdynamicresponseisnotinstantaneous.

Example11.1 The output of an LVDT is connected to a 5 V voltmeterthrough an amplifier of amplification factor 250. Thevoltmeterscaleshas100divisionsandthescalecanbereadto1/5thofadivision.Anoutputof2mVappearsacrosstheterminalsoftheLVDTwhenthecoreisdisplacedthroughadistance of 0.5 mm. Calculate (a) the sensitivity of theLVDT,(b)thatofthewholesetup,and(c)theresolutionoftheinstrumentinmm.

Solution(a)Foradisplacementof0.5mm,theoutputvoltageis2mV.

Hence,thesensitivityoftheLVDTis mV/mm=4mV/mm

(b)Duetotheamplifier,thissensitivityisamplified250timesintheset-up.Hencethesensitivityoftheset-upis4×250=1V/mm

(c)Theoutputofthevoltmeteris5Vwith100divisionsEachdivisionscorrespondsto Since thofa

divisioncanberead,theminimumvoltagethatcanbereadis0.01Vwhichcorrespondsto0.01mm.Hence,theresolutionoftheinstrumentis0.01mm.

11.4 STRAINGAUGES

The strain gauge is an electrical transducer; it is used to measure mechanical surfacetension.Straingaugecandetectandconvertforceorsmallmechanicaldisplacementintoelectrical signals. On the application of force a metal conductor is stretched orcompressed, its resistance changes owing to the fact both length and diameter ofconductorchange.Also,thereisachangeonthevalueofresistivityoftheconductorwhenit is strained and this property of the metal is called piezoresistive effect. Therefore,resistance strain gauges are also known as piezoresistive gauges. The strain gauges areused for measurement of strain and associated stress in experimental stress analysis.Secondly,manyotherdetectorsandtransducers,forexampletheloadcell, torquemeter,flowmeter,accelerometeremploystraingaugeasasecondarytransducer.

TheoryofResistanceStrainGaugesThechangeinthevalueofresistancebytheapplicationofforcecanbeexplainedbythenormaldimensionalchangesofelasticmaterial.Ifapositivestrainoccurs,itslongitudinaldimension (x-direction) will increase while there will be a reduction in the lateraldimension(y-direction).Thereversehappensforanegativestrain.Sincetheresistanceofa conductor is directlyproportional to its length and inverselyproportional to its cross-sectionalarea,theresistancechanges.Theresistivityofaconductorisalsochangedwhenstrained.Thispropertyisknownaspiezoresistiveeffect.

Let us consider a strain gauge made of circular wire. The wire has the dimensions:

length L, area A, diameter D before being strained. The material of the wire has aresistivityρ.

LetatensilestressSbeappliedtothewire.ThisproducesapositivestraincausingthelengthtoincreaseandtheareatodecreaseasshowninFigure11.3.LetΔL=Changeinlength,ΔA=Changeinarea,ΔD=ChangeindiameterandΔRisthechangeinresistance.

Figure11.3Changeindimensionsofastrain-gaugeelementwhensubjectedtoatensileforce

InordertofindhowΔRdependsuponthematerialphysicalquantities,theexpressionforRisdifferentiatedwithrespecttostressS.Thus,

DividingEq.(11.1)throughoutbyresistance itbecomes

ItisclearfromEq.(11.2),thattheperunitchangeinresistanceisduetothefollowing:

Perunitchangeinlength=

Perunitchangeinarea= and

Perunitchangeinresistivity=

or,

puttingthisvalueof inEq.(11.2),itbecomes

Now,Poisson’sratio

Forsmallvariations,theaboverelationshipcanbewrittenas

The gauge factor is defined as the ratio of per unit change in resistance to per unitchangeinlength.

whereε= =Strain

11.5 ELECTROMAGNETICFLOWMETER

Magnetic flowmeters have beenwidely used in industry formany years.Unlikemanyothertypesofflowmeters, theyoffer truenon-invasivemeasurements.Theyareeasytoinstall and use to the extent that existing pipes in a process can be turned intometerssimply by adding external electrodes and suitable magnets. They can measure reverseflows and are insensitive to viscosity, density, and flow disturbances. Electromagneticflowmeterscan rapidly respond to flowchangesand theyare lineardevices forawiderangeofmeasurements.Inrecentyears,technologicalrefinementshaveresultedinmuchmoreeconomical,accurate,andsmallerinstrumentsthanthepreviousversions.

Asinthecaseofmanyelectricdevices,theunderlyingprincipleoftheelectromagneticflow meter is Faraday’s law of electromagnetic induction. The induced voltages in anelectromagneticflowmeterarelinearlyproportionaltothemeanvelocityofliquidsortothevolumetricflowrates.Asisthecaseinmanyapplications,ifthepipewallsaremadefromnonconductingelements,thentheinducedvoltageisindependentofthepropertiesofthefluid.

Figure11.4showstheschematicdiagramofaMagneticMeter(Magmeter),whereVisthevelocityoftheliquidflowthroughthepipe,Distheinternaldiameterofthepipe,BisthefluxdensityofthemagneticfieldandEs istheinducedvoltageattheelectrodesduetheflowoftheliquidthroughthepipeplacedinthemagneticfield.

Figure11.4TheMagmeteranditscomponents

The accuracy of thesemeters can be 0.25%at the best and, inmost applications, anaccuracyof1%isused.Atworst,5%accuracyisobtainedinsomedifficultapplicationswhereimpuritiesofliquidsandthecontactresistancesoftheelectrodesareinferiorasinthecaseoflow-puritysodiumliquidsolutions.

11.5.1Faraday’sLawofInductionThis law states that if a conductor of length l (m) is moving with a velocity v (m/s),perpendiculartoamagneticfieldoffluxdensityB(Tesla)thentheinducedvoltageacrosstheendsofconductorcanbeexpressedby

TheprincipleofapplicationofFaraday’slawtoanelectromagneticflowmeterisgiveninFigure11.5.Themagnetic field, thedirectionof themovementof theconductor,andtheinducedemfareallperpendiculartoeachother.

Figure 11.6 illustrates a simplified electromagnetic flow meter in greater detail.Externally located electromagnets create a homogeneous magnetic field (B) passingthroughthepipeandtheliquidinsideit.Whenaconductingflowingliquidcutsthroughthemagnetic field, a voltage is generated along the liquid path between two electrodespositionedontheoppositesidesofthepipe.

Figure11.5Operationalprincipleofelectromagneticflowmeters

Figure11.6Constructionofpracticalflowmeters

Inthecaseofelectromagneticflowmeters,theconductoristheliquidflowingthroughthepipe,andthelengthoftheconductoristhedistancebetweenthetwoelectrodes,whichisequaltothetubediameter(D).Thevelocityoftheconductorisproportionaltothemeanflowvelocity(v)oftheliquid.Hence,theinducedvoltagebecomes

Ifthemagneticfieldisconstantandthediameterofthepipeisfixed,themagnitudeoftheinducedvoltagewillonlybeproportionaltothevelocityoftheliquid.Iftheendsoftheconductor, in this case the sensors, are connected to anexternal circuit, the inducedvoltagecausesacurrent, i to flow,whichcanbeprocessedsuitablyasameasureof theflow rate. The resistance of themoving conductor can be represented byR to give theterminalvoltageasvT=e−iR.

Electromagnetic flowmeters areoften calibrated todetermine thevolumetric flowoftheliquid.Thevolumeofliquidflow,Qcanberelatedtotheaveragefluidvelocityas

Writingthearea,Aofthepipeas

givestheinducedvoltageasafunctionoftheflowrate.

Equation (11.11) indicates that in a carefully designed flow meter, if all otherparametersarekeptconstant,thentheinducedvoltageislinearlyproportionaltotheliquidflowonly.

BasedonFaraday’slawofinduction,therearemanydifferenttypesofelectromagneticflowmetersavailable,suchasac,dc,andpermanentmagnets.Thetwomostcommonlyusedonesaretheacanddctypes.Thissectionconcentratesmainlyonacanddctypeflowmeters.

Although the inducedvoltage is directlyproportional to themeanvalueof the liquidflow,themaindifficultyintheuseofelectromagneticflowmetersisthattheamplitudeofthe induced voltage is small relative to extraneous voltages and noise. Noise sources

include•Strayvoltageintheprocessliquid

•Capacitivecouplingbetweensignalandpowercircuits

•Capacitivecouplinginconnectionleads

•Electromechanicalemfinducedintheelectrodesandtheprocessfluid

•Inductivecouplingofthemagnetswithintheflowmeter

AdvantagesofElectromagneticFlowMeter•Theelectromagneticflowmetercanmeasureflowinpipesofanysizeprovidedapowerfulmagneticfieldcanbe

produced.

•Theoutput(voltage)islinearlyproportionaltotheinput(flow).

•Themajoradvantageofelectromagneticflowmeteristhatthereisnoobstacletotheflowpathwhichmayreducethepressure.

•Theoutputisnotaffectedbychangesincharacteristicsofliquidsuchasviscosity,pressureandtemperature.

Limitations•Theoperatingcostisveryhighinanelectromagneticflowmeter,particularlyifheavyslurries(solidparticlein

water)arehandled.

•Theconductivityoftheliquidbeingmeteredshouldnotbelessthan10µΩ/m.Itwillbefoundthatmostaqueoussolutionsareadequatelyconductivewhileamajorityofhydrocarbonsolutionsarenotsufficientlyconductive.

11.5.2ComparisonofdcandacExcitationofElectromagneticFlowMeter

Themagneticfieldusedinelectromagneticflowmetercaneitherbeacordcgivingrisetoacoradcoutputsignalrespectively.Thedcexcitationisusedinfewapplicationsduetothefollowinglimitationsofthedcexcitation.

Whendcexcitationisusedformaterialsofverylowconductivityandflowingatslowspeeds, theoutput emf is too small tobeeasily readoff.Thedcamplifiersused in thispurposesarealsohavesomeinherentproblemsespeciallyatlowlevel.

Manyhydrocarbonoraqueoussolutionsexhibitpolarisationeffectswhentheexcitationis dc. The positive ionsmigrate to the negative electrode and disassociate, forming aninsulatingpocketofgaseoushydrogen,thereisnosuchphenomenawhenacisused.

ThedcfieldmaydistortthefluidvelocityprofilebyMagnetoHydroDynamic(MHD)action.Anacfieldofnormalfrequency(50Hz)haslittleeffectonvelocityprofilebecausefluidinertiaandfrictionforcesat50Hzandsufficienttopreventanylargefluidmotion.

Sincetheoutputofelectromagneticflowmetersisquitesmall(afewmV),interferingvoltageinputsduetothermocoupletypeofeffectsandgalvanicactionofdissimilarmatelsused inmeter constructionmay be of the same order as the signal. Since the spuriousinterferring inputsaregenerallydriftsofvery low frequency, the50Hz systemcanusehighpassfilterstoeliminatethem.

While ac system predominates, dc types of systems have been used for flowmeasurementsof liquidmetals likemercury.Here,nopolarisationproblemexists.Also,aninsulatingpipeoranonmetallicpipeisnotneededsincetheconductivityoftheliquidmetalisverygoodrelativetoanordinarymetalpipe.Thismeansthatthemetalpipeisnot

veryeffectiveasashortcircuitforthevoltageinducedintheflowingliquidmetal.Whenmetallic pipes are used as with dc excitation no special electrodes are necessary. Theoutput voltage is tapped off the metal pipe itself at the points of maximum potentialdifference.

11.6 TEMPERATURETRANSDUCERS

Applicationofheatoritswithdrawalfromabodyproducesvariousprimaryeffectsonthisbodysuchas

•Changeinitsphysicalorchemicalstatesuchasphasetransition

•Changeinitsphysicaldimensions

•Variationsinitselectricalproperties

•Generationofanemfatthejunctionoftwodissimilarmetals

•Changeintheintensityoftheemittedradiation

Anyoftheseeffectscanbeemployedtomeasurethetemperatureofabody,thoughthefirstoneisgenerallyusedforstandardisationoftemperaturesensorsratherthanfordirectmeasurementoftemperature.

11.6.1ResistanceThermometersResistancetemperaturedetectors,orresistancethermometers,employasensitiveelementofextremelypureplatinum,copperornickelwirethatprovidesadefiniteresistancevalueateachtemperaturewithinitsrange.Therelationshipbetweentemperatureandresistanceofconductorsinthetemperaturerangenear0°Ccanbecalculatedfromtheequation

whereRt=resistanceoftheconductorattemperaturet(°C)

Rref =resistanceatthereferencetemperature,usually0°Cα =temperaturecoefficientofresistanceΔt =differencebetweenoperatingandreferencetemperature

Almostallmetallicconductorshaveapositivetemperaturecoefficientofresistancesothat their resistance increaseswith an increase in temperature. Somematerials, such ascarbonandgermanium,haveanegativetemperaturecoefficientofresistancethatsignifiesthattheresistancedecreaseswithanincreaseintemperature.Ahighvalueofαisdesirablein a temperature sensing element so that a substantial change in resistance occurs for arelatively small change in temperature.This change in resistance (ΔR) canbemeasuredwithaWheatstonebridge,whichmaybecalibratedtoindicatethetemperaturethatcausedtheresistancechangeratherthantheresistancechangeitself.

Figure11.7indicatesthevariationofresistancewithtemperatureforseveralcommonlyused materials. The graph shows that the resistance of platinum and copper increasesalmostlinearlywithincreasingtemperature,whilethecharacteristicfornickelisdecidedlynonlinear.

Figure11.7Relativeresistance(RT/R0)versustemperatureforsomepuremetals

Thesensingelementofaresistancethermometerisselectedaccordingtotheintendedapplication.Table11.1summarises thecharacteristicsof the threemostcommonlyusedresistancematerials. Platinumwire is used formost laboratory work and for industrialmeasurementsofhighaccuracy.Nickelwireandcopperwirearelessexpensiveandeasierto manufacture than platinum wire elements, and they are often used in low-rangeindustrialapplications.Table11.1Resistancethermometerelements

Resistancethermometersaregenerallyoftheprobetypeforimmersioninthemediumwhosetemperatureistobemeasuredorcontrolled.Atypicalsensingelementforaprobe-typethermometerisconstructedbycoatingasmallplatinumorsilvertubewithceramicmaterial, winding the resistance wire over the coated tube, and coating the finishedwinding again with ceramic. This small assembly is then fired at high temperature toassureannealingofthewindingandthenitisplacedatthetipoftheprobe.TheprobeisprotectedbyasheathtoproducethecompletesensingelementsasshowninFigure11.8.

Figure11.8Resistancethermometerinprotectingcover

Practically,allresistancethermometersforindustrialapplicationsaremountedinatubeor well to provide protection against mechanical damage and to guard againstcontamination and eventual failure. Protecting tubes are used at atmospheric pressure;

when they are equipped inside a pipe thread bushing, theymay be exposed to low ormedium pressures. Metal tubes offer adequate protection to the sensing element attemperatures up to 100°F, although they may become slightly porous at temperaturesabove1500°Fandthenfailtoprotectagainstcontamination.

Protectingcoversaredesignedforuseinliquidorgasesathighpressuresuchasinpipelines,steampowerplants,pressure tanks,pumpingstations,etc.Theuseofaprotectingcover becomes imperative at pressures above three times of atmospheric pressure.Protectivewellsaredrilledfromsolidbarstock,usuallycarbonsteelorstainlesssteel,andthe sensing element is mounted inside. A waterproof junction box with provision forconduitcouplingisattachedtothetopofthetubeorwell.

A typical bridge circuit with resistance thermometer Rt in the unknown position isshowninFigure11.9.Thefunctionswitchconnectsthreedifferentresistorsinthecircuit.RRefisafixedresistorwhoseresistanceisequaltothatofthethermometerelementatthereferencetemperature(say,0°C).Withthefunctionswitchinthe‘REFERENCE’position,thezero adjust resistor is varied until the bridge indicator reads zero.Rfs is another fixedresistorwhoseresistanceequalsthatofthethermometerelementforfull-scalereadingofthecurrentindicator.Withthefunctionswitchinthe ‘FULLSCALE’position, thefullscaleadjustresistorisvarieduntiltheindicatorreadsthefullscale.Thefunctionswitchisthensettothe‘MEASUREMENT’position,connectingtheresistancethermometerRtinthecircuit.When the resistance temperaturecharacteristicof the thermometerelement is linear, thegalvanometerindicationcanbeinterpolatedlinearlybetweenthesetofvaluesofreferencetemperatureandfullscaletemperature.

The Wheatstone bridge has certain disadvantages when it is used to measure theresistance variations of the resistance thermometer. These are the effects of contactresistances of connections to the bridge terminals, heating of the elements by theunbalance current and heating of the wires connecting the thermometer to the bridge.Slight modifications of the Wheatstone bridge, such as the double slide wire bridgeeliminatesmostoftheseproblems.Despitethesemeasurementdifficulties,theresistancethermometermethodissoaccuratethat it isoneof thestandardmethodsof temperaturemeasurementwithintherange–150°to650°C.

Figure11.9Wheatstonebridgecircuitwitharesistancethermometerasoneofthebridgeelements

11.6.2ThermocoupleThomasSeebeckdiscovered in1821 thatwhen twodissimilarmetalswere incontact,avoltage was generated where the voltage was a function of temperature. The device,consisting of two dissimilar metals joined together, is called a thermocouple and the

voltageiscalledtheSeebeckvoltage,accordingtothenameofthediscoverer.

Asanexample,joiningcopperandconstantanproducesavoltageontheorderofafewtensofmillivolts(Figure11.10)withthepositivepotentialatthecopperside.Anincreaseintemperaturecausesanincreaseinvoltage.

Figure11.10Thermocoupleoutputvoltageasafunctionoftemperatureforvariousthermocouplematerials

Thereareseveralmethodsofjoiningthetwodissimilarmetals.Oneistoweldthewirestogether. This produces a brittle joint, and if not protected from stresses, this type ofthermocouplecan fracture and break apart.During thewelding process, gases from thewelding can diffuse into the metal and cause a change in the characteristic of thethermocouple.Anothermethodofjoiningthetwodissimilarmetalsistosolderthewirestogether.Thishasthedisadvantageofintroducingathirddissimilarmetal.Fortunately,ifboth sidesof the thermocoupleareat the same temperature, theSeebeckvoltagedue tothermocoupleactionbetweenthetwometalsofthethermocoupleandthesolderwillhaveequalandoppositevoltagesandtheeffectwillcancel.Amoresignificantdisadvantageisthat inmanycases the temperatures tobemeasuredarehigher thanthemeltingpointofthesolderandthethermocouplewillcomeapart.

Itwould appear to be a simplematter tomeasure the Seebeck voltage and create anelectronicthermometer.Todothis,wirescouldbeconnectedasshowninFigure11.11tomakethemeasurement.Thisconnectionofthewirescausesaproblemofmeasurement,asshowninFigure11.12.

Figure11.11Effectsofadditionalparasiticthermocouple

Assumethatthemeterusescopperwiresasshown.Inthiscase,wherethetwocopperwirescome incontact there isnoproblem,butwhere thecoppercomes incontactwithanothermetal,suchastheconstantanthermocouplewire,thetwodissimilarmetalscreateanotherthermocouple,whichgeneratesitsownSeebackvoltage.Forthisexample,copperinterconnectingwireswere used and the thermocouplewas copper and constantan.Thecompositionof thewires is immaterial, as any combinationwill produce theseparasiticthermocoupleswiththeproblemsofadditionalSeebackvoltages.Itisaninescapablefactthattherewillbeatleasttwothermocouplejunctionsinthesystem.Tocontendwiththis,it is necessary that the temperature of one of the junctions be known and constant.Therefore, there is a fixed offset voltage in themeasuring system. In early times, it ismandatory to place this junction in a mixture of ice and water, thus stabilising thetemperatureto0°CasshowninFigure11.13.Inmodern-ageelectronicreferencejunctionis used and it is called the reference or cold junction because this junction wastraditionallyplacedintheicebath.

Figure11.12Connectionofwires

Figure11.13Applicationofareferencejunction

Theclassicmethodofmeasuringthermocouplevoltageswastheuseofapotentiometer.Thiswas amechanicaldevice and isno longerused.Completely electronicdevices areused to measure thermocouple voltages and to convert from the Seeback voltage totemperature,andtocompensateforthereferencejunction.

11.6.3ErrorsoccurringDuringtheMeasurementusingThermocouple

1.OpenJunctionThere aremany sources of an open junction. Usually, the error introduced by an openjunction is of such an extreme magnitude that an open junction is easily spotted. Bysimply measuring the resistance of the thermocouple, the open junction is easilyidentified.

2.InsulationDegradationThe thermocouple isoftenusedatveryhigh temperatures. Insomecases, the insulationcanbreakdownandcausesasignificant leakageresistancewhichwillcauseanerror inthe measurement of the Seeback voltage. In addition, chemicals in the insulation candefuseintothethermocouplewireandcausedecalibration.

3.ThermalConductionThethermocouplewirewillshuntheatenergyawayfromthesourcetobemeasured.Forsmall temperature to be measured, small diameter thermocouple wire could be used.However, the small diameter wire is more susceptible to the effects. If a reasonablecompromise between the degrading effects of small thermocouplewire and the loss ofthermal energy and the resultant temperature error cannot be found, thermocoupleextensionwirecanbeused.Thisallowsthethermocouple tobemadeofsmalldiameterwire,whiletheextensionwirecoversmajorityoftheconnectingdistance.

4.GalvanicActionChemicalscomingincontactwiththethermocouplewirecancauseagalvanicaction.Thisresultant voltage can be as much as 100 times the Seebeck voltage, causing extremeerrors.

5.DecalibrationThis error is a potentially serious fault, as it can cause slight error that may escapedetection. Decalibration is due to altering the characteristics of the thermocouple wire,thus changing the Seeback voltage. This can be caused due to subjecting the wire toexcessivelyhightemperatures,diffusionofparticlesfromtheatmosphereintothewire,orbycoldworkingthewire.

11.6.4ThermistorsThermistors (construction of thermal resistor) are semiconductors which behave asresistorswithahighnegativetemperaturecoefficientofresistance.

Manganese,nickelorcobaltoxidesaremilled,mixedinproperproportionwithbinders,passesintodesiredshapesandthensinteredtoformthermistorsintheformofbeads,rodsor discs. Sometimes, a glass envelope is provided to protect a thermistor formcontaminations.

TheresistanceRTofathermistorattemperatureT(Kelvin)canbewrittenas

whereRTandR0aretheresistancesinohmsofthethermistoratabsolutetemperaturesT

and T0.β is a thermistor constant ranging from 3500 K to 5000 K. The referencetemperatureT0isusuallytakenas298Kor25°C.

Nowthetemperaturecoefficientoftheresistance

AtT=298K,thevalueofαis

Thisisevidentlyaratherhightemperaturecoefficientbecauseforaplatinumresistancethermometerthecorrespondingfigureis0.0035/°C.

Theplotofresistivity(ρ)versustemperature(Figure11.14)willalsodemonstrate thiscomparison.

Equation(11.13)canberearrangedtotheform

whereAandBareconstants.Eq.(11.16)mayalternativelybeusedtofindtemperaturesbyevaluatingAandBfromtwopairsofknownvaluesofRTandT.

Figure11.14Comparisonofresistivityofplatinumwiththatofthermistors

Thermistorsareverypopularastemperaturetransducersbecause(i)theyarecompact,rugged, inexpensive,(ii) theircalibrationisstable,(iii) theyhaveasmallresponsetime,(iv)theyareamenabletoremotemeasurements,andaboveall,(v)theiraccuracyishigh.

Example11.2 Fora certain thermistorβ=3100Kand its resistanceat20°C is known to be 1050 Ω. The thermistor is used fortemperature measurement and the resistance measured is2300Ω.Findthemeasuredtemperatureifthetemperature-resistancecharacteristicsofthethermistorisgivenby

whereTisinKelvin.

SolutionHere,R0=1050Ω,T0=293K.hencefromEq.(11.15),weget

whichgivesT=272.8K 0°C

Example11.3 Theresistanceofathermistoris800Ωat50°Cand4kΩatthe ice-point.Calculate thecharacteristic constants (A,B)for the thermistorandthevariations inresistancebetween30°Cand100°C.

SolutionFormEq.(11.16),wegetthefollowingconditions:

A+Bin800=

A+Bin4000=

whichgivesA=7.4084×10-4andB=3.5232×10-4.

Thevariationinresistancecanbecalculatedfromtherelation

11.7 PRESSUREMEASUREMENT

Thepressure, or force,measurement canbedoneby converting the appliedpressureorforce into a displacement by elastic elements which acts as a primary transducer. Thedisplacement of the elastic element which is a function of the applied force may bemeasured by the transducer which acts as a secondary transducer. The output of thesecondary transducer is a function of the displacement, which in turn is a function ofpressureorforcewhichisthemeasurand.Somemechanicalmethodsareusedtoconverttheappliedpressureofforceintodisplacement.Thesemechanicaldevicesarecalledforcesummingdevices.

Themostcommonlyusedsummingdevicesare1.Flatorcorrugateddiaphragms

2.Pivottorque

3.Straighttube

4.Singleordoublemasscantileversuspension

5.CircularortwistedBourdontube

6.Bellows

Among these, pressure transducers generally use flat or corrugated diaphragms,bellows, circular or twisted Bourdon tubes and straight tubes. Single or double masscantilever suspension and pivot torque types are found in accelerometer and velocitytransducers.DifferentkindsofforcesummingdevicesareshownintheFigure11.15.

SecondaryTransducersThedisplacementproducedbytheactionoftheforcesummingdevicesisconvertedintoachangeofsomeelectricalparameter.Thevarioustransducersusedforthispurposeareofthefollowingtypes:

1.Resistive

2.Inductive

3.Differentialtransformer

4.Capacitive

5.Photo-electric

6.Piezo-electric

7.Ionization

8.Oscillation.

Figure11.15Differenttypesofsummingdevices

11.7.1ResistiveTransducersThe electrical strain gauges attached to a diaphragmmay be used for measurement ofpressure.Thediagram is shown inFigure11.16. The output of these strain gauges is afunctionoftheappliedstrain,whichinturn,isafunctionofthediaphragmdeflectionandthe differential pressure. The deflection generally follows a linear variation withdifferentialpressureP=P2−P1 (when thedeflection is less than1/3of thediaphragmthickness).Oneofthedisadvantagesofthismethodissmallphysicalareaisrequiredformounting the strain gauges. Change in resistance of strain gauges on account ofapplicationofpressure is calibrated in termsof thedifferential pressure.Gaugesof thistypearemadeinsizeshavingalowerrangeof100kN/m2to3MN/m2toanupperrange

of100kN/m2to100MN/m2.

11.7.2InductiveTransducersThistypeoftransducershasbeensuccessfullyusedassecondarytransducersalongwithadiaphragmformeasurementofpressure.Figure11.17showsanarrangementwhichusestwocoils;anupperandalowercoilwhichformthetwoarmsofanacbridge.Thecoilshaveequalnumberof turns.Theother twoarmsof thebridgeare formedby twoequalresistances eachof valueR.The diaphragm is symmetrically placedwith respect to thecoilsandsowhenP1=P2,Thereluctancesofthepathofmagneticfluxforboththecoilsareequalandhencetheinductancesofthecoilsareequal.

Figure11.16Differentialpressuremeasurementwithdiaphragmandstraingauges

Figure11.17Pressuremeasurementwithdiaphragmandinductivetransducer

Now, I initial self-inductance = N2/R0, where Number of turns, and R0 = Initialreluctanceofthefluxpath.Underthisconditionthebridgeisbalancedandtheoutput,E0,ofthebridgeiszero.NowforanyparticularmomentP2isgreaterthanP1and thereforethedifferentialpressureP=P2−P1,deflectsthediaphragmupwardsthroughadistanced.forsmalldisplacementofdiaphragms,thereluctanceofthefluxpathoftheuppercoilisR1 =R0 +K(D −d) and that of the lower coil isR2 =R0 +K(D +d).WhereK is aconstant,Distheinitialdistanceofthediaphragmfromthecoilsanddisthedisplacementofthediaphragmsduetoforce.Hence,theinductanceoftheuppercoil

andthatofthelowercoilis

Thebridgebecomesunbalancedandthevalueofoutputvoltageisgivenby

Since K, R0, D and ei are constant, the output voltage is directly proportional todisplacementd,ofthediaphragm.Displacementd, isdirectlyproportionaltodifferentialpressureP =P2 − P1 Hence the output voltage e0 may be calibrated in terms of thedifferentialpressureP.

If thevalueof thedeflectiond issmall thenthereexistsa linearrelationshipbetweenoutputvoltagee0andthedifferentialpressure.ItispossibletodeterminewhetherP2>P1orP1 >P2with reference to thephaseof theoutput voltage,e0,with respect to sourcevoltageei.

11.7.3DifferentialTransformersThelinearvariabledifferentialtransformers(LVDT)isusedasasecondarytransducerformeasuringthepressurewithbellowsorbourdontubeactingasaprimarytransducers,i.e.,asaforcesummingdevice.ThepressureisconvertedintodisplacementwhichissensedbytheLVDTandtransformedintoavoltage.ThetwoarrangementsareshowninFigure11.18and11.19.

Figure11.18PressuremeasurementwithbellowsandLVDT

Figure11.19PressuremeasurementwithBourdontubeandLVDT

11.7.4CapacitiveTransducersInthistypeoftransducers,alinearcharacteristicscanbeachievedbyusingadifferential

arrangement for the capacitive displacement transducers. The arrangement using threeplatesisshowninFigure11.20.P1andP2arefixedplatesandMisthemovableplatetowhichthedisplacementtobemeasuredisapplied.Thus, twocapacitorsaretherewhosedifferentialoutputistaken.

Figure11.20Differentialarrangementofcapacitivetransducer

LetthecapacitanceofthesecapacitorsbeC1andC2respectively,whentheplateMismidwaybetweenthetwofixedplates,underthisconditionthecapacitancesC1andC2areequal.

Whereε=Permittivityofthemediumbetweentheplates,A=Cross-sectionalareaoftheplates,D=Distancebetweentheplates.

AnacvoltageE is appliedacrossplatesP1andP2 and thedifferenceof thevoltagesacrossthetwocapacitancesismeasured.WhenthemovableplateismidwaybetweenthetwofixedplatesC1=C2andthereforeE1=E2=E/2.

Therefore,differentialoutputwhenthemovableplateismidwayΔE=E1-E2=0

Letthemovableplatebemovedupduetodisplacementx,thereforethevaluesC1andC2becomedifferentresultinginadifferentialoutputvoltage.

Therefore,theoutputvoltagevarieslinearlyasthedisplacementx.

The use of a three-terminal variable differential circuit capacitor is shown in Figure11.21.Sphericaldepressionsofadepthofabout0.025mmaregroundintotheglassdiscs.The depressions are coated with gold to form the two fixed plates of the differentialcapacitor.Athinstainlesssteeldiaphragmclampedbetweenthediscsactsasthemovable

plate.

Figure11.21Capacitivetransducerandbridgecircuit

Whenequalpressuresareapplied(i.e.,P1=P2),thediaphragmisintheneutralpositionand the bridge is balanced. The output voltage e0, is zero under this condition. If onepressure is made greater than the other, the diaphragm deflects in proportional to thedifferentialpressure,givinganoutputvoltagee0, from thebridge terminals.Thisoutputvoltageisproportionaltothedifferentialpressure.Foranoppositepressuredifference,theoutputvoltageshowsa180°phaseshift.

The use of capacitive transducers is not common because of low sensitivity. Alsocapacitive transducers require high carrier frequencies (typically, 2.5 kHz) for dynamicpressuremeasurement.

11.7.5PhotoelectricTransducersThepropertiesofaphotoemissivecellorphototubeareusedinphotoelectrictransducers.Thevacuumphotoelectric cell consistsof a curved sheetof thinmetalwith its concavesurfacecoatedwithaphotoemissivematerial,whichformsthecathode,andtherodanodemountedatthecentreofcurvatureofthecathode.ThewholeassemblyismountedinanevacuatedglassenvelopeasshowninFigure11.21.Thematerial,coatedcathode,emitselectronswhen light radiation strikes them.The emitted electrons from the cathode arecollectedbyapositiveelectrode(anode)forminganelectriccurrent.

Figure11.22 also shows the current versus voltage characteristics of a typical highlyevacuatedphototube.Itisfoundfromthecurvethatforthevoltageaboveapproximately20V,theoutput isnearlyindependentof theappliedanodevoltagebutentirelydependsupontheamountofincidentlight(denotedbyitswavelengthinFigure11.21).Thecurrentthroughthephototubeproducedasaresultofincidentlightisverysmall.Thiscurrentistheoutputofthephoto-electrictransducers.AsthecurrentisintheorderofsomefewμA,itmustbeamplifiedtoprovideausableoutput.

Figure11.22Photoemissivecellanditsvoltagevscurrentcharacteristic

Thephotoelectric transducerusesaphototubeanda lightsourceseparatedbyasmallwindow, whose aperture is controlled by the force summing device of the pressuretransducer (Figure 11.23). The displacement of the force summing devices modulatesquantityofincidentlightfallingonthephototube.Appliedpressureorforcechangesthepositionof theforcesummingdevicewhich in turnchanges thepositionof thewindowthuscausingachangeinincidentlight.AccordingtocurvesinFigure11.22achange inlight intensity varies the photoemissive property at a rate approximately linear withdisplacement. These transducers either use a stable source of light or an acmodulatedlight.

Figure11.23Pressuremeasurementusingphotoelectrictransducer

11.7.6PiezoelectricTransducersWhen piezoelectric crystals are under the influence of some external force or pressure,theyproduceanemf.Theforceordisplacementorpressuretobemeasuredisappliedtothecrystal.Thepressure isapplied to thecrystal througha force summingdevice.Thiscausesadeformationwhichproducesanemfwhichisafunctionofthedeformation.Thisoutputemfmaybemeasuredtoknowthevalueofappliedforceandhencethepressure.

11.7.7IonisationTransducersIonisationistheprocessofremovinganelectronfromanatomproducingafreeelectronandapositivelychargedion.Ionisationmaybeproducedbythecollisionofahighspeedelectron from the atom. Figure 11.24 shows the essential features of an ionisation-typegauge. Electrons are emitted from heated cathode using a filament and are acceleratedtowardsthegrid,whichispositivelycharged.Someof theelectronsarecapturedbythe

grid, producing grid current IG. Electrons having high kinetic energy pass through andcauseionizationofgasatoms.

Figure11.24Ionisationtypevacuumgaugeformeasurementoflowpressure

Thepositiveionssoproducedareattractedtotheplate,whichisatnegativepotentialand a current Ip is produced in the plate circuit. It is found that the pressure of gas isproportionaltoratioofplatetogridcurrent,

whereS=constantofproportionality

S iscalled thesensitivityof thegauge.AtypicalvalueofSfornitrogenis20 torr–1.However, the exact value must be determined by calibration of particular gauge sincesensitivitySisafunctionofthegeometryofthetubeandthegasfilledinit.Pressurethatcanbemeasuredbyionisationgaugerangesform10–3to10–8mmofHg.

11.7.8OscillationTransducersThesetypesof transducersuseaforcesummingdevicetochangethecapacitance,C,orinductance,L,ofanLCoscillationcircuit.Figure11.25shows thebasicelementsofLCtransistoroscillatorwhoseoutputfrequencyisaffectedbyachangeintheinductanceofacoil. The change in inductance is caused by the force summing device acting upon aninductivedevice.Theoutputofoscillatorisamodulatedoutputandcanbedemodulatedandcalibratedintermsofthepressureorforceapplied.

Figure11.25Basicelementsofanoscillationtransducer

EXERCISE

Objective-typeQuestions1.Capacitivetransducershavetheadvantagesof

(a)veryhighinputimpedance

(b)veryhighinputimpedance,excellentfrequencyresponse,highsensitivityandnotbeingaffectedbystaymagneticfields

(c)both(a)and(b)

(d)noneoftheabove

2.Thetransducerthatconvertsmeasurandintotheformofpulseiscalledthe_______transducers.

(a)digital

(b)active

(c)analog

(d)pulse

3.A______iscommonlyusedforthemeasurementoftemperature

(a)photodiode

(b)straingauge

(c)piezocrystal

(d)thermistor

4.LVDTwindingsarewoundon

(a)copper

(b)ferrite

(c)aluminium

(d)steelsheets(laminated)

5.Thestraingaugesshouldhavelow

(a)resistancetemperaturecoefficient

(b)resistance

(c)gaugefactor

(d)alloftheabove

6.Whichofthefollowingdevicescanmeasurepressuredirectly?

(a)Bourdontube

(b)Rotometer

(c)Both(a)and(b)

(d)Neither(a)nor(b)

7.Thelowerlimitofusefulworkingrangeofatransducerisdeterminedby

(a)transducererrorandnoise

(b)minimumusefulinputlevel

(c)dynamicresponse

(d)cross-sensitivity

8.Whichoneofthefollowinggivesthegaugefactorofastraingauge?

9.Self-generatingtypeoftransducersare

(a)Inverse

(b)active

(c)passive

(d)secondary

10.Thesensitivityfactorofstraingaugeisnormallyoftheorderof

(a)1to1.5

(b)1.5to2.0

(c)0.5to1

(d)5to10

11.Apairofactivetransducersis

(a)thermocouple,thermistors

(b)thermistors,solarcell

(c)solarcell,LVDT

(d)thermocouple,solarcell

12. Thetransducersthatconvert theinputsignalintotheoutputsignal,whichisacontinuousfunctionoftime,areknownas

(a)analog

(b)digital

(c)active

(d)passive

13.Astraingaugewitharesistanceof250Ωundergoesachangeof0.150Ωduringatest.Thestrainis1.5×10-4.Thenthegaugefactoris

(a)4

(b)3

(c)2

(d)100

14.Considerthefollowingtransducers:

1.LVDT

2.Piezoelectric

3.Thermocouple

4.Photovoltaiccell

5.Straingauge

Whichoftheseareactivetransducers?

(a)2,3and5

(b)1,3and4

(c)1,2and5

(d)2,3and4

15.LVDTcanbeusedfor

(a)angularvelocitymeasurementofacolumn

(b)loadmeasurement

(c)vibrationmeasurement

(d)forcemeasurementinabeam

16.Thermocouples

(a)requirereferencejunctioncompensation

(b)aremostcommonlyusedastemperaturetransducer

(c)haveanionoutputvoltagelevel

(d)alloftheabove

17.Athermocoupletemperatureindicatorwithreferencejunctionatroomtemperaturehasatimeconstantof1s.Itisdipped in a hot bath of 120°C. If the room temperature is 20°C, after 1 s the thermocouple type temperatureindicatorwillread

(a)63.2°C

(b)100°C

(c)120°C

(d)140°C

Short-answerQuestions1. What is the definition and importanceofprimary sensing element?. Enlist some of themost commonly used

primarysensingelements.

2.Namedifferentelasticspressureelementsandgivetheirusefulworkingrangeandothercharacteristics.

3.Distinguishbetweenactiveandpassiveelectricaltransducersandgivesomeexamplesofthem.

4.Whatarethedifferencesbetweensensorsandtransducers?

5.Describeamethodformeasurementofdifferentialpressure.

6. What isanelectrical transducer?Whatare thebasic requirementsofa transducer?Give theclassificationofatransducer.

7.Explainhowthermistorcanbeusedfortemperaturemeasurement.

8.WhataretheadvantagesandusesoftheLVDT?

9.Whatarecapacitivetransducers?Whataretheiradvantagesanddisadvantages?

Long-answerQuestions1. What are thermistors? Explain theworking, construction and applications of thermistors. Compare resistance

temperaturecharacteristicsofatypicalthermistorandplatinum.

2.Writedowntheconstructionandworkingprincipleofathermocouple.Comparedifferentthermocouplematerials.Describetheadvantages,disadvantagesandapplicationsofthermocouple.

3. What is an LVDT? Explain its working principle with necessary diagrams and characteristics.What are itsadvantagesanduses?

4.Explaintheworkingprincipleofalinearvariabledifferentialtransformer(LVDT).Showhowitcanbeusedformeasuringsmallmechanicaldisplacements.

5. Describewithsuitablediagramstheworkingprincipleofstraingauges.DescribethetermsPoisson’sratio andgaugefactor.

6. Withaneatsketch,brieflydescribetheprincipleofelectromagneticflowmeter.Whataretheadvantagesofanelectromagneticflowmeter?

7.(a)Whataretheerrorsthatoccurthatduringthemeasurementusingathermocouple?

(b)Whatarethesecondarytransducersusedforpressuremeasurement?Explainanyonethembriefly.

12.1 INTRODUCTION

Magneticquantitiesaremeasuredusingavarietyofdifferenttechnologies.Eachtechniquehas unique properties that make it more suitable for particular applications. Theseapplications can range from simply sensing the presence or change in the field to theprecise measurements of a magnetic field’s scalar and vector properties. Magneticmeasurements are most difficult to make and essentially less accurate than electricalmeasurements for two reasons.First, inmagneticmeasurement, flux isnotmeasuredassuch,butonlysomeeffectproducedbyit,suchasthevoltageinducedbyachangeofflux.Asasecondandgreaterdifficulty, fluxpathsarenotdefinedasareelectricalcircuits—difficultiesaredefinitelyfacedinprecisionacbridgesinmakingtheelectricalcircuits,butthemagneticsituationisradicallyworseandnotsubjecttothesamecontrol.

12.2 TYPESOFMAGNETICMEASUREMENTS

Magneticmeasurementscanbedividedintotwogeneralclasses:direct-current(dc)testsand alternating-current (ac) tests. Although quite different methods and objectives arefound, these are the twomostdistinctlydefinedclassesof tests.Thedcbranchmaybefurthersubdividedintomeasurementoffieldstrength,flux,permeability,B-Hcurvesandhysteresis loops. Such tests are most generally made upon solid materials, the ac testmethodsbeingusedchieflyforlaminatedmaterials.Theacmeasurementsareconcernedmainlywithlossesinmagneticmaterialsunderconditionsofalternatingmagnetisation.

12.3 THEBALLISTICGALVANOMETER

Theballisticgalvanometerisusedtomeasurethequantityofelectricitypassedthroughit.Thisquantityinmagneticmeasurementsistheresultofanemfinstantaneouslyinducedinasearchcoilconnectedtothegalvanometerterminals,whenthemagneticfluxinterlinkingwiththesearchcoilischanged.SuchagalvanometerisusuallyaD’Arsonvaltype,sincethistypeisleastaffectedbyexternalmagneticfields.Itdoesnotshowasteadydeflectionwhen in use, owing to the transitory nature of the current passing through, but gives a“throw”whichisproportionaltothequantityofelectricityinstantaneouslypassedthroughit. In the ballistic case the current flow takes place in a short period of time. The coilreceivesamomentaryimpulse,whichcausesittoswingtoonesideandthenreturntorest,eithergraduallyorafterseveraloscillations,dependingonthedamping.Thedeflectionis

readattheextremepointofthefirstthrow.

The discharge through the ballistic galvanometermust occur in a short time, that is,beforethecoilhasmovedappreciablyfromitsrestposition,inorderthatthethrowshallbedirectlyproportional to thequantityofelectricdischarge.Galvanometers forballisticusearedesigned,accordingtohavealongerperiodthanthatofordinarytype.Thelongperiodissecuredbylargeinertiaofthemovingsystemandsmallrestrainingtorqueofthesuspension.Theinertiahasbeensecuredinsomegalvanometersbytheadditionofdeadweighttothemovingsystem.Itispreferabletodesignthecoilforgreaterwidthsothattheaddedcoppernotonlyincreasestheinertiabutalsoenhancesthesensitivity.

Equations describing the behaviour of a ballistic galvanometer may be derived asfollows.Thetorquedevelopedbythecoilatanypointoftimeis

whereL,Wandnarerespectively,thelength,widthandnumberofturnsofthecoil,andBistheairgapfluxdensity.

Thetorqueofaccelerationis

whereJ is themomentof inertiaof thecoilabout itsaxisandw is theangularvelocity.Nowifthecoilisclosetoitszeropositionduringthetimethedischargetakesplace,thetorque of the suspension is practically zero, and if the damping torque is negligible incomparisonwiththedrivingtorqueduringthistime,thevalueofderivedtorquemaybeequal.Therefore,duringthisshortdischargeperiod

Byintegrating,weget,

where,thesubscriptzeroreferstoconditionsattheendofthedischargetime.TheintegralformontherightsideofEq.(12.4)isthequantityofchargethathaspassedthroughthecoilduringthisperiod.Therefore,

The above expression indicates that the velocity which the coil acquires from theimpulseandwithwhichitbegins itsswingisproportional to thequantityofchargethatpassed through it. This depends on Eq. (12.3), which in turn, is true only if the entiredischargetakesplacebeforethecoilhasmovedappreciablyfromitsrestposition.Thisisthereasonfortherequirementofalongperiodforthegalvanometerswing.

Duringtheactualmotion,thedeflectiontoqueiszeroandtheequationofmotionis

where,Disdampingconstant,Sisthecontrolconstantandθisthedeflectioninradians.

Thesolutionofthisequationis

where,AandBareconstantsandm1,m2 .Here,thedampingissmallandasa

result,m1andm2areimaginary.Inthepresentapplication,theinitialconditionsare

Underthiscondition,thesolutionmaybewrittenas

where,

Notice inEq. (12.9) thatdeflectionsareproportional toω0,which fromEq. (12.5) isproportional toQ. The deflection of the galvanometer may accordingly be used as ameasureofquantityofelectricitydischargedthroughit.

Theamplitudeofthefirstswingθ1,for“undamped”case(D≈0)isfromEq.(12.9)

TheratioofsuccessiveswingswithdampingpresentisfoundbyexponentialmultiplierinEq.(12.9)foratimeintervalsuchthatβt= ort= /β.Theratioofsuccessiveswingsis

The natural logarithm of this ratio is referred to as “logarithmic decrement” of thegalvanometerandhasthevalue

Thethirdswingmaybefoundinthesamemannerasfollows.

Ingeneral,

Incaseofcriticaldamping,Eq.(12.9)willbemodifiedasfollows.

Maximumdeflectionisfoundfor ort=2J/DfromEq.(12.16).SubstitutethisvalueinEq.(12.15)andcallthedeflectionθ1;then

Since,D2/4J2=S/Jforcriticalcase.

ItisinterestingtocompareEq.(12.18)withEq.(12.10).Thedeflectioninthecriticallydampedcaseis1/eor36.8%oftheundampeddeflection,butitisstilladirectmeasureofω0 orQ. The loss of sensitivity is not much serious, since conditions can usually bearrangedtogiveampledeflection.

Summarising the resultsof this study in the followingequationof thechargepassingthroughthegalvanometer,

TheusualworkingunitsinEq.(12.19)are

K2 =galvanometersensitivityinmicrocoulombs/millimetredeflectionθ =deflectioninmillimetresQ =chargeinmicrocoulombs

Intheoreticalstudy,θwasinradiansandQincoulombs,buttheunitsaboveareonesincommon use in laboratory work. The sensitivityK2 has been shown to depend on thedamping.Curvesmaybefoundshowingtherelationshipofsensitivitytodampinginorderto give an idea of the nature of variation. The sensitivity for a set of measurements,however,shouldbeobtainedbycalibratingconductedundertheactualconditionsofuse.

12.3.1MeasurementofMagneticFluxbyBallisticGalvanometerTosensemagneticfluxofabarmagnet,itissurroundedbyasearchcoilorpick-upcoilthatisconnectedinserieswithavariableresistorandagalvanometer.Thecircuitdiagramof thismeasurement scheme is shown in Figure 12.1. The series resistor is set to givecritical damping and itmay also be used to control sensitivity. The sensitivitymay becontrolled satisfactorily by adjusting the number of turns in the search coil.When themagnetissuddenlywithdrawnfromthecoil,animpulseofshortdurationisproducedinthegalvanometerandthefirstdeflectionofthegalvanometermaybetakenasameasureoftheflux.Theinducedvoltageinthesearchcoilintheprocessis

where,fluxismeasuredinweabersandNisthenumberofturnsinthesearchcoil.IfRisthe total resistanceof thecircuit, includingsearchcoil,seriesresistorandgalvanometer,themomentarycurrentflowingthroughthecircuitis

Neglectingthesign,thequantityofchargepassedthroughthegalvanometeris

Deflectionofthegalvanometeris

Whileperformingthistest,twopointsshouldbenoted:first,thechangeoffluxmustbemadeinashorttimeintervalincomparisonwiththeperiodoftheinstrument;second,thegalvanometer is here used in a closed circuit and hence is subject to electromagneticdamping.Thesensitivityfactor,K2,mustbeproperlyevaluatedfortheresistanceusedinthetestmeasurements.

Figure12.1Measurementofmagneticfluxbyballisticgalvanometer

12.3.2CalibrationoftheBallisticGalvanometerThismaybecarriedoutinanumberofways.Someofthemethodsareasfollows:

1.ByMeansofaCapacitorA capacitor which has been charged to a known voltage is discharged through thegalvanometer.ThecircuitdiagramoftheschemeisshowninFigure12.2.TheresistorandS2 switch are used to bring the galvanometer to rest quickly after a deflection. Thecapacitorischargedbytheupperpositionof theS1switchanddischargedbytemporarycontactinthelowerposition.Thequantityofelectricitydischargecanbecalculatedfromthe known voltage and capacitance of the capacitor i.e.Q =CE, so the constantK2 isderived from the charge divided by the observed deflection. This, as described, is theundamped sensitivity, because, the galvanometer circuit has infinite resistance.A shuntmaybe added, as shownby thedotted line and anewcalibration canbeobtained.Theshuntalsogivesdamping,andiftheshuntismuchbelowthecriticalvalue,theactionissluggish. Damping conditions may be improved by a combination of shunt and seriesresistances.

Thismethod isnot ingeneralusedowing to thedifficultyofdeterminingexactly thecapacitance of the capacitor under all conditions and also because of the fact that thedampingofthegalvanometerduringcalibrationisdifferentfromthatduringtesting.

Figure12.2Calibrationofaballisticgalvanometerbycapacitor

2.ByMeansofaStandardSolenoidThismethodismostcommonlyusedforcalibrationpurposes.Astandardsolenoidconsistsofalongcoilofwirewoundonacylinderofinsulatingandnonmagneticmaterial.Theremay be one ormore layers ofwire, but the design is such that the axial length of thesolenoidis largecomparedwithitsmeandiameter.Usually, theaxial lengthisat least1metre,whilethemeandiameterisoftheorderof10cm.Thewindingshouldbeuniformandthenumberofturnspermetreaxiallengthshouldbesuchthatafieldstrength,H,of10,000 A/m or more is obtained at the centre of the coil when carrying its maximumallowablecurrent.Thistypeofdimensionssetapracticallyuniformfieldnearthecentre.Thetestcoilorsearchcoilwoundcloselyaround(orelseplacedinside)themiddleofthelongsolenoidasshowninFigure12.3.Here,thecalibrationisdoneforfluxmeasurementsbymeansofaknownflux,andthecalibrationanddampingremainconstantif thesametotalresistanceinthegalvanometercircuitismaintainedatalltimes.

Thefluxlinkingthesearchcoilisgivenby

where,N1=primaryturnspermetrelengthofsolenoid

I1 =primarycurrentinamperesA =crosssectionareaoftestcoilinsquaremetres,ifplacedinside=crosssectionareaofsolenoid,iftestcoiliscloselywoundoutside.

Thus, the circuit is operated by throwing the reversing switch from one position toother.Asa result, thisarrangementcreatesa fluxchange twiceasgreatasabove,sobysubstitutionin(12.23)

where,N2=turnsonthetestcoil

R=resistanceofthetestcoilandgalvanometercircuit

ThesensitivityfactorK2canthusbeestablishedfromQandtheobserveddeflection.Thecalibrationforfluxmeasurementsmaybeplacedinconvenientform,onceK2isevaluated.Ifthegalvanometerisusedtomeasureanunknownflux,itmaybewrittenthat

where,Φx=unknownfluxchange

θ1x =deflectioninmillimetresNx =numberofturnsusedinthesearchcoil

Figure12.3Calibrationofballisticgalvanometerbysolenoid

3.ByMeansofaMutualInductanceThesolenoidandsearchcoilprovideacalculablemutualinductance,butitisacommonpractice touseavariablemutual inductor.Thisprocedurehas theadvantagethata largerangeofcalibrationpointscanbeobtained,andthemutualinductorisusuallysmallerandmoreconvenientthanthelongsolenoid.Thistestispracticallysameastheearliertest,butexpressed in a somewhat differentway. If themutual inductance between test coil andsolenoidisknown,followingthecircuitconnectionasshowninFigure12.4,adeflectionθ1producedbythereversalofaknownprimarycurrentIisobserved.

Bychangingprimarycurrent,

Figure12.4Calibrationofballisticgalvanometerbymutualinductor

LetRbethetotalresistanceofgalvanometercircuit.

Galvanometercurrent,

Byintegration,

So,

12.4 FLUXMETER

A fluxmeter is superior over the ballistic galvanometer for some kinds of magneticmeasurements.Itisaspecialformofballisticgalvanometerwithsomemodifications,like,thetorqueofthesuspensionismadeverysmall,andtheelectromagneticdampingisveryheavy.Apartfromportability,ithastheadvantagethatunlikeaballisticgalvanometer,theflux change for short time is not necessary. The deflection obtained for a given fluxchangedoesnotdependonthetimetakenmakingthechangeofflux.

TheconstructionofthemetreisshowninFigure12.5.Thecoil issupportedbyasilkfibre from a spring support. The current connections are made by spirals having themaximumpossiblespringeffect.Tomaketherestoringtorqueofthesystemasnearlyzeroaspossible,thesuspensionandspiralsarepresentintheconstruction.Thesearchcoilandmoving coil are of low resistance to get a heavily overdampedmoving system duringelectromagneticaction.Themetrecoilfollowsfluxchangesveryrapidlyandispracticallydeadbeat in its action.Afterbeingdeflected, thecoil staysalmost stationaryandmovesextremelyslowlytowardthezeroposition;thus,thefluxmeterismucheasiertoreadthanaballistic galvanometer.Amechanical or electrical return arrangementmust beused tobringthepointerbacktozero.Fluxmetersareusuallyofportabletype,carryingapointerandscale.

Figure12.5Constructionofafluxmeter

The derivation for the ballistic galvanometer was based on the assumption thatdischargethroughthecoiltakesplacebeforeitmovesappreciablyfromtherestpositionandthedampinghasanegligibleeffectduringthisperiod.Thisisnottrueforafluxmeterbecauseof theheavydampingaction.Witha lowcircuit resistance,a largeacceleratingtorqueactson themetrecoilwhenever thesearch-coilvoltageexceeds thebackvoltagecausedbythemotionofmetrecoil.Asaresult,themetrecoilrespondsquicklyandiswellalonginitsmovementwhilethefluxchangeisunderprogress,regardlessofwhetherthefluxchange is fastor slow.Thealmostcompleteabsenceofacounteracting suspensiontorquepermitsthemetretoaddtheeffectsofaseparatefluxchangesoverashortperiodoftimeandgivesindependenceoftheoveralltime,withinreasonabletime.

The voltage generated in the fluxmeter coil by its motion becomes the controllingelement in this metre because of the low resistance of the moving system and of theabsenceoftorquefromthesuspension.Thecoilvoltagecouldbeexpressedasthechangeof the flux linkages, but since the turns and magnet strength are constant it is more

convenientforthispurposetorelatevoltagetocoilvelocityor

whereK1=BLnWisthecoilconstant.

Figure12.6Analysisoffluxmeteraction

The quantities required in the analysis are shown in the Figure 12.6. The voltageinducedin thesearchcoil is indicatedbyasmallgeneratormarkedegand thebackemfcaused by the motion of the fluxmeter coil by another generator, em. In the electricalcircuit,

UsingEq.(12.34)inEq.(12.35)andsolvingfori,

Theequationofcoilmotioncanbewrittenwiththetermforsuspensiontorqueomitted.Thenettorqueisequatedtotheamountproducedbythecurrent

where,J=momentofinertia

D=constantoffrictionandairdamping

Substitutingiandaftersimplifying,

Now,integratingallwithrespecttotime.

where,R=Rc+RmTheair-dampingeffectandtheresistancearebothsmall,andaccordingly,thefirstterm

isnearlyequaltoK1.Therefore,

Equation(12.40)indicatesaninterestingphysicalfact.Thequantityontherightisthechangeoffluxlinkagewithsearchcoil,andthequantityontheleftisthechangeoffluxlinkage with the metre coil. If the operator withdraws a magnet from the search coil,reducingthefluxlinkagewiththatpartofthecircuit,themetrecoilmovesinadirection

to restore the flux linkages and thus to keep the total constant for the circuit. Thefluxmeter does this within the limits set by the degree to which air damping andsuspensiontorquearenegligible.

TheeffectofshuntingthemetrebyasimplifiedformasshowninFigure12.7,canbederived.Sinceinducedtermsdonotappearintheresult,atthestartingtheyaredroppedinstudy.

Figure12.7Simplifiedcircuitforashuntedfluxmeter

Accordingtotheabovefigure,twocircuitequationscanbewritten,

BysubstitutingforisinEq.(12.41)ofitsvaluefromEq.(12.42),

IfitissolvedforimfromEq.(12.43),substitutingthevalueinEq.(12.37)

andintheapproximateform

ComparisonofEq.(12.40)andEq.(12.45)showsthatthemaineffectoftheshuntistoapplyashuntingfactorRs/(Rc+Rs)tothereading.Theresistancecircuit,asshowninthecorrectionterminEq.(12.39)orEq.(12.44),isnotofextremeimportance.However,foraccuratework,thetotalresistanceshouldbebroughttothesamevalueusedincalibrationbytheadditionofaseriesresistanceifnecessary.

12.5USESOFBALLISTICGALVANOMETERANDFLUXMETER

Fluxmeasurementsmaybedoneinopenorcloseframeelectromagnetswhenthecurrentinthemagnetcoilbeeitherswitchedonandofforreversed.Asearchcoilwithsuitablenumberof turnsneeds tobewoundaroundthemagnet. If theflux in thefieldpoleofalarge motor or generator is being measured, even a single-turn search coil may give

enough deflection, and it will be necessary to shunt the metre. The fluxmeter has theadvantage in suchmeasurements that the fluxneednot tobechanged ina short time—changesshouldbemadetoorapidly,particularlyinlargemachines.

Thefluxofapermanentmagnetcanbemeasuredifthesearchcoilcanmoveonandoffthemagnet.Itshouldbeplacedalwaysinthesamepositionwithrespecttothemagnettogetconsistentresult.

Thefieldstrengthbetweenmagnetpolescanbemeasuredifthereisroomtoinsertandremove the search coil.Anothermethod,used in fieldsof considerable extent is a “flipcoil”,whichisacoilmountedsothatitcanberotatedanexact180°inashortperiodoftime.Thefluxmeterindicationcanthenbeinterpretedintermsoffieldstrength.

B-H curves of a ring-shaped samples of magnetic material may be obtained by aballistic galvanometer or fluxmeter in conjunction with search and magnetising coilswould around the sample. Similar tests are run on straight-strip samples by means of“permeameter”.

12.6 MEASUREMENTOFFLUXDENSITY

Measurementoffluxdensityinsideaspecimencanbedonebywindingasearchcoiloverthespecimen.Thissearchisknownasa“B-coil”.Thissearchcoilisthenconnectedtoaballisticgalvanometeror toa fluxmeter.Schemeofmeasuring thefluxdensity ina ringspecimen is shown in Figure 12.8. Let, the current I is flowing through magnetisingwinding wound around the specimen. A search coil with suitable number of turns iswoundaroundthespecimenandconnectedthrougharesistanceandcalibratingcoil,toaballisticgalvanometer.

Thecurrentthroughthemagnetisingcoilisreversedandthereforethefluxlinkagesofthesearchcoilchangeinducinganemfinit.Thisemfsendsacurrentthroughtheballisticgalvanometercausingittodeflect.

Figure12.8Circuittomeasurefluxdensityofaringspecimen

φ =fluxlinkingthesearchcoilR =resistanceoftheballisticgalvanometercircuitN =numberofturnsinthesearchcoil

andt=timetakentoreversetheflux

Averageemfinducedinthesearchcoil

So,averagecurrentthroughtheballisticgalvanometeris,

Chargepassingthroughit,

Letθ1be thedeflectionof thegalvanometer.Charge indicatedby thegalvanometer=K2θ1

Inuniformfieldandwithsearchcoilturnsatrightanglestothefluxdensityvector,thefluxdensity,

where,As=cross-sectionareaofthespecimen.

Thus,observingthethrowoftheballisticgalvanometer,fluxdensitymaybemeasured.

For the above analysis, it is assumed that the flux remains uniform throughout thespecimenandthattheeffectivecross-sectionareaofthesearchcoilisequaltothecross-section area of the specimen. However, search coil is usually of larger area than thespecimenandthusthefluxlinkingthesearchcoil is thesumof thefluxconfinedin thespecimenandthefluxwhichispresentinairspacebetweenthespecimenandthesearchcoil.

So, Flux observed = Actual flux in the specimen + Flux in the air space betweenspecimenandsearchcoil.

or,

B’AS=BAS+µ0H(Ac-As)

Hence,actualvalueofthefluxdensity

where,B’=apparentorobservedvalueofthefluxdensity

B =actualortruevalueofthefluxdensityinthespecimenAs =cross-sectionareaofthespecimenAc =cross-sectionareaofthecoil

12.7 MEASUREMENTOFMAGNETISINGFORCE(H)

Aballisticgalvanometerandasearchcoilmaybeusedtomeasurethemagnetisingforceofaconstantmagneticfield.ThevalueofH insidethespecimenmayeitherbeobtainedfrom the calculations with data of magnetising coil and the specimen or frommeasurementsmade fromoutside the specimen.Directmeasurement cannotbedone. Ifthemagnetisingforceistobedeterminedintheairgap,thesearchcoilisplacedintheairgap itself. In case of testing ferromagneticmaterials, themagnetising force, within thespecimenmaybedeterminedbymeasuringthemagnetisingforceonitssurface,sincethetangential components of the field are of equal in magnitude for both sides of theinterface.Thesearchcoil,asplacedinFigure12.9,measuresfluxdensityinair,B0.Thissearchcoiliscalledan“Hcoil”.Whilethefluxdensitiesencounteredinirontesting,thereisusuallynotroubleingettingagoodsensitivitybyusingaB-coilofsufficientturnsbutthere is some difficulty in achieving adequate sensitivity in the H coil placed at thesurface. At the first instance, its cross-sectional area is much smaller than the coilsurrounding the specimen and thenH is not constant across the section. Secondly, thepermeabilityofironisverylargeascomparedtothatofairandthereforefluxdensityB0,in thesearchcoil, isverysmallcomparedto that in thespecimen.Thevalueof thefluxdensityB0inHcoilismeasuredinasimilarwayasdescribedbeforeformeasuringofBinaspecimen.

Magnetisingforce,H=B0/µ0

Figure12.9Circuitdiagramtomeasuremagnetisingforce

TestingRingandBarSpecimensTheballisticmethodswhicharedoneonringspecimensgivehighestaccuracyprovidedthetestconditionsarecontrolledproperly.Themainadvantageofringspecimensisthattheendeffectsareabsentinringspecimensandtesterrorsduetomagneticleakagearenotencountered.

Toavoidmagneticleakage,auniformdistributionofmmfismaintainedbyauniformlywound magnetising winding on the ring sample. The magnetising force is usuallycalculatedintermsofmeandiameteroftheringandthemmfinthemagnetisingwinding.Since, the inner periphery of ring specimen is smaller than the outer periphery, themagnetisingforceandthefluxdensitybecomenonuniformover thecross-sectionof thering.Theerrorinvolveddependsupontheratioofmeandiametertotheradialwidthofthering. But, when this ratio is more, both magnetising force and the flux density aresufficiently uniform over the cross-section of the specimen and as a result, the errorinvolvedintestresultisnotsignificant.

Theringspecimensmaytakeonofthefollowingshapes:

1.LaminatesIt is the common form for isotropic sheet material. The ring is assembled with thedirection of rolling of individual laminations distributed radially, in order that the testshouldexhibitresultscorrespondingtomeanpropertiesofthematerial.

2.Clock-springAlongstripofmaterialmaybewoundintheformofspiraltoformaring.Thisformissuitablefortestinganisotropicmaterials,i.e.,grain-orientedsteel.

3.SolidSolid rings are prepared by either casting or forging.Ring specimens are also used fortestingpowderordustcorematerial.

Theringispreparedforthetestbyfirstwindingonitathinlayerofinsulatingtapeand

then a search coil of a suitable number of turns, evenly distributed around the ring.Insulatingtapeisappliedoverthesearchcoil,andthenthemagnetisingcoiliswoundonthe ring. The magnetising coil should be spaced uniformly around the ring and mustconsistofasuitablenumberofturnsofwireofadequatecurrent-carryingcapacitytogivethenumberofampere-turnsrequiredforthetests.

12.8 DETERMINATIONOFMAGNETISINGCURVE

There are two methods used to determine the magnetising curve or B-H curve of aspecimen.

1.MethodofReversalA ring specimenwith known dimensions is used for the test.At first, ring specimen ispreparedbyplacingsearchcoil,andmagnetisingcoilwithproperinsulationarrangementasmentionedearlier.ThearrangementofthetestcircuitisshowninFigure12.8.

Afterdemagnetising the test isstartedbysetting themagnetisingcurrent to its lowesttest level.At that time, thegalvanometer switch is closed, the iron specimen isbroughtintoareproduciblecyclicmagneticstatebythrowingthereversingswitchSbackwardandforward about twenty times. The K switch is now opened and the value of fluxcorrespondingofthisvalueofHismeasuredbyreversingtheswitchSandrecordingthethrow of galvanometer. The value of flux density corresponding to this H can becalculatedbydividingthefluxbythecross-sectionareaofthespecimen.ThisprocedureisrepeatedforvariousvaluesofHtomaximumtestingpoint.TheB-HcurvemaybeplottedfromthemeasurementvaluesofBcorrespondingtothevariousvaluesofH.

2.Step-by-stepMethodFor this test, thecircuitdiagramisshowninFigure12.10. In this test themagnetisationwinding of the ring specimen is supplied from a potential divider having few tappings.ThetappingsarearrangedsothatthemagnetisationforceHmaybeincreasedinsuitablenumber of steps, upto desiredmaximumvalue.Before testing the specimen, itmust bedemagnetised.

KeepingtheswitchS2onthetap1position,theswitchS1isclosed.Currentflowinthemagnetisingwinding sets up amagnetising force,H1 which in turns increases the fluxdensity in the specimen, from zero to some value B1, and corresponding throw ofgalvanometer is observed. The B1 value can be calculated from the throw of thegalvanometer.H1valuemaybecalculatedfromthereadingoftheammetre,connectedtothemagnetisingwindingcircuit.ThemagnetisingforceisthenincreasedtosomevalueH2byswitchingS2suddenlytothetapping2andthecorrespondingincreaseinfluxdensityΔB is determined from the throw of the galvanometer. Then the flux density B2corresponding to magnetising force H2 is calculated asB2 =B1 + ΔB. The process isrepeatedforothervaluesofHuptothemaximumpointandthecompleteB-HcurvethusdrawnasshowninFigure12.11.

Figure12.10Circuittomeasuremagnetisingcurve

Figure12.11Magnetisingcurve

12.9 DETERMINATIONOFHYSTERESISLOOP

1.Step-by-stepMethodThe determination of the hysteresis loop by this method is carried out simply bycontinuing the procedure described in the previous section where the B-H curve wasobtained. After reaching the point of maximum H with S2 on the tapping 8, themagnetisingcurrentisthenreduced,instepstozerobymovingS2downthroughtappingpoints8,7,6…2,1.Afterthereductionofthemagnetisingforcetozero,negativevaluesofHareobtainedbyreversingthereversingsupplytothepotentialdividerandthenmovingtheswitchS2instepsasbefore.

2.ByMethodofReversalThecircuitconnectionsforthetestareshowninFigure12.12.Thistestiscarriedoutbymeansofanumberofsteps.Thefluxdensityischangedinstepsfromthemaximumvalue

+Bmaxdowntosomelowervalue,theironspecimenbeingpassedthroughthereminderofthemagnetisation cycle back to the flux density +Bmax. InFigure 12.12,R1 is there toadjustgalvanometercircuit;whereas,R2andR4aretheretoadjustthemagnetisingcircuit.R3 is avariable shunting resistor, connectedacross themagnetisingwindingbymovingovertheswitchS2,thusreducingthecurrentinthiscircuitfromitsmaximumvaluedowntoanydesiredvalue—dependinguponthevalueofR3.

Figure12.12Circuittomeasurehysteresisloop

ThevalueofHmaxrequiredtodevelopBmaxtobeusedduringthetestistakenfromthepreviously obtainedB-H curve of the specimen.R2 andR4 are then varied so that themagnetisingcurrentissuchthatthisvalueofHisobtainedwhenS2isintheOFFposition.SinceH=NI/l.Whenthemaximumvalueofthemagnetisingisreversed,togetasuitabledeflectionofthegalvanometer,R1isadjusted.R3isadjustedtosuchavaluethatasuitablereduction of the current in themagnetisingwinding is obtainedwhen this resistance isswitchedinthecircuit.SwitchRS2isthenplacedoncontacts11’andtheshort-circuitingkey K opened. Since at this moment, maximum magnetising current is flowing, themagnetisation of the specimen corresponds to the pointA on the loop shown in Figure12.13.

Inthenextstep,theswitchS2isquicklythrownoverfromtheOFFpositiontocontactX, thus shunting themagnetisingwinding byR3 and reducing themagnetising force toHc(say). The corresponding reduction in flux density, −ΔB, is obtained from thegalvanometer throw, and hence the pointC on the loop is obtained. The keyK is nowclosed,andtheswitchRS2reversedontocontacts22’.SwitchS2isthenopenedandRS2movedbackagaintocontacts11’.Inthisprocedure,thespecimenundergoesacycleofmagnetisation and back to the pointA and it is ready for the next step in the test. ThesectionADoftheloopisfoundbycontinuationofthisprocedure.

Figure12.13Hysteresisloop

TofindoutDEFsectionoftheloop,withKclosedandS2intheOFFposition,RS2isplaced on contacts 1 1’. Then throwS2 on the contactY position, open the keyK andrapidlyreverseRS2ontocontacts22’.Fromthis throw, thechangeinfluxΔB’ (Figure12.13)maybeobtained,sincetheswitchingoperationsdescribedcauseH tobechangedfrom+Hmaxto-Hk(say).TobringthemagnetisationofthespecimenbacktothepointA,closethekeyK,openS2andreverseRS2ontocontacts11’.Bycontinuingthisprocess,otherpointsonthesectionDEFofthelooparefound.ThesectionFGLAoftheloopmaybe obtained by drawing in reverse of ADEF, since the two halves are identical. Bymeasuring the area of the hysteresis loop so obtained, by means of a planimeter, andexpressing this area in B-H units of area, the hysteresis loss for the material may beobtained,since,hysteresisloss/cycle/m3injoules=areaoftheloopinB-Hunits.

12.10TESTINGOFSPECIMENSINTHEFORMOFRODSORBARS

It is obviouslymuch easier to prepare a specimen in the form of a rod or bar than toprepare a ring specimen. However, if test methods described for ring specimens areemployed to bar specimens, some difficulties and inaccuracies arise in testing. Barspecimens suffer from the disadvantage of “self-demagnetisation”. When a bar ismagnetisedelectromagnetically,polesareproducedattheends,andthesepolesproduce,insidetherod,amagnetisingforcefromthenorthpoletothesouthwhichisinoppositionto theappliedmagnetising force, thus rendering the truevalueofH actingon thebarasomewhat uncertain quantity. For accurate results, therefore, if the methods ofmeasurementusingaballisticgalvanometer areused, thisdemagnetisingeffectmustbecorrectedfor,or,sincetheeffectisleastwhentheratioofdiametertolengthoftherodissmall, thedimensionsof the specimen shouldbechosen so that the effect isnegligible.Thedemagnetisingforceduetothis“endeffect”isgivenbytheexpression

where,Bfistheferricinduction,i.e.thefluxdensityduetothemagnetisationoftheironpieceitself,andFisaconstantwhichdependsupontherelativedimensionoftherod.Foran ellipsoid or very long rod, the value of the coefficientF can be calculated from theexpression

where,

a =minoraxisoftheellipsoidb =majoraxisoftheellipsoid

ToobtainthetruevalueofthemagnetisingforceHactingonthebarspecimen,HdmustbesubtractedfromthevalueofHcalculatedfromtheampere-turnspermetrelengthofthemagnetisingwinding. It has been seen that the length-to-diameter ratio of the specimenmustbeoftheorderof25ormorefortohaveanegligibleinfluenceuponthevalueofH.

Onaccountofthisdemagnetisingeffect,thevalueofHisoftenmeasuredbymeansofsearchcoilswoundonthinstripsofglassandplacedwiththeglasslyingflatonthebarspecimen.Thefluxdensityintheairatthesurfaceofthespecimen(whichissameasHinthe specimen) ismeasured by thismeans instead of relying upon calculated values andcorrections.

12.11 PERMEAMETERS

There are various formsof “permeameters” that have been devised to avoid difficultiesincurredtoteststraightspecimens.Permeametersprovidecontrollablefieldconditionstotestbarspecimens.Theyconsistgenerallyofafixedsteelframetowhichstraightsamplescanbefitted,butdifferwidely in thearrangementofmagnetisingandpick-uporsearchcoilsandinthemeansofguardingagainstleakagefluxesandmmfdropsatthejoints.Allpermeametersusereturnpathsoflargecross-sectionareainordertomakethereluctanceofthepathsnegligible.Mostofthepermeametersincorporatemodificationsofthebarandyoke arrangements first described by Hopkinson. The following discussion shall belimitedonlyonafewofmanyformsofpermeameters.

12.11.1HopkinsonPermeameter(Bar-and-YokeMethod)This method is used for the testing of bar specimens and the demagnetising effect islargelyeliminatedbytheuseofheavy-sectionyokes.Asearchcoil iswoundaroundthebar specimen at its centre, and the bar is then clamped between the two halves of amassive iron yoke, whose reluctance is small compared with that of the specimen, asshowninFigure12.14.Themagnetisingwindingisfixedinsidetheyoke,asshown,thespecimenfittinginsideit.

Figure12.14Barandyokemethod

Let,N=numberofturnsofthemagnetisingwinding

I =currentinthemagnetisingwindingl =lengthofspecimenbetweentwohalvesoftheyokeA =cross-sectionofthespecimen

µs=µsrµ0=permeabilityofthespecimenwhenthemagnetisingcurrentisI,µsrbeingtherelativepermeabilityofthespecimen

Ry =reluctanceoftheyokeRj =reluctanceofthetwojointsbetweenbarspecimenandyokeΦ =fluxinthemagneticcircuit

Then,

Reluctanceofthespecimen,Rs=l/µsA

So,fluxΦ=mmf/reluctanceofmagneticcircuit

Fluxdensityinthespecimen,

Magnetisingforce,

Let,m=Reluctanceofyokeandjoints/Reluctanceofthespecimen

Thevalueofmismadesmallbykeepingthereluctanceoftheyokeandthejointstoasmallvalue.Thiscanbeachievedbycarefullyfittingthespecimenintotheyokesothatairgapbetweenthebarandyokeisnegligibleandmakingtheyokeoflargecross-section.

Soifmissmall,

whichmeansthattheactualvalueofHinthespecimendiffersfromthevaluecalculatedfromthemagnetisingampere-turnsandlengthofspecimenbytheamountmNI/l.Thefluxdensitymaybemeasuredbyaballisticgalvanometerintheusualway.

12.11.2EwingDoubleBarPermeameterInthispermeameter,twoexactlysimilarbarspecimensofthematerialundertestareused,withtwopairsofmagnetisingcoils,onepairofthelatterbeingexactlyhalfthelengthoftheotherpair.Thenumberof turns,perunitaxial length, issameforbothpairsofcoil.Twoyokesofannealedsoftiron,withholestoreceivetheendsofthebarspecimens—thefitbeingtight—areused.ThearrangementofthebarandyokeisshowninFigure12.15.

Thepurposeofthearrangementistheeliminationofthereluctanceofyokeandjoints.Thetestsaredone,onewithlengthofspecimen=landtheotherwithlength=I/2.Itisassumedthatforbothpositions,thereluctanceoftheyokesandjointsissameforagivenfluxdensity.

Figure12.15Ewingdoublebarmethod

Let,n=numberofturnsperunitlengthofmagnetisingcoils

I1 =currentinthecoilswhenthespecimenlengthislI2 =currentinthecoilswhenthespecimenlengthisl/2H1 =apparentmagnetisingforcewhenlengthislH2 =apparentmagnetisingforcewhenlengthisl/2a =mmfrequiredfortheyokesandairgapsineachcaseB =fluxdensityinthespecimen(thesameineachcase)

Then

and

IfHbethetruemagnetisingforceintheironforafluxdensityB,

Hl=nI1l−a=H1l−a

andHl/2=nI2l.2−a=H2l/2-a

Hence,a=l(H2-H2)

and

ThefluxdensitycorrespondingtothisactualvalueofHismeasuredbymeansofsearchcoilsandballisticgalvanometerinordinaryway.Thecompletetest isperformedbyfirst

obtaining and plotting aB-H curve for the specimen with a length of l—the apparentvaluesofHbeingplotted.Thespecimensarethendemagnetised,andasecondB-Hcurveisobtained,andplotted,withaspecimenlengthofl/2,thetwocurvesbeingplottedonthesame axis. The true B-H curve is obtained from these two, the true value of H,correspondingtoanyvalueofB,beingobtainedfromtheexpressionderivedabove.

Thedisadvantagedofthismethodare1.thereluctanceoftheyokesandjointsisnotexactlysameforthetwopositionsoftheyoke,

2.thetestrequirestwoexactlysimilarbars,and

3.thistestissomewhatlengthy.

12.11.3IllioviciPermeameterAsshowninFigure12.16, it consistsof abar specimenclampedagainst aheavyyoke.Thebariswoundwithamagnetisingwindingandasearchcoil.AballisticgalvanometerBG1 is connected across the search coil. A magnetic potentiometer is connected to asectionXY of thebar specimen.Theyoke isprovidedwithcompensatingwinding. It isconnected inparallelwith themagnetisingwindingacross a reversing switch.Whennomagneticpotentialdropisindicatedbythemagneticpotentiometer,themmfofXYsectionisprovidedbythemagnetisingwindingwhilefortheremainingpartofthespecimen,theyokeandthejoints,isprovidedbythecompensatingwinding.ThisconditionisachievedbyadjustingthecurrentinthemainwindingtotherequiredtestvalueandthenadjustingthecurrentinthecompensatingwindingsothattheballisticgalvanometerBG2showsnothrowwhenthecurrentsarereversed.Underthiscondition,thereisano-fluxthroughthemaneticpotentiometerand, therefore,nodifferenceofmagneticpotentialexistsbetweenpointsXandY.Thus,themagnetisingforceforlengthXYisgivenbyH=NI/l,where,Nisthe number of turns in the magnetising winding, I is the current in the magnetisingwindingandlislengthofXY.

ThefluxdensityinthespecimenisfoundbynotingthethrowofBG1whenthecurrentsin magnetising winding and compensating winding are reversed simultaneously. Thepermeameterhasthefollowingdisadvantages:

1.Since,thereislackofsymmetryinthearrangement,theresultsobtainedarenotsatisfactory.

2.Thisarrangementdoesnotincludeadirecttestofuniformityofmagnetisationalongthespecimen.

3.Sincecompensatingwindingneedstobeadjustedforeachreading,theoveralloperationbecomescomplicated.

4.Someleakagebetweentheyokeandspecimenandthemagneticpotentiometermaybeaffectedbyleakagefluxwhichcanintroduceerrorinthetestresults.

Figure12.16Illiovicipermeameter

12.11.4BurrowsPermeameterThispermeameter,whichwas firstdevelopedbyCWBurrows,hasbeenadoptedas thethestandardapparatusforthetestingofbarspecimens.Theeffectofmagneticleakageatthejointsbetweentheyokeandspecimeniseliminatedinthispemeametrebytheuseofanumberofcompensatingwindingswhichapplycompensatingmmfsatdifferentpartsofthe magnetic circuit, these mmfs being just sufficient to drive the flux through thereluctanceofthepartuponwhichthecoilsareplaced.

Figure 12.17 shows the arrangement of the magnetic circuit and coils. S1 is the barspecimen under test and S2 is a bar of identical dimensions to S1. These bars aresurroundedbymagnetisingcoilsM1andM2.Magnetisingwindingsareuniformlywoundalongthelengthofthebars.C1,C2,C3andC4arecompensatingcoilsforeliminatingtheleakageeffectsat thejointsbetweenthetwobarsandthemassiveyokesYY’ intowhichthebarsfit;cxandcyaretwoexactlysimilarsearchcoilswoundatthecentresofthetwobars,whiled1andd2aretwosimilarsearchcoilswoundinthepositionsshown,onthetestbar,andeachhavingexactlyhalfthenumberofturnsofthesearchcoilcx.Coilsd1andd2areconnectedinseries.FourcoilsC1,C2,C3andC4arealsoinseries.ThedimensionsofthecoilsM1andM2aresuchthatHinthespecimenisaround104timesthecurrentinthewindings, themaximumvalueofH forwhich theapparatus isusedbeingabout40,000A/m.Thedimensionsofthebarsarearound30cmlongand1cmindiameter.ThecoilsC1,C2,C3 and C4 are supplied from a separate battery source, coilM1 from anotherbatteryandM2fromanother.Toperformthetest,itisnecessary,toensurethatforagivenvalue of the current inM1, i.e. ofH in the test bar, the flux threading through all four

searchcoilscx,cy,d1andd2isthesame,thecurrentinthecompensatingcoils,andinM2,beingadjusteduntilthisconditionissatisfied.Ifthefluxthreadingcoilsd1andd2 is thesame as that of the threadings cx and cy, there can be no appreciable leakage of fluxthrough the air in the joints. Thismeans that themmf for the joints is supplied by thecompensating coils and that themmf in coilM1 is used upmerely in driving the fluxthroughthebarspecimenS1insideit.Thus,HinthespecimenisgivenbyNI/l,where,Nis the number of turns onM1, and I is current throughM1 and l is the length of thespecimeninmetres.

Figure12.17MagneticcircuitofBurrowsdouble-barandyokepermeameter

Itmayinsomecases,benecessarytomakecorrectionsforthefactthatthemagnetisingsolenoids are not infinitely long, but such corrections are usually negligible. Theprocedureforgettingequalfluxthreadinginallfoursearchcoilsisasfollows.

As shown inFigure12.18, first, the specimenhavingbeendemagnetised, the currentthroughthemagnetisingcoilM1issetattherequiredtestinglevel.Searchcoilscxandcyarethenconnectedinseries,butinopposition,toaballisticgalvanometer,ThecurrentsinM1 and M2 are then simultaneously reversed. A throw will be observed on thegalvanometer.ThecurrentinM2isadjusteduntilnothrowisobtainedwhentwocurrentsare reversed. Since search coils cx andcy have equal number of turns, thismeans thatequal fluxes are now threading through them. Next, the search coil cx is connected inserieswith,butinoppositionto,coilsd1andd2andthentotheballisticgalvanometer.Thecurrent incompensatingcoilsC1,C2,C3 andC4 is then adjusted until no galvanometerdeflectionisobtaineduponsimultaneousreversalofthecurrentsinthesecoilsandinM1andM2.Then,sinced1andd2togetherhavethesamenumberofturnsasthecoilcx, thefluxthreadingallthreecoilsissame.ThefluxdensitycorrespondingtothevalueofHinM1 can bemeasured by connecting the coil cx alone to the ballistic galvanometer, andrecording the throw when the currents in the twomagnetising coils and compensatingcoils are simultaneously reversed.Figure12.18 gives a diagram of connection showinghowtheswitchingmaybearrangedforconvenienceincarryingoutthetestasdescribedabove.

Figure12.18CircuitforBurrowsdoublebarandyokepermeameter

12.12 MEASUREMENTOFMAGNETICLEAKAGE

Indynamo-electricmachinery,themagneticfluxperpolewhichcrossestheairgap—the“useful flux”—is less than the flux in thebodyof thepole.This is due to the fact thatsomelinesofforce,calledleakageflux,passfromthepoletotheadjacentpoleswithoutcrossingtheairgaptothearmature.Thefluxattherootofthepoleiscalledtotalfluxandtheratiooftotalfluxtousefulfluxistheleakagefactorofthepole.

Leakage factor can bemeasured bymeans of a fluxmeter.Here, galvanometer is notsuitableonaccountof thehigh inductanceof the fieldwinding,which results ina slowrateofincreaseoffluxwhenthevoltageisswitchedontothefieldwinding.Thetotalfluxmaybemeasuredbywindingtwosearchcoilsontheyokeofthemachine—incaseofadcmachinewithstationaryfield—oneoneithersideofthepoleasshowninFigure12.19.Astheyokecarrieshalfofthetotalflux,thesesearchcoilsmustbeconnectedinseriessothatthefluxmetermeasurethefluxembracedbybothofthem.Thefluxsomeasuredwillbethetotalflux.Anothersearchcoil,placedonthestationaryarmatureinsuchapositionthatitembracestheusefulfluxfromthepole,isthenconnectedtothefluxmeterandtheusefulflux ismeasured. The leakage factor is obtained from these twomeasurements. It willusually be found that search coils of one turnwill bemost suitable, inwhich case thefluxmeterreadinggivesthefluxdirectly.

Figure12.19Measurementofmagneticleakagefactor

12.13 MAGNETICTESTINGWITHALTERNATINGCURRENT

When iron issubjected toanalternatingmagnetic field,apower loss takesplacedue tohysteresiseffects in the iron.Eddycurrentswhicharesetupin the ironfurther increasethe power loss in the material. Although the hysteresis loss per cycle in iron may bedeterminedfromhysteresisloopobtainedindctests,thislossmaybesomewhatdifferentundertheactualalternatingmagnetisationconditionwithwhichitwillbeworking.Also,eddycurrentlossescanonlybemeasuredbytheuseofalternatingfield.Forthesereasons,inspection tests upon sheet steelwhich is to be used in themanufacturing process of atransformerandotheracapparatusareverycommonactests.It isusuallyconvenienttomeasurethehysteresisandeddycurrentlossincombinedform,calledironloss.

SeparationofIronLossesItisoftensufficient,inacceptancetestsofsheetmaterial,tomeasurethetotallossatthestandardfrequencyandwithmaximumfluxdensityofabout1weberpersquaremetreastheseparationofthelossesintotheirtwocomponentsinvolvesarathermorelengthytest.

Hysteresislosscanbeexpressedas

Wh=k.f.B1.6maxwhere,Whis the loss inwattspercubicmetreofmaterial, fbeing thesupplyfrequency,Bmax themaximumfluxdensity,andkaconstantforanygivenmaterial.This lawholdsgoodforvaluesofBmaxbetween0.1and1.2Wb/m2.

Eddy current loss, provided the sheets are sufficiently thin for skin effect to benegligible,isgivenbytheexpression

We=k’Kf2f2t2B1.6maxwhere,Weisthelossinwattspercubicmetre,fisthefrequency,tisthethicknessofthesheet,andBmaxisthemaximumfluxdensity,andKfistheformfactorofthealternatingfluxanddependsupontheshapeofthewave.

Thus, if the form factor remains constant throughout the test and themaximum flux

densityiskeptconstant,thetotalpowerlossbeingmeasuredatdifferentfrequencies,maybewrittenas

Wt=Mf+Nf2

where,M=KB1.6max

andN=k’Kf212B2maxbothMandNbeingconstantforthistest.

These constants may be determined, and the total loss thus split up into its twocomponents,foranyfrequency,byplottingW/fagainstfisshowninFigure12.20.Then

,sothattheinterceptontheverticalaxisgivesM,andNcanbeobtainedfromtheslopeof thegraph.M is the hysteresis loss per cycle and the eddy-current loss for anyfrequency fx is given by the intercept ED, as shown in Figure 12.21. Again, if thefrequency and Bmax are kept constant and form factor is varied, the total loss beingmeasuredforvariousvaluesofformfactorsisthen

Wt=C+DKf2

Figure12.20Separationofironlosses

Figure12.21Separationofironlosses

IfWt is now plotted along the y-axis against the values ofKf2 along the x-axis, theconstantsCandDmaybeobtained.TheinterceptupontheverticalaxisgivesC,andtheslopeofthelinegivesD.

12.14 BRIDGEANDacPOTENTIOMETERMETHODS

Theacbridgeoracpotentiometermethodsaresuitableformaterialsworkingatlowfluxdensities.Anumberofbridgecircuitsareusedwherematerialsworkatlowfluxdensitiesand a small quantity of material is available. The test is to be performed at audiofrequencies.

12.14.1Maxwell’sBridgeMethodFigure12.22showsthecircuitdiagramoftheMaxwellbridgewhichisusedtomeasureironlossandpermeability.R1,R2arefixedvaluedresistorsandR3isavariableresistor.InserieswithR3avariable inductorLof resistancer isconnected. Itmaybenecessary toconnectR3inserieswiththewindingonthesampleifresistanceofthelatterissmall.Thespecimen, in ring form, iswoundwith awindingwhose inductance isLs and effectiveresistanceRs.Thiseffectiveresistancecontainsanironlosscomponent.Rwistheactualresistanceofthewindingonthering.Gisavibrationgalvanometerortelephone,andanammetre.This supply froman ac source shouldbehaving apure sinusoidalwaveform.ThebalanceofthebridgeisobtainedbyadjustingLandR3.

Figure12.22acbridgeforironlossmeasurement

Atbalance,

I1R1=I2R2andI1(Rs+jωLs=I2[(r+R3)+jωL]

where,ω=2 ×Frequency

Theironlossinthesampleisgivenby

RsI12−RwI12

Now,thecurrent,I=I1+I2Here,I1andI2areinphase.

IfN=numberofturnsonthespecimen

l =lengthofmeancircumferenceofthespecimen(inmetres)a =crosssectionofspecimeninsquaremetresµr =relativepermeabilityofthespecimen

Thentheinductanceis

Fromwhich,µrcanbecalculatedwhenLshasbeenmeasured.

12.14.2TheacPotentiometerMethodThe circuit connection for measurement of iron loss with a potentiometer is shown inFigure 12.23. The used potentiometer is of co-ordinate type. Here, the ring specimencarriestwowindings,theprimarywindingwithN1turnsandthesecondarywithN2turns,Theprimarywindingissuppliedfromanalternatorthrougharegulatingtransformer.Thealternatorisalsosupplyingtotwopotentiometerslide-wirecircuits.TheprimarywindingcircuitcontainsaregulatingresistorandastandardresistorRisconnectedinserieswithit.This resistor is introduced in the circuit to sense the current in the primarywinding bymeasuringthepotentialdropacrossit.AvibrationgalvanometerGisusedinthetest.Atfirst, thepotentiometer is standardised.The supply is fed to theprimarywindingof thespecimen,asaresult,thevoltageE2isinducedinthesecondarywinding.

Figure12.23Ironlossmeasurementbyacpotentiometer

where,E2=4KffΦmaxN2=4KffBmaxAsN2In the above expression,Kf = Form factor = 1.11 for sinusoidal supply, f = Supply

frequency,Bmax=maximumfluxdensity,As=Cross-sectionareaof thespecimen,N2=Numberofturnsinthesecondarywinding.

Andmaximumfluxdensity,

The voltage E2 is measured by placing the switch S on the contact x, setting thequadraturepotentiometeratzeroandadjusting the in-phasepotentiometer tillbalance isobtained.Thesettingofthein-phasepotentiometerindicatesthevalueofE2directly.

The switch is then placed to contact y. At this position, the potential drop in thestandardresistorRismatchedagainstthein-phaseandquadraturepotentiometers.Thesetwopotentiometersareadjustedtoachievethebalancedcondition.Thereadingofthein-phasepotentiometergivesthevalueIeRwhereIe is the losscomponentof thecurrent intheprimarywinding:

Ie=readingofin-phasepotentiometer/R

ThereadingofthequadraturepotentiometerindicatesthevalueofImR,where,Imisthemagnetisingcomponentofthecurrentintheprimarywinding.

Im=readingofquadraturepotentiometer/R

Theironloss=IeE2N1/N2Thismethodissuitableforacmagnetictestingatlowfluxdensities,sincemagnetising

andiron-losscomponentsofexcitingcurrentaremeasuredseparately

12.15 MAGNETICSHIELDING

Magneticshielding isan important issue topreventmagnetic field frominterferingwithelectricaldevices.Magneticshieldingisaprocessofreducingthecouplingofamagneticfield between two locations.A number ofmaterials are used for this purpose includingsheetmetal,metalmesh,ionisedgas,orplasma.Unlikeelectricity,magneticfieldscannotbe blocked or insulated.As a result,magnetic shielding is verymuch essential to stopmalfunctioning of electrical and electronics devices and equipments if they are put inservice in such an environment where a chance of magnetic interference is prevailing.According toMaxwell’s equations,del.B = 0,whichmeans that there are nomagneticmonopoles.Asaresult,magneticfieldlinesmustterminateontheoppositepole.Thereisnowaytoblockthesefieldlines;naturefindsapathtoreturnthemagneticfieldlinesbacktoanoppositepole.Evenifanonmagneticobject—forexample,glass—isplacedbetweentwooppositepolesofamagnet,themagneticfieldwillnotchange.

Themainconceptofmagneticshielding is tore-route themagneticfield linesaroundthe object or device under threat of magnetic interference. This can be achieved bysurroundingthedevicewithamagneticmaterialwithhigherpermeabilitythatthatofthedeviceinsideunderthreat.Bydoingso,themagneticfieldlinestendtofindaneasierpathalong the shielding material, thus avoiding the object inside. This technique merelyredirects the magnetic field lines to a material having high permeability, instead ofstoppingorblockingmagneticfieldlines.

It is important that materials used in magnetic shielding purpose should have highpermeability,but it isalsoimportant that theythemselvesshouldnotdeveloppermanentmagnetisation. Keeping these points in consideration, the most effective magneticshieldingmaterialavailable ismu-metal, analloycontaining77%nickel,16% iron,5%copper,and2%chromium,whichisthenannealedinahydrogenatmospheretoincreaseits permeability.Mu-metal is extremely expensive, that’swhy other alloyswith similarcompositionsaresoldformagneticshielding,usuallyinrollsoffoil.

ImportantAreasforMagneticShieldingMagneticshieldingisessentiallyemployedinhospitals,wheredevicessuchasMagneticResonance Imaging (MRI) equipment generate powerful magnetic flux which caninterferewithsurroundinginstrumentsormetres.

Magnetic shielding rooms are also used in electron beam exposure rooms wheresemiconductorsaremade,orinresearchfacilitiesusingmagneticflux.

Applications of magnetic shielding are common in home theatre systems. SpeakermagnetscandistortaCathodeRayTube(CRT)televisionpicturewhenplacedclosetotheset,sospeakersintendedforthatpurposeusemagneticshielding.

Magneticshieldingisalsousedtocountersimilardistortiononcomputermonitors.

Magnetic shielding is quiet essential in laboratories and factorieswhere high-voltagetestsoroperationsareperformed.Normally,shieldingnetsarepreferredforthispurpose.

EXERCISE

Objective-typeQuestions

1.Whichofthefollowingmeasuresthemagneticfluxdensity?

(a)Ballisticgalvanometer

(b)Grassotfluxmeter

(c)Permeameter

(d)Alloftheabove

2.Whenamagneticmaterialissubjectedtoalternatingfield,lossofpoweroccursowingto

(a)hysteresisonly

(b)eddycurrentonly

(c)bothhysteresisandeddycurrents

(d)noneoftheabove

3.Theareaofthehysteresisloopinmagneticspecimenindicates

(a)hysteresisandeddycurrentloss

(b)hysteresisloss

(c)hysteresislossperunitvolume

(d)hysteresislossperunitvolumepercycleoffrequency

4.Theratiooftotalfluxtotheusefulfluxinamagneticcircuitiscalled

(a)formfactor

(b)leakagefactor

(c)utilityfactor

(d)dispersionfactor

5.Maxwell’sbridgemethodisusedtomeasure

(a)ironlossandpermeability

(b)copperloss

(c)copperlossandironloss

(d)noneofthese

Short-answerQuestions1.Whyaremagneticmeasurementsnotasaccurateasothertypesofmeasurementsinelectricalengineering?

2.Whyareringspecimenspreferredoverrodsorbarsformagnetictesting?

3. Why is the fluxmeter employed to measure leakage factor in electric machinery rather than ballisticgalvanometer?

4. What are the components of power loss that occur in ferromagnetic materials when subjected to alternatingmagneticfields?

5.WhataErethemethodsusedformeasuringironlosses?

Long-answerQuestions1. What are the different types of magnetic measurement? How is ballistic galvanometer used in magnetic

measurement?Explaintheworkingprincipleofaballisticgalvanometer.

2.Explainhowaballisticgalvanometerisusedtomeasurefluxchangesoccurringinmagneticcircuitsandindicatetheessentialconditionstobesatisfiedbytheballisticgalvanometerchosenforthispurpose.

3. Howis themagnetic fluxmeasuredbyaballisticgalvanometer?Whatare thedifferentmethods tocalibrateaballisticgalvanometer?

4. Whatareballistictestsusedfortestingofmagneticmaterials?Howisfluxdensitydeterminedintheringtypespecimenofmagneticmaterial?

5.Explaintheworkingprincipleofafluxmeterwiththehelpofaneatdiagram.

6.Givetheadvantagesanddisadvantagesofringandbarspecimensusedinmagnetictestingofmaterials.

7.BrieflydescribeamethodformeasurementofB-Hcurveofamagneticsubstanceofbarform.

8.Withthehelpofacircuitdiagram,describethestep-by-stepproceduretodrawthecompleteB-Hloopofaringspecimen.

9. Describe theprocedure todeterminehysteresis loopby themethodof reversal, and suggest precautions tobefollowed.

10.DiscusstheprincipleandadvantageofapermeameterforthedeterminationofB-Hcurveofasample.

11.Howisthebar-and-yokemethodemployedtomeasurethemagnetisingforceofaspecimen?

12.DescribetheconstructionandworkingofaBurrowspermeameterbringingitsrelativeadvantagesoverothertypesfortestingabarspecimen.

13.Whatareironlosses?Howdotheyvarywithfrequency?Explaintheprocedureforseparationofironlosses.

14.Explaintheacpotentiometermethodofdeterminationofironlosses.

15.Writeshortnotesonthefollowing:

(a)Fluxmeasurement

(b)Ewingdoublebarpermeameter

(c)Illiovicipermeameter

(d)Maxwell’sbridgemethodforironlossmeasurement

13.1 INTRODUCTION

Signalgeneratorsprovideavarietyofwaveformsfortestingofelectroniccircuitsatlowpower levels. There are various types of signal generators, but the followingcharacteristicsarecommontoalltypes:

1.Alwaysastablegeneratorwithdesiredfrequencysignalsshouldbegenerated.

2.Generatedsignalamplitudeshouldberegulatedoverawiderangefromverysmalltorelativelylargelevel.

3.Generatedsignalshouldbefreefromanydistortions.

Therearemanyvariationsof theaboverequirements,especiallyforspecialisedsignalgeneratorssuchas functiongenerators,pulsegeneratorsandpulse frequencygenerators.Sine wave generators, both in audio and radio frequency ranges are called oscillators.Although, the terminology is not universal, the termoscillator is generally used for aninstrument thatprovidesonlya sinusoidaloutput signal.The term functiongenerator isapplied to an instrument that provides several output waveforms, including sine wave,square wave, triangular wave and pulse trains as well as amplitude modulation of theoutputsignal.

13.2 OSCILLATORS

Oscillator is the basic element of ac signal sources and generates sinusoidal signals ofknown frequency and amplitude. Themain applications of oscillators are as sinusoidalwaveformsourcesinelectronicmeasurementwork.Oscillatorscangenerateawiderangeoffrequencies(fewHztomanyGHz)aspertherequirementoftheapplication.Althoughan oscillator can be considered as generating sinusoidal signal, it is to be noted that itmerelyactsasanenergyconverter.Itconvertsadcsourceofsupplytoalternatingcurrentofdesiredfrequency.

Oscillatorsaregenerallyanamplifierwithpositivefeedback.Anoscillatorhasagainequal to or slightly greater than unity. In the feedback path of the oscillator, capacitor,inductor or both are used as reactive components. In addition to these reactivecomponents, an operational amplifier or bipolar transistor is used as amplifying device.Noexternalacinputisrequiredtocausetheoscillatortoworkasthedcsupplyenergyisconvertedbytheoscillatorintoacenergy.

Oscillatorsmay be classified in a number ofways.Here they are classified on three

bases:(a)thedesignprincipleused,(b)thefrequencyrangeoverwhichtheyareused,and(c)thenatureofgeneratedsignals.

1.ClassificationAccordingtoDesignPrinciple(a)Positivefeedbackoscillators(b)Negativefeedbackoscillators

2.ClassificationAccordingtoFrequencyBandoftheSignals(a)AudioFrequency(AF)oscillators—frequencyrageis20Hzto20kHz

(b)RadioFrequency(RF)oscillators—frequencyrangeis20kHzto30MHz

(c)VideoFrequencyoscillators—frequencyrangeisdcto5MHz

(d)HighFrequency(HF)oscillators—frequencyrangeis1.5MHzto30MHz

(e) VeryHigh Frequency (VHF) oscillators—frequency range is 30MHz to 300MHz

3.ClassificationAccordingtoTypesofGeneratedSignals(a)SinusoidalOscillatorsTheseareknownasharmonicoscillatorsandaregenerallyLCtuned-feedbackorRCtuned-feedbacktypeoscillatorthatgeneratesasinusoidalwaveformwhichisofconstantamplitudeandfrequency.

(b)Non-sinusoidalOscillators These are known as relaxation oscillators and generatecomplex non-sinusoidal waveforms that changes very quickly from one condition ofstability to another such as square-wave, triangular-wave or sawtooth-wave-typewaveforms.

13.2.1FeedbackCircuitEmployedinOscillatorsIt is theuseofpositivefeedback that results ina feedbackamplifierhavingclosed-loopgainAfgreaterthanunityandsatisfiesthephasecondition.

In a system assuming, Vin and Vout as the input and output voltages respectively.Withoutfeedbackoropen-loopgain,

TakingtheforwardpathgainofthesystemasAandβasfeedbackfactor

Withfeedback,theoutputvoltageofthesystem,

Figure13.1Basicfeedbackcircuitemployedinoscillators

Oscillatorsgenerateacontinuousvoltageoutputwaveformatarequiredfrequencywiththe values of the inductors, capacitors or resistors forming a frequency selective LCresonant(ortank)feedbacknetwork.Theoscillatorfrequencyisregulatedusingatunedorresonant inductive/capacitivecircuitwith theresultingoutput frequencybeingknownasthe oscillation frequency. So, the feedback path of the oscillator is made reactive. Thephaseangleofthefeedbackwillvaryasafunctionoffrequencyandthisiscalledphaseshift. Certain conditions are required to fulfill for sustained oscillations and theseconditionsarethat(a)theloopgainofthecircuitmustbeequaltoorgreaterthanunity,and(b)thephaseshiftaroundthecircuitmustbezero.ThesetwoconditionsforsustainedoscillationsarecalledBarkhausencriteria.

13.2.2ResonanceIf a constant voltage with varying frequency is impressed to a circuit consisting of aninductor,capacitorandresistor,thenthereactanceofboththecapacitor-resistor(RC)andinductor-resistor (RL) paths are to change both in amplitude and in phase of the outputsignalascomparedtotheinputsignal.Athighfrequenciesthereactanceofacapacitorisverylowanditactsasashortcircuitwhilethereactanceoftheinductorishighanditactsasanopencircuit.At lowfrequencies, the reverse is true,meaning the reactanceof thecapacitoractsasanopencircuitandthereactanceoftheinductoractsasashortcircuit.Betweenthesetwoboundaries,thecombinationoftheinductorandcapacitorproducesatuned or resonant circuit that has a resonant frequency (fr) inwhich the capacitive andinductivereactancesareequalandcancelouteachother,leavingonlytheresistanceofthecircuittoopposetheflowofcurrentandasaresultofthat,thereisnophaseshiftasthecurrent is in phase with the voltage. Based on this concept subsequent sections of thechapterareexplained.

13.2.3BasicLCOscillatoryCircuitAsshowninFigure13.2,thecircuitconsistsofaninductivecoilLandacapacitorC.Thecapacitorstoresenergyintheformofanelectrostaticfieldandwhichproducesapotentialor static voltage across it, while the inductive coil stores its energy in the form of amagnetic field. The capacitor is charged up to the dc supply voltageV by putting theswitchinthepositionA.Whenthecapacitorisfullycharged,theswitchisthrowntothepositionBandthechargedcapacitorisnowconnectedinparallelacrosstheinductivecoilso the capacitor begins to discharge itself through the coil. The voltage acrossC startsfallingasthecoil.ThevoltageacrossCstartsfallingasthecurrentthroughthecoilbeginstorise.ThisrisingcurrentsetsupanelectromagneticfieldaroundthecoilandwhenC iscompletely discharged, the energy that was originally stored in the capacitor C as anelectrostaticfieldisnowstoredintheinductivecoilLasanelectromagneticfieldaroundthecoilwindings.Asthereisnownoexternalvoltageinthecircuittomaintainthecurrentwithinthecoil,itstartstofallastheelectromagneticfieldbeginstocollapse.Abackemfisinducedinthecoil(e=−Ldi/dt)keepingthecurrentflowingintheoriginaldirection.ThiscurrentnowchargesthecapacitorCwiththeoppositepolaritytoitsoriginalcharge.Ccontinuestochargeuntilthecurrenthasfallentozeroandtheelectromagneticfieldofthecoilhascollapsedcompletely.Theenergyoriginallyintroducedintothecircuitthrough

the switch has been returned to the capacitorwhich again has an electrostatic potentialacrossit,althoughitisnowoftheoppositepolarity.Thecapacitornowstartstodischargeagainbackthroughthecoilandthewholeprocessisrepeated,withthepolaritieschangedand continues as the energy is passed back and forth producing an ac type sinusoidalvoltageandcurrentwaveform.

Figure13.2BasicLCoscillatorcircuit

ThisoscillatoryactionoftransferringenergyfromthecapacitorCtotheinductor,Landvice versa,would continue indefinitely if there is no loss of energy in the circuit. But,energyislostintheresistanceoftheinductorcoil,inthedielectricofthecapacitor,andinradiation from the circuit; so the oscillation steadily decreases until it dies awaycompletely. Then in a practical LC circuit, the amplitude of the oscillatory voltagedecreases at each half cycle of oscillation and will eventually die away to zero. Theoscillationsarethensaidtobedamped.Thequalityfactorofthecircuitsetstheamountofdamping. InFigure13.3,dampedoscillationsareshowninboth thecases,withsmallRandwithlargeR.

ThefrequencyoftheoscillatoryvoltagedependsuponthevalueoftheinductanceandcapacitanceintheLCcircuit.Weknowwhenresonancehastooccur,boththecapacitiveXCandinductiveXLreactancesmustbeequalandoppositetocancelouteachother.Asaresult, the resistance in the circuit remains to oppose the flow of current. Then thefrequencyatwhichthiswillhappenisgivenas

ResonantfrequencyinatunedLCcircuit,theoutputfrequency,

Tomaintaintheoscillationskeepingtheamplitudeataconstantlevel,inanLCcircuit,itisrequiredtoreplacetheenergylostineachoscillation.Theamountofenergyreplacedmust be equal to that lost during each cycle. Alternatively, if the amount of energyreplacedistoosmall,theamplitudewoulddecreasetozeroovertime.ThesimplestwayofreplacingthisenergyistotakepartoftheoutputfromtheLCcircuit,amplifyitandthenfeeditbackintotheLCcircuitagainandthiscanbeachievedusingavoltageamplifier.Toproduceaconstantoscillation,theleveloftheenergyfedbacktotheLCnetworkmustbe

accurately controlled. Then there must be some form of automatic amplitude or gaincontrolwhentheamplitudetries tovaryfromareferencevoltageeitherupordown.Tomaintainastableoscillationtheoverallgainofthecircuitmustbeequalto1orunity.Anylessandtheoscillationswillnotstartordieawaytozero,anymoretheoscillationswilloccur but the amplitude will become clipped by the supply rails causing distortion. Acircuitcontainingthisfeatureisconsideredinthenextsection.

Figure13.3Dampedoscillations

13.2.4BasicTransistorLCOscillatorCircuitABJTisusedastheoscillatoramplifierandthetunedLCcircuitactsasthecollectorloadas shown in Figure 13.4.A second coilL2 is connected between the base and emitter.ElectromagneticfieldofL2ismutuallycoupledwiththatofthecoilL.Mutualinductanceexists between two circuits. The changing current in one circuit induces byelectromagnetic induction a potential in the other due to transformer action. So as theoscillationstakeplaceinthetunedcircuit,electromagneticenergyistransferredfromthecoilL to the coilL2 and a voltage of the same frequency as that in the tuned circuit isappliedbetweenthebaseandemitterofthetransistor.Inthisway,thenecessaryautomaticfeedback voltage is obtained. The amount of feedback can be varied by changing thecouplingbetweencoilsLandL2.Whenthecircuitisoscillating,itsimpedanceisresistiveandthecollectorandbasevoltagesare180°outofphase.Inordertomaintainoscillations,thevoltageappliedtothetunedcircuitmustbein-phasewiththeoscillationsoccurringinthe tunedcircuit.So, it isnecessary to introduceanadditional180°phase shift into thefeedbackpathbetweenthecollectorandbase.ThisisdonebywindingthecoilofL2inthecorrect direction relative to the coil L giving us the correct amplitude and phaserelationshipsfortheoscillatorcircuitorbyintroducingaphaseshiftnetworkbetweentheoutputandinputoftheamplifier.

Figure13.4BasictransistorLCoscillator

LC oscillators are actually sinusoidal oscillators or harmonic oscillators that cangenerate high-frequency sinewaves for use inRadioFrequency (RF)Type applicationswiththetransistoramplifierbeingaBJTorFET.TherearedifferentwaystoconstructLCfilternetworksandamplifiers.Asa result,harmonicoscillatorscome indifferent formsandthemostcommonformsareHartleyLCoscillator,ColpittsLCoscillator,Armstrongoscillator,Clapposcillator,etc.

13.2.5OscillatorSummaryAfewbasicrequirementsforanoscillatorycircuitaregivenasfollows:

1.Thecircuitshouldcontainareactiveorfrequencydependentcomponent—eitheranInductor(L)oraCapacitor(C)andadcsupplyvoltage.

2.Overallgainoftheamplifiercircuitmustbeatleastunity.

3.Self-regenerativeorpositivefeedbackresultsoscillations.

4.Oscillationsofthecircuitbecomedampedduetocircuitlosses.

5.Toovercomethesecircuitlosses,voltageamplificationisnecessary.

6.Desiredoscillationscanbemaintainedbyusingsomepartoftheoutputvoltageasfeedbacktothetunedcircuitthatisofthecorrectamplitudeandin-phase(0°).

7. To keep the output signal in phase with the input, the overall phase shift of thecircuitmustbezero.

13.3 HARTLEYOSCILLATOR

ThebasicLCoscillatorcircuitdoesnothavetheoptionofcontrollingtheamplitudeoftheoscillations. A weak electromagnetic coupling between L and L2 results in insufficientfeedback and the oscillations would eventually die away to zero. Similarly, a strongfeedback causes the oscillations to increase in amplitude until they are limited by thecircuitconditionsproducingdistortion.Itispossibletofeedbackexactlytherightamountof voltage for constant amplitude oscillations. If the feedback is more than what isnecessary, theamplitudeof theoscillationscanbecontrolledbybiasing theamplifier insuchawaythatiftheoscillationsincreaseinamplitude,thebiasisincreasedandthegainof the amplifier is reduced. If the amplitude of the oscillations decreases, the biasdecreasesandthegainoftheamplifierincreases,thus,increasingthefeedback.Thisisthemethod to keep oscillations constant and it is known as automatic base bias. Efficientoscillatorcanbeimplementedbyemployingaclass-Borevenclass-Cbiasasthecollectorcurrent flows during only part of the cycle and the quiescent collector current is verysmall. Then this self-tuning base oscillator circuit forms the basic configuration for theHartleyoscillatorcircuit.

IntheHartleyoscillator,thetunedLCcircuitisconnectedbetweenthecollectorandthebase of the transistor amplifier and as far as the oscillatory voltage is concerned, theemitterisconnectedtoatappingpointonthetunedcircuitcoil.AHartleyoscillatorcanbe

implemented from any configuration that uses either a single-tapped coil or a pair ofseries-connectedcoilsinparallelwithasinglecapacitor.

13.3.1BasicHartleyOscillatorCircuitFigure13.5showsthebasicHartleyoscillatorcircuit.Duringoscillation,thevoltageatthepointX(collector),relativetothepointY(emitter),is180°out-of-phasewiththevoltageatthepointZ(base)relativetothepointY.Atthefrequencyofoscillation,theimpedanceofthecollectorloadisresistiveandanincreaseinbasevoltagecausesadecreaseinthecollectorvoltage.Thenthereisa180°phasechangeinthevoltagebetweenthebaseandcollectorand thisalongwith theoriginal180°phaseshift in thefeedbackloopprovidesthecorrectphaserelationshipofpositivefeedbackforoscillationstobemaintained.Thepositionoftappingpointoftheinductorsetstheamountoffeedback.Ifitismovednearerto the collector, the amount of feedback is increased, but the output taken between thecollectorandgroundisreducedandviceversa.ResistorsR1andR2aretherefortheusualstabilisingdcbiasforthetransistorinthenormalmannerwhilethecapacitorsactasdc-blockingcapacitors.Inthiscircuit,thedccollectorcurrentflowsthroughapartofthecoilandforthisreason,thecircuitissaidtobeseries-fedwiththefrequencyofoscillationoftheHartleyoscillatorbeinggivenas

where,L=L1+L2.

Note:Listhetotalinductanceiftwoseparatecoilsareused.

Figure13.5BasicHartleyoscillator

ThefrequencyofoscillationscanbeadjustedbyvaryingthetuningcapacitorCorbyvarying the tap position of the inductive coil, giving an output over a wide range offrequencies making it very easy to tune. In the series-fed Hartley oscillator, it is alsopossible to connect the tuned tank circuit across the amplifier as a shunt-fed oscillatordiscussedasfollows.

13.3.2Shunt-fedHartleyOscillatorCircuitAs shown in Figure 13.6, in the shunt-fed Hartley oscillator, both the ac and dccomponentsof thecollectorcurrenthaveseparatepathsaround thecircuit.Here,averysmallamountofpoweriswastedinthetunedcircuit.Sincethedccomponentisblockedby the capacitorC2, no dc component flows through the inductive coil, L. The RadioFrequencyCoil(RFC)L2isanRFchokewhichoffersahighreactanceatthefrequencyofoscillationssothatmostoftheRFcurrentisappliedtotheLCtuningtankcircuitviathecapacitor,C2asthedccomponentpassesthroughL2tothepowersupply.AresistorcouldbeusedinplaceoftheRFCcoilbuttheefficiencywouldbeless.

Figure13.6Shunt-fedHartleyoscillator

Example13.1OneHartleyoscillatorcircuithastwoinductorsof0.5mHandeachistunedtoresonatewithacapacitorwhichcanbevaried from 100 pF to 500 pF. Determine the upper andlower frequencies of oscillation and the oscillatorbandwidth.

SolutionThecircuitconsistsoftwoinductivecoilsinseries.

Thetotalinductanceisgivenas:

Upperfrequency,

Lowerfrequency,

Oscillatorbandwidth

13.4 COLPITTSOSCILLATORS

TheColpittsoscillatorissomewhatoppositetotheHartleyoscillatorasthecentretappingismadefromcapacitivevoltagedividernetworkinsteadoftappedinductivecoilasshowninFigure13.7.Similar to theHartleyoscillator, the tuned tankcircuitconsistsofanLCresonancecircuitconnectedbetweenthecollectorandbaseofthetransistoramplifier.

Figure13.7BasicColpittsoscillatorcircuit

TheemitterofthetransistoramplifierisconnectedtothejunctionofcapacitorsC1andC2 which are connected in series with the required external phase shift obtained in asimilarmannertothatintheHartleyoscillator.TheamountoffeedbackiscontrolledbytheratioofC1andC2whicharegenerallygangedtogethertoprovideaconstantamountof feedback. Once again, the frequency of oscillations for a Colpitts oscillator isdeterminedbytheresonantfrequencyoftheLCtankcircuitandisgivenas

whereCTisthecapacitanceofC1andC2connectedinseriesandisgivenas.

A common emitter-amplifier configuration is employed here, with the output signal180° out of phase with respect to the input signal. The two capacitors are connectedtogetherinseriesbutinparallelwiththeinductivecoilresultinginoverallphaseshiftofthecircuitbeingzero.ResistorsR1andR2areusedfortheusualstabilisingdcbiasforthetransistorinthenormalmannerwhilethecapacitoractsasdc-blockingcapacitors.

Example13.2OneColpittsoscillatorcircuithastwocapacitorsof10pFand 100 pF respectively connected in parallel with aninductorof10mH.Determinethefrequencyofoscillationsofthecircuit.

SolutionThecircuitconsistsoftwocapacitorsinseries.

So,thetotalcapacitanceisgivenas

Iftheinductorisof10mHthenthefrequencyofoscillationis

Thenthefrequencyofoscillationsfortheoscillatoris527.8kHz.

13.5 THERCOSCILLATOR

Sofar,onlyLCtunedcircuitsthatcausephaseshiftof180°duetoinductiveorcapacitivecouplinginadditiontoa180°phaseshiftproducedbythetransistororop-amp,havebeendiscussed.SuchLC oscillators are employed togeneratehigh-frequencyoscillationsbuttheycannotbeemployedforgenerationoflowfrequencyoscillationsastheybecometoobulkyandexpensive.RCoscillatorsarecommonlyusedforgeneratingaudio-frequenciesas they provide good frequency stability and waveform. When an RC network isconnected in class-A configuration, a single stage amplifierwill produce 180° of phaseshift between its output and input signals. If an oscillator has to oscillate a sufficientpositivefeedbackofthecorrectphasemustbeprovidedwiththeamplifierbeingusedasaninvertingstagetoachievethis.InanRCoscillator,theinputisshifted180°throughtheamplifierstageand180°againthroughasecondinvertingstagegiving360°(180°+180°)ofphaseshiftwhich is thesameas0° therebyproviding therequiredpositivefeedback.ThismethodofphaseshiftbetweentheinputtoanRCnetworkandtheoutputfromthesame network is employed in a resistance-capacitance oscillator or simply an RCoscillator.

Figure13.8RCphase-shiftnetwork

In Figure 13.8, the circuit on the top shows a single resistor-capacitor network andwhoseoutputvoltage leads the inputvoltagebysomeangle less than90°.An idealRCcircuitwouldproduceaphaseshiftofexactly90°,asitisknownthattheamountofactualphaseshiftinthecircuitdependsuponthevaluesoftheresistor,capacitorandthechosenfrequencyofoscillations.Thephaseangle(Ф)isgivenas

In this simpleexampleabove, thevaluesofRandC havebeenchosen so that at therequired frequency, theoutputvoltage leads the inputvoltagebyanangleofabout60°.

ThenbycascadingorconnectingtogetherthreesuchRCnetworksinseries,itispossibletoproduceatotalphaseshiftinthecircuitof180°atthechosenfrequencyanditformsthebasisofanRCoscillatorcircuit.Itisknownthatinanamplifiercircuit,eitherusingaBJTorOp-AMP,itwillproduceaphase-shiftof180°betweenitsinputandoutput.IfanRCphase-shiftnetworkisconnectedbetweenthisinputandoutputoftheamplifier,thetotalphaseshiftwillbecome360°,i.e.thefeedbackisin-phase.

13.5.1BasicRCOscillatorCircuitThe RC oscillator as shown in Figure 13.9, which is called a phase-shift oscillator,producesasine-waveoutputsignalusingregenerativefeedbackfromtheresistor-capacitorcombination.

Figure13.9BasicRCoscillatorcircuit

ThisregenerativefeedbackfromtheRCnetworkispossibleduetothecapabilityofthecapacitor to store an electric charge. The resistor-capacitor feedback network can beconnectedasshownabovetoproducealeadingphaseshiftorinterchangedtoproducealaggingphaseandtheoutcomeisstillthesameasthesine-waveoscillationsonlyoccuratthe frequency at which the overall phase shift is 360°. By varying one ormore of theresistors or capacitors in the phase-shift network, the frequency can be varied andgenerally this is doneusing a 3-gangedvariable capacitor. If all the resistorsR and thecapacitors C are equal in value then the frequency of oscillations produced by theoscillatorisgiven

wherefistheoutputfrequencyinHz,Ristheresistanceinohms,Cisthecapacitanceinfarads,NisthenumberofRCstagesandinourexample,N=3

13.5.2TheOp-ampffCOscillatorOperational Amplifier (Op-amp) RC oscillators are more common than their bipolartransistorcounterparts.TheRCnetwork thatproduces thephaseshift isconnected fromtheop-ampsoutputbacktoitsnon-invertinginputasshowninFigure13.10.

Figure13.10Operational-amplifierRCoscillators

The feedback is connected to thenon-inverting input and theoperational amplifier isconnectedinitsinvertingamplifierconfigurationwhichproducestherequired180°phaseshift. The RC network produces the other 180° phase shift at the required frequency.AlthoughitispossibletocascadetogethertwoRCstagestoprovidetherequired180°ofphaseshift,butinthatcasethestabilityoftheoscillatoratlowfrequenciesispoor.OneofthemostimportantcharacteristicsofanRCoscillatorisitsfrequencystability.Thisistheability of an oscillator to provide a constant frequency output under varying loadconditions.Sotoobtainhigherfrequencystability,threeorevenfourRCstagestogetherarecascaded.RCoscillatorswithfourstagesarewidelyusedbecausecommonlyavailableoperationalamplifierscomeinquadICpackages.So,designinga4-stageoscillatorwith45°ofphase shift relative toeachother is comparativelyeasy.RC oscillators are stableand provide a well-shaped sine-wave output with the frequency being proportional to1/RC.Usingavariablecapacitor,awiderfrequencyrangeispossible.However,theuseofRC oscillators are restricted to low-frequency applications, because of their bandwidthlimitationstoproducethedesiredphaseshiftathighfrequencies.

Example13.3 Determine the frequencyof oscillationsof aRCoscillatorcircuit having three-stages each with a resistor andcapacitorofequalvalues.R=10kΩandC=500pF

SolutionHere,R=10kΩ,C=500pF,N=3

Therefore,thefrequencyofoscillationisgivenas

13.6 WIENBRIDGEOSCILLATORS

TheWienbridgeoscillatorisanothertypeofoscillatorwhichusesaRCnetworkinplaceoftheconventionalLCtunedcircuittoproduceasinusoidaloutputwaveform.TheWienbridgeoscillatorisatwo-stageRCcoupledamplifiercircuit thathasgoodstabilityat itsresonantfrequency,lowdistortionandisveryeasytotunemakingitapopularcircuitasanaudiofrequencyoscillator.ThephaseshiftoftheoutputsignalisconsiderablydifferentfromthepreviousRCoscillators.

TheWienbridgeoscillatoremploysafeedbackcircuitconsistingofaseriesRCcircuitconnected with a parallelRC of the same component values producing a phase delay-

advance(lag-lead)circuitdependinguponthefrequencyasshowninFigure13.11.

TheaboveRCnetworkisa typicalsecond-orderfrequencydependentband-passfilterwithhighqualityfactor(Q).Itconsistsofalow-passfilter(seriesRCnetwork)andanotherhigh-passfilter(parallelRCnetwork).Atlowfrequencies, thereactanceXcoftheseriescapacitorisveryhighsotheseriescapacitoractslikeanopencircuitandblocksanyinputsignalVinandthereforethereisnooutputsignalVout.Athighfrequencies,thereactanceoftheparallelcapacitor isverylowsotheparallelcapacitoracts likeashortcircuitontheoutput, so again there is no output signal. However, between these two extremes, theoutputvoltagereachesamaximumandthefrequencyatwhichthishappensiscalledtheresonant frequency (fr) as the circuit’s reactance equals its resistance Xc = R. At thisresonantfrequency,theoutputvoltageisonethird(1/3)oftheinputvoltage.

Figure13.11RCphaseshiftnetwork

Figure13.12Outputgainandphaseshift

ItcanbeseenasinFigure13.12thatatverylowfrequencies,thephaseanglebetweenthe input and output signals is positive, i.e. leading in nature, while at very highfrequencies the phase angle becomes negative, i.e. lagging in nature. In the middle ofthesetwopointsthecircuitisatitsresonantfrequency(fr)withthesignalsbeingin-phaseor0°.Theexpressionofresonantfrequencyisasfollows:

This frequency-selective RC network forms the basis of the Wien Bridge oscillatorcircuit.TheWienbridgeoscillatorcircuitisproducedbyplacingthisRCnetworkacrossanon-invertingamplifier.AsinFigure13.13,theoutputoftheoperationalamplifierisfedback to the inputs in-phasewith part of the feedback signal connected to the invertinginput terminalvia the resistordividernetworkofR1 andR2,while theother part is fedbacktothenon-invertinginputterminalviatheRCnetwork.Thenattheselectedresonantfrequency(fr),thevoltagesappliedtotheinvertingandnon-invertinginputswillbeequaland in-phase.So thepositive feedbackwill cancel thenegative feedback signal causing

thecircuittooscillate.Alsothevoltagegainoftheamplifiercircuitshouldbe3assetbytheresistornetwork,R1andR2.

Figure13.13Wienbridgeoscillatorwithop-amp

Example13.4 Determine the maximum and minimum frequency ofoscillations of a Wien bridge oscillator circuit having aresistorof10kΩandavariablecapacitorof1nFto1000nF.

SolutionThefrequencyofoscillationsforaWienbridgeoscillatorisgivenas:

Lowestfrequency,

Highestfrequency,

13.7 CRYSTALOSCILLATORS

Frequencystabilityisthemostimportantfeatureofanoscillator.Frequencystabilityistheability toprovideaconstant frequencyoutputundervarying loadconditions.FrequencystabilityoftheoutputsignalcanbeimprovedbyproperselectionofthecomponentsusedfortheresonantfeedbackcircuitincludingtheamplifierbutthereisalimittothestabilitythatcanbeobtainedfromnormalLCandRCtankcircuits.Someofthefactorsthataffectthe frequency stability of an oscillator include temperature, variations in the load andchangesinthepowersupply.Forveryhighstability,aquartzcrystalisgenerallyusedasthefrequency-determiningdevicetoproduceatypicaltypeofoscillatorcircuitknownascrystaloscillators.

Thecrystaloscillatorsareimplementedusingthepiezo-electriceffect.Thisisactuallyrealisedwhenavoltagesourceisappliedtoasmallthinpieceofcrystalquartz.Thequartzcrystal begins to change shape.This piezo-electric effect is thepropertyof a crystal bywhich an electrical charge produces a mechanical force by changing the shape of thecrystal.Inreversesense,amechanicalforceappliedtothecrystalproducesanelectricalcharge.Thispiezo-electriceffectproducesmechanicalvibrationsoroscillationswhichareused to replace theLC tank circuit and can be seen inmany different types of crystal

substances with the most important of these for electronic circuits being the quartzmineralsbecauseoftheirsuperiormechanicalstrength.

Thequartzcrystalisaverysmall,thinpieceorwaferofcutquartzwiththetwoparallelsurfacesmetalisedtomaketheelectricalconnectionsinacrystaloscillator.Thephysicalsizeandthicknessofapieceofquartzcrystalistightlycontrolledsinceitaffectsthefinalfrequencyofoscillationsandiscalledthecharacteristicfrequencyofthecrystal.Oncecutandshaped,thecrystalcannotbeusedatanyotherfrequency.Thecrystal’scharacteristicorresonantfrequencyisinverselyproportionaltoitsphysicalthicknessbetweenthetwometalisedsurfaces.Amechanicallyvibratingcrystalcanberepresentedbyanequivalentelectrical circuit consistingof low resistance, large inductance and small capacitance asshowninFigure13.14.

Figure13.14Quartzcrystal

Likeanelectricallytunedtankcircuit,aquartzcrystalhasresonantfrequencywithveryhighQfactorduetolowresistance.Thefrequenciesofquartzcrystalsrangefrom4kHzto10MHz.Thecutofthecrystalalsodetermineshowitwillvibrateandbehaveassomecrystals will vibrate at more than one frequency. Also, if the crystal is of varyingthickness, ithas twoormoreresonantfrequencieshavingbothafundamental frequencyand harmonics such as second or third harmonics. However, usually the fundamentalfrequency ismore pronounced than the others and this is the one used. The equivalentcircuitaboveconsistsofthreereactivecomponentsandtherearetworesonantfrequencies,thelowestisaseries-typefrequencyandthehighestaparallel-typeresonantfrequency.

In a crystal oscillator circuit, the oscillatorwill oscillate at the crystal’s fundamentalseriesresonantfrequencyasthecrystalalwaysintendstooscillatewhenavoltagesourceisappliedtoit.Itisalsopossibletotuneacrystaloscillatortoanyevenharmonicofthefundamental frequencies, (2nd,4th,8th, etc.) and these are knowngenerally as harmonicoscillators while overtone oscillators vibrate at odd multiples of the fundamentalfrequencies,(3rd,5th,11th,etc).Crystaloscillatorsthatoperateatovertonefrequenciesdosousingtheirseriesresonantfrequency.

13.7.1ColpittsCrystalOscillator

ThedesignofaColpittscrystaloscillatorisverysimilartotheColpittsoscillator.TheLCtankintheColpittoscillatorcircuithasbeenreplacedbyaquartzcrystalasshownbelowinFigure13.15.Theinputsignaltothebaseofthetransistorisinvertedatthetransistorsoutput. The output signal at the collector is then taken through 180° phase shiftingnetworkwhichcontainsthecrystaloperatinginaseriesresonantmode.

The output is fed back to the input which is inphase with the input providing thenecessarypositivefeedback.ResistorsR1andR2 bias the transistor in class-AoperationandtheresistorReistakensothattheloopgainisslightlyhigherthanunity.CapacitorsC1andC2aremadeaslargeaspossibleinordertogetthefrequencyofseriesresonantmodeofthecrystal.

This frequency does not depend upon the values of these capacitors. The circuitdiagramaboveof theColpitts crystal oscillator circuit shows that capacitorsC1 andC2shunttheoutputofthetransistorwhichreducesthefeedbacksignal.Therefore,thegainofthetransistorlimitsthemaximumvaluesofC1andC2.Anotherimportantpointisthattheoutputamplitudeshouldbekeptlowinordertoavoidexcessivepowerdissipationinthecrystal,otherwise,thecrystalcoulddestroyitselfbyexcessivevibration.

Figure13.15Colpittscrystaloscillator

13.8 PIERCEOSCILLATOR

ThePierceoscillatorisanothercommondesignofacrystaloscillator.Itusesthecrystalaspartofitsfeedbackpathinsteadoftheresonanttankcircuit.AJFETisusedasamplifierasit provides a very high input impedance with the crystal connected between the drain(output)terminalandthegate(input)terminalasshowninFigure13.16.

Figure13.16Piercecrystaloscillator

Intheabovecircuit,thecrystaldeterminesthefrequencyofoscillationsandoperatesonits series resonant frequency giving a low-impedance path between output and input. Itgives 180° phase shift at resonance and makes the feedback positive. The maximumvoltagerangeatthedrainterminalsetstheamplitudeoftheoutputsinewave.ResistorR1regulates the amount of feedback and crystal drive. The voltage across the RadioFrequency Choke (RFC) reverses during each cycle. The Pierce oscillator can beimplemented using the minimum number of components. Because of this, Pierceoscillatorsareusedtodesignmostdigitalclocks,watchesandtimers,etc.

13.9 MICROPROCESSORCLOCKS

Thecrystalquartzoscillatoristhemostsuitablefrequency-determiningdeviceinvirtuallyall microprocessors, microcontrollers, PICs and CPUs, used to generate their clockwaveforms. Crystal oscillators provide the highest accuracy and frequency stabilitycompared to resistor-capacitor or inductor-capacitor oscillators. TheCPU clock dictateshowfasttheprocessorcanprocessthedata,andamicroprocessorhavingaclockspeedof3MHzmeansthat itcanprocessdatainternally3milliontimesasecondateveryclockcycle. Generally, all that is needed to produce a microprocessor clock waveform is acrystal and two ceramic capacitors of values ranging between15 to 33 pF as shown inFigure13.17.

Figure13.17Microprocessoroscillator

Most microprocessors, microcontrollers and PICs have two oscillator pins labelledOSC1andOSC2 toconnect toanexternalquartzcrystal,RCnetworkorevenaceramicresonator.Inthisapplication,thecrystaloscillatorproducesatrainofcontinuoussquare-wave pulses whose frequency is controlled by the crystal which in turn executes theinstructionsthatcontrolthedevice.

Table13.1Oscillatorswiththeiroperatingfrequencyrange

Typeofoscillator Approximatefrequencyrange

Crystaloscillator Fixedfrequency

Wienbridgeoscillator 1Hzto1MHz

Phase-shiftoscillator 1Hzto10MHz

Hartleyoscillator 10kHzto100MHz

Colpittsoscillator 10kHzto100MHz

13.10 SQUAREWAVEANDPULSEGENERATORS

Wave shape, or wave profile, of a single pulse is shown in Figure 13.18. Thecharacteristicsofasinglepulsearegivenbelow.

•Thevoltagerisesveryrapidlyfromzerotoitsmaximumvalue.

•Itstayssteadyatthemaximumvalueforatime.

•Itthenfallsveryrapidlybacktozero.

•Thedurationofapulsecanbeanywherefromaverylongtime(days)toaveryshorttime(picosecondsorless).

•Pulsesdonotriseandfallinstantaneouslybuttaketime(whichmaybeveryshort).

•Theyarecalledtheriseandfalltimes.

Figure13.18Waveshapeofasingle-pulse

Figure13.19Waveformofpulsetrain

AsshowninFigure13.19,afewcharacteristicsofpulsetrainsarestatedbelow:•Ifpulsesoccuroneafteranother,theyarecalledapulsetrain.

•Thedurationtimeofapulseiscalledthemark.

•Thetimebetweenpulsesiscalledthespace.

•Therelativetimesareexpressedasthemark-to-spaceratio.

•Marktospaceratiosmayvary.

13.10.1TypicalSquareWaveGeneratorA continuous signal with regular wave shape is one requirement in a wide range ofapplications.Oneofthemostimportantoftheseisasquare-wavegenerator.

The circuit in Figure 13.20 uses an op-amp as comparator with both positive and

negativefeedbacktocontrolitsoutputvoltage.Becausethenegativefeedbackpathusesacapacitor while the positive feedback path does not, there is a time delay before thecomparator is triggered to change state. As a result, the circuit oscillates, or keepschangingstatebackandforthatapredictablerate.

Figure13.20Squarewavegeneratorcircuitusingop-amp

Sincenoforceorexcitationisgiventolimittheoutputvoltage,itwillswitchfromoneextremetotheother.Ifitisassumedthatoutputvoltagestartsat−12voltsthenthevoltageatthepositiveornon-invertinginputterminalwillbesetbyR2andR1toaFigure13.20fixedvoltageequalto−12R1/(R1+R2)volts.Now,itbecomesthereferencevoltageforthecomparator,andtheoutputwillremainunchangeduntilthenegativeorinvertinginputterminalbecomesmorenegativethanthisvalue.Buttheinvertingterminalisconnectedtoacapacitor(C)whichisgraduallycharginginanegativedirectionthroughtheresistorRf.SinceCischargingtowards−12volts,butthereferencevoltageatthenon-invertinginputis necessarily smaller than the−12 volt limit, eventually the capacitor will charge to avoltage that exceeds the reference voltage. When that happens, the circuit willimmediatelychangestate.Theoutputwillbecome+12voltsandthereferencevoltagewillabruptlybecomepositiveratherthannegative.Nowthecapacitorwillchargetowards+12volts,andtheotherhalfofthecyclewilltakeplace.Theoutputfrequencyisgivenbytheapproximateequation:

In the practical field, the circuit-component values are chosen such that R1 isapproximatelyRf/3,andR2isintherangeof2to10timesR1.

13.10.2OP-AMPAstableMultivibratorandMonostableMultivibratorCircuits

Relaxation oscillators are normally non-sinusoidalwaveform generators. The relaxationoscillator using an op-amp shown in Figure 13.21 is a square-wave generator. Squarewavesarerelativelyeasytogenerate.

ThefrequencyofoscillationofacircuitisdependentonthecharginganddischargingofacapacitorCthroughthefeedbackresistorRf.Themaincomponentoftheoscillatorisaninverting op-amp working as comparator. A comparator circuit has positive feedbackwhichincreases thegainof theamplifier.Acomparatorcircuithavingpositivefeedbackofferstwoadvantages.

First,thehighgaincausestheop-amp’soutputtoswitchveryquicklyfromonestatetoanotherandviceversa.Second,theuseofpositivefeedbackgivesthehysteresisloopinthecircuitoperation.

Figure13.21Op-ampsquare-wavegenerator

AsshowninFigure13.21,intheop-ampsquare-wavegenerator,theoutputvoltageVoutisconnectedtogroundthroughtwoZenerdiodesZ1andZ2,connectedback-to-backandislimitedtoeitherVZ2orVZ1.Afractionoftheoutputisfedbacktothenon-inverting(+)inputterminal.AcombinationofRfandCactasa low-passRCcircuitwhichisusedtointegratetheoutputvoltageVoutThecapacitorvoltageVcisappliedtotheinvertinginputterminalinsteadofexternalsignal.

Atthatpointoftime,thedifferentialinputvoltageisgivenasVin=Vc−βVout.

WhenVinis+veVout=−VzlandwhenVinis−ve,Vout=+Vz2.

Consideran instantwhenVin < 0.At this instant,Vout =+Vz2, and thevoltage at thenon-inverting (+) input terminal is βVz2, the capacitorC charges exponentially towardsVz2,witha timeconstantRfC.Theoutputvoltage remainsconstant atVz2untilvcequalβVz2.Whenithappens,comparatoroutputreversesto−Vz1.Nowvcchangesexponentiallytowards−Vz1with the same timeconstantandagain theoutputmakesa transition from−Vz1to+Vz2whenVcequals−βVz1LetVz1=Vz2The time period, T of the output square wave is determined using the charging and

dischargingphenomenaofthecapacitorC.ThevoltageacrossthecapacitorVcwhenitischargingfrom−BVzto+Vzisgivenby

Vc=[1−(1+β)]e−T/2τ

whereτ=RfC

ThewaveformsofthecapacitorvoltagevcandoutputvoltageVout(orvz)areshowninFigure13.22.

Whent=t/2,

Vc=+βVzor+βVout

Therefore,βVz=Vz[1−(1+β)e−T/2τ]

ore−T/2τ=(1−β)/(1+β)

orT=2τloge[(1−β)/(1+β)]=2Rfcloge[1+(2R3/R2)]

Figure13.22Outputandcapacitorvoltagewaveforms

Here,thefrequency(f=1/T),ofthesquarewaveisindependentoftheoutputvoltageVout.Thiscircuit isalsoknownas free-runningorastablemultivibrator.Thiscircuithastwoquasi-stablestatesasshowninFigure13.22.TheoutputremainsinonestateforthetimeT1andthenarapidtransitiontothesecondstateandremainsinthatstatefortimeT2.ThecyclerepeatsitselfaftertimeT=(T1+T2).where,Tisthetimeperiodofthesquare-wave.Theop-ampsquare-wavegeneratoroffersgoodperformanceinthefrequencyrangeofabout10Hz−10kHz.But,athigherfrequencies,theslewrateoftheop-amplimitstheslope of the output squarewave. Thematching of twoZener diodesZ1 andZ2 decidessymmetryof theoutputwaveform.Theunsymmetricalsquarewave(T1notequaltoT2)canbeobtainedbychoosingdifferentchargingtimeconstantsforchargingthecapacitorCto+Voutand−Vout

Figure13.23Pulsegenerator/monostablecircuitandwaveforms

Apulse generator circuit, as shown inFigure13.23, is amonostablemultivibratorAMonostableMulti Vibrator (MMV) has one stable state and one quasi-stable state. Anexternal triggering pulse pushes the circuit to operate in the quasi-stable state from thestablestate.ThecircuitcomesbacktoitsstablestateafteratimeperiodT.Asaresult,asingleoutputpulseisgeneratedinresponsetoaninputpulseandisreferredtoasaone-shot or mono shot. The monostable multivibrator circuit shown in Figure 13.23. isobtainedbymodifyingthepreviouscircuitbyconnectingadiodeD1acrossthecapacitorCsoastoclampvcatvdduringpositiveexcursion.

Atsteadystate,thecircuitwillremaininitsstablestateandtheoutputwillbeVOUT=+VOUT or+Vz.ThecapacitorC is clampedat thevoltageVD (=0.7V). The voltageVDmust be less thanβVOUT forVin < 0. The circuit can be switched to the other state byapplyinganegativepulsewithamplitudegreaterthanβVOUT−VDtothenon-inverting(+)terminaloftheop-amp.IfatriggerpulsewithamplitudegreaterthanβVOUT−VDisgiven,Vingoespositivecausingatransitioninthestateofthecircuitto−Vout.ThecapacitorCstartschargingexponentiallywithatimeconstantofτ=RfCtowardsVOUTanddiodeD1becomes reverse-biased. When the capacitor voltage vc becomes more negative than−βVOUT,Vinbecomesnegativeand,therefore,theoutputswingsbackto+VOUTwhichis

thesteady-stateoutput.Thecapacitornowchargestowards+VOUTtillvcattainsVDandcapacitorCbecomesclampedatVD.The triggerpulse, capacitorvoltagewaveformandoutputvoltagewaveformareshowninFigure13.23(b),23(c)and23(d)respectively.

ThetriggerpulsewidthTmustbemuchsmaller thanthedurationof theoutputpulsegenerated,i.e.TP=Tandforreliable,operationthecircuitshouldnotbetriggeredagainbeforeT.

During the quasi-stable state, the exponential profile of the capacitor voltage isexpressedas,

vc=−VOUT+(VOUT+VD)e−t/τ

At,t=T,vc=−βVOUT

So−βVOUT=−VOUT+(VOUT+vD)e−T/τ

or,T=RfCloge(1+VD/Vout)/1−β

Normally,VD<<VOUTandtakingR2=R3Thefactor,β=R3/(R2+R3)=1/2

So,T=RfCloge2=0.693RfC

13.11 TRIANGULARWAVEGENERATOR

Simply integrating the generated squarewave can produce a triangularwave.With thebasic squarewave-generator circuit, if a gradually charging capacitor is used to set thetimingorfrequencyofthecircuitthenthedesiredtriangularsignalmaybeobtained.Sincethe capacitor is charging through a resistor, the charging profile necessarily follows alogarithmiccurve,ratherthanalinearramp.

AsshowninFigure13.24,intherightpartofthecircuit,aseparateintegratorisusedtogenerate a ramp voltage from the generated squarewave. As a result, bothwaveformsfromasinglecircuitcanbeobtained.Notethattheintegratorinvertsaswellasintegrating,soitwillproduceanegative-goingrampforapositiveinputvoltage,andviceversa.

Figure13.24Triangularwavegenerator

Since an op-amp is in use in the integrator, to get the triangle wave, a logarithmicresponseisnotobtainedanywhereinthecircuit.Asaresult,theequationfortheoperatingfrequencyis

Thesquare-waveamplitude isstill the limitofvoltage transition,whichareassumingheretobe±12volts.Thetrianglewave’samplitudeissetbytheratioofR1/R2.

ThecircuitshowninFigure13.25isanexampleofarelaxationoscillatordesignedwithtwo op-amps. The integrator output waveform will be triangular if the input to it is asquare wave. So, a triangular-wave generator can be formed by simply cascading anintegratorandasquare-wavegenerator,asillustratedinFigure13.13.25(a).Toimplementthe circuit, a dual op-amp, two capacitors, and at least five resistors are required. Therectangular-waveoutput swingsbetween+Vsatand−Vsatwith a timeperioddetermined.Thefrequencyoftriangular-waveformandthesquarewaveformaresame.

Figure13.25Basiccircuitoftriangular-wavegenerator

TheinputtotheintegratorA2isasquarewaveanditsoutputisatriangularwaveform,theoutputoftheintegratorwillbeatriangularwaveonlywhenR4C2>T/2;whereT isthetimeperiodofthesquarewave.Asageneralrule,R4C2shouldbeequaltoT.Toobtainastabletriangularwave,itmayalsobenecessarytoshuntthecapacitorC2withresistanceR5=10R4andconnectanoffsetvoltcompensatingnetworkatthenon-inverting(+)inputterminal of the op-ampA2. As usual, the frequency of the triangular-wave generator islimitedbytheop-ampslewrate.Itisbettertouseahighslewrateop-amp(likeLM301),togeneratetriangularwaveformsofrelativelyhigherfrequency.

Withfewercomponents,anothertriangular-waveformgeneratorcanbeformedandthecircuitofthatisshowninFigure13.26(a).ThearrangementconsistsofaSchmitttriggerinnon-invertingconfigurationfollowedbyanintegrator.TherectangularwaveoutputoftheSchmitttriggerdrivesanintegrator.Theintegratorgeneratesatriangularwave,whichisfedbackandusedtodrivetheSchmitttrigger.Thus,thefirstpartofthecircuitdrivesthesecondpartof thecircuit,and theseconddrives thefirst.But thequestionarisesonhowthecircuitgetsstartedattheoutset.Thispartisexplainedasfollows.

Figure13.26(a)FeedbackcircuitwithSchmitttriggerandintegratorproducingtriangularoutputwaveform(b)TransfercharacteristicofSchmitttrigger(c)Outputwaveforms

The fact is that the moment the Schmitt trigger is connected to power supplies, theoutputof theSchmitt triggermustbe either at low stateor at high state. If theSchmitttriggeroutputislowthentheoutputoftheintegratorwillbearisingrampandforSchmitttrigger of high output, the integrator will produce a falling ramp. In any case, thetriangularwaveformwillstarttogenerate,andthepositivefeedbacktotheSchmitttriggerinputkeepsitgoing.ThetransfercharacteristicoftheSchmitttriggerisshowninFigure13.26(b).Whentheoutputislow,theinputmustincreasetotheupperthresholdvoltagetoswitch the output to high.Likewise,when the output is high, the inputmust fall to thelowerthresholdvoltagetoswitchtheoutputtolow.ThetriangularwaveproducedbytheintegratoriscapableofdrivingtheSchmitttrigger.WhentheoutputoftheSchmitttriggeris low, the integrator develops a rising ramp which increases till it reaches the upperthresholdvoltage,asillustratedinFigure13.26(c).Atthispoint,theoutputoftheSchmitttrigger switches to thehigh state and forces the triangularwave to reverse in direction.Thenegativeorfallingrampproducedbytheintegratornowfallstillitreachestheupperthresholdvoltage,whereanotherSchmittoutputchangeoccurs.

13.12 SINEWAVEGENERATOR

The demand of sine waves in many electronic applications is very high. The circuit,showninFigure13.27 is thescheme to implementamathematical relationshipbetweenthesineandcosinetrigonometricfunctions.Byintegratingasinewave,aninvertedcosinewaveisobtained.Acosinewaveformisactuallythesamewaveformasthesinewavebutshifted 90° in phase. If that cosine wave is integrated and another 90° phase shift isachieved,itproducesanegativesinewave.Ofcourse,eachop-ampintegratorintroducesaninversionaswell,sotheoutputofthefirstintegratorisactuallyanon-invertedcosinewave.Thisisreversedagainbythesecondintegrator,soitsoutputisstillanegativesinewave.Byinvertingthenegativesinewave,theoriginalsinewavecanberestored.

Inthiscircuit,R1 isadjustedtoensurethatoscillationsstartandtohelpsettheoutput

amplitude.TheZenerdiodesservetolimittheoutputsignalamplitudebylimitingthegainofthecosineamplifierbeyondthedesiredlevel.Thispreventsthecircuitfromamplifyingthesignalbeyondits±12voltlimits.

Figure13.27Asine-wavegeneratorcircuit

TheclippingeffectcausedbytheZenerdiodesdoesintroducesomedistortion,butwitha reasonable setting ofR1 this effect is very slight, and the distortion it causeswill besignificantlyreducedbythesecondintegrator.

Figure13.28Asine-waveoscillator

AclassicoscillatorcircuitisshowninFigure13.28.Inthiscircuit, theop-ampoffsetsmust be precisely balanced; otherwise, theywill accumulate on the two integrators andgraduallydampouttheoscillations.Thiscircuitcanbeimplementednicelyusingadualopampsuchasthe1458.Allthreecapacitorsarethesame,andRt is takenveryslightlyless thanR to ensure that the oscillations start themoment power is applied.Here, thefrequency of oscillations is f = 1/2 RC. The frequency response of the op amps in usedetermines the maximum frequency of oscillations. In the circuit, the loop gain willdecrease as frequency increases, andoscillations cannotbe sustained if the loopgain islessthan1.Theloopgainofthiscircuitmustbegreaterthan1toensureoscillations.Thiscircuit will also tend to clip the output waveforms. However, the same double-Zenerclippingscheme in thecircuitcanbeapplied to thecosine integrator, to limit thesignalamplitudeandpreventeitheropampfromgettingsaturated.

Asbothsineandcosinewavesareavailable,thiscircuitisalsoknownasaquadratureoscillator.

13.13 FUNCTIONGENERATORS

Afunctiongeneratorisasignalsourcethathasthecapabilityofproducingdifferenttypesofwaveformsas itsoutputsignal.Themostcommonoutputwaveformsaresinewaves,triangularwavessquarewavesandsawtoothwaves.Thefrequenciesofsuchwaveformsmaybeadjustedfromafractionofahertztoseveralhundredkilohertz.

Actually, the functiongeneratorsareveryversatile instrumentsas theyarecapableofproducingawidevarietyofwaveformsand frequencies. In fact, eachof thewaveformstheygenerate are particularly suitable for a different groupof applications.Theuses ofsinusoidal outputs and square-wave outputs have already been described in the earlierSections. The triangular-wave and sawtooth wave outputs of function generators arecommonlyusedforthoseapplicationswhichneedasignalthatincreases(orreduces)ataspecific linear rate.Theyarealsoused indrivingsweeposcillators inoscilloscopesandtheX-axisofX-Yrecorders.

Many function generators are also capable of generating two different waveformssimultaneously (fromdifferentoutput terminals,ofcourse).Thiscanbeauseful featurewhen two generated signals are required for a particular application. For instance, byprovidinga squarewave for linearitymeasurements in anaudio-system, a simultaneoussawtooth output may be used to drive the horizontal deflection amplifier of anoscilloscope,providingavisualdisplayofthemeasurementresult.Foranotherexample,atriangularwaveandasinewaveofequalfrequenciescanbeproducedsimultaneously.Ifthezerocrossingsofboththewavesaremadetooccuratthesametime,alinearlyvaryingwaveformisavailablewhichcanbestartedatthepointofzerophaseofasinewave.

Another important feature of some function generators is their capability of phaselockingtoanexternalsignalsource.Onefunctiongeneratormaybeusedtophaselockasecond function generator, and the two output signals can be displaced in phase by anadjustableamount.Inaddition,onefunctiongeneratormaybephaselockedtoaharmonicof the sine wave of another function generator. By adjustment of the phase and theamplitudeoftheharmonics,almostanywaveformmaybeproducedbythesummationofthe fundamental frequency generated by one function generator and the harmonicsgeneratedbytheotherfunctiongenerator.Thefunctiongeneratorcanalsobephaselockedto an accurate frequency standard, and all its output waveforms will have the samefrequency,stabilityandaccuracyasthestandard.

TheblockdiagramofafunctiongeneratorisgiveninFigure13.29.Inthisinstrument,thefrequencyiscontrolledbyvaryingthemagnitudeofcurrentthatdrivestheintegrator.Thisinstrumentprovidesdifferenttypesofwaveforms(suchassinusoidal,triangularandsquarewaves)asitsoutputsignalwithafrequencyrangeof0.01Hzto100kHz.

The frequency-controlled voltage regulates two current supply sources. The currentsupply source 1 supplies constant current to the integrator whose output voltage riseslinearlywithtime.Anincreaseordecreaseinthecurrentincreasesorreducestheslopeoftheoutputvoltageandthus,controlsthefrequency.

Figure13.29Functiongeneratorblockdiagram

Thevoltagecomparatormultivibratorchangesstateatapredeterminedmaximumlevel,of theintegratoroutputvoltage.Thischangecutsoff thecurrentsupplyfromthesupplysource 1 and switches to the supply source 2. The current supply source 2 supplies areverse current to the integrator so that its output drops linearly with time. When theoutput attains a predetermined level, the voltage comparator again changes state andswitchesontothecurrentsupplysource.Theoutputoftheintegratorisatriangularwavewhosefrequencydependsonthecurrentsuppliedbytheconstant-currentsupplysources.Thecomparatoroutputprovidesasquarewaveofthesamefrequencyastheoutput.Theresistancediodenetworkchangestheslopeofthetriangularwaveasitsamplitudechangesandproducesasinusoidalwavewithlessthan1%distortion.

Voltage-controlledOscillator

Figure13.30blockdiagramofvoltage-controlledoscillator

Inmost cases, the frequency of an oscillator is determined by the time constantRC.However, in cases or applications such as FM, tone generators, and Frequency-ShiftKeying(FSK),thefrequencyistobecontrolledbymeansofaninputvoltage,calledthecontrolvoltage.ThiscanbeachievedinaVoltage-ControlledOscillator(VCO).AVCOisacircuitthatprovidesanoscillatingoutputsignal(typicallyofsquarewaveortriangularwaveform)whosefrequencycanbeadjustedoverarangebyadcvoltage.AnexampleofaVCO is the566 ICunit as shown inFigure13.30which provides simultaneously thesquare-waveandtriangular-waveoutputsasafunctionofinputvoltage.ThefrequencyofoscillationissetbyanexternalresistorR1andacapacitorC1andthevoltageVcappliedto

thecontrolterminals.Figure13.20showsthatthe566ICunitcontainscurrentsourcestochargeanddischargeanexternalcapacitorCvataratesetbyanexternalresistorR1andthe modulating dc input voltage. A Schmitt trigger circuit is employed to switch thecurrentsourcesbetweencharginganddischargingthecapacitor,andthetriangularvoltageproducedacross thecapacitorandsquarewavefromtheSchmitt triggerareprovidedasoutputs through buffer amplifiers. Both the output waveforms are buffered so that theoutputimpedanceofeachis50 f2.Thetypicalmagnitudeofthetriangularwaveandthesquarewaveare2.4Vpeak.to-peakand5.4Vpeak.to.peak.Thefrequencyoftheoutputwaveformsisapproximatedby

fout=2(V+−Vc)/R1C1V+

13.14 RFSIGNALGENERATOR

AnRFoscillatorisemployedforgeneratingacarrierwaveformwhosefrequencycanbeadjustedtypicallyfromabout100kHzto30MHz.Carrierwavefrequencycanbevariedandindicatedwiththehelpofarangeselectorswitchandavernierdialsetting.Rangeisselectedbyemployingfrequencydividers.Frequencystabilityoftheoscillatoriskeptveryhighatallfrequencyranges.

•Thefollowingmeasuresaretakeninordertoachievestablefrequencyoutput.

• Frequency of output voltage changes with the change in supply voltage soregulatedpowersupplyisused.

• Bufferamplifiersareused to isolate theoscillatorcircuit fromoutputcircuit sothatanychangeinthecircuitconnectedtotheoutputdoesnotaffectthefrequencyandamplitudeoftheoscillatoroutput.

• Temperature also causes change in oscillator frequency, so temperature-compensatingdevicesareused.

• Q-factorof theLC circuit should be very high, say above20,000.This canbeachievedbyemployingquartzcrystaloscillatorinplaceoftheLCoscillator.

• An audio-frequency modulating signal is generated in another very stableoscillator, called themodulation oscillator. Provision ismade in themodulationoscillator for changing the frequency and the amplitude of the signal beinggenerated.

Inthisoscillator,provisionisalsomadetogetvarioustypesofwaveformssuchasthesquare, triangular waves or pulses. The radio-frequency and the modulation-frequencysignals are fed to a wide-band amplifier, called the output amplifier. Percentage ofmodulation(canalsobeadjustedanditisindicatedbythemeter.

Modulation level can be adjusted up to 95% by a control device. The output of theamplifier is then fed to an attenuator and finally the signal goes to theoutput of signalgenerator.Theoutputmeterisprovidedtoreadthefinaloutputsignal.

The accuracy to which the frequency of the RF oscillator is known is an importantspecificationofthesignalgeneratorperformance.Mostlaboratory-typemodelsareusuallycalibratedtobewithin0.5−1.0%ofthedialsetting.Thisaccuracyisusuallysufficientfor most measurements. For greater accuracy, if needed, a crystal oscillator, whosefrequency is known to be within 0.01% or better, may be used as an internal RFcalibrationsource.

Another key specification of signal generators is their amplitude stability. It is veryimportantthattheamplitudeoftheoutputsignalremainsconstantastheRFfrequencyisvaried.

13.15 SWEEPFREQUENCYGENERATOR

A sweep frequency generator is a special type of signal generator which generates asinusoidaloutputwhosefrequencyisautomaticallyvariedorsweptbetweentwoselectedfrequencies.Onecompletecycleofthefrequencyvariationiscalledasweep.Therateatwhich the frequency is varied can be either linear or logarithmic, depending upon thedesignofaparticularinstrument.However,theamplitudeofthesignaloutputisdesignedtoremainconstantovertheentirefrequencyrangeofthesweep.

Sweep-frequencygeneratorsareprimarilyemployed formeasurementof responsesofamplifiers,filters,andelectricalcomponentsovervariousfrequencybands.Thefrequencyrange of a sweep-frequency generator usually extends over three bands: 0.001Hz−100kHz (low frequency to audio), 100 kHz−1,500 MHz (RF range), and 1 − 200 GHz(microwave range). Performance of measurement of bandwidth over a wide frequencyrangewithamanuallytunedoscillatorisatime-consumingtask.Withtheuseofasweep-frequencygenerator,a sinusoidal signal that isautomaticallysweptbetween twochosenfrequenciescanbeappliedtothecircuitundertestanditsresponseagainstfrequencycanbedisplayedonanoscilloscopeorX-Yrecorder.

Thus,themeasurementtimeandeffortisconsiderablyreduced.SweepgeneratorsmayalsobeemployedforcheckingandrepairingamplifiersusedinTVandradarreceivers.

Theblockdiagramof an electronically tuned sweep frequencygenerator is shown inFigure13.31

As shown inFigure13.31, themain component of a sweep-frequency generator is amasteroscillator,usuallyanRFtype,withseveraloperatingrangeswhichareselectedbyarangeswitch.Thefrequencyoftheoutputsignalofthesignalgeneratormaybevariedeithermechanicallyorelectronically.

In themechanically variedmodels, the frequency of the output signal of themasteroscillatorisvaried(tuned)byamotor-drivencapacitor.

Intheelectronicallytunedmodels, thefrequencyofthemasteroscillatoriskeptfixedand a varying frequency signal is produced in another oscillator, called the VoltageControlledOscillator (VCO).TheVCOcontainsanelementwhosecapacitancedependsuponthevoltageappliedacrossit.Thiselementisemployedforvaryingthefrequencyof

the sinusoidal output of the VCO. The output of the VCO is then combined with theoutputofthemasteroscillatorinaspecialelectronicdevice,calledthemixer.Theoutputof themixer is sinusoidal,whose frequencydependson thedifferenceof frequenciesoftheoutputsignalsofthemasteroscillatorandVCO.Forexample,ifthemasteroscillatorfrequencyisfixedat10.00MHzandthevariablefrequencyisvariedbetween10.01MHzto35MHz,themixerwillgivesinusoidaloutputwhosefrequencyissweptfrom10kHzto25MHz.

Figure13.31Electronicallytunedsweepgenerator

The sweep rates of sweep frequency generators can be adjusted to vary from 100 to0.01secondspersweep.AvoltagevaryinglinearlyorlogarithmicallyaccordingtosweepratecanbeusedfordrivingtheX-axisofanoscilloscopeorX-Yrecordersynchronously.In the electronically tuned sweep generators, the same voltage which drives the VCOservesasthisvoltage.

Thefrequencyofvariouspointsalongthefrequency-responsecurvecanbeinterpolatedfrom thevaluesof theend frequencies if it isknownhowdoes the frequencyvary (i.e.linearlyorlogarithmically).

A basic system for the sweep generator is shown in Figure 13.32. A low-frequencysawtooth wave is generated from some form of oscillator or waveform generator. TheinstantaneousvoltageofthesawtoothwavecontrolsthefrequencyofanRFoscillatorwithitscentrefrequencysetatthecentrefrequencyofthedeviceundertest(filterorIFchanneletc).Overasinglesweepoffrequency,RFoutputvoltagefromthedevice,asafunctionoftime, is a plot of the filter response. By rectifying and RF filtering in a simple AMdetector, the output is converted to a dc voltage varying as a function of time and thisvoltage is applied to the vertical input of theCRO.By synchronising the sweep of theCROwiththesawtoothoutput,thedeviceresponseisplottedontheCROscreen.

Figure13.32Basicsweep-generatorarrangement

Toachievethisforarangeoffrequencies,itiseasiesttosweepasinglefrequency(say1 MHz) and heterodyne this to the test frequency required. The system developed isshownintheblockdiagramofFigure13.32.A1MHzoscillatorisfrequencymodulatedby theoutputofasawtoothgeneratoroperatingat33Hz.Themodulatedoutput isbeatwithanexternal signalgenerator set toprovide thedifference frequencycentreedat thecentrefrequencyofthefilterorIFcircuitundertest.TheoutputofcircuitundertestisfedtoasimpleAMdetectorwhichprovidesvaryingdcoutputleveltofeedtheCROverticalinput.BysynchronisingtheCROsweepcircuittothe33Hzsweepgenerator,aplotoftestcircuitresponseisdisplayedintermsofamplitudeversusfrequency.

Figure13.33Theheterodynesweepgeneratorsystem—sweepfrequencywidthisindependentofoutputfrequency

TheHeterodyneSweepGeneratorCircuitdetailoftheheterodynesweepgeneratorisshowninFigure13.34.Theoperationisdescribedasfollows:

TheXR205sawtoothgeneratorNIdrivesavoltage-controlledoscillatorN2operatingatafixedcentrefrequencyof1MHz.ThisisaverystableICpackagetypeXR2209whichcanoperateat1MHzwithitsfrequencysetbyexternalRandCcomponents.ItsoutputatPin8isatriangularwaveformandthisisshapedtoasinewavebyLPfilterL1,C10,L2andC11.Thesweep-frequencyspaniscontrolledbytheamplitudeofthesawtoothwaveandthisissetbythepotentiometerR8.

The1MHzsweepoutput ismixedwithanexternalvariable signal source (suchasastandardsignalgenerator)inadoublebalancedmixerN3.Thisbalancesoutthetwoinputsignalsanddeliverstwofrequencieswhicharethesumanddifferenceoftheinputsignalfrequencies.Thewell-knownMC1496isusedforthisfunctionandprovidesahighoutputlevel of mixed signals up to around 20 MHz with output falling off as 25 MHz isapproached.Itslow-frequencyperformanceislimitedtoaround100kHzbytheprimaryinductanceofcouplingtransformerTI,woundonasmallferritetoroidalcore.Outputlevelis set by the potentiometer R24 coupled via emitter follower stage V1 to provide lowoutput impedance. For satisfactory operation, the signal level from the external signalsourceneedstobearound0.1to0.5VPP.

To set up for a givenoutput frequency, it is onlynecessary to set the external signalgenerator to a frequency 1 MHz removed from the required frequency. No tuning isrequired in the sweep generator itself. Of course, there is always a second imagefrequencycomponentat theoutput,butasthefilterorIFchannelbeingtestedis itselfa

selectiveband-limitingdevice,theimagecomponentisrejectedfromreachingthedetectorcircuit.

Figure13.34Heterodynesweepgenerator(100kHzto25MHz)showingsawtoothgenerator,voltagecontrolledoscillatorandmixercircuits

From an operational point of view, the precise centre frequency of the fixed internalsweeposcillator is not important.However, by setting it right at 1MHz, the frequencyrequiredfromtheexternaloscillatorbecomesobviouswithoutputtingpencil topaperorreferringtothecalculator.Theprecisefrequencyoftheoscillatorcanbesetto1MHzbytrimming the value of C7. The XR2209 is a very stable oscillator provided its supplyvoltageisheldconstant.Hence,the12Vsupplytothesweepgeneratormustberegulated.

TheMC1496(N3)usedwastheTO5packageandthepinnumbersshownareforthatpackage.Thepinnumbers for theDILpackagewouldbedifferent.PackagesN1andN2arebothDILtypes.

13.16 WAVEANALYSER

It is well known that any periodic waveform can be represented as a sum of a dccomponent and a series of sinusoidal harmonics. Analysis of a waveform consists ofdeterminationof thevalues of amplitudes, frequency and sometimesphase angle of theharmoniccomponents.Graphicalandmathematicalmethodsmaybeusedforthepurposebutmethods are quite laborised. The analysis of a complexwaveform can be done byelectrical means using a bandpass filter network to single out the various harmoniccomponents.Networksofthesetypespassanarrowbandoffrequencyandprovideahighdegreeofassumptionstoallotherfrequencies.

Awave analyser, in fact, is an instrument designed tomeasure relative amplitude ofsinglefrequencycomponentsinacomplexwaveform.Basically,theinstrumentactsasa

frequency selective voltmeter which is turned to the frequency of one signal whilerejecting all other signal components.The desired frequency is selected by a frequencycalibrateddialtothepointofmaximumamplitude.TheamplitudeisindicatedeitherbyasuitablevoltmeteroraCRO.

There are two types of wave analyser, depending upon frequency ranges used: (i)frequencyselectivewaveanalyserand(ii)heterodynewaveanalyser.

13.16.1FrequencySelectiveWaveAnalyserThis wave analyser is employed in audio-frequency-range (20 Hz to 20 kHz)measurement.Itconsistsofanarrowbandpassfilterwhichcanbetunedtothefrequencyofinterest.TheblockdiagramofthisanalyserisshowninFigure13.35.Thewaveformtobeanalysedintermsofitsseparatefrequencycomponentsisappliedtoaninputattenuatorthat is set by the meter range switch on the front panel. A driver amplifier feeds theattenuated waveform to a high-Q active filter. The filter consists of a cascadedarrangementofRCresonantsectionsandfilteramplifiers.ThepassbandofthewholefiltersectioniscoveredindecadestepsovertheentireaudiorangebyswitchcapacitorsintheRC sections.Close-tolerance polystyrene capacitors are generally used for selecting thefrequency ranges. Precision potentiometers are used to tune the filter to any desiredfrequencywithin the selection passband.The final amplifier stage supplies the selectedsignaltothemetercircuitandtoanunturnedbufferamplifier.Thebufferamplifiercanbeusedtodrivearecorderoranelectroniccounter.Themeterisdrivenbyanaveragetypedetectorandusuallyhasseveralvoltagerangesaswellasadecibelscale.Thebandwidthisverynarrow,typicallyabout1%oftheselectedfrequency.Figure13.36showsatypicalattenuationcurveofawaveanalyser.

13.16.2HeterodyneWaveAnalyserThis wave analyser is used to measure the frequency in megahertz range. The blockdiagramofthiswaveanalyserisshowninFigure13.37.Thesignalasinputisfedthroughan attenuator and amplifier before being mixed with a local oscillator signal. Thefrequencyof this oscillator is adjusted to give a fixed frequencyoutputwhich is in thepass bandof the amplifier. In thenext stage, this signal ismixedwith a second crystaloscillator, whose frequency is such that the output from themixer is centreed on zerofrequency. The subsequent active filter has a controllable bandwidth, and passes theselectedcomponentofthefrequencytotheindicatingmeter.Goodfrequencystabilityinawaveanalyserisachievedbyusingfrequencysynthesisers,whichhavehighaccuracyandresolution,orbyautomaticfrequencycontrol.Inanautomaticfrequencycontrolsystem,thelocaloscillatorlockstothesignal,andsoeliminatesthedriftbetweenthem.

Figure13.35Blockdiagramofafrequencyselectivewaveanalyser

Figure13.36Attenuationofawaveanalyser

Figure13.37Blockdiagramofaheterodynewaveanalyser

13.16.3ApplicationsofWaveAnalysers

Waveanalysershaveveryimportantapplicationsinthefieldofi)electricalmeasurements,ii)soundmeasurements,andiii)vibrationmeasurements.

Wave analysers are used industrially to detect and reduce the sound and vibrationgeneratedbyrotatingelectricalmachinesandequipment.Agoodspectrumanalysiswithawaveanalysershowsvariousdiscretefrequenciesandresonancesthatcanberelatedtothemotionofmachines.

13.17 HARMONICDISTORTIONANALYSERS

Generally, the output waveform of an electronic device, such as an amplifier, shouldbecomeanexactreplicaoftheinputwaveform.However,inmostofthecasesthatdoesnothappendue to the introductionofvarious typesofdistortions.Distortionsmaybearesult of the inherent non-linear characteristics of components used in the electroniccircuit. Non-linear behaviour of circuit elements introduces harmonics in the outputwaveformandtheresultantdistortionisoftentermedHarmonicDistortion(HD).

TypesofDistortionThevarioustypesofdistortionswhichoccurareexplainedbelow.

1.FrequencyDistortionThis distortion occurs due to the amplification factor of the amplifier is different fordifferentfrequencies.

2.Phasedistortion

Thisdistortionoccursduetothepresenceofenergy-storageelementsinthesystem,whichcause the output signal to be displaced in phasewith the input signal. If signals of allfrequencies are displaced by the same amount, the phase shift distortion would not beobserved.However,inactualpractice,signalsatdifferentfrequenciesareshiftedinphasebydifferentanglesandtherefore,thephase-shiftdistortionbecomesnoticeable.

3.AmplitudeDistortionHarmonicdistortionoccursdue to thefact that theamplifiergeneratesharmonicsof thefundamentalof the inputsignal.Harmonicsalwaysgive rise toamplitudedistortion, forexample,whenanamplifierisoverdrivenandclipstheinputsignals.

4.Inter-modulationDistortionThis type of distortion occurs as a consequence of interaction or heterodyning of twofrequencies, giving an output which is the sum or difference of the two originalfrequencies.

5.Cross-overDistortionThistypeofdistortionoccursinpush-pullamplifierduetoincorrectbiaslevels.

6.TotalHarmonicDistortionAnon-linearsystemproducesharmonicsofaninputsinewave,theharmonicsconsistsof

asinewavewithfrequencieswhicharemultiplesofthefundamentaloftheinputsignal.TheTotalHarmonicDistortion(THD)ismeasured in termsof theharmoniccontentsofthewave,asgivenby

In a measurement system, noise is read in addition to harmonics, and the totalwaveform, consisting of harmonics, noise and fundamental, is measured instead of thefundamental alone. Therefore, the measured value of the total harmonic distortion(THDM)isgivenby

Figure13.38showstheblockdiagramofaharmonicdistortionanalyserwhichisusedtomeasureTHD.The signal sourcehasvery lowdistortionand this canbecheckedbyreadingitsoutputdistortionbyconnectingdirectlyintotheanalyser.Thesignalfromthesource is fed into the amplifier under test. This generates harmonics and the originalfundamental frequency.The fundamental frequency is removed by a notch filter. In themanualsystem,asshowninFigure13.38(a),theswitchSisfirstplacedintheposition1andthetotalcontentoffundamentalandharmonics(ET)ismeasured.Thentheswitchismovedtotheposition2tomeasurejusttheharmonicsEH.thevalueofTHDisthenfoundusingfollowingequation:

Figure13.38Simplifiedblockdiagramsoffundamentalsuppressionharmonicdistortionanalysers:(a)Manualreading(b)Ratioreading

Themeter canbecalibratedbyputting the switch in theposition1andadjusting the

reading for full scale deflection.With the switch position 2, the meter reading is nowproportionaltoTHD.Figure13.28(b)showsanalternativearrangement,wherethevalueofETandEHarereadsimultaneouslyandtheirratiocalculatedanddisplayedasTHDonthe indicator.Forgoodaccuracy, thenotch filtermusthaveexcellent rejectionandhighpass characteristics. It should attenuate the fundamental by 100 db or more and theharmonics by less than 1 db. The filter also needs to be tuned accurately to thefundamentalofthesignalsource.Thisisdifficulttoachievemanuallyandmostdistortionanalysers do this automatically.A common form of notch filter is aWien bridge. Thisbalancesatonefrequencyonlyandatthisfrequency,theoutputvoltageatthebridgenulldetectorisminimum.

13.18 SPECTRUMANALYSER

Aspectrumanalyserisawideband,verysensitivereceiver.Itworksontheprincipleof“superheterodynereceiver”toconverthigherfrequencies(normallyranginguptoseveral10sofGHz)tomeasurablequantities.Thereceivedfrequencyspectrumisslowlysweptthrough a range of pre-selected frequencies, converting the selected frequency to ameasurabledc level (usually logarithmicscale),anddisplaying thesameonaCRT.TheCRTdisplaysreceivedsignalstrength(y-axis)againstfrequency(x-axis).

Figure13.39Simplifiedblockdiagramofasuper-heterodynereceiver

AsseenfromFigure13.39,itconsistsofthefollowingparts:1.Front-endmixer

2.Voltagecontrolledoscillator

3.Sawtoothgenerator

4.IFamplifier

5.Detector

6.Videoamplifier

7.CathodeRayTube(CRT)

Thefront-endmixeriswheretheRFinputiscombinedwiththelocaloscillator(VCO)frequencytogiveIF(IntermediateFrequency)output.TheIFfrequenciesarethenfedtoanIFamplifier,thentoadetector.Theoutputofthedetectorisfedtothevideoamplifier.TheoutputfromthevideoamplifierisgiventoCRT(verticalaxis),andtheoutputofthesawtooth generator is given to the horizontal axis of theCRT. Thus,we see the signal

amplitudeagainstthetimesweep(whichinturnrepresentsthefrequency).

Normally,thefrequencyconversiontakesplaceinmultiplestages,andband-passfiltersareusedtoshapethesignals.Also,precisionamplifiersanddetectorsareusedtoamplifyanddetectthesignals.

Obviously,signalsthatareweakerthanthebackgroundnoisecouldnotbemeasuredbyaspectrumanalyser.Forthisreason,thenoisefloorofaspectrumanalyserincombinationwithRBWisavitalparametertobeconsideredwhenchoosingaspectrumanalyser.Thereceived signal strength is normally measured in decibels (dbm). (Note that 0 dBmcorresponds to 1 mWatt of power on a logarithmic scale). The primary reasons formeasuring the power (in dBm) rather than voltage in spectrum analysers are the lowreceivedsignalstrength,andthefrequencyrangeofmeasurement.Spectrumanalysersarecapableofmeasuringthefrequencyresponseofadeviceatpowerlevelsaslowas−120dBm. These power levels are encountered frequently in microwave receivers, andspectrum analysers are capable of measuring the device characteristics at those powerlevels.

13.18.1SpectrumAnalyserVsOscilloscope1.Aspectrumanalyserdisplaysreceivedsignalstrength(y-axis)againstfrequency(x-

axis).Anoscilloscopedisplaysreceivedsignalstrength(y-axis)againsttime(x-axis).

2. A Spectrum analyser is useful for analysing the amplitude response of a deviceagainst frequency. The amplitude is normally measured in dBm in spectrumanalysers,whereasthesameismeasuredinvoltswhenusingoscilloscopes.

3.Normally,anoscilloscopecannotmeasureverylowvoltagelevels(say,−100dBm)and are intended for low-frequency, high-amplitude measurements. A spectrumanalyser caneasilymeasurevery lowamplitudes (as lowas−120dBm), andhighfrequencies(ashighas150GHz).

4. The spectrum analyser measurements are in frequency domain, whereas theoscilloscopemeasurementsareintimedomain.

5.Also,aspectrumanalyserusescomplexcircuitrycomparedwithanoscilloscope.Asaresultofthis,thecostofaspectrumanalyserisusuallyquitehigh.

A signal is usually defined by a time-varying function carrying some sort ofinformation.Sucha functionmostoften representsa time-changingelectricormagneticfield, whose propagation can be in free space or in dielectric materials constrained byconductors(waveguides,coaxialcables,etc.).Asignalissaidtobeperiodicif itrepeatsitselfexactlyafteragiventimeTcalledtheperiod.TheinverseoftheperiodT,measuredinseconds,isthefrequencyfmeasuredinhertz(Hz).

A periodic signal can always be represented in terms of a sum of several (possiblyinfinite)sinusoidalsignals,withsuitableamplitudeandphase,andhavingfrequenciesthatareintegermultiplesofthesignalfrequency.Assuminganelectricsignal,thesquareoftheamplitudesofsuchsinusoidalsignalsrepresentsthepowerineachsinusoid,andissaidtobe thepower spectrumof the signal.Theseconcepts canbegeneralised toanaperiodicsignal; in this case, its representation (spectrum) will include a continuous interval of

frequencies, instead of a discrete distribution of integer multiples of the fundamentalfrequency.Therepresentationofasignal in termsof its sinusoidalcomponents iscalledFourier

analysis.The(complex)functiondescribingthedistributionofamplitudesandphasesofthe sinusoids composing a signal is called its Fourier Transform (FT). The Fourieranalysiscanbereadilygeneralisedtofunctionsoftwoormorevariables;forinstance,theFT of a function of two (spatial) variables is the starting point of many techniques ofimage processing. A time-dependent electrical signal can be analysed directly as afunctionoftimewithanoscilloscopewhichissaidtooperateinthetimedomain.Thetimeevolutionofthesignalisthendisplayedandevaluatedontheverticalandhorizontalscalesofthescreen.

Thespectrumanalyserissaidtooperateinthefrequencydomainbecauseitallowsonetomeasure the harmonic content of an electric signal, that is, the power of each of itsspectral components. In this case, the vertical and horizontal scales read powers andfrequencies. The two domains are mathematically well defined and, through the FTalgorithm,itisnottoodifficulttoswitchfromoneresponsetotheother.

Theirgraphical,easilyperceivablerepresentationisshowninFigure13.40,where thetworesponsesareshownlyingonorthogonalplanes.ItistrivialtosaythattheeasiestwaytomakeaFourieranalysisofatime-dependentsignalistohaveitdisplayedonaspectrumanalyser. Many physical processes produce (electric) signals whose nature is notdeterministic,butratherstochastic,orrandom(noise).SuchsignalscanalsobeanalysedintermsofFT,althoughinastatisticalsenseonly.Atimesignalissaidtobeband-limitedifitsFTisnonzeroonlyinafiniteintervaloffrequencies,say(Fmax−Fmin)=B.Usually,this is the case and an average frequencyF0 can be defined.Although the definition issomewhatarbitrary,a(band-limited)signalisreferredtoasRF(radiofrequency)ifF0isintherange100kHzto1GHzandasamicrowavesignalintherange1to1000GHz.Thedistinctionisnotfundamentaltheoretically,butithasverystrongpracticalimplicationsininstrumentationandspectralmeasuringtechniques.Aband-limitedsignalcanbedescribedfurtherasnarrowband,ifB/F0<=1,orwidebandotherwise.

Figure13.40Howthesamesignalcanbedisplayed

Thefirststepinperformingaspectralanalysisofanarrow-bandsignalisgenerallytheso-called heterodyne down-conversion: it consists in themixing (beating) of the signalwithapuresinusoidalsignaloffrequencyFL,calledLocalOscillator(LO).Inprinciple,

mixingtwosignalsoffrequencyF0andFLinanynonlineardevicewillresultinasignaloutputcontainingtheoriginalfrequenciesaswellasthedifference(F0−FL)andthesum(F0+FL)frequencies,andalltheirharmonic(multiple)frequencies.Inthepracticalcase,apurelyquadraticmixerisused,withanLOfrequencyFL<F0; theoutputwill includethe frequencies (F0 − FL), 2FL, 2F0, and (F0 + FL), and the first term (called theintermediatefrequencyorIF)willbeeasilyseparatedfromtheothers,whichhaveamuchhigher frequency. The bandwidth of the IF signal will be the same as the originalbandwidthB;however,topreservetheoriginalinformationfullyintheIFsignal,stringentlimitsmustbe imposedon theLO signal, because anydeviation fromapure sinusoidallawwill show up in the IF signal as added phase and amplitude noise, corrupting theoriginal spectral content. The process of down converting a (band-limited) signal isgenerallynecessarytoperformspectralanalysis inthevery-high-frequency(microwave)region, toconvert thesignal toa frequencyrangemoreeasilyhandled technically.Whenthe heterodyne process is applied to a wideband signal (or whenever FL > Fmin),“negative”frequencieswillappearintheIFsignal.Thisprocessiscalleddoublesidebandmixing,becauseagivenIFbandwidthB(i.e.,(FL+B/2)willincludetwoseparatebandsoftheoriginalsignal,centreedatFL+IF(“upper”sideband)andFL− IF(“lower”side-band).Thisformofmixingisobviouslyundesirableinspectrumanalysis,andinputfiltersaregenerallynecessarytosplitawide-bandsignalinseveralnarrow-bandsignalsbeforedownconversion.Alternatively,specialmixerscanbeusedthatcandelivertheupperandlowersidebands toseparate IFchannels.Aband-limitedsignal in thefrequency interval(Fmax−Fmin)=BissaidtobeconvertedtobasebandwhentheLOisplacedatFL=Fmin,sothatthebandisconvertedtotheinterval(B−0).Nofurtherloweringoffrequencyisthenpossible,unlessthesignalissplitintoseparatefrequencybandsbymeansoffilters.After down conversion, the techniques employed to perform power-spectrum analysisvary considerably depending on the frequencies involved. At lower frequencies, it ispossible to employ analog-to-digital converters (ADC) to get a discrete numericalrepresentation of the analog signal, and the spectral analysis is then performednumerically, either by direct computation of the FT (generally via the fast Fouriertransform,FFT,algorithm)orbycomputationofthesignalautocorrelationfunction,whichis directly related to the square modulus of the FT via the Wiener-Khinchin theorem.ConsideringthattheADCmustsamplethesignalatleastattheNyquistrate(i.e.attwicethehighestfrequencypresent)andwithadequatedigitalresolution,thisprocessisfeasibleand practical only for frequencies (bandwidths) less than a few megahertz. Also, thepossibility of a real-time analysis with high spectral resolution may be limited by theavailability of very fast digital electronics and special-purpose computers. The digitalapproachistheonlyonethatcanprovideextremelyhighspectralresolution,uptoseveralhundredthousandchannels.Forhighfrequencies,severalanalogtechniquesareemployed.

13.18.2APracticalApproachtoSpectrumAnalysisSpectrumanalysisisnormallydoneinordertoverifytheharmoniccontentofoscillators,transmitters, frequency multipliers, etc. or the spurious components of amplifiers andmixers. Other specialised applications are possible, such as the monitoring of RadioFrequency Interference (RFI), Electromagnetic Interference (EMI), andElectromagneticCompatibility(EMC).Theseapplications,asarule,requireanantennaconnectionanda

low-noise, external amplifier. Which are then the specifications to look for in a goodspectrumanalyser?Wewouldsuggestthefollowing:1.Itshoulddisplayselectable,verywidebandsoftheEMradiospectrumwithpower

andfrequencyreadablewithgoodaccuracy.

2.Itsselectivityshouldrange,indiscretesteps,fromafewhertztomegahertzsothatsidebandsofaselectedsignalcanbespottedandshownwiththenecessarydetails.

3.Itshouldpossessaverywidedynamicrange,sothatsignalsdifferinginamplitudesixtoeightordersofmagnitudecanbeobservedatthesametimeonthedisplay.

4. Its sensitivitymust be compatiblewith themeasurements to be taken.As alreadymentioned, specialised applications may require external wide-band, low-noiseamplifiersandanantennaconnection.

5.Stabilityandreliabilityaremajorrequestsbuttheyaremetmostofthetime.

Occasionally,abattery-operatedoptionforportablefieldapplicationsmaybenecessary.AblockdiagramofacommercialspectrumanalyserisshowninFigure13.41.

ReferringtoFigure13.41,wecansaythatweareconfrontedwitharadio-receiver-likesuperhetwithawide-bandinputcircuit.Thehorizontalscaleoftheinstrumentisdrivenbyarampgeneratorwhichisalsoappliedtothevoltage-controlledLO[2].

A problem arises when dealing with a broadband mixing configuration like the oneshownabove,namely,avoidingreceivingtheimageband.

The problem is successfully tackled here by upconverting the input band to a high-valued IF.Aneasilydesigned input low-pass filter, not shown in theblockdiagram forsimplicity,willnowprovidethenecessaryrejectionoftheunwantedimageband.

Figure13.41Blockdiagramofacommercialspectrumanalyser

Nowadays,withtheintroductionofYIGbandpassfilterpreselectors,tunableoververywideinputbands,upconversionisnotalwaysnecessary.Tracesofunwantedsignalsmay,however,showuponthedisplayalthoughatverylowlevel(lessthan−80dBc)ongoodanalysers.

A block diagram of a commercial spectrum analyser exploiting both the mentionedprinciples is shown in Figure 13.41. This instrument includes a very important featurewhich greatly improves its performance: theLO frequency is no longer coming from afree-runningsourcebutratherfromasynthesisedunit referenced toaverystablequartzoscillator.TheimprovedqualityoftheLO,bothintermsofitsownnoiseandfrequency

stability,optimisesseveralspecificationsoftheinstrument,suchasfrequency-determiningaccuracy,finerresolutionondisplay,andreducednoiseingeneral.

Further,astableLO generates stableharmonicswhichcan thenbeused towiden theinput-selected bands up to themillimetre region.As already stated, this option requiresexternaldevices,e.g.amixer.Thepowerreferenceonthescreenisthetophorizontallineofthereticle.Duetotheverywidedynamicrangeforeseen,theuseofalogscale(e.g.,10dB/square)seemsappropriate.Conventionally,1mWistakenasthezeroreferencelevel:accordingly, dBm is used throughout. The noise power level present on the displaywithoutaninputsignalconnected(noisefloor)isduetotheinputrandomnoisemultipliedbytheIFamplifiergain.Suchanoiseisalwayspresentandvarieswithinputfrequency,IFselectivity,andanalyser sensitivity (in termsofnoise figure13.13.).The“on-displaydynamicrange”oftheanalyseristhedifferencebetweenthemaximumcompression-freeleveloftheinputsignalandthenoisefloor.Asaguideline,thedynamicrangeofagoodinstrumentcouldbeoftheorderof70to90dB.

An input attenuator, always available on the front panel, allows one to apply morepower to the analyser while avoiding saturation and nonlinear readings. The onlydrawback is the obvious sensitivity loss.One should not expect a spectrum analyser togiveabsolutepower-levelreadingstobebetterthanacoupleofdB.

Fortheaccuratemeasurementofpowerlevels,thesuggestionistouseapowermeter.An erratic signal pattern on display and a fancy level indicationmay be caused by thewrongsettingofthe“scantime”knob.Itmustberealisedthathigh-resolutionobservationofawideinputbandrequiresproperscanningtime.Anincorrectparametersettingyieldswrong readings but usually an optical alarm is automatically switched on to warn theoperator.

13.18.3SpectrumAnalyserApplications1.DeviceFrequencyResponseMeasurementsYoucanusespectrumanalysersformeasuringtheamplituderesponse(typicallymeasuredindbm)againstfrequencyofthedevice.Thedevicemaybeanythingfromabroadbandamplifiertoanarrowbandfilter.

2.MicrowareTowerMonitoringYou can measure the transmitted power and received power of a microware tower.Typically, you use a directional coupler to tap the power without interrupting thecommunications.Inthisway,youcanverifythatthefrequencyandsignalstrengthofyourtransmitterareaccordingtothespecifiedvalues.

3.InterferenceMeasurementsAnylargeRFinstallationsnormallyrequiresitesurvey.Aspectrumanalysercanbeusedto verify and identify interferences.Any such interfering signals need to beminimisedbefore going ahead with the site work. Interference can be created by a number ofdifferent sources, such as telecom microwave towers, TV stations, airport guidancesystems,etc.

Other measurements that could be made using a spectrum analyser include the

following:•Return-lossmeasurement

•Satelliteantennaalignment

•Spurioussignalsmeasurement

•Harmonicmeasurements

•Inter-modulationmeasurements

Givenbelowaresomeimportantfeaturesavailablewithfewportablespectrumanalyserof9kHzto26.5GHz:

•Colourdisplay

•Continuous30Hzto26.5GHzsweep

•Fastdigitalresolutionbandwidthsof1,3,10,30and100Hz

• Adjacent channel power, channel power, carrier power, occupied bandwidth percentage and time-gatedmeasurementsstandard

•Precisiontimebaseand1Hzcounterresolution

•Measurementpersonalitiesfordigitalradioandphasenoisemeasurements

•EasilytransferscreenimageortracedatatoPC

Note: The above specifications are given as an example only, andmay not accuratelyrepresenttheactualequipmentspecifications.

EXERCISE

Objective-typeQuestions1.Whichoneofthefollowingoscillatorsisusedforgenerationofhighfrequencies?

(a)RCphaseshift

(b)Wienbridge

(c)LCoscillator

(d)Blockingoscillator

2.Atriangularwavecanbegeneratedby

(a)integratingasquarewave

(b)differentiatingasquarewave

(c)integratingasinewave

(d)differentiatingasinewave

3.Harmonicdistortionisdueto

(a)changeinthebehaviourofcircuitelementsduetochangeintemperature

(b)changeinthebehaviourofcircuitelementsduetochangeinenvironment

(c)linearbehaviourofcircuitelements

(d)nonlinearbehaviourofcircuitelements

4.Aspectrumanalyserisacombinationof

(a)narrowbandsuper-heterodynereceiverandCRO

(b)signalgeneratorandCRO

(c)oscillatorandwaveanalyser

(d)VTVMandCRO

5.Aspectrumanalyserisusedacrossthefrequencyspectrumofagivensignaltostudythe

(a)currentdistribution

(b)voltagedistribution

(c)energydistribution

(d)powerdistribution

Short-answerQuestions1.Whatistheinitialconditionforanoscillatortostart?

2.WhataretheBarkhausenconditionsofoscillations?

3.WhyareLCresonantcircuitsimpracticalataudiofrequencies?

4.Whyisacrystaloscillatorpreferredincommunicationtransmittersandreceivers?

5.Whatisafunctiongenerator?

6.Whatisthebasicdifferencebetweenasquare-wavegeneratorandpulsegenerator?

7.WhatisaSchmitttriggercircuit?DiscusstheapplicationsofaSchmitttriggercircuit.

8.WhatisaVCO?Explainitsworkingprinciple.

Long-answerQuestions1.Classifyoscillatorsonthebasisofdesignprinciple.Howcananamplifierbeconvertedintoanoscillator?Whatis

theroleofresonanceinanoscillatorcircuit?

2.Whatisanoscillator?Howdoesitdifferfromanamplifier?Whatarethemajorpartsofanoscillatorcircuit?

3.DrawthecircuitdiagramofaHartleyoscillatorandexplainitsoperation.

4.DrawthecircuitdiagramofaColpittsoscillatorandexplainitsoperation.

5.EnumeratetheadvantagesofRCoscillators.ExplaintheworkingofanRCphaseshiftoscillator.

6.DrawandexplainthecircuitoftheWienbridgeoscillator.Derivetheexpressionforfrequencyofoscillationforsuchanoscillator.Willoscillationstakeplaceifthebridgeisbalanced?

7.Whataretherequirementsofpulse?Drawacircuitdiagramofageneratorwhichproducessuchpulses.

8. Explain theworkingof a functiongeneratorproducing sine, squareand triangularwaveforms.Draw itsblockdiagram.

9.Drawthecircuitdiagramofastablemultivibrator.Howdoesitgeneratesquarewave?

10.Describewithablockdiagramasweep-frequencygeneratoranditsapplications.

11.Discusstheworkingofawaveanalyser.

12.Withthehelpofablockdiagram,explaintheworkingofaharmonicdistortionanalyser.

13.Whatisawaveanalyser?Explaintheworkingprincipleofaheterodynewaveanalyser.

14.Distinguishtheprinciplesoftheworkingofaspectrumanalyserandawaveanalyser.Drawtheblockdiagramofaspectrumanalyser.Indicatethecommonapplicationsofaspectrumanalyser.

14.1 INTRODUCTION

Adataacquisitionsystemisadeviceoranintegratedsystemusedtocollectinformationaboutthestateorconditionofvariousparametersofanyprocess.Forexample,collectingday-to-day temperature of a particular location can be termed data acquisition. Say, apersonrecordingthelevelofmunicipalwater-storingtankintoapieceofpaper,isactuallyperforming the task of a data acquisition system. With the advancement of digitalelectronics, various electronic devices have been developed to perform this kind ofrecordingorloggingjob.

Nowadays,mostdataacquisitionsystemsareintegratedwithcomputer,sensors,signalconditioningdevices,etc.andthefunctionofthesekindofdataacquisitionsystemsvariesforsimplerecordingofprocessparametertocontrolofindustrialsystem.Thesekindsofsystemsbasicallyhaveahardware anda softwarepart.Thehardwarepart consistsof asensor, signal conditioning, analog-to-digital converter, memory, processor, switches,digital-to-analogconverter,etc.andthesoftwarepartconsist,ofoperatingsystem,editor,graphdisplayprogramanddataprocessingsoftware,etc..

A data acquisition system is used in various applications, starting from industry toscientificlaboratories.

The actual definition of a data acquisition system also varies; here is a commondefinitionofdataacquisitionsystem.

“Dataacquisitionistheprocessbywhichphysicalphenomenafromtherealworldaretransformedintoelectricalsignalsthataremeasuredandconvertedintoadigitalformatforprocessing,analysing,andstoragebyacomputer”.

14.2 BASICCOMPONENTSOFDATAACQUISITIONSYSTEMS

The basic elements of a data acquisition system, as shown in the functional diagram(Figure14.1)areasfollows:

SensorsandtransducersFieldwiringSignalconditioningDataacquisitionhardwarePC(operatingsystem)Dataacquisitionsoftware

Figure14.1(a)and(b)Functionaldiagramofadataacquisitionsystem

Wecanthinkofadataacquisitionsystemasacollectionofsoftwareandhardwarethatconnects us to the physical world. A typical data acquisition system consists of thesecomponents.Table14.1Componentsofadataacquisitionsystem

Components Description

DataacquisitionhardwareThemainfunctionofthishardwareistoconvertana-logsignalstodigitalsignals,andtoconvertprocesseddigitalsignalstoanalogsignals.

Sensorsandactuators(transducers)

Transducer/Sensorconvertsinputenergyfromoneformtoanotherform.Forexample,athermocoupleconvertsheatenergyintoelectrical.Anactuatoralsoconvertsenergyfromoneformtoanother,whichisoftenconnectedattheoutputofadataacquisitionsysteminordertomanipulatethefinalcontrolelement.

Signalconditioninghardware

Sensorsignalsareoftennotcompatiblewithdataacquisitionhardware.Toovercomethisincompatibility,thesignalmustbeconditioned.Forexample,wemayneedtoconditionthethermocoupleoutputsignalbyamplifyingitorbyremovingunwantedfrequencycomponents.Outputsignalsmayalsoneedconditioning.

Computer Thecomputerprovidesaprocessor,asystemclock,abus

totransferdata,andmemoryanddiskspacetostoredata.

Software

Itallowsexchanginginformationbetweenthecomputerandthehardware.Forexample,typicalsoftwareallowsustoconfigurethesamplingrateofourboard,andacquireapredefinedamountofdata.

14.3COMPONENTSOFATYPICALPC-BASEDDATAACQUISITIONSYSTEM

Earlier, expensive mainframe computers were used extensively for gathering multiplechannelsofdata,primarilyinlargeindustrialorscientificapplications.Theywereseldomusedinsmallprojectsbecauseoftheirrelativelyhighcost.Buttheintroductionofsmallrack-mountedminicomputersthatdevelopedinthe1960’sandlaterdesktoppersonal-typecomputers thathousedmicroprocessors andproliferated in the1970’s justified theirusefor smaller projects. Soon, data acquisition plug-in cards (aswell as hundreds of othertypesofplug-in cards) for these small computerswere a commonmeans to collect andrecorddataofalltypes.

14.3.1DAQHardwareADataAcquisitionSystem(DAQ)isacombinationofcomputerhardwareandsoftwarethatgathersstoresorprocessesdatainordertocontrolormonitorsomesortofphysicalprocess. A typical data acquisition system comprises a computer system with DAQhardware,whereintheDAQhardwareistypicallypluggedintooneoftheI/Oslotsofthecomputer system. The DAQ hardware is configured and controlled by DAQ softwareexecuting on the computer system. Data acquisition hardware is either internal andinstalleddirectlyintoanexpansionslotinsideyourcomputer,orexternalandconnectedtoyourcomputerthroughanexternalcable,whichistypicallyaUSBcable.

At the simplest level, data acquisition hardware is characterised by the subsystems itpossesses. A subsystem is a component of data acquisition hardware that performs aspecialisedtask.Commonsubsystemsinclude

AnaloginputAnalogoutputDigitalinput/outputCounter/timer

Hardwaredevicesthatconsistofmultiplesubsystems,suchastheonedepictedbelow,arecalledmultifunctionboards.

1.AnalogInputSubsystemsAnalog inputsubsystemsconvert real-worldanalog inputsignals fromasensor intobitsthat can be read by your computer. Perhaps the most important of all the subsystemscommonly available, they are typically multichannel devices offering 12 or 16 bits ofresolution.

Analog input subsystems are also referred to as AI subsystems, A/D converters, or

ADCs.

Analog-to-DigitalConversion Indata acquisition systems, it isnecessary to convertoneorseveralanalogsignalsintooneorseveraldigitalsignalscapableofbeingstoredinadigitalmemoryandprocessedbyadigitalprocessor.Analogsignalsmustbedigitisedbeforetheycanbeusedbyacomputerasabasis for supportingcomputations.Ananalog-to-digitalconverterisanelectricaldevicethatconvertsananalogsignaltoadigitalsignal.Whentheanalog signal has been converted to a digital signal, it can be processed and stored bycomputersystems.Ananalog-to-digitalconverterisoftenfabricatedonasingleintegratedcircuit.Thedetailsofananaloginputsubsystemwillbediscussedinlatter.

2.AnalogOutputSubsystemsAnalog output subsystems convert digital data stored on your computer to a real-worldanalog signal. These subsystems perform the inverse conversion of analog inputsubsystems. Typical acquisition boards offer two output channels with 12 bits ofresolution, with special hardware available to support multiple channel analog outputoperations.

Analogoutput subsystems are also referred to asAO subsystems,D/Aconverters, orDACs.

3.DigitalInput/OutputSubsystemsDigital input/output (DIO) subsystems are designed to input and output digital values(logic levels) to and fromhardware.These values are typically handled either as singlebitsorlines,orasaport,whichtypicallyconsistsofeightlines.

While most popular data acquisition cards include some digital I/O capability, it isusuallylimitedtosimpleoperations,andspecialdedicatedhardwareisoftennecessaryforperformingadvanceddigitalI/Ooperations.

4.Counter/TimersSubsystemsCounter/Timer subsystems are designed to count the number of pulses coming fromexternal devices and the timers are normally used to provide strict time count of delaytime

14.3.2SensorsandTransducersTransducer/Sensorconvertsinputenergyfromoneformtoanotherform.Accordingtothetype,outputsensorsareclassifiedintwotypes:digitalsensorsandanalogsensors.

Thesensorswhichcanproduceadigitaloutputsignal,thatisadigitalrepresentationoftheinputsignal,havingdiscretevaluesofmagnitudemeasuredatdiscretetimes,arecalleddigital sensors. A digital sensor must output logic levels that are compatible with thedigitalreceiver.Examplesofdigitalsensorsincludeswitchesandpositionencoders.

Analogsensorsproduceanoutputsignalthatisdirectlyproportionaltotheinputsignal,and is continuous in both magnitude and in time. Most physical variables such astemperature,pressureandaccelerationarecontinuousinnatureandarereadilymeasuredwith an analog sensor. For example, some common analog sensors and the physicalvariablestheymeasurearelistedbelow.

Table14.2Commonanalogsensors

Sensor PhysicalVariable

Thermocouple Temperature

Microphone Pressure

Pressuregauge Pressure

Photodiode Lightintensity

Straingauge Force

LVDT Displacement

Whenchoosingthebestanalogsensortouse,youmustmatchthecharacteristicsofthephysicalvariableyouaremeasuringwiththecharacteristicsof thesensor.Thetwomostimportantsensorcharacteristicsare

ThesensoroutputThesensorbandwidth

14.3.3SignalConditioningMost sensors and transducers generate signals that must be conditioned before ameasurementorDAQdevicecanreliablyandaccuratelyacquirethesignal.Thisfront-endprocessingisreferredtoassignalconditioning.Asignalconditionermaycreateexcitationforcertaintransducerssuchasstraingaugesandresistancetemperaturedetectors,whichrequire external excitation voltages or currents. The main tasks performed by signalconditioningareasfollows:

FilteringAmplificationLinearisationIsolationExcitation

FilteringInnoisyenvironments,itisverydifficulttoacquirelowmagnitudesignalsreceivedfromsensorssuchassignalsfromthermocouplesandstraingauges(intheorderofmV).Ifthenoiseisofthesameorgreaterorderofmagnitudethantherequiredsignal,thenoisemustfirstbefilteredout.Signalconditioningequipmentoftencontainlow-passfiltersdesignedtoeliminatehigh-frequencynoisethatcanleadtoinaccuratedata.

Filtering isaprocessbywhich theunwantednoise frequenciesare removed from thesourcesignal.ThisisdonebeforethesignalisamplifiedtofeedtotheDAQsystem.

Ideally, a filter should have a very sharp cut-off frequency, in order to separate theuseful frequencies from the noise frequencies. However, most practical filters do notaccuratelyattenuatetheundesiredfrequenciesbeyondthedesiredrange.

Ingeneral,analogfilterhardwareconsistsoftwotypesoffilters—namelyactivefiltersandpassivefilters.

While active filters use components likeOP-AMPs, passive filters consist of passivecomponents like capacitors, inductors and resistors. They provide cheap hardware for

filteringaction.However,suchfiltersarenotidealandtheydonotaccuratelyattenuatethenoiseamplitudes.In intelligent signal-conditioningmodules, however, integratingA/D converters go a

longwaytoaveraging(filtering)outanycyclicalnoiseappearingattheinput.

Alternatively,softwareaveragingmayalsobeusedtoeliminateperiodicsystemnoisessuchasmainshum.

Filtershavecertainattributeswhichdefinethem.Theyareasfollowing:

1.Cut-offFrequencyIt is thefrequencybeyondwhichthefilterattenuatesall thefrequencies.Itcanbehigh-passorlow-passcut-offfrequencyasrequiredbythedevice.Ingeneral,cut-offfrequencyis considered as frequencywhere the normalised gain of the signal drops below 0.707timesthemaximumgain.

2.RollOffThisistheslopeoftheamplitudeversusthefrequencygraphattheregionofthecut-offfrequency.Thischaracteristicdifferentiatesanidealfilterfromanon-idealfilter.

3.QualityFactorThisfactordeterminesthegainofthefilterattheresonantfrequencyandtheroll-offofthetransfercharacteristicsonbothsidesoftheresonantfrequency.

Activefiltersaremorefrequentlyusedasagainstthepassivefiltersduetotheirsharperroll-ofandbetterstability.

4.TypesofFiltersTherearefourkindsoffilters,namely

Low-passfilterHigh-passfilterBand-passfilterBand-stopfilter

(a)Low-PassFilterAlow-passfilterallowsthelowfrequenciestopasswhileattenuatesthehigherfrequencies.Figure14.2showstheideallow-passfiltercharacteristics,whereωpisthefiltercut-off frequency.Figure14.3 shows thecircuitdiagramofanactive low-passfilter.Theactualfilterresponsedeviatesfromtheoriginalwhenimplemented.Figure14.4showsthepracticalfiltercharacteristics.

Figure14.2Ideallow-passfiltercharacteristics

Figure14.3Circuitdiagramofanactivelow-passfilter

Figure14.4Practicallow-passfiltercharacteristics

Figures14.2 and 14.3 shows the circuit diagram and the transfer characteristics of alow-passfilterrespectively.Aswecansee,alow-passfilterallowsthelowfrequenciestopasswhileattenuatesthehigherfrequencies.

(b)High-PassFilter Ahigh-passfilterallowsthehighfrequenciestopasswhileattenuatesthelowerfrequencies.Figure14.5shows the idealhigh-pass filtercharacteristics,wherewpisthefiltercut-offfrequency.Figure14.6showsthecircuitdiagramofanactivehigh-passfilter.Theactualfilterresponsedeviatesfromtheoriginalwhenimplemented.Figure14.7showsthepracticalfiltercharacteristics.

Figure14.5Idealhigh-passfiltercharacteristics

Figure14.6Circuitdiagramofanactivehigh-passfilter

Figure14.7Practicalhigh-passfiltercharacteristics

(c) Band-Pass (selective) Filter These are filters which allow frequencieswithin a certainrange, bound by an upper (wp2) and a lower (wp1) cut-off frequency to pass through,attenuatingotherfrequencies.Thesearealsoknownasselectivefiltersandtheycombinealow-pass and a high-pass filter in series to give selected band of frequency allowance.Figure14.8and14.9showsthecharacteristicsofband-passfilter foran idealandarealfilterrespectively.

Figure14.8Idealband-passfiltercharacteristics

Figure14.9Practicalband-passfiltercharacteristics

(d)Band-stop(Notch)FiltersThiskindoffilterattenuatesacertainbandoffrequenciesandletsallotherfrequenciestopassthrough.Theyuseaparallelcombinationofahighandlow-pass filters togive the requiredattenuationof abandof frequencies.Theyare alsoknown as notch. Figure 14.10 and 14.11 show the ideal and practical band-stop filtercharacteristicsofaband-stopfilter.

Figure14.10Idealband-stopfiltercharacteristics

Figure14.11Idealband-stopfiltercharacteristics

(e)ButterworthFilterThisisakindofactivefilterwhichprovidesabetterleveloflow-passfiltering.Thisisachievedbycascadingtwoormorestagesoflow-passfilters.Thenumberofstagesoffilteringdetermineshowsharptheroll-offisatthecut-offfrequency.Figure14.12showsatwo-stageButterworthfilter.

Figure14.12Atwo-stageButterworthfilter

5.AmplificationIt is a process by which an input signal of weak signal strength (low amplitude) isconvertedintoasignalofhighersignalstrength(highamplitude),soastobereadablebytheprocessingdevices.

Insignalconditioning,amplificationservestwomainpurposes:

IncreasesresolutionoftheinputsignalIncreasesSignal-to-Noiseratio(SNR)

Amplification mainly serves for increasing resolution of the input signal. If, forexample,alow-levelsignaloftheorderofafewmVisfedtoa12-bitADC,therewillbealossofprecisionastheresolutionoftheADCisoftheorderof2mV.However,ifthesignalisamplifiedtotheorderof10V(fullscalevoltageforADC),wegetthemaximumprecision.ThehighestpossibleresolutioncanbeachievedbyamplifyingtheinputsignalsothatthemaximuminputvoltageswingequalsthemaximuminputrangeoftheADC.

Another important function of amplification is to achieve high signal-to-noise ratio.Amplifyingasignalbeforesending it throughacable to the receivingendenableshighSNR to the noises introduced in the path having noise interference. This ensures theimprovedprecisionofthemeasurement.If,however,thesignalisamplifiedafterthenoiseinterferencecauses lowSNRwhich implies thenoisecausesa considerableerror in theinputsignal.

6.Linearisation

Itisthemodificationofasystemsothatitsoutputsareapproximatelylinearfunctionsofitsinputs,inordertofacilitateanalysisofthesystem.

It isseen thatsometimes thedataoutputby transducersbearanon-linearrelationshipwiththemeasuredphenomenonoverarangeofthemeasuredvariable.Agoodexampleofsuch relation is thermocouples. Such non-linear relationships need to be properlylinearisedforanalysisofdata.Typically,theDAQsoftwarefacilitatesthelinearisationofthe signals.However, if the signal has a periodic and repeatable non-linear relation, anintelligent signal conditioning hardware may as well provide such linearisation. Thishowever,requires thesignalconditioningmodule tobemodifiedforaparticular typeoftransducer.TheresultthencanbesentdirectlytothehostPCdirectlywithoutundergoinglinearisationasthesignalisdirectlyrelatedtothemeasuredphenomenon

7.IsolationSignal-conditioningequipmentcanalsobeusedtoprovideisolationoftransducersignalsfrom the computer where there is a possibility that high-voltage transients may occurwithin the system being monitored, either due to electrostatic discharge or electricalfailure. Isolation protects expensive computer equipment from damage and computeroperatorsfrominjury.Inaddition,wherecommon-modevoltagelevelsarehighorthereisa need for extremely low common-mode leakage current, as for medical applications,isolationallowsmeasurementstobeaccuratelyandsafelyobtained.

Isolation in signal conditioning refers to the transmission signal from the source tomeasuring device without physical connection. The most common methods of circuitisolation includeopto-isolation,magneticorcapacitive isolation.Whileopto-isolation isused for digital signals,magnetic and capacitive isolations are used for analog signals.Magneticorcapacitiveisolationinvolvesthemodulationofthesignalconvertingitfromvoltagetofrequencysignalandthetransmittingitoveratransformeroracapacitor,whenitisagainconvertedbacktoavoltagesignal.

Isolation of the signal source is very crucial where there is a risk of high voltagetransientscausedbyelectrostaticdischarge, lightning,orhigh-voltageequipmentfailure,whichmayruintheexpensiveDAQequipmentifnotisolatedfromthesignalsourceandmayalsocause serious injuries tohumanshandling theequipment.Alsousing isolationpreventscomplexitiescausedbycommon-modevoltagesandgroundloops.

Systemisolationcanbecarriedoutinthefollowingways:

Byusingisolationtransformerinordertorejectthecommon-modevoltageappearingonthesignallinesByusingbufferamplifierstoisolatetheinputsignalsfromgroundnoiseByisolatingsystemgroundreferences

8.ExcitationThe transducers generally provide for the excitation signals required by the DAQhardwareanddatamanipulation.However,insomecases,thetransducersrequireexternalexcitationduetoweaksignalgeneration,non-electricalsignalgenerationorduetonoiseinterference and other factors. The signal-conditioning hardware provides for suchexcitationsignals.Thetransducerswhichconvertthenon-electricalvaluesintoelectrical

(voltage or current) signals are known as active transducers. These transducers do notgenerallyrequireexternalexcitation.Otherdevicesknownaspassivetransducerschangean electrical network value, such as resistance, inductance or capacitance, according tochangesinthephysicalquantitybeingmeasured.Straingauges(resistivechangetostress)andLVDTs(inductancechangetodisplacement)aretwoexamplesofthis.Tobeabletodetectsuchchanges,passivedevicesrequireexternalexcitation.

14.3.4TheComputerThePCusedinadataacquisitionsystemcangreatlyaffectthespeedsatwhichdatacanbecontinuouslyandaccuratelyacquired,processed,andstoredforaparticularapplication.Where high-speed data acquisition is performed with a plug-in expansion board, thethroughputprovidedbybusarchitectures,suchas thePCIexpansionbus, ishigher thanthatdeliveredbythestandardISAorEISAexpansionbusofthePC.

The particular application, the microprocessor speed, hard-disk access time, diskcapacityand the typesofdata transferavailable,canallhavean impacton thespeedatwhichthecomputerisabletocontinuouslyacquiredata.AllPCs,forexample,arecapableofprogrammedI/Oandinterrupt-drivendatatransfers.TheuseofDirectMemoryAccess(DMA),inwhichdedicatedhardwareisusedtotransferdatadirectlyintothecomputer’smemory, greatly increases the system throughput and leaves the computer’smicroprocessorfreeforothertasks.Innormaloperation,thedataacquired,fromaplug-indata acquisition board or otherDAQ hardware (e.g. data logger), is stored directly tosystemmemory.Where the available systemmemory exceeds the amount of data tobeacquired,datacanbe transferred topermanentstorage,suchasaharddisk,atany time.Thespeedatwhichthedataistransferredtopermanentstoragedoesnotaffecttheoverallthroughputofthedataacquisitionsystem.

If real-time processing of the acquired data is needed, the performance of thecomputer’s processor is paramount.Aminimum requirement for high-frequency signalsacquired at high sampling rates would be a 32-bit processor with its accompanyingcoprocessor, or alternatively a dedicated plug-in processor. Low frequency signals, forwhich only a few samples are processed each second,would obviously not require thesamelevelofprocessingpower.Alow-endPCwould,therefore,besatisfactory.Clearly,the performance requirements of the host computer must be matched to the specificapplication.Aswithallaspectsofadataacquisitionsystem,thechoiceofcomputerisacompromisebetweencostandthecurrentandfuturerequirementsitmustmeet.

One final aspect of the personal computer that should be considered is the type ofoperating system installed. This may be single-tasking (e.g. MS-DOS) or multitasking(e.g. Windows 2000). While the multitasking nature of Windows provides manyadvantagesforawiderangeofapplications,itsuseindataacquisitionisnotasclear.

Thecomputerprovidesaprocessor,asystemclock,abustotransferdata,andmemoryand disk space to store data. The processor controls how fast data is accepted by theconverter.The system clock provides time information about the acquired data.Data istransferredfromthehardwaretosystemmemoryviaDynamicMemoryAccess(DMA)orinterrupts.DMAishardwarecontrolledandthereforeextremelyfast.Interruptsmightbeslowbecauseof the latency timebetweenwhenaboardrequests interruptservicingand

when the computer responds. Themaximum acquisition rate is also determined by thecomputer’sbusarchitecture.

14.3.5SoftwareRegardlessofthehardwareyouareusing,youmustsendinformationtothehardwareandreceive information from the hardware. You send configuration information to thehardware suchas the sampling rate, and receive information from thehardware suchasdata, statusmessages, and errormessages.Youmight alsoneed to supply thehardwarewith information so that you can integrate it with other hardware and with computerresources.Thisinformationexchangeisaccomplishedwithsoftware.Therearetwokindsofsoftware:

DriversoftwareApplicationsoftware

1.DriverSoftwareItallowsustoaccessandcontrolthecapabilitiesofhardware.Amongotherthings,basicdriversoftwareallowsusto

BringdataontoandgetdataofftheboardControltherateatwhichdataisacquiredIntegratethedataacquisitionhardwarewithcomputerresourcessuchasprocessorinterrupts,DMAandmemoryIntegratethedataacquisitionhardwarewithsignal-conditioninghardwareAccessmultiplesubsystemsonagivendataacquisitionboardAccessmultipledataacquisitionboards

2.ApplicationSoftwareItprovidesaconvenientfrontendtothedriversoftware.Itallowsusto

ReportrelevantinformationsuchasthenumberofsamplesacquiredManagethedatastoredincomputermemoryConditionasignalPlotacquireddata

14.4 ANALOGINPUTSUBSYSTEM

Many data acquisition hardware devices contain one or more subsystems that convert(digitise)real-worldsensorsignalsintonumberswhichcomputerscanread.Suchdevicesare called analog input subsystems (AI subsystems,A/D converters, orADCs).Analoginputsubsystemsconvertreal-worldanaloginputsignalsfromasensorintobitsthatcanbe read by our computer. Perhaps themost important of all the subsystems commonlyavailable,theyaretypicallymultichanneldevicesoffering12or16bitsofresolution.

14.4.1NyquistCriterionAnalog signals are continuous in time and in amplitude (within predefined limits).

Samplingtakesa“snapshot”ofthesignalatdiscretetimes,whilequantisationdividesthevoltage(orcurrent)valueintodiscreteamplitudes.

Sampling frequency has to be at least twice the frequency of the event that requirescapture.

This rule is called the Nyquist Criterion. If one fails to follow this rule then aphenomenoncalledaliasingoccurs.Aliasingiswhenafrequencyhigherthanhalfofoursampling frequency gets “folded” back onto a frequency that is less than half of oursamplingfrequency.Thiscreatesaghostsignalthatcanreallymessupourresults.

14.4.2A/DConversionA process of converting an analog signal into a digital signal comprisesmeasuring theamplitudeoftheanalogsignalatconsistenttimeintervalsandproducingasetofsignalsrepresenting the measured digital value. The information in the digital signals and theknown time interval enablesone to convert thedigital signal back to the analog signal.Analog todigital conversionof a continuous input signalnormallyoccurs in two steps:sampling and quantisation. The sampler takes a time-varying analog input signal andconverts it to a fixed voltage, current, electrical charge, or other output level. Thequantiser takes the constant sampled level and compares it to the closest level from adiscreterangeofvaluescalledquantisationlevels.Theperformanceofanaloganddigitalconverters is typically quantified by two primary parameters, speed (in samples persecond)andresolution(inbits).HigherresolutionA/Dconverterstypicallyrequirealargesignal-to-noise ratio and good linearity. A/D converters with high sampling rates arefrequentlydesired,butgenerallyhavelowerresolution.Therearetwobasictechniquesforperforming analog-to-digital conversion: an open-loop technique and a feedbacktechnique.

14.4.3DifferentTypesofA/DConvertersWhileallanalog-to-digitalconvertersareclassifiedbytheirresolutionornumberofbits,howtheA/Dcircuitryachievesthisresolutionvariesfromdevicetodevice.TherearefourprimarytypesofA/Dconvertersusedforindustrialandlaboratoryapplications:

SuccessiveapproximationFlash/ParallelIntegratingRamp/Counting

Industrialandlabdataacquisitiontaskstypicallyrequire12to16bits—12arethemostcommon.As a rule, increasing resolution results in higher costs and slower conversionspeed.Table14.3ComparisonofdifferentA/Dconverters

1.SuccessiveApproximationAsuccessiveapproximationADCisatypeofanalog-to-digitalconverterthatconvertsacontinuous analog waveform into a discrete digital representation via a binary searchthroughallpossiblequantisationlevelsbeforefinallyconverginguponadigitaloutputforeachconversion.ItisthemostcommonA/Dconverterdesignusedforgeneralindustrialandlaboratoryapplications(Figure14.13).Thisdesignprovidesaneffectivecompromiseamong resolution, speed, and cost. An internal digital-to-analog (D/A) converter and asinglecomparator—essentiallyacircuitdetermineswhichoftwovoltagesishigher—areusedtonarrowinontheunknownvoltagebyturningbitsintheD/Aconverteronuntilthevoltagesmatchtowithintheleastsignificantbit.

Figure14.13A/Dconversionbysuccessiveapproximation

2.Flash/ParallelAflashA/Dconverterincludesareferencevoltagegeneratorforgeneratingapluralityofreference voltages, a first group of amplifiers having a plurality of amplifiers. Each ofthese amplifies a difference voltage between each reference voltage (generated by thereference voltage generator and a voltage of an input signal) and a second group ofamplifiers having a plurality of amplifiers. It is used when higher speed operation isrequired. This design usesmultiple comparators in parallel to process samples atmorethan 100MHz with 8 to 12-bit resolution. Conversion is accomplished by a string ofcomparatorswithappropriatereferencesoperatinginparallel(Figure14.14).

The downside of this design is the large number of relatively expensive comparatorsthatarerequired—forexample;a12-bitconverterrequires4,095comparators.

Figure14.14A/DConversionbyFlash/Paralleltechnique

3.IntegratingIntegratinganalog-to-digital converters (ADCs)providehigh resolutionandcanprovidegood line frequency and noise rejection. This type of A/D converter integrates anunknowninputvoltageforaspecificperiodof timeand then integrates itbackdowntozero.Thistimeiscomparedtotheamountoftimetakentoperformasimilarintegrationon a known reference voltage. The relative times required and the known referencevoltage then yields the unknown input voltage. Integrating converterswith 12 to 18-bitresolutionareavailable,atrawsamplingratesof10–500kHz.Thesetypesofconvertersoften includebuilt-indrivers forLCDorLEDdisplays andare found inmanyportableinstrumentapplications,includingdigitalpanelmetersanddigitalmultimeters.

It also smoothesout signalnoisebecause this typeofdesigneffectively averages theinputvoltageovertime.And,ifanintegrationperiodischosenthatisamultipleoftheacline frequency, excellent common-mode noise rejection is achieved.More accurate andmore linear than successiveapproximationconverters, integratingconverters areagoodchoiceforlow-levelvoltagesignals.

4.Ramp/CounterThe flash (simultaneous)A/D converter uses several voltage comparators that comparereference voltages with the analog input voltage. These converters use one comparatorcircuitandaD/Aconverter(Figure14.15).Thisdesignprogressivelyincrementsadigitalcounter and with each new count generates the corresponding analog voltage andcompares it to the unknown input voltage. When agreement is indicated, the countercontainsthedigitalequivalentoftheunknownsignal.Theadvantageofthiscircuitisthatitprovidesafastermethodofanalog-to-digitalconversion.

Avariationonthecountermethodistherampmethod,whichsubstitutesanoperationalamplifier or other analog ramping circuit for the D/A converter. This technique issomewhatfaster.

Figure14.15A/DConversionbycounting/ramptechnique

14.4.3PerformancePerformanceofaADCisjudgedbyobtainingfollowingparameters:

1.ResolutionCentral totheperformanceofanA/Dconverter is itsresolution,oftenexpressedinbits.AnA/Dconverteressentiallydividestheanaloginputrangeinto2Nbits,whereN is thenumberofbits. Inotherwords, resolution is ameasureof thenumberof levelsused to

representtheanaloginputrangeanddeterminestheconverter’ssensitivitytoachangeinanalog input. Amplification of the signal, or input gain, can be used to increase theapparentsensitivityifthesignal’sexpectedmaximumrangeislessthantheinputrangeofthe A/D converter. As higher resolution A/D converters cost more, it is especiallyimportanttonotbuymoreresolutionthanoneneeds—ifonehas1%accurate(1in100)temperature transducers, a 16-bit (1 in 65,536) A/D converter has probably moreresolutionthanoneneeds.

2.VoltageStabilityAbsoluteaccuracyof theA/Dconversion isa functionof the referencevoltagestability(theknownvoltagetowhichtheunknownvoltageiscompared)aswellasthecomparatorperformance.Overall,itisoflimitedusetoknowtheaccuracyoftheA/Dconverteritself.Accuracy of the system, together with the associated multiplexer, amplifier, and othercircuitryistypicallymoremeaningful.

3.SpeedTheotherprimaryA/Dconverterperformanceparameterthatmustbeconsideredisspeed-throughputforamulti-channeldevice.Overall,systemspeeddependsontheconversiontime, acquisition time, transfer time, and the number of channels being served by thesystem.

4.AcquisitionAcquisitionisthetimeneededbythefront-endanalogcircuitrytoacquireasignal.Alsocalledaperturetime,itisthetimeforwhichtheconvertermustseetheanalogvoltageinordertocompleteaconversion.Conversionisthetimeneededtoproduceadigitalvaluecorrespondingtotheanalogvalue.Transferisthetimeneededtosendthedigitalvaluetothe host computer’s memory. Throughput, then, equals the number of channels beingserveddividedbythetimerequiredtodoallthreefunctions.

Example14.1 Ananalogtodigitalconverter(ADC)measuresvoltagesintherangeof0to25Vandhas12-bitaccuracy.WhatisthesmallestvoltagestepthattheADCcanresolve?

Solution12bits=212=4096

Therefore, the ADC can measure 4096 different values of voltage (from 0 to 4095inclusive), the number of voltage steps is thus 4095 (one fewer than the number ofdifferent values available).Assuming thatwe set digital 0 to be equivalent to 0V anddigital4095tobeequivalentto25V,eachvoltagestepissimplygivenby

25V/4095=0.006105V=6.105mV

Example14.2 Determine thenumberofoutputbits required foranADCsothatquantisingerrorlessthan1%.

SolutionFor1%quantisingerror,count≥100.

Forn=6,N=26–1=63

Forn=7,N=27–1=127

Example14.3 A ramp-type ADC system uses a 10MHz clock generatorandarampvoltagethat increases from0Vto1.25Vinatime of 125 ms. Determine the number of clock pulsescounted into the register when V = 0.9 V, and when it is0.75V.

SolutionForVr=1.25V,tr=125ms

Example14.4 If3.45Visappliedtoa4-bitsuccessive-approximation-typeA/D converterwhich has a reference voltage of 5V,whatwillbethedigitaloutputoftheADC?

Setd3=1,Output5/21=2.5V.Now,3.45>2.5andsetd3=1

Setd2=1,Output=2.5+ =3.75Now,3.45<3.75andsetd2=0

Setd1=1,Output=2.5+ =3.125Now,3.125<3.45andsetd1=1

Setd0=1,Output=3.125+ =3.4375Now,3.4375<3.45andsetd0=1.

Thus,theoutputoftheA/Dconverteris1011.

14.5 ANALOGOUTPUTSUBSYSTEM

Analog outputs commonly are used to operate final control elements in industrialenvironments like valves andmotors. An analog output subsystemmainly consist of aDigital-to-Analog (D/A) converter, which is functionally opposite to anA/D converter.Similar to analog input configurations, a commonD/Aconverter often is shared amongmultiplexedoutputsignals.Standardanalogoutputrangesareoftensameasanaloginputstandards:±5Vdc,±10Vdc,0–10Vdc,and4–20mAdc,etc.

1.KeySpecificationsofanAnalogOutputSubsystem(a) Settling Time Period required for aD/Aconverter to respond to a full-scale set pointchange.

(b)Linearity This refers to thedevice’s ability to accuratelydivide the referencevoltageintoevenlysizedincrements.

(c)RangeThereferencevoltagesetsthelimitontheoutputvoltageachievable.

2.D/AConversionAdigital-to-analogconverter,or simplyDAC, is a semiconductordevice that isused toconvertadigitalcode intoananalogsignal.Digital-to-analogconversion is theprimarymeansbywhichdigitalequipment suchascomputer-basedsystemsareable to translatedigitaldataintoreal-worldsignalsthataremoreunderstandabletooruseablebyhumans,such as music, speech, pictures, video, and the like. It also allows digital control ofmachines,equipment,householdappliances,andthelike.

Essentially,thelogiccircuitryforananalogvoltageoutputusesadigitalwordorseriesofbits,todropin(ordropout,dependingonwhetherthebitis1or0)aseriesofresistorsfromacircuitdrivenbyareferencevoltage.Thisladderofresistorscanbemadeofeitherweighted-valueresistorsoranR-2Rnetworkusingonlytworesistorvalues—oneifplacedin series (Figure 14.16). While operation of the weighted-value network is moreintuitivelyobvious, theR-2R scheme ismorepractical.Becauseonlyone resistor valueneedbeused, it iseasier tomatchthetemperaturecoefficientsofanR-2R ladder thanaweighted network, resulting inmore accurate outputs. Plus, for high resolution outputs,veryhighresistorvaluesareneededintheweighted-resistorapproach.

Figure14.16Weightedvalueandsingle-valueresistornetworksforD/Aconversion

By the Nyquist–Shannon sampling theorem, sampled data can be reconstructedperfectlyprovidedthatitsbandwidthmeetscertainrequirements(e.g.,abase-bandsignalwith bandwidth less than the Nyquist frequency). However, even with an idealreconstruction filter, digital sampling introduces quantisation error that makes perfectreconstructionpracticallyimpossible.Increasingthedigitalresolution(i.e.,increasingthenumberofbitsusedineachsample)orintroducingsamplingdithercanreducethiserror.

14.5.1DifferentTypesofDACsThemostcommontypesofelectronicDACsarethefollowing:

1.PulseWidthModulatorItisthesimplestDACtype.Astablecurrentorvoltageisswitchedintoalow-passanalogfilterwithadurationdeterminedbythedigitalinputcode.Thistechniqueisoftenusedfor

electricmotorspeedcontrol,andisnowbecomingcommoninhigh-fidelityaudio.

2.OversamplingDACsorInterpolatingDACsTheyuseapulsedensityconversiontechnique.TheoversamplingtechniqueallowsfortheuseofalowerresolutionDACinternally.Asimple1-bitDACisoftenchosenbecausetheoversampledresultisinherentlylinear.TheDACisdrivenwithapulsedensitymodulatedsignal,createdwiththeuseofalow-passfilter,stepnonlinearity(theactual1-bitDAC),andnegativefeedbackloop,inatechniquecalleddelta-sigmamodulation.Thisresultsinan effective high-pass filter acting on the quantisation (signal processing) noise, thussteeringthisnoiseoutofthelowfrequenciesofinterestintothehighfrequenciesoflittleinterest, which is called noise shaping (very high frequencies because of the oversampling). The quantisation noise at these high frequencies are removed or greatlyattenuatedbyuseofananaloglow-passfilterattheoutput(sometimesasimpleRC low-pass circuit is sufficient).Most very-high-resolutionDACs (greater than 16 bits) are ofthis type due to high linearity and low cost. Higher oversampling rates can relax thespecificationsoftheoutputlow-passfilterandenablefurthersuppressionofquantisationnoise.Speedsofgreater than100 thousand samplesper second (for example, 192kHz)andresolutionsof24bitsareattainablewithDelta-SigmaDACs.

3.BinaryWeightedDACItcontainsoneresistororcurrentsourceforeachbitoftheDACconnectedtoasummingpoint.Theseprecisevoltagesorcurrentssumtothecorrectoutputvalue.Thisisoneofthefastestconversionmethodsbutsuffersfrompooraccuracybecauseof thehighprecisionrequiredforeachindividualvoltageorcurrent.Suchhigh-precisionresistorsandcurrentsources are expensive, so this type of converter is usually limited to 8-bit resolution orless.

4.R-2RLadderDACItisabinaryweightedDACthatusesarepeatingcascadedstructureofresistorvaluesRand2RasshowninFigure14.17.Thisimprovestheprecisionduetotherelativeeaseofproducingequal-valuedmatchedresistors(orcurrentsources).However,wideconvertersperformslowlyduetoincreasinglylargeRC-constantsforeachaddedR-2Rlink.

Figure14.17R-2RladderDAC

5.ThermometerCodedDACIt contains an equal resistor or current source segment for each possible value ofDACoutput.An8-bitthermometerDACwouldhave255segments,anda16-bitthermometerDACwouldhave65,535segments.ThisisperhapsthefastestandhighestprecisionDACarchitecturebutattheexpenseofhighcost.Conversionspeedsof>1billionsamplespersecondhavebeenreachedwiththistypeofDAC.

6.HybridDACItusesacombinationoftheabovetechniquesinasingleconverter.MostDACintegratedcircuits are of this type due to the difficulty of getting low cost, high speed and highprecisioninonedevice.

14.5.2DACPerformanceDACsareatthebeginningoftheanalogsignalchain,whichmakesthemveryimportantto system performance. The most important characteristics of these devices are thefollowing:

1.ResolutionThis is thenumberof possibleoutput levels theDAC is designed to reproduce.This isusuallystatedasthenumberofbitsituses,whichisthebasetwologarithmofthenumberoflevels.Forinstance,a1bitDACisdesignedtoreproduce2(21)levelswhilean8bitDACisdesignedfor256(28)levels.ResolutionisrelatedtotheEffectiveNumberofBits(ENOB)whichisameasurementoftheactualresolutionattainedbytheDAC.

2.MaximumSamplingFrequencyThis is ameasurementof themaximumspeedatwhich theDACscircuitry canoperateandstillproducethecorrectoutput.AsstatedintheNyquist–Shannonsamplingtheorem,asignalmustbesampledatovertwicethefrequencyofthedesiredsignal.Forinstance,toreproducesignalsinalltheaudiblespectrum,whichincludesfrequenciesofupto20kHz,

itisnecessarytouseDACsthatoperateatover40kHz.TheCDstandardsamplesaudioat44.1 kHz, thus,DACsof this frequency are often used.A common frequency in cheapcomputersoundcardsis48kHz—manyworkatonlythisfrequency,offeringtheuseofothersampleratesonlythrough(oftenpoor)internalresampling.

3.MonotonicityThis refers to theabilityofDAC’sanalogoutput to increasewith an increase indigitalcode or the converse. This characteristic is very important for DACs used as a low-frequencysignalsourceorasadigitallyprogrammabletrimelement.

4.THD+NThisisameasurementofthedistortionandnoiseintroducedtothesignalbytheDAC.Itisexpressedasapercentageofthetotalpowerofunwantedharmonicdistortionandnoisethat accompany the desired signal. This is a very important DAC characteristic fordynamicandsmall-signalDACapplications.

5.DynamicRangeThisisameasurementofthedifferencebetweenthelargestandsmallestsignalstheDACcanreproduceexpressedindecibels.ThisisusuallyrelatedtoDACresolutionandnoisefloor.

Example14.5 Given a 3-bit DAC with a 1 V full-scale voltage andaccuracy±0.2%, find its resolutionandaccuracy in termsofvoltage.

Example14.6 An 8-bitD/A converter has+Vref = 5 V and –Vref = 0 V(Referencevoltages).WhatistheoutputvoltagewhenBin=10110100?FindalsoVLSB.

Solution

Example14.7 A 6-bit D/A converter has a reference voltage of 10 V.Calculate theminimumvalueofRsuch that themaximumvalueof output current doesnot exceed10mA.Findalsothesmallestquantisedvalueofoutputcurrent.

Solution

Example14.8 A6-bitD/Aconverterhaving320kWresistancesisinLSBposition.Theconverter isdesignedwithweightedresistivenetwork. The reference voltage is 10 V. The output of theresistive network is connected to an OP-AMP with afeedbackresistanceof5kW.Whatistheoutputvoltageforabinaryinputof111.010?

Solution

14.6 DIGITALINPUTANDOUTPUTSUBSYSTEM

We saw that analog transducers sense continuous variables such as pressure andtemperature and send the output in a continuous form to the ADC (analog to digitalconverter)viaasignalconditioningdevice.Incontrasttothat,manytransducersprovideanoutputthatisoneoftwostates:highorlow,openorclosed,onoroff,etc.Forexample,pressuremightbetoohighoratemperaturetoolow,triggeringclosureofaswitch.Thiskindofinputwhichisprovidedtothecomputerbythetransducerisknownasthedigitalinput.

Outputs,too,arenotalwaysstrictlyanalog.Forexample,solenoidvalvestypicallyareopenedorclosed;manypumpsandheatersaresimplyturnedonoroff.Theoutputofaprinterisalsopurelydigitalinnature.

Digital I/O interfaces are commonly used in PC based DAQ systems to providemonitoring and control for industrial processes, generate patterns for testing in thelaboratoryandcommunicatewithperipheralequipmentsuchasdataloggersandprinterswhichhaveparalleldigitalI/Ocapabilities.

Itisclearthatthesetypesofdigital,ordiscrete,inputsandoutputs(I/O)aremucheasierformicroprocessor-baseddataacquisitionsystemstodealwiththananalogsignalsasthecomputerhasafullybinaryenvironment.Similartoanalog-to-digitalconvertersusedfor

analog I/O, digital I/O is designed to deal directly with Transistor-to-Transistor Logic(TTL)levelvoltagechanges.TTLtypicallysetsthelow-voltagelevelbetween0and0.8Vandthehigh-voltagelevelbetween2.0and5.0V.Voltagelevelsbetween0.8and2.0Varenotallowed.Avoltagechange,then,fromthehighrangetothelowrange(orviceversa)representsadigitalchangeofstatefromhightolow,ontooff,etc.andbecauseacquiringananalogsignal ismorecomplex thanacquiringadigitalone,analogI/Ochannelsalsoaremoreexpensive.AclearcomparisonofthecomplexityinacquiringasignalinanaloganddigitalformsisshowninFigure18.

Figure14.18Comparisonofdigitalandanaloginput

14.6.1DigitalInputsMany types of digital input signals from switch closures, relay contacts, or TTLcompatibleinterfacescanbereaddirectlybydigitalI/Ocards(Figure14.18).Othertypesofinputsmayrequiresomesignal-conditioning,mostlikelytoreducehigherlevelvoltagechangestoTTLlevels.Avarietyofsignal-conditioningmodulesareavailabletoprovideisolationandotherdigital-conditioningfunctions.Themostcommontypeofdigitalinputisthecontactclosure(Figure14.19).Essentially,asensororswitchofsometypeclosesoropens a set of contacts in accordancewith some process change. An applied electricalsignalthendetermineswhetherthecircuitisopenorclosed.Currentflowsifthecircuitisclosed, registering a “1” in a transistor at the computer interface. Conversely, an opencircuitretainsahighvoltage(andnocurrent),registeringa“0”atthetransistor.

Figure14.19Contacttypedigitalinput

14.6.2DigitalOutputsAt its simplest, a digital output provides a means of turning something on or off.Applications range fromdriving a relay to turning on an indicator lamp to transmittingdatatoanothercomputer.Forlatchingoutputs,a“1”typicallycausestheassociatedswitchorrelaytolatch,whilea“0”causestheswitchtounlatch.Devicescanbeturnedonoroff,

depending on whether the external contacts are normally open or normally closed.StandardTTLlevelsignalscanbeusedtodrive5Vrelaycoils;aprotectivediodeisusedtoprotectthedigitaloutputcircuitry(Figure14.20).Becausedataacquisitionboardscantypicallysupplyonly24mAofdrivingcurrent,theyareintendedprimarilytodriveotherlogic circuits, not final control elements.Scalingmaybeneeded so that logical voltagelevelsare sufficient tocauseswitching in larger relays.Outputs intended todrive largersolenoids,contactors,motors,oralarmsalsomayrequireaboost.

Figure14.20Contacttypedigitalinput

14.6.3Counter/TimerandPulseI/OAsomewhat separate classof digital I/O is pulse inputs andoutputs,which typically isassociated with frequency, counting or totalisation applications. Pulse inputs might beusedtocounttherotationsofaturbineflowmeter;pulseoutputsmightbeusedtodriveasteppingmotor.

Pulseinputsarehandledinmuchthesamewayasdigitallogicinputs,buttheoutputofthesensingcircuitisnormallyconnectedtoacounterratherthanaspecificbitpositionintheinputregister.Successivepulsesincrementordecrementthecounter.Addanelapsedtime measure and a frequency or pulse rate can readily be determined. Similar to ananalog-to-digital converter, a counter is characterised by its number of bits—an N-bitcountercanaccumulateupto2Ndiscreteevents.Thus,a16-bitcountercancountto216=65,536.

14.7 IEEE488INTERFACE

In 1965, Hewlett-Packard designed the Hewlett-Packard Interface Bus ( HP–IB ) toconnect programmable instruments with computers. A high transfer rate around 1Mbytes/secondwaspossibletorealiseandduetothishightransferrate,thisinterfacebusquickly gained popularity. It was later accepted as IEEE Standard 488-1975, and hasevolvedtoANSI/IEEEStandard488.1-1987.Today,thenameGeneralPurposeInterfaceBus (GPIB) ismorewidely used thanHP-IB.ANSI/IEEE 488.2-1987 strengthened theoriginalstandardbydefiningpreciselyhowcontrollersandinstrumentscommunicate.

Up to15devices canbe connected in a single IEEE488busbydaisy-chaining.Thespeed is determined by the slowest device participating in the control and data-transferhandshakes.TheGPIBbusisan8-bitwideparallelinterfacesystem.Thebusconsistsof5

controllines,3handshakelines,8bi-directionaldatalines.Ithasatotalof24lines,withthe remaining lines occupied by ground wires. Additional features include TTL logiclevels (negative true logic). It has the ability to communicate in a number of differentlanguageformats,andnominimumoperationaltransferlimit.Themaximumdata-transferrateisdeterminedbyanumberoffactors,oftenitisrealisedin1Mb/s.Devicesconnectedinthebuscanbeclassifiedinthefollowingcategory:

1. Controller2. Talker3. Listener

Figure14.21showstheconnectionofthesethreetypesofdevices.

Figure14.21ConnectiondiagramofdifferentdeviceswithIEEEGPIBbus

Asingledeviceconnectedcanhaveallthethreeoranytwooratleastanyoneofthesefeatures, but only one option will be active at a time. The first function of the buscontroller(whichisonlyoneatatime)istodeterminwhichdeviceisactiveonthebus.Theremaybemanynumbersofactivelistenersexistingonthebuswithanactivetalkeraslongasnomorethen15devicesareconnectedtothebus.Thecontrollersendsinterfacemessages over the bus to a particular active instrument. Each individual device isassociatedwithaunique5-bitBCDcode(IDnumber).Byusingthiscode,thecontrollercancoordinate the activitieson thebus and the individualdevices canbemade to talk,listen(un-talk,unlisten)asdeterminedbythecontroller.

1.DataLinesTheeightdata lines,DIO1 throughDIO8,carrybothdataandcommandmessages.ThestateoftheAttention(ATN)linedetermineswhethertheinformationisdataorcommands.Allcommandsandmostdatausethe7-bitASCIIorISOcodeset,inwhichcasetheeighthbit,DIO8,iseitherunusedorusedforparity.

2.HandshakeLinesThree lines asynchronously control the transfer ofmessage bytes between devices. Theprocessiscalleda3-wireinterlockedhandshake.Itguaranteesthatmessagebytesonthedatalinesaresentandreceivedwithouttransmissionerror.

(a)NRFD(NotReadyForData)Thisindicateswhenadeviceisreadyornotreadytoreceiveamessagebyte.The line isdrivenbyalldeviceswhenreceivingcommands,byListenerswhenreceivingdatamessages,andbytheTalkerwhenenablingtheHS488protocol.

(b) NDAC (Not Data Accepted) This indicates when a device has or has not accepted amessage byte. The line is driven by all devices when receiving commands, and bylistenerswhenreceivingdatamessages.

(c)DAV(DataValid)Thistellswhenthesignalsonthedatalinesarestable(valid)andcanbeacceptedsafelybydevices.TheControllerdrivesDAVwhensendingcommands,andtheTalkerdrivesDAVwhensendingdatamessages.

3.InterfaceManagementLinesFivelinesmanagetheflowofinformationacrosstheinterface:

(a) ATN (Attention) The Controller drives ATN true when it uses the data lines to sendcommands,anddrivesATNfalsewhenaTalkercansenddatamessages.

(b)IFC(InterfaceClear) TheSystemControllerdrivestheIFClinetoinitialisethebusandbecomeCIC.

(c)REN(RemoteEnable)TheSystemControllerdrivestheRENline,whichisusedtoplacedevicesinremoteorlocalprogrammode.

(d) SRQ (Service Request) Any device can drive the SRQ line to asynchronously requestservicefromtheController.

(e)EOI (Endor Identify) TheEOI linehas twopurposes—theTalkeruses theEOI line tomarktheendofamessagestring,andtheControllerusestheEOIlinetotelldevicestoidentifytheirresponseinaparallelpoll.

Figure14.22Pin-outdescriptionofGPIBbus

Figure14.22pin-outdescriptionofGPIBbus

4.GPIBDataTransferOperationThethree lines(DAV,NRFDandNDAC)areusedtoformthreehandshakelineswhichcontrolthepassageofdata.Theactivetalkercontrolsthe‘DAV’line(DataValid)andthelistener(s) control the ‘NRFD’ (Not Ready For Data), and the ‘NDAC’ (Not DataAccepted)line.Inthesteadystatemode,theTalkerhold‘DAV’high(nodataavailable)whilethelistenerhold‘NRFD’high(readyfordata)and‘NDAC’low(nodataaccepted.After the talker placed data on the bus it then takes ‘DAV’ low (data valid). TheListener(s) then send ‘NRFD’ low and send ‘NDAC’ high (data accepted). Before theTalkerliftsthedataoffthebus,‘DAV’istakenhighsignifyingthatdataisnolongervalid.If the ‘ATN’ line (attention) is high while this process occurs, the information isconsidereddatabutwith the“ATN’line low, the information is regardedasan interface

message.Theotherfivelinesonthebus(‘ATN’included)arethebus-managementlines.These linesenable theControllerandotherdeviceson thebus toenable, interrupt, flag,andhalttheoperationofthebus.

All lines in theGPIBare tri-stateexceptfor‘SQR’, ‘NRFD’,and‘NDAC’whichareopen-collector.Thestandardbusterminationisa3Kresistorconnectedto5voltsinserieswitha6.2Kresistortoground—allvalueshavinga5%tolerance.

Thestandardalsoallowsforidentificationofthedevicesonthebus.Eachdeviceshouldhaveastringof1or2lettersplacedsomewhereonthebodyofthedevice(nearorontheGPIBconnector).TheseletterssignifythecapabilitiesofthedeviceontheGPIBbus.Table14.4DevicecapabilitiesontheGPIBbus

C Controller

T Talker

L Listener

AH AcceptorHandshake

SH SourceHandshake

DC DeviceClear

DT DeviceTrigger

RL RemoteLocal

PP ParallelPoll

TE TalkerExtended

LE ListenerExtended

Devices are connected together on the bus in a daisy-chained fashion.Normally, theGPIB connector (after being connected to the devicewith themale side) has a femaleinterface so that another connectormaybe attached to it.This allows thedevices tobedaisychained.Devicesareconnectedtogetherineitheralinearorstarfashion.

EXERCISE

Objective-typeQuestions1.Thefunctionofdataacquisitionsystemis

(a)acquiringphysicalphenomenafromtherealworld

(b)sendingsignaltorealworld

(c)processingandanalysingofsignal

(d)alloftheabove

2.Identifytheelementwhichisnotpartofadataacquisitionsystem:

(a)Digitaltoanalogconverter

(b)Filter

(c)Display

(d)Timer

3.WhichA/Dconverterhashighestconversiontime?

(a)Flashtype

(b)Dualslopeintegrating

(c)Successiveapproximation

(d)Ramp/Counting

4.HowmanydevicescanbeconnectedinasingleIEEE488bus?

(a)15

(b)16

(c)32

(d)Infinite

5. Asignalhasminimumandmaximumvaluesof–5Vand+5Vrespectively.Torecorda0.01Vchangeofthesignalvalue,whatbitlengthofA/Dconverterisrequired?

(a)4bit

(b)8bit

(c)10bit

(d)Noneofthese

6.Thefunctionofnotchfilteris

(a)passhighfrequencysignal

(b)passaparticularbandofsignal

(c)passlowfrequencysignal

(d)noneofthese

7. Ifasignalhasabandwidthof20Hzto20kHz,whatwillbetheminimumsamplingfrequencytoacquire thesignalsothatthesignalcanbereproducedproperly?

(a)20Hz

(b)>20Hzbut<20kHz

(c)<20kHz

(d)>20kHz

8.ThecorrectTTLlogiclevelsare

(a)0–0.8Vand2.0–5.0V

(b)0–0.4Vand2.4–5.0V

(c)0Vand5V

(d)0–0.1Vand4.9–5.0V

9.AnIEEE488buscontains

(a)8datalinesand1aAddresslines

(b)5controllines,3handshakelinesand8datalines

(c)3controllines,5handshakelinesand8datalines

(d)5controllines,3handshakelines,8datalinesand4addresslines

10.Whichmaynotbethefeatureofadataacquisitionapplicationsoftware?

(a)Managethedatastoredincomputermemory

(b)Plotacquireddata

(c)Reportrelevantinformationsuchasthenumberofsamplesacquired

(d)Acquiredatafromrealworld

Short-answerQuestions1.DefineadataacquisitionsystemanddrawthefunctionalblockdiagramofatypicalDAQ.

2.WhatarethedifferentcomponentsofaDAQ?Brieflydiscussthose.

3.Whatarethedifferentsignal-conditioningunitsadataacquisitionsystemcontains?Brieflydiscussthose.

4.WhatarethedifferentprocessesforisolationoffieldinstrumentfromDAQhardware?

5.StatethedifferentfunctionsofdriversoftwareofatypicalDAQsystem.

6.Comparesuccessiveapproximation,flash,integratingandrampADC.

7.CompareR-2RDACwithabinaryweightedDAC.

8.HowarethedigitalinputandoutputsystemconnectedwithdigitalI/OpinsofDAQhardware?

9.HowdothedevicesconnectedwithIEEE488buscommunicatewitheachother?

10.Writedownthedifferentfunctionsof5controlsignalsofIEEE488bus.

Long-answerQuestions1.An8-bitADCisconvertingatemperaturesignalwhichhasameasuringrangeof0degCto800degC.Calculate

theresolutionofthetemperature-measuringinstrument.

2.Supposea10-bitADChas+Vrefand–Vrefof+5Vand–5Vrespectively.IftheADCisbeingusedtoconvertasignalhavingminimumandmaximumvalueof–1Vand+1VthenwhatamountofsmallestvoltagechangecantheADCdistinguish?

3.Aramp-typeADCsystemusesa20MHzclockgeneratorandarampvoltagethatincreasesfrom0Vto5Vinatimeof0.5sec.DeterminethenumberofclockpulsescountedintotheregisterwhenV=1V,andwhenitis2.5V.

4.A4-bitD/Aconverterhas320kWresistancesinLSBposition.Theconverterisdesignedwithweightedresistivenetwork.Thereferencevoltageis+5V.Theoutputof theresistivenetworkisconnectedtoanOP-AMPwithafeedbackresistanceof5kW.Whatistheoutputvoltageforabinaryinputof101.110?

5.An8-bitD/Aconverterhas–Vref=–5Vand+Vref=+5Vrespectively.Thencalculatetheoutputvoltagewhenaninputof14010(decimal)isgivenintheinputofDAC.Also,findtheVLSB.

15.1 INTRODUCTION

Aftercollectinginformationaboutthestateofsomeprocess,thenextconsiderationishowtopresentitinaformwhereitcanbereadilyusedandanalysed.Thischapter,therefore,startsbycoveringthetechniquesavailabletoeitherdisplaymeasurementdataforcurrentuseor record it for futureuse.Following this, standardsofgoodpractice forpresentingdata in either graphical or tabular form are covered, using either paper or a computermonitorscreenasthedisplaymedium.

Nowadays, a wide variety of recorders are used in industry, laboratory and variousfieldsCoveringalltheseinachapterisaformidabletask.Anattempthasthereforebeenmade to classify the more common types of chart recorders. The definition of a chartrecorderis“adeviceforproducing,asapermanentrecordinanalogform,thechangeofavariablesignal(x)againsttime(t)(whetherthisbecontinuousorintermittent)”.Inthissection, only electrically actuated recorders will be considered, although in manyapplications, such as the recordingof pressure,mechanically actuateddevices are used.However, with the increasing requirement for display as well as recording at a remotecentralpoint,wheretheinformationisalsorequiredtobepassedfordataprocessing,thereisagreatertendencynowadaystouseelectricalmethodsemployingsuitabletransducers.

Many techniques now exist for recording measurement data in a form that permitssubsequent analysis, particularly for looking at the historical behaviour of measuredparameters in fault diagnosis procedures. The earliest recording instruments used werevarious formsofmechanical chart recorders.Whilstmanyof these remain inuse,mostmodern forms of chart recorder exist in hybrid forms in which microprocessors areincorporatedtoimproveperformance.Thesectionsbelowdiscussthese,alongwithothermethodsofrecordingsignalsincludingdigitalrecorders,magnetictaperecorders,digital(storage)oscilloscopesandhard-copydevicessuchasdot-matrix,inkjetandlaserprinters,X-Yrecorders,ultravioletrecordersandthermalarrayrecorders.

ClassificationofRecordersTherearemanywaysforclassifyingrecorders;thepopularoneisaccordingtothetypeofsignaltoberecorded,whichisasfollows:

1.Analogrecorders

a.Graphicrecorder

i.Stripchartrecorder

•Galvanometertype

•Nulltype

•Potentiometricrecorders

•Bridgerecorders

•LVDTrecorders

ii.Circularchartrecorders

iii.X-YRecorders

b.Magnetictaperecorders

c.Oscillographicrecorders

d.Others[hybrid,paperless,ultravioletandthermaldotmatrixrecorder]

2.Digitalrecorders

15.2 ANALOGRECORDERS

Thesekindsofrecordersareusedtorecordanalogsignalsintheformofachartpaperforkeepingtherecordpermanently.Despitethepresentemphasisbytheelectronicsindustryondigitalinstrumentation,theuseofanalogrecordersisstillpopular.Astheypresentaninstantaneous visual indication of the data being recorded, they it it in an analogway,which isoftenmoremeaningful thandigital indication topeople in the laboratoryorontheproductionline.Therearebasicallythreetypesofanalogrecordersavailable:graphic,oscillographicandmagnetictaperecorders.

15.2.1GraphicRecordersAgraphicrecorderisbasicallyameasuringdevicewhichisabletoproduceinrealtimeahard copy of a set of time functionswith the purpose of immediate and/or later visualinspection.Thecurves/linesaremostlydrawnona(long)stripofpaper(fromaroll),oftencalledstripchart recorder.When thecurvesaredrawnonacircularpaper, it iscalledacircularchartrecorder,andwhentwoindependentvariablesaretoberecordedonapieceofpaperwithrespecttoeachother,itiscalledanX-Yrecorder.

1.StripChartRecorderAstripchart recorder recordsphysicalvariablewith respect to the independentvariabletimeon a longpaper kept in the formof a roll.The independent variable time (t) thencorrespondstothestrip-lengthaxisandthephysicalvariablesmeasured(y)arerelatedtothechartwidth.Tracingsareobtainedbyawritingprocessatsitesonthechartshortaxis(y) corresponding to the physical variables magnitudes with the strip being moved atconstant velocity to generate the time axis. Graphs cannot be interpreted if essentialinformationisabsent;scalesandreferencelevelsforeachphysicalvariablerecordedandfortimeareallnecessities.Additionalinformationconcerningtheexperimentalconditionsof the recording is also necessary and is preferably printed by the apparatus (data,investigateditem,typeofexperiment,etc.).Figure15.1showsdifferentcomponentsofa

stripchartrecorder.AtypicalindustrialstripchartrecorderisshowninFigure15.2

Stripchartrecordersconsistofarollorstripofpaperthatispassedlinearlybeneathoneormorepens.Asthesignalchanges,thepensdeflectproducingtheresultantchart.Stripchartrecordersarewellsuitedforrecordingofcontinuousprocesses.

Figure15.1Stripchartrecorder

Figure15.2Industrialstripchartrecorder[Manf:OmegaCorporation]

Astripchartconsistsofthefollowing:

(a)Chart/PaperLonggraphpaperkeptontworollers,lowerrollerdragsthepaperverticallywiththehelpofamotor.

(b)ChartSpeedSelectorControlsthespeedoftherolleratsomespecifiedspeedselectedbytheoperatorandhencecontrolsthetimescale.

(c) Range Selector Amplifier or attenuator which is to be adjusted according to theamplitudelevelofphysicalvariable.Ifthephysicalvariabletoberecordedisofverylowamplitude then itneeds tobeamplifiedwithpropergain.Thegainvalue is adjustedbyselectingproperrange.

(d) Stylus Driving System Moves the stylus in proportion to the physical variable to berecorded,inmostrecorders,asynchronousmotorisusedfordrivingthepaper.

(e)Stylus Createmarking/impression on themoving graph paper [most recorders use apointerattachedtothestylus,which(pointer)movesoveracalibratedscalethusshowinginstantaneousvalueofthequantitybeingmeasured].

Themostcommonlyusedmechanismsemployedformakingmarksonthepapersare

(i) Penandink:Markingwithink-filledstylus

(ii) Thermaltype:Markingwithheatedstylusontemperaturesensitivepaper(e.g.faxpaper)

(iii) Impacttype:Markingwithpressuresensitivepaper(e.g.carbonpaper)

(iv) Electrostaticstylus:Markingwithchargedstylusonplainpaper

(v) Opticaltype:Markingwithlightrayonphotosensitivepaper

Stripchartrecordersarecommonlyusedinlaboratoryaswellasprocessmeasurementapplications.Modernstripchartrecordershavethefacilityof

(i) Simultaneousrecordinganddisplayofmultipointdata

(ii) Universal input: The recorders accept wide range of dc voltage, all commonthermocoupleandRTD.Oftentheserangescanbeprogrammedforeachchannel.

(iii) Universalpowervoltageof100Vacto240Vac,50/60Hz

(iv) AlarmDisplay/Printings

(v) Chart illumination convenient to confirm printed signal in the night or in darkplaces.

Therearevariouskindsofstripchartrecorders.Accordingtotheirworkingprinciples,these are divided in mainly two categories. One works on the principle of thegalvanometerandotheriscallednulltype.

(a)GalvanometricType Galvanometric instrumentsusuallyusead’Arsonvalgalvanometeras the basicmovement. This galvanometer consists of amoving coil (shown in Figure15.3)suspendedeitheronpivotsoratautligament.Thecoil is thenabletorotateinthefieldproducedbyapermanentmagnet.Whenasmallcurrentisappliedtothecoil,afieldiscreatedwhichreactswiththatofthepermanentmagnet,andthecoilrotates.Acontrolspring in a pivoted instrument and the ligament with a taut suspension provide anopposingtorque.Thus,dependingonthecurrentapplied,equilibriumwillbeestablished.Apointer shows thedeflection. In practice, this principle is applied in severalways. Indirect-writingmoving-coilinstruments,anarmwithapenattached,whichisfedfromaninkreservoir, isdirectlyconnected to themovingcoil.Thepen thenwrites insympathywith the coilmovementon a chart,whichmaybe either in strip formor circular from.Suchinstrumentsarecapableofrecordingfull-scaledeflectionsfromupwardsofl00mVdcand500mVac.Correspondingcurrentsare500mAdcand1mAac.Direct-writinginstruments can be fitted with a variety of chart-drive mechanisms ranging from analternating-current synchronous motor, with or without spring wound reserve (whichenables the recorder to continue to operate for a reasonable period), to a completely

mechanically driven clock mechanism. This latter feature, of course, makes theinstruments portable and for suitable for field use. There aremany possible variations.Somemanufacturersofferuptoasmanyassixmovementswritingindependentlyononechart. With the use of shunts and current and voltage transformers, ranges may beextendedforhighervalues.Onsometypes,controlfacilitiesforhighandlowalarmsarealsofitted.

(b)PotentiometricTypeWiththedevelopmentofacamplifiertechniquesinthemid1930s,therequirementforincreasedsensitivityinprocesscontrolcouldbesatisfiedbytheuseofa closed-loop recorder. In addition, themechanism, thoughmore complicated, could bemade much less susceptible to vibration. The self-balancing potentiometer type ofinstrumentconsistsofabridgecircuit.Acrossonearmofthebridgeisareferencevoltage,andacrosstheotherarmisafeedbacknetwork(showninFigure15.4).Initially,thebridgeisadjustedsothattheservoamplifieranditsmotorareinbalanceandstationary.Whenasignal is fed to the amplifier, the output causes the servomotor to drive a balancingpotentiometer,which in turn refers a feedbackvoltage to the amplifier input.When thetwosignalsareequalandopposite,thesystembalancesandtheservomotorstops.Ifapenunitisattachedtothemotor/potentiometermechaniseddrive,atthepointofbalance,thepen will show the proportional value of the input signal. As with galvanometricinstruments,thisprinciplemaybeappliedinvariousways.

Figure15.3Galvanometertyperecorder

Figure15.4Potentiometrictyperecorder

Thiskindofrecordershavingveryhighinputimpedance,infinityatbalanceconditions,andahighsensitivity.

Themostcommonapplicationofpotentiometricrecorderisforrecordingandcontrolofprocess temperatures.Self-balancingpotentiometersareundulyusedin industrybecauseofthefollowingreasons:

(i)

Theiractionisautomaticandthuseliminatestheconstantoperationofanoperator.

(ii) Theydrawacurveofthequantityofbeingmeasuredwiththehelpofarecordingmechanism.

(iii) Theycanbemountedontheswitchboardorpanelandthusactasmountingdevicesforthequantityundermeasurement.

(c) Single-Point and Multi-point Recorders Instruments that record changes of only onemeasuredvariablearecalledsingle-pointrecorders.

Amulti-point recordermay have asmany as 24 inputs, with traces displaced in sixcolours.

2.CircularChartRecorderAcircularchartrecorderrecordsdatainacircularformat.ThepaperisspunbeneathoneormorepensasshowninFigure15.5.Thepensaredeflectedinproportiontothevaryingsignal resulting inacircularchart.Circularchart recordersare ideal forbatchprocesseswhereasetprocesstimeisknown.Thechartsarenormallydesignedtorotateinstandardtimeperiods,suchas1hour,24hours,7days,etc.,althoughmanyrecordersareflexibleenoughtoaccommodatenon-standardtimeperiods.

These recorders were developed mainly to take advantage of the availability andconvenience of a spring-wound clock and synchronous motor movements to drive thechartinacirculardirection.Thecircularchartusedherehasconcentriccirclesruledonitto form its scales as shown inFigure15.5. In addition, there areprinted arcs extendingfromthecentreof thechart to thepaper’sedge.As thepenof therecorder ismoved, itswingsalongthesearcs;thesearcsarecalledthe‘timearcs’.Thespeedoftherotationofthe chart is usually one revolution per 24 hours or per seven days or any other speed,which can be conveniently obtained by using a synchronous motor with suitable gearassembly.Theradialpositionofthepenatanytimeindicatestheinstantaneousvalueofthequantityundermeasurement.AtypicalindustrialcircularrecorderisshowninFigure15.6.

Figure15.5Circularchartrecorder

Figure15.6Industrialcircularchartrecorder[Manf:Omega]

Chartdiameter is limited to amaximumof0.3m.Speedof the chart is also limited,resolutionalong the scale length isusuallynon-uniformand thechartsdonot run for alongperiod.Magnitudeofseveralvariablescanberecordedonasinglechartwhichmakesiteasyandconvenienttoanalysetheinterrelationshipofvariousmeasurementsandalsosavesthepanelmountingspace.

Thevariousdrivesforcircularchartsareclassifiedasfollows:

(a)Mechanical(springclockdrive)

(b)Pneumatic(airlockdrive)

(c)Electric(synchronousregulateddcmotorormotorwoundspring)

(d)Dualpowereddrive(duplex),i.e.asynchronousmotorandspringclockmechanicaldrive

(e)Externallycontrolleddrives

Circular chart recorders are particularly suitable for direct actuation by a number ofmechanicalsensorssuchasbellows,bourdontubes,etc.

3.X-YRecorderWiththedevelopmentofthepotentiometricprinciple,userswereawarethatarecordwasoften required as the resultant of two varying signals, and thus the X-Y plotter wasintroduced (Figure 15.7). Today, X-Y plotters are as flexible as conventionalpotentiometric instruments, except that they have two completely independent servo-systemstooperatetheXandYchannels.ThetwomostpopularsizesareA4andA3(297mm×210mm,420mm×297mm,respectively).SensitivitiessimilartothoseobtainablewithY-t instruments are achieved, and, often, themore comprehensive instruments arealsofittedwithatimeaxist,whichprovidessingleorrepetitivetimesweepsagainsttheYaxis.

XYrecordersaccepttwoinputsandcreateachartorgraphofoneinputversustheother.They are commonly used to determine the relationship between the two inputs. Forexample, in a chemical process, an XY recorder might be used to monitor the effecttemperaturehasonthepressureoftheprocess.AtypicalindustrialXYrecorderisshown

inFigure15.7.

Figure15.7IndustrialXYrecorder[Manf:Omega]

This system has a penwhich can be positioned along the two axeswith thewritingpaperremainingstationary.Therearetwoamplifierunits,oneamplifieractuatesthepenintheY-directionastheinputsignalisapplied,whilethesecondamplifieractuatesthepeninthe X-direction. The movements of the pen in X-and Y-directions are automaticallycontrolledbymeansofamotor,pulleysandalinearpotentiometer.Obviously,traceofthemarkingpenwillbeduetothecombinedeffectsoftwosignalsappliedsimultaneously.Intheserecorders,anemfisplottedasafunctionofanotheremfTherearemanyvariationsofX-Yrecorders.Withthehelpoftheserecordersandappropriatetransducers,aphysicalquantity may be plotted against another physical quantity. Figure 15.8 shows a blockdiagramofatypicalanalogX-Yrecorder.

Asignalentersineachofthetwochannels.

The signals are attenuated to the inherent full-scale range of the recorder (often 0.5mA).The signal then passes to a balance circuitwhere it is comparedwith an internalreferencevoltage.

Theerrorsignal(i.e.thedifferencebetweentheinputsignalvoltageandthereferencevoltage)isfedtoa“chopper”whichconvertsdcsignaltoanacsignal.

Thesignalisthenamplifiedinordertoactuateaservomotorwhichisusedtobalancethesystemandholditinbalanceasthevalueofthequantitybeingrecordedchanges.

Theactiondescribedabovetakesplaceinboththeaxessimultaneously.Thus,wegetarecordofonevariablewithrespectofanother.

Figure15.8DifferentcomponentsofanXYrecorder

Advantages

1. Theinstantaneousrelationshipbetweentwophysicalquantitiescanberecorded.2. Therelationshipbetweeneitherelectricalornon-electricalquantitiescanberecorded.3. Inmodemtypesofrecorders,zerooffsetadjustmentsareavailable.

ApplicationsAfewexamplesinwhichuseofX-Yrecordersareusedareasunder:

1. Plottingofstress-straincurves,hysteresiscurvesandvibrationsamplitudeagainstsweptfrequency

2. Pressure-volumediagramsforLCengines3. Pressure-flowstudiesforlungs4. Liftdragwindtunneltests5. Electricalcharacteristicsofmaterialssuchasresistanceversustemperature6. Plottingtheoutputfromelectroniccalculatorsandcomputers7. Speed-torquecharacteristicsofmotor8. Regulationcurvesofpowersupplies9. Plottingofcharacteristicsofvacuumtubes,zenerdiodes,rectifiersandtransistors,

etc.

4.HybridRecordersHybrid chart recorders represent the latest generation of chart recorder and basicallyconsist of a potentiometric chart recorder with an added microprocessor. Themicroprocessor provides for selection of range and chart speed, and also allowsspecification of alarmmodes and levels to detect whenmeasured variables go outsideacceptable limits.Additional information can also be printed on charts, such as names,timesanddatesofvariables recorded.Microprocessor-based,hybridversionsofcircular

chart recorders also now exist. A typical industrial hybrid recorder is shown in Figure15.9.

Ahybridrecordercanfunctionasarecorderordatalogger.Likeastandardrecorder,thehybridrecordercangenerateachartoftheinputs.However,itcanalsoproduceadigitalstampofthedatasimilartoadatalogger.Theyarecommonlyavailableinmultichanneldesigns although one print head normally handles all channels. This makes the hybridrecorderacost-effectivesolutionformultichannelsystemsalthoughtheresponsetimeisnotasfastasrecorderswhichhaveauniquepenforeachchannel.

5.PaperlessRecordersPaperless recorders are one of the latest types of recorders to emerge on the market.Paperlessrecordersdisplaythechartontherecorders’graphicdisplayratherthanprintthechartonpaper.Thedatacannormallyberecordedininternalmemoryortoamemorycardforlatertransfertoacomputer.Themajorbenefitofpaperlessrecordersisconservationofpaperandeasytransfertoacomputer.AtypicalindustrialpaperlessrecorderisshowninFigure15.10.

Figure15.9Industrialhybridrecorder[Manf:Omega]

Figure15.10Industrialpaperlessrecorder[Manf:Omega]

6.UltravioletRecordersThelimitedbandwidthproblemofgalvanometricrecordersareduetosystemmomentofinertiaandspringconstantscanbereducedlimited to themaximumbandwidth toabout100Hz.Ultraviolet recordersworkonverysimilarprinciples to standardgalvanometricchart recorders, but achieve a very significant reduction in system inertia and springconstantsbymountinganarrowmirrorratherthanapensystemonthemovingcoil.This

mirrorreflectsabeamofultravioletlightontoultravioletsensitivepaper.Itisusualtofindseveralofthesemirror-galvanometersystemsmountedinparallelwithinoneinstrumenttoprovide a multi-channel recording capability, as illustrated in Figure 15.11. Thisarrangement enables signals at frequencies up to 13 kHz to be recordedwith a typicalinaccuracyof±2%fullscale,while it ispossible toobtainsatisfactorypermanentsignalrecordings by this method. Special precautions are necessary to protect the ultraviolet-sensitivepaper fromlightbeforeuseand tospraya fixing lacqueron itafter recording.Such instruments must also be handled with extreme care, because the mirrorgalvanometersandtheirdelicatemountingsystemsareeasilydamagedbyrelativelysmallshocks. In addition, ultraviolet recorders are significantlymore expensive than standardchartrecorders.

Figure15.11InternalrecordingcomponentsofUVrecorder

7.ThermalDotArrayRecordersThermal dot array recorders have the advantage of not having any moving parts. Thewritingmechanismisanarrayofequidistantwritingpointswhichcoversthetotalwidthofthepaper.Forwriting,mediumthermo-sensitivepapersaregenerallyused. In thisarraythe writing system consists of miniature electrically heated coils. Maximum writingfrequencyisdeterminedbythermalpropertiesofthecoilswhichareinclosecontactwiththe chart paper and the electric activating pulse. Heating of the thermo-sensitive paperresults in a black dot with good long-term stability. The heating pulse is controlled inrelation to the chart velocity in order to obtain sufficient blackness at high velocities.Tracing blackness or line thickness is seldom used for curve identification; andalphanumericannotationismostlyapplied.Differenttypesofgridpatternscanbeselectedby the user. Moreover, alphanumeric information can be printed for indicatingexperimental conditions. Ordinate axis resolution is determined by the dot array:primarily,8dots/mm;exceptionally,12dots/mm(as in standard laserprinters).Mostofthedotarrayinstrumentsareintendedforhigh-signal-frequencyapplications:perchannelsamplingfrequenciesof100,200,andeven500kHzareusedinrealtime.Thesesamplingfrequencies largely exceed the writing frequencies; during the writing cycle, data are

storedinmemoryandforeachchannelwithineachwritinginterval,adottedverticallineisprintedbetweentheminimalandthemaximalvalue.Forexample,asinewavewithafrequency largelyexceeding thewritingfrequency is representedasablackbandwithawidth equal to the sine amplitude. In this way, the graphs indicate the presence of aphenomenonwithafrequencycontentexceedingthewritingfrequency.

15.2.2MagneticDiskandTapeTypeRecorderAtpresent,magneticrecordingtechnologydominatestherecordingindustry.Itisusedintheformsofharddisk,floppydisk,removabledisk,andtapewitheitherdigitaloranalogmode. In its simplest form, it consists of amagnetic head and amagneticmedium, asshowninFigure15.12.Theheadismadeofapieceofmagneticmaterialinaringshape(core),withasmallgapfacingthemediumandacoilawayfromthemedium.Theheadrecords (writes) and reproduces (reads) information, while the medium stores theinformation.TherecordingprocessisbasedonthephenomenonthatanelectriccurrentigeneratesamagneticfluxfasdescribedbyAmpere’slaw.Thefluxfleaksoutoftheheadcoreatthegap,andmagnetisesthemagneticmediumwhichmovesfromlefttorightwithavelocityVundertheheadgap.Dependingonthedirectionoftheelectriccurrenti, themediumismagnetisedwithmagnetisationMpointingeitherleftorright.Thispatternofmagnetisationisretainedinthememoryofthemediumevenaftertheheadmovesaway.Magnetictapesarestillpopularinseveralareassuchas

1. Medicalresearch2. Patientmonitoring3. Surveillance4. Spying5. Productioncontrol

Figure15.12Magnetictaperecording

1.TheMagneticTapeBeforeactuallygoing into thedetailsof themagnetic tape recorder, it isbetter toknowaboutthetapewhichisusedforthispurpose.Actually,thetapeismadeoutofaspecialtypeofplasticmaterialwhichisstableandcanwithstandcontinuousrubbingagainstthehead.Normally,thismaterialiseitherPVCorMylarwhicharequiteresistanttowearandstretchingisnecessaryforthetapetoremainusefulforalongperiodoftime.Ontopofthis plastic base, there is a thin layer of magnetic material, usually iron oxide. Theparticlesofthismagneticmaterialareshapedintheformoftinyneedlesandoccupythetop portion of the plastic base. The typical thickness of the tape is of the order of 25micrometres.

Duringrecording,anelectricalsignalcausescurrenttoflowthroughthecoilproducing

amagnetic field in thegap,asshownby theblue linesof force inFigure15.12.As theelectricalsignalvaries inamplitudeand frequency, sodoes themagnetic field.The tapeconsistsofaplasticfilmcoatedwithamaterialthatismagnetisedbythefieldasitpassesoverthegap.Asthemagneticfieldvariesinstrength,sodoesthemagnetismstoredonthetape.Duringplayback,thetapepassesoverthesamehead(itiscalledtherecord/playbackhead).Thistimethemagnetismstoredonthetapeinducesavoltageintheheadcoil.Thisvoltageisamplifiedandusedforretrievaloftherecordedsignal.

(a)PrinciplebehindMagneticRecording—HysteresisLoopThoseofyouwhohavestudiedphysicsmustsurelyrememberthattherearetwomagnettypes,namelypermanentmagnet and temporarymagnet. In a temporarymagnet, themagnetism is induced as aresultofsomeforcewhichalignsthemagneticparticlesalongaspecificaxis.Thisforcecouldbeduetorubbingofanothermagneticmaterialoranelectromagneticfieldappliedusingavaryingcurrent.

TakealookatthetypicalmagnetisationcurveinFigure15.13,whichshowsthegraphofthemagnetisingforceHagainstthefluxdensityB.Whenamaterialisinpurelynon-magnetisedstateandamagnetisingforceisapplied,thefluxdensityrisesalongthedottedlineOAC.Butnowifthecurrentisbroughttozero,thefluxdoesnotreducetozerobutaresidualfluxremainsandthecurrenthastobeextendedintothenegativeregion(oppositedirection)tobringBtozeroagain.

Hence,aloopisformedoftheoverallprocessascanbeseenfromthediagramandthisisknownas themagnetisationcurve for thematerial or is alsoknownas thehysteresisloop. Now this property may be undesirable in several situations but here you canintuitively imagine agreat use for the same.Once the signal is applied to themagnetictapeviatherecordinghead,thesectionofthetapegetsmagnetisedinaccordancewiththesignalwhichleavesaresidualfluxonthetape.Thisacts tostore thatsignalonthetapewhichcanbeplayedbackusingtheplaybackhead.

Figure15.13Hysteresisloop

(b)TheBasicArrangement The basic circuit of amagnetic recording and playbacksystem isquite simple andcanbeunderstoodby seeingFigure15.14,which shows theentire arrangement.Of course, this is a highly simplified sketchwithout the insidenutsandbolts,yetitisusefultotakeabroadviewofthesystem.

Asyoucansee,theentiresystemconsistsoftwoportions—amechanicalarrangement

tomakethemagnetic tapemoveacross twopoints,andanelectricalsystemwhichdoesthe real job.Themechanicalmovement is achievedwith the help ofmotor drive and acombinationofrollersandbelts.Theelectricalpartistakencareofbyappropriatecircuitswhichdotheworkofrecording,playbackandamplificationofsound.Therearetwoheadswhichareusedforrecordingandplaybackofthesignalsrespectively.

(c)RecordingandPlayback Thebasicprincipleofoperation isquite simple.As thetaperubsagainst therecordinghead, itappliesamagneticfieldwhichisproportional totheinputsignal.Thissignalorientsthemagneticparticlesinaspecificformatwhichactsasindicatorstothepatternofsignalstored.Whentheplaybackheadrubsagainstthetape,the signal is reproduced since now the particles induce similarmagnetic patterns in thehead. If youwant to readmore technicaldetails about thisprocessyoucan refer to thenextarticleonthistopic(comingsoonandwillbelinkedhere).

Figure15.14Magnetictaperecordingmechanism

There are several types of recording techniques which are used for recording onmagnetictapesandthesecanbe

DirectrecordingFrequencymodulationrecordingPulsedurationmodulationrecordingDigitalrecording

Wewilltakealookatallthesemethodsofrecordingonmagnetictapes

2.DirectRecordingIf the signals are recorded in an analog manner in a way so that the amplitude andfrequencyofthesignalisrecordedlinearlyasavariationoftheamplitude,magnetisationand wavelength on the magnetic tape, such a system of recording is known as directrecording. Since low distortion is required on the playback signal, this is achieved byaddingahigh-frequencyacbiassignaltothesignalbeingrecorded.

Thismethodofrecordingismostsuitedforaudiosignalsratherthananyotherpurpose.Thisissobecausethehumanearhasanin-builtmechanismwhichaveragestheamplitudevariationerrors.

3.FMRecordingWehavelearntaboutfrequencymodulationinapreviousarticleandknowthatfrequencymodulationisallaboutusingasinewavecarriersignalandmodulatingormodifyingitas

per the signal to be loadedon that carrier signal.Similarly, in caseofFM recording inmagnetic tapes, a frequencymodulator is used to feed the input signal onto the carriersignal.Thissignal is thenrecordedonto themagnetic tapeeitherwithorwithout theacbiassignalasdescribedintheprevioussectionofdirectrecording.

Figure15.15showsasimplifiedviewofsucharecordingsystemwithoutshowingtheinternal details.Asyou can see,when the signal is now reproducedusing theplaybackhead,itneedstobepassedthroughademodulatorwhichseparatesthesinecarrierwavefromtherecordedsignalandthenreproduced.

Figure15.15FMrecordingmechanism

Thissystemismorecomplicatedinitsconstructionandexpensivetobuildbecauseofthevarious extra circuitries involved in it.Hence, normally it is onlyused in situationswhere amplitude-variation errors are not acceptable, such as instrumentationwhere theparametersofsomedelicate industrialprocessare recorded.Despite thisadvantage, thissystemhasapoorhigh-frequencyresponseandrequiresahighertapespeedwhichneedstobepreciselycontrolled.

4.PDMRecordingInthistypeofmagnetictape-recordingsystem,theinputsignalisconvertedintoapulsesignal. The duration of the pulse is in tunewith the amplitude of the signal; hence thename pulse duration modulation since the duration of the pulse varies with the inputsignal.

Obviously,sincethecontinuousinputsignalisdividedintodiscretepulses,thistypeofrecordingsystemisevenmorecomplicatedandexpensivethantheFDMsystemdescribedpreviously. Yet it is used in situations which require special quality recording such assituationswherealargenumberofvariablesaremonitoredandtheychangeveryslowly.Theadvantagesofsuchasystemare

(a)Multichannelrecording

(b)Greatdegreeofaccuracy

(c)Verylowsignal/noiseratio

5.BenefitsofMagneticRecordingNowwewill takealookatsomeoftheadvantagesanddrawbacksofthemagnetictapesystems.

(a)Thefrequencyrangeofthesignalsstoredonthetapehasaverywiderangeandspectrum,andanequallygooddynamicrange.

(b)hereisverylessdistortionofsignalsstoredonthetape.Thisisspecificallyusefulforaudio/videopurposes

(c)Tapescanbeusedtostoremultiplesignalsalongthesamelength,thusincreasingefficiency.

(d)Eventhoughyoumightthinkthatelectronicmemoriesaregettingcheaper,thetapestillisawinnerintermsofcostperbitofstorage.Thisismainlyduetolargesurfaceareaofthetapeandveryhighdatadensity.

(e)Timebaseofthestoredsignaldatacanbevariedasperrequirement.Thismeansthatsignalsrecordedatfastspeedcanbeplayedbackatslowerspeedandviceversa,whichisusefulinseveralapplications

15.2.3OscillographicRecordersAlthough,strictlyspeaking,oscillographsaredirect-writinginstruments,theyalsoemploya moving coil, but the writing element uses much more power and is fed from an acamplifier feedingadriverpoweramplifier.Thewritingelement,usuallyreferred toasa“penmotor”,canconsumemorethan100W.Theangulardeflectionofthemotorisoftenrestricted to as little as 17°with the result that response times of up to 150Hz can beobtained.Oscillographsaresuitableforrecordinghightransientsignalssuchasoccurringinstrain-gaugemeasurementsandinmedicalapplicationssuchasmeasuringheartbeatandbrain-response(ECGsandEEGs).Therecordingisusuallymadeoninklesspaperusingaheatedstylus.

Used primarily for applications in the test and research fields, the capabilities ofoscillographic recorders and thenewerdigital oscilloscopeshave expandedgreatlyoverthepastseveralyears.Anoscillographisadevicefordeterminingwaveformsbyplottinginstantaneousvaluesofaquantitysuchasvoltageasafunctionoftime.Adecadeago,thisimplied either a recording galvanometer or a CRT recorder—analog instruments thataffordedtheneededbandwidthsinexcessof20kHz.

Asinotherrecorderdevelopments,however,digitalisthebuzzwordtodayandDigitalStorage Oscilloscopes (DSOs) or simply digital oscilloscopes have proliferated. Thesemaybe defined as oscilloscopes that digitise an input signal for storage inmemory forlaterdisplayoranalysis.Itisalogicalandrelativelysimplesteptousethestoreddatatoprovideachartrecord,andmanyDSOsdojustthat,essentiallyactingasdataloggers.

A recent survey lists some 30 different suppliers ofDSOs,many of them PC-based.Theycoverarangeofbandwidths—somearound40to50MHzwhileothersgoashighas350MHz.ThesearesophisticatedelectronicinstrumentsthathavecapabilitiesfarbeyondtraditionalanalogCRT-basedoscilloscopes,whichhavebeenaroundformanydecades.

15.3 DIGITALRECORDERS

Digital recorder record the data in the form of ‘1’ and ‘0’. There are several types ofdigital recorders.Thefollowingsectiondiscussesdata loggersandmagnetic-typedigitalrecorders.

15.3.1DataLoggerDataloggersareisastand-alonedevicesthatcanrecordinformationelectronicallyfrominternalorexternalsensorsorotherequipmentthatprovidedigitalorserialoutputs.

1.KeyFeaturesofDataLoggers(a)Stand-aloneOperationMostdataloggersarenormallyconfiguredwithaPC,somemodels canbe configured from the front panel providedby themanufacturer.Once thedataloggersareconfigured,theydon’tneedthePCtooperate.

(b)Support forMultipleSensorTypes Data loggersoftenhaveuniversal input typewhichcanacceptinputfromcommonsensorslikethermocouple,RTD,humidity,voltage,etc.

(c)LocalDataStorageAlldataloggershavelocaldatastorageorinternalmemoryunit,soallthemeasureddataisstoredwithintheloggerforlatertransfertoaPC.

(d) Automatic Data Collection Data loggers are designed to collect data at regularintervals,24hoursadayand365daysayearifnecessary,andthecollectionmodeisoftenconfigurable.

Data logging and recording are both analog terms in the field ofmeasurement.Datalogging is basically measuring and recording of any physical phenomena or electricalparameter over a period of time. The physical phenomena can be temperature, strain,displacement, flow, pressure, voltage, current, resistance, power, and many otherparameters.TypicalindustrialdataloggersareshowninFigure15.16.

Figure15.16Typicaldataloggers[Manf:NationalInstrumentandOmegaCorp.]

Thedata logger collects information about the state of any physical system from thesensors.Thenthedata loggerconverts thissignal intoadigitalformwiththehelpofanA/Dconverter.Thisdigitalsignalisthenstoredinsomeelectronicstorageunit,whichcanbeeasilytransferredtothecomputerforfurthertheanalysis,theschematicdiagramofadata-loggingapplicationinindustrialenvironmentisshowninFigure15.17.

Figure15.17Industrialdatalogginganddisplay

Afewbasiccomponents thateverydata loggermusthaveareshowninFigure15.17,whichare:

1. Hardwarecomponentslikesensors,signalconditioning,andanalog-to-digitalconverter,etc.

2. Long-termdatastorage,typicallyonboardmemoryoraPC3. Softwareforcollectingdata,analysingandviewing

2.FunctionsofDataLoggersBeyondtheacquiringandstoringdata,adataloggeroftenperformsvariouskindsofotherjobs like offline and online analysis, display, sharing datawith other devices connectedwiththenetwork,reportingeventsandprovidingalarmwheneversomecriticalsituationarises.Acompletedata-loggingapplicationtypicallyrequiresmostoftheelementsshowninFigure15.18.

Figure15.18Differentcomponentsofdataloggers

15.3.2DigitalTapeRecordingThe verymention of the namedigital tape recording brings the picture of hard drives,flashmemories,etc.toourmind,butthisalsoreferstoanothermethodofrecordingonthegoodoldmagnetictapeaswell.Figure15.19showsthedigitaltaperecordingmechanism.

Figure15.19Digitaltaperecordingmechanism

Theonlydifferenceis that thesignalsarerecordedintheformof0sand1swhicharetypicalofthedigitalworld.Obviously, itwouldrequiremodulationofsomeformorthe

other,toconvertanalogtodigitalsignalsandhencethereareseveralmethodsofmagnetictaperecordingwhichfallunderthecategoryofdigitalrecording.Someofthesemethodsare

1. Return-to-biasmethod2. Return-to-zeromethod3. Non-Return-to-zeromethod

Thedetaileddescriptionof thesemethodswouldbeabit toocomplicatedheresowewilljustgothroughthebasicsofoneofthese,letussaytheReturn-to-Bias(RB)method.Figure (15.19) schematically shows the digital recording/reproducing process. First, alluserdataareencodedintoabinaryformat—aserialof1sand0s.Thenawritecurrentiissent to the coil. This current changes its direction whenever a 1 is being written.Correspondingly, a change of magnetisation, termed a transition, is recorded in themedium for each 1 in the encoded data. During the reproducing process, the electricvoltage induced in the head coil reaches a peak whenever there is a transition in themedium.Apulsedetectorgeneratesapulseforeachtransition.Thesepulsesaredecodedtoyieldtheuserdata.TheminimumdistancebetweentwotransitionsinthemediumisthefluxchangelengthB,andthedistancebetweentwoadjacentsignaltracksisthetrackpitchW,whichiswiderthanthesignal trackwidthw.Thefluxchangelengthcanbedirectlyconvertedintobitlengthwiththepropercodeinformation.Thereciprocalofthebitlengthiscalledlineardensity,andthereciprocalof thetrackpitchis termed trackdensity.Theinformationstorageareadensityinthemediumistheproductofthelineardensityandthetrackdensity.Thisareadensityroughlydetermineshowmuchinformationausercanstoreinaunitsurfaceareaofstoragemedium,andisafigureofmeritforarecordingtechnique.Much effort has been expended to increase the areal density. For example, it has beenincreased50timesduring90’s.

15.4 DISPLAYSYSTEM

Thedisplaysystemactsasafinallinkbetweenthemeasuringprocessandtheuser.Ifthedisplayisnoteasytoseeandeasytounderstandthenthatprocess iscompromised.Theuser’ssensorycapabilitiesandcognitivecharacteristics,therefore,mustbothbeaddressedin display-system selection. Furthermore, display technologies and performancecapabilities are easier to evaluate in the context of their intended application. Thefollowingsectiondiscussesvariouskindofcommonlyuseddisplaysystem.

15.4.1CathodeRayTube(CRT)TheCathodeRayTube(CRT)wasdevelopedfor televisionin the40s.Nowithaswiderangeofapplicationsinoscilloscopes,radarandmonitors,etc.

Itconsistsofaglassenvelopemadefromaneckandcone.Allairhasbeenextractedsothat it contains a vacuum.At the narrow end are pinswhichmake connectionwith aninternal electron gun, as shown in Figure 15.20. Voltages are applied to this gun toproduceabeamofelectrons.Thiselectronbeamisprojectedtowardstheinsidefaceofthe

screen.

Different basic component of CRTs are electron gun, electron accelerating anode,horizontal and vertical electric field coils, electron beam and a screen coated withphosphor.Theelectrongungeneratesanarrowbeamofelectrons.Theanodesacceleratethe electrons. Deflecting coils produce an extremely low-frequency electric field thatallowsforconstantadjustmentofthedirectionoftheelectronbeam.Therearetwosetsofdeflectingcoils:horizontalandvertical.(Inthefigure,onlyonesetofcoilsisshownforsimplicity).Theintensityofthebeamcanbevaried.Theelectronbeamproducesatiny,brightvisiblespotwhenitstrikesthephosphor-coatedscreen.Thescreeniscoveredwithafinelayerofphosphorescentelements,calledphosphors,whichemitlightbyexcitationwhenelectronsstrikethem,creatingalit-updotcalledapixel.

Figure15.20InternalcomponentsofaCRT

Toproduceanimageonthescreen,complexsignalsareappliedtothedeflectingcoils,andalsototheapparatusthatcontrolstheintensityoftheelectronbeam.Thiscausesthespottoraceacrossthescreenfromrighttoleft,andfromtoptobottom,inasequenceofhorizontallinescalledtheraster.AsviewedfromthefrontoftheCRT,thespotmovesinapatternsimilartothewayyoureyesmovewhenyoureadasingle-columnpageoftext.Butthescanningtakesplaceatsucharapidratethatyoureyeseesaconstantimageovertheentirescreen.

The illustration shows only one electron gun. This is typical of a monochrome, orsingle-colour CRTs. However, virtually all CRTs today render colour images. Thesedevices have three electron guns, one for the primary colour red, one for the primarycolour green, and one for the primary colour blue. The CRT thus produces threeoverlappingimages:oneinred(R),oneingreen(G),andoneinblue(B).Thisistheso-calledRGBcolourmodel.

In computer systems, there are several display modes, or sets of specificationsaccordingtowhichtheCRToperates.ThemostcommonspecificationforCRTdisplaysisknownasSVGA(SuperVideoGraphicsArray).Notebookcomputerstypicallyuseliquidcrystaldisplay.ThetechnologyforthesedisplaysismuchdifferentthanthatforCRTs.

ColdCathodeDisplayAcathodeisanyelectrodethatemitselectronsasdiscussedinthesectiononCRTdisplay.Generally, the cathode is heated so that electron emission occur at lower potentialdifferencethesecathodearecalledhotcathodeandarewidelyusedinvacuumtubeCRTmonitor oscilloscope, etc. By taking advantage of thermionic emission, electrons can

overcome thework functionof the cathodewith lower electric field.But in the caseofcold cathode, sufficient voltage is provided so that electrons can overcome the workfunction and come out from the cathode at ambient temperature. Because it is notdeliberately heated, such a cathode is referred to as a cold cathode. Although severalmechanismsmayeventuallycause thecathode tobecomequitehotonce it isoperating.Mostcoldcathodedevicesarefilledwithagaswhichcanbeionised.Afewcoldcathodedevicescontainavacuum.

15.4.2LightEmittingDiode(LED)OneofthecheapestandconvenientwaystodisplayinformationelectronicallyisbyusingLight-EmittingDiodes(LEDs).Itisbasicallyap-njunctionphotodiodewhenexcitedatforward-bias condition emits light (basic theory of LEDs are discussed in chapter on“FibreOpticMeasurements”).Itcanbeeasilyinterfacedwithasimpleelectroniccircuitandisdurableandreliable.TheseLEDsareoftenarrangedindifferentformatstodisplayinformation.Among these, the seven segmentsconfigurationanddotmatrixdisplayareverycommonandwidelyused.Theseven-segmentconfigurationofanLEDarrangedintheformofthedigit8canberestrictiveinthatitdoesnotadequatelyallowthedisplayofsome alphanumeric characters. By contrast, the versatility of a dot-matrix arrangementallowsanLEDunit todisplaymorecomplicatedshapes.Thefollowingsectionsdiscusstheaboutseven-segmentanddot-matrixLEDdisplay.

1.TheSevenSegmentDisplayOnecommonrequirementformanydifferentdigitaldevicesisavisualdisplay.IndividualLEDscanofcoursedisplaythebinarystates,i.e.‘ON’orOFF’.Butwhensomenumbersorcharactersare tobedisplayed thensomearrangementof theLEDsare required.Onepossibility is a matrix of LEDs in a 7 × 5 array. However, if only numbers are to bedisplayed then this becomes a bit expensive. A much better way is to arrange theminimumpossiblenumberofLEDsinsuchawaythatitcanrepresentanumberrequiringonly 7 LEDs. A common technique is to use a shaped piece of translucent plastic tooperateasaspecialisedoptical fibre, todistribute the light fromtheLEDevenlyoverafixed bar shape. The seven bars are laid out as a squared-off figure “8”. The result isknownasaseven-segmentLED.

Seven-segment displays having a wide range of applications. They used in clocks,watches,digitalinstruments,digitalbalancesandmanyhouseholdappliancesalreadyhavesuchdisplays.

There are basically two type of seven-segment displays—common cathode andcommonanode.Thecommon-anodetypeisshowninFigure15.21,where‘a’,‘b’,‘c’,‘d’,‘e’, ‘f’and ‘g’ represent individualLEDswhicharearrangedasshown in the figure. Inordertodisplaynumbersoftendecimalpointhavetobedisplayed.Forthat,anotherLEDhasbeenadded,whichisrepresentedby‘dp’(decimalpoint).

Figure15.21Commonanodeconnectionofsevensegmentdisplayunit

Atypicalseven-segmentdisplayunitisshowninFigure15.22.Figure15.23showsthepindiagramofacommonanodetypeseven-segmentdisplay.Thatmeansthatthepositivelegof eachLED is connected to a commonpointwhich is thePin3 in this case.EachLEDhasanegativelegthatisconnectedtooneofthepinsofthedevice.Tomakeitwork,youneedtoconnectthepin3to5volts.Thentomakeeachsegmentlightup,connectthegroundpinforthatLEDtoground.Aresistorisrequiredtolimitthecurrent.RatherthanusingaresistorfromeachLEDtoground,youcanjustuseoneresistorfromVcctothepin3tolimitthecurrent.

Figure15.22Typicalsevensegmentdisplayunit

Figure15.23Pindiagramofsevensegmentdisplayunit

Table15.1showshowtoformthenumbers0to9andthelettersA,B,C,d,E,andF.‘0’meansthatpinisconnectedtoground.‘1’meansthatpinisconnectedtoVcc.

Table15.1Formingnumbersandletters.

2.DotMatrixDisplayLEDsarearrangedinmatrixform—commonconfigurationsare5×7,5×8and8×8,asshowninFigure15.4.Basedontheelectrodeconnections,twokindsofLEDmatricesarepossible,one iscommonanode.All theLEDs ina rowhaving theanodeareconnectedtogether. The other one is common cathode, having all LEDs in a row, the commoncathodeorcathodesareshorted. It iseasier tounderstand theconstructionand interfacecapabilities of an LED matrix using an illustration. Figure 15.24 depicts a matrixconstruction of the common-anode type.A singlematrix is formedby thirty-fiveLEDsarrangedinfivecolumnsandsevenrows(5×7).TheanodesofthefiveLEDsformingonerowareconnectedtogether.Similarly,thecathodesofthesevenLEDsofacolumnareconnected together. In this arrangement ofLEDs, the cathodes are switched to turn theLEDsofarowonoroff.

The matrix (unit) illustrated in Figure 15.25 can be used to display a singlealphanumeric character. Several such units can be placed next to each other to form alargerpaneltodisplayastringofcharacters.

Figure15.24LEDMatrixwithcommon-anodearrangement

Figure15.255×7and8×8dotmatrixdisplay

3.DisplayofInformationusingLEDMatrixFromFigure15.26 it isclear thatswitching/multiplexingofrowsis required todisplayacharacteronthematrixunit.Theseareoftendonebyusingexternalhardwarelikelatches.EachrowoftheLEDisdrivenforabriefperiodbeforeswitchingtothenextrow.Asthehumaneyeretainsavisualimpressionofanobjectforashortdurationaftertheobjectisremoved. Retention time depends on the brightness of the image. Due to this visualphenomenon termed persistence of vision, the human eye considers that the LEDs areglowingcontinuouslyandcanvisualisethecharacters.

Rapid switching between rows produces the illusion that all the rows areON at thesametime.Tofunctionasintended,twoadditionalrequirementsmustbemet:

1. TheLEDsmustbeoverdrivenproportionatelyortheycanappeardim.ThedimnessoccursbecausearowisONforonlyafractionoftime.

2. Therowsmustbeupdatedoftenenough(e.g.eachrowisscannedabout30–40timespersecond),toavoiddisplayflicker.Foractualcharacterdisplay,itisnecessarytomaptheshapeofthecharactertothe5x7LEDmatrix.Figure15.26illustratesthecharactersAandB.

Figure15.26IllustrationoftheCharactersAandB

Foranygivencharacter, a correspondingpatternofLEDONandLEDOFFmustbegenerated, for example, the character A, as displayed in the figure, is formedwith thepatternshowninTable15.2.Table15.2DisplayPatternfortheCharacterA

Othercharacters/objectscanbedevelopedinasimilarmannerandstoredinthememorytobeusedwhiledisplaying.ByfrequentlyswitchingtherowsorcolumnswiththeproperselectionofLEDON/OFFpatterns,thehumaneyeperceivesthedisplayascontinuous.

15.4.3LiquidCrystalDisplay(LCD)The Liquid Crystal Display ( LCD) has been one of the enabling technologies of thecurrent electronic revolution. It is anessentialpartof everymobilephone, every laptopand every personal organiser.Liquid crystal is an organic compound that polarises anylight thatpasses through it.A liquidcrystalalsoresponds toanappliedelectric fieldbychanging the alignment of itsmolecules, and in so doing changing the direction of thelightpolarisation that it introduces.Liquid crystals canbe trappedbetween twoparallelsheets of glass, with a matching pattern of transparent electrode on each sheet. Figure15.27showsdifferent layersofa typicalLCDdisplay.Whenavoltage isapplied to theelectrodes,theopticalcharacterofthecrystalchangesandtheelectrodepatternappearsinthecrystal.AhugerangeofLCDshasbeendeveloped, includingthosebasedonseven-segment digits or dot matrix formats, as well as a variety of graphical forms. Manygeneral-purposedisplaysareavailablecommercially.

Theliquidcrystalfluidistheactivemediumthatisusedtocreateanimage.Itconsistsof a very large number of elongated crystals suspended in a fluid. This reservoir issandwiched between two thin sheets of glass. Each piece of glass has a transparentconductivepatternbondedtoit.Thecrystalsarealignedinaspiralpatternuntilanelectricfieldisimpressedontheconductors.

Figure15.27DifferentlayersofatypicalLCDdisplay

Asheetofpolarisingmaterial isbonded to theoutside surfacesofboth the front andrear glass covers.As incident light of randompolarisation enters the top polarizer, it isstoppedexcept for thatwhich ispolarised in theproperdirection.Withnoelectric fieldapplied, the light is twisted or its polarisation is changed by the spiral pattern of thecrystals.Thebottompolariserisalignedoppositeofthetoponebutthe“twisted”lightisnowalignedwiththebottompolariserandpassesthrough.Thedisplayisnowtransparentandappearslight.

Asimpleblack-or-whiteLCDdisplayworksbyeitherallowingdaylighttobereflectedbackoutat theviewerorpreventing it fromdoingso—inwhichcase theviewer seesablack area. The liquid crystal is the part of the system that either prevents light frompassingthroughitornot.

Thecrystalisplacedbetweentwopolarisingfiltersthatareatrightanglestoeachotherandtogetherblocklight.Whenthereisnoelectriccurrentappliedtothecrystal,ittwistslightby90°,whichallowsthelighttopassthroughthesecondpolariserandbereflectedback.Butwhen thevoltage isapplied, thecrystalmoleculesalign themselves,and lightcannotpass through thepolariser: the segment turnsblack, thisphenomena is shown inFigure15.28.

Many other types of LCD displays are being developed for the laptop and CRTreplacement market including full colour versions. These include double and TripleTwistedNematic (DSTN and TSTN) displays and theActive-matrix Thin-filmTwistedNematic andMetal-Insulated-Metal TwistedNematic (TFT-TN andMIM-TN) displays.Unfortunately,theseadvanceddisplayaretooexpensiveformostofthecalculatormarket.TNLCDs almost completely dominate today’s calculatormarket due to their extremelylowpowerrequirements,thinsizeandlowcost.

Figure15.28WorkingprincipleofLCD

Table15.3ComparisonofCRTandLCD

CathodeRayTubes LiquidCrystalDisplays

Advantages

FastresponseandhighresolutionpossibleFullcolour(largemodulationdepthofE-beam)SaturatedandnaturalcolorsInexpensive,maturedtechnologyWideangle,highcontrastandbrightness

Advantages

SmallinsizeLightweight(typ.1/5ofCRT)Lowpowerconsumption(typ.1/4ofCRT)Completelyflatscreen—nogeometricalerrorsCrisppictures—digitalanduniformcoloursNoelectromagneticemissionFullydigital,signalprocessingpossibleLargescreens(>20inch)ondesktops

Disadvantages

Largeandheavy(typ.70×70cm,15kg)Highpowerconsumption(typ.140W)HarmfuldcandacelectricandmagneticfieldsFlickeringat50–80Hz(nomemoryeffect)Geometricalerrorsatedges

Disadvantages

Highprice(presently3×CRT)Poorviewingangle(typ.+/–50degrees)Lowcontrastandluminance(typ.1:100)Lowluminance(typ.200cd/m2)

15.4.4FlatPanelDisplayFlat-screenmonitors, often termedFlat PanelDisplays (FPDs), are becomingmore andmorepopular,astheytakeuplessspaceandarelessheavythantraditionalCRTmonitors.OthergreateradvantagesofFPDsaretheyconsumelessenergywhencomparedtoCRTmonitors, andalsohave lesselectromagnetic radiation.Therearebasically two typesofFlatPanelDisplay(FPD)—thepopularoneisLiquidCrystalDisplay(LCD)andtheotheroneisPlasmaDisplayPanel(PDP).

ThetheoryofLiquidCrystalDisplayswasdiscussedintheLCDsection.Here,Plasma

DisplayPanel(PDP)willbediscussedinbrief.

PlasmaDisplayPanel(PDP)APlasmaDisplayPanel (PDP) is a typeof flat paneldisplaynowcommonlyused forlargeTVdisplays(typicallyabove32¢¢).Itisoftenusedinthehomeenvironmentandisbecomingincreasinglypopularinmoderncultures.

Figure15.29Workingprincipleofplasmadisplay

Aplasmadisplaypanel is basedon emitting lightby excitinggases.Thegasused inplasma screens is amixture of argon (90%) and xenon (10%).Gas is containedwithincells,eachonecorrespondingtoapixel thatcorrespondstoarowelectrodeandcolumnelectrode,which excite the gaswithin the cell.A typical green colour cell is shown inFigure 15.29, where red and blue colour cells are located nearby. By modulating thevoltage applied across the top and bottom electrodes and by changing the frequency ofexcitation, the inert gas can be excited. The gas excited this way produces ultravioletradiation (which is invisible to the human eye). With blue, green, and red phosphorsdistributedamongthecells,theultravioletradiationisconvertedintovisiblelight,sothatpixels(madeupof3cells)canbedisplayedinupto16millioncolors(256×256×256).

Plasmatechnologycanbeused tocreate large-scalehigh-contrastscreens,butplasmascreensarestillexpensive.What’smore,powerconsumptionismorethan30timeshigherthan for anLCDscreen.A typical plasmaTVofSAMSUNGCorp. is shown inFigure15.30.

Figure15.30PlasmaTV[Manf.SAMSUNGCorp.]

15.4.5NixieTubeNixietubesarenonplanarelectronicdevicesthatusetheprinciplesofglowdischargefordisplayingnumeralsorotherinformation.Theseareactuallygaseousglowtubesmadeofglass thatcontain twoelectrodes.Theanode is in theformofawiremeshandmultiplecathodesthatareshapedasnumeralsorothersymbolsthataretobedisplayed.Whenthecathodecorrespondingtothenumeraltobedisplayedisactivated,itgetssurroundedbyanorange gaseous glowdischarge.The glass tube is generally filledwith neon gas at lowpressure,withalittlemercury.ThephotographofaNixietubeisshowninFigure15.31.

Whenasufficientpotentialofaround170voltsisappliedbetweentheselectedcathodeand theanodeplate, thegas surrounding the selectedcathodegets ionisedandemits anorangeglow.ANixietubeshouldnotbeconfusedwithavacuumtubesinceoperationofthe Nixie tube does not depend on thermionic emissions of electrons from a heatedcathode. The operating temperature ofNixie tube rarely exceeds 40°C.Nixie tubes arethusalsocalledcold-cathodetube.

ThemostcommonlyavailableNixietubehastencathodesintheshapesofthenumerals0 to 9, and may be a decimal point. These cathodes displaying different numbers arearrangedonebehindanother.Thus,whenthecharactersglowoneatatime,eachcharacterappearsatadifferentdepth.

Figure15.31Nixietube(Courtesy,www.123rf.com)

Nixietubeswereusedinearlierdaysasdisplayunitsinvoltmeters,ammetersandotherelectricalandelectronicmeasuringinstruments.

EXERCISE

Objective-typeQuestions1.Astripchartrecorderisa/an

(a)analogrecorder

(b)magnetictaperecorder

(c)oscillographicrecorder

(d)noneoftheabove

2.PrintingmechanismofaFAXmachineisof

(a)thermaltype

(b)impacttype

(c)electrostatictype

(d)opticaltype

3.Whichisnotthefunctionofdataloggers?

(a)Display

(b)Onlineanalysis

(c)Reporting

(d)Control

4.Thebandwidthofamagnetictaperecorderis

(a)higherthanelectronicrecorder

(b)higherthanstripchartrecorder

(c)lowerthanstripchartrecorder

(d)higherthanultravioletrecorder

5.PowerconsumptionofanLEDdisplayis

(a)higherthanLCDdisplay

(b)lowerthanLCDdisplay

(c)almostequaltoLCDdisplay

(d)ApproximatelytwolineshigherthansamesizeLCD

6.InaCRT,theelectronbeamisdeflectedby

(a)electricfield

(b)magneticfield

(c)bothmagneticandelectricfield

(d)gravitationalfield

7.Servomechanismisusedin

(a)potentiometrictyperecorder

(b)galvanometrictyperecorder

(c)magnetictapetyperecorder

(d)ultravioletrecorder

8.TheresponsetimeofCRTdisplayis

(a)higherthatLCDdisplay

(b)lowerthanLCDdisplay

(c)higherthanplasmadisplay

(d)lowerthanplasmadisplay

9.Thegasusedinplasmascreensisamixtureof

(a)nitrogenandoxygen

(b)nitrogenandxenon

(c)argonandnitrogen

(d)argonandxenon

10.Timescaleofastripchartrecorderiscontrolledby

(a)controllingspeedofthechartpaper

(b)controllingthestylusdrivemechanism

(c)controllingtherangeselector

(d)controllingthestylus

Short-answerQuestions1.Classifydifferenttypesofrecorders.

2.Whatarethedifferentcomponentsofastripchartrecorder?Brieflydiscussthose.

3.Compareapotentiometricwithgalvanometricrecorder.

4.Statetheworkingprincipleofultravioletrecorders.

5.Whataretheadvantagesofamagnetictaperecorderovertheotherrecordingsystem?

6.Drawafunctionalblockdiagramofadatalogger.Alsodiscussabouteachelement.

7.Comparecoldcathodedisplaywithhotcathodedisplay.

8.HowDoesasimpleblack-and-whiteLCDdisplaywork?

9.Statetheworkingprincipleofplasmadisplay.

10.HowarecharactersdisplayedinanLEDdotmatrixdisplayunit?

16.1 INTRODUCTION

Rising costs and the inflexibility of hard-wired relay systems have stimulated thedevelopmentofProgrammableLogicControllers(PLCs)asanalternative.ThePLCcanbedefinedasauser-friendly;microprocessor-basedspecialisedequipmentthatcarriesoutcontrolfunctionsofmanytypesandlevelsofcomplexityforuseinindustry.Itspurposeistomonitorcrucialprocessparametersandadjustprocessoperationsaccordingly.Itcanbeprogrammed, controlled, and operated by users. PLCs use a programmablememory tostoreinstructionsandtoimplementfunctionssuchaslogic,sequencing,timing,countingand arithmetic in order to control machines and processes. PLCs are designed to beoperated by users with perhaps a limited knowledge of computer and computinglanguages.Generally, a PLC’s operator draws the lines and devices of ladder diagramswith a keyboard into a display screen. Then, the resulting drawing is converted intocomputermachinelanguageandrunasauserprogram.

Inatraditionalindustrialcontrolsystem,allcontroldevicesarewireddirectlytoeachotheraccording tohow thesystem is supposed tooperate.ThePLCreplaces thewiringbetweenthedevices.Thus,insteadofbeingwireddirectlytoeachother,allequipmentiswired to the PLC. Then, the control program inside the PLC provides the wiringconnectionbetweenthedevices.Thecontrolprogramis thecomputerprogramstoredinthePLC’smemory that tells thePLCwhat’s supposed to be goingon in the system. Ifanybody wants a PLC system to behave differently or to control a different processelement, just thecontrolprogram is required tochange. Ina traditional system,makingthistypeofchangewouldinvolvephysicallychangingthewiringbetweenthedevices,acostlyandtime-consumingendeavour.

Theexistingpushbuttons,limitswitches,andothercommandcomponentscontinuetobeused,andbecome inputdevices to thePLC. In likemanner, thecontactors,auxiliaryrelays,solenoids,indicatinglamps,etc.,becomeoutputdevicescontrolledbythePLC.Ifone understands the interface between the hardware and the software, the transition toPLCsisrelativelyeasytoaccomplish.

16.2 ADVANTAGESOFPLCs

PLCs have been gaining popularity on the factory floor and will probably remainpredominantforsometimetocome.Mostofthisisbecauseoftheadvantagestheyoffer.

Costeffectiveforcontrollingcomplexsystems.

Flexibleandcanbereappliedtocontrolothersystemsquicklyandeasily.Computationalabilitiesallowmoresophisticatedcontrol.Troubleshootingaidsmakeprogrammingeasierandreducedowntime.Reliablecomponentsmaketheselikelytooperateforyearsbeforefailure.Expandability.Abilitytowithstandharshenvironments.Smallspacerequirements.PLCcircuit’soperationcanbeseenduringtheoperationdirectlyonamonitor.

16.3 THECONTROLPROGRAM

ApersonknowledgeableinrelaylogicsystemscanmasterthemajorPLCfunctionsinafewhours.Thesefunctionsincludecoils,contacts,atimerandcounters.Thesameistrueforapersonwithadigital-logicbackground.Forapersonunfamiliarwithdigitalandrelaylogics,however,thelearningprocesstakesmoretime.PLCsarenotdesignedsothatonlycomputerprogrammerscansetuporchangetheprograms.Thus,thedesignersofthePLChavepre-programmeditsothatthecontrolprogramcanbeenteredusingasimple,ratherintuitiveformoflanguage.So,thecontrolprograminstructsthePLCsystemhowtoreactto each input signal from, say, switches and give the required outputs to, say, lamps,motorsandvalves.Aprogrammighthaveaformasfollows:

IfswitchAorBclose

Thenoutputtolampcircuit

IfswitchAandBclose

Outputtomotorcircuit

Figure16.1Contactsandcoils

InaPLC,switches,sensorsorinputdevicesarerealisedascontactsandoutputcircuitsas coils.The term logic in aPLC is usedbecause programming is primarily concernedwithimplementinglogicandswitchingoperations.Inputdevicessuchassensors,switchesandoutputdevicesinthesystembeingcontrolled,e.g.lamp,motoretc.,areconnectedtothePLC.Theoperatorthenentersasequenceofinstructions,i.e.acontrolprogram,intothememoryofthePLC.Thecontrollerthenmonitorstheinputs(contacts)andoutputs(coils)according to thiscontrolprogramandcarriesout thecontrol rule forwhich ithasbeenprogrammed.

16.4 FUNCTIONOFEACHPARTINPLC

APLCconsistsoftheCPU,memoryandcircuitsforinputsandoutputs.Inputandoutputcircuitsdealwithreceivinginputdataandsendingdatatooutputdevicesrespectively.APLCmaybeconsideredtobeacollectionofalargenumberofrelays,counters,timersanddata-storage locations.Thesecomponents (timers, counters, etc.)donot existphysicallybut,areusedaslogicalcomponents.TheblockdiagramoftheinternalstructureofaPLCisshowninFigure16.2.

1.InputRelays(Contacts)These components are actually transistors, exist physically and aremeant for receivingsignalfromsensors,switches,etc.

2.InternalUtilityRelays(Contacts)Theyarelogical(simulated)relaysandarethemaintoolsofaPLCwhicheliminatetheuseofconventionalphysicalrelaysandfinally,hard-wiredrelaycontrolcircuits.Theseareusefulcomponentstoimplementcontrollogicprograms.

3.OutputRelays(Coils)They do exist physically, made of transistors, conventional relay, etc., depending uponapplicationsandareusedtosendon/offsignalstolamps,solenoidsetc.

4.CountersThese are programmed to count the number of events (pulses). They do not existphysically. These logical components are used for the sake of implementing controlprogramscontainingtheneedofcountingupordownorboth,aseriesofevents.

5.TimersTheseexist logically.Theseareused to introduce timedelaybetween theoccurrenceoftwoevents.Timersareofdifferenttypes,like,on-delaytimers,off-delaytimers,retentivetype,etc.

6.DataStorageThese are basically a group of registers, used to store data to carry out arithmetic andlogicaloperationswiththem.ThisisaveryessentialpartofaPLC.

Figure16.2BlockdiagramoftheinternalstructureofPLC

16.5 HARDWAREOFPLC

Typically,aPLCsystemhasthreebasicfunctionalcomponents.Thethreemajorpartsarecentral processing unit (CPU), Input/outputmodule and programming terminals. Figure

16.3showshowthesethreepartsareinterconnected.

Figure16.3BlockdiagramofPLChardware

16.5.1TheCentralProcessingUnit(CPU)CPUcontrolsandprocessesalltheoperationswithinthePLC.Itissuppliedwithaclockfrequencyoftypicallybetween1and8MHz.ThisfrequencydecidestheoperatingspeedofaPLCandprovidesthetimingandsynchronisationforallelementsinthesystem.TheCPUactsasthe“brain”ofthesystem,whichhasthreesubparts:

1.ProcessorItcontainsthemicroprocessor.Thisinterpretstheinputsignalsandcarriesoutmathematicand logic operations to set the control actions, according to the program stored in thememory,andfinally,communicatesthedecisionsasactionsignalstotheoutput.Thispartdoesthefollowingfunctions:

(a)UpdatingInputsandOutputs ThisfunctionallowsaPLCtoreadthestatusofitsinputterminalsandactivateorde-activateitsoutputterminals.

(b)Performing Logic andArithmeticOperations For this anArithmetic and LogicUnit (ALU) is there. It is responsible for datamanipulation and carryingout arithmeticoperationsofadditionandsubtractionandlogicoperationsofAND,OR,NOT,XOR.

(c)CommunicatingwithMemoryAsdataandprogramsarestoredinthememory,theCPUneedstocommunicatewiththememorythroughouttheoperation.

(d)ScanningApplicationProgramsThescanningfunctionallowsthePLCtoexecutetheapplicationprogramasspecifiedbytheprogrammer.

(e)CommunicatingwithaProgrammingTerminalTheprogrammingterminalisusedtoloadprogramsanddataintotheCPU.So,inPLCprogrammingmode,theCPUhastoconstantlycommunicatewiththeprogrammingterminal.

APLCusesfourbusestocarryoutcommunicationprocesswhenbinaryinformationistransferred fromone location toanother.Thosebusesaredatabus, addressbus, controlbusandsystembus.

DatabuscarriesthedatausedintheprocessingcarriedoutbytheCPU.ThisisabidirectionalbusastheCPUhastoperformbothdata/instructionreadandwriteoperationthroughthisbus.AddressbususedtocarrytheaddressofmemorylocationsorI/OdevicestoidentifyaparticularmemoryregisterorI/Odevicewithwhichtheread/writeoperationis

conductedbyCPU.ControlbuscarriesthesignalsusedbytheCPUforcontrolactions,e.g.toinformmemorydeviceswhethertheyaretoreceivedatafromaninputdeviceortosenddatatoanoutputdevice.Thisbusisemployedtocarrytimingsignalsusedtosynchroniseactions.Systembusisusedforcommunicationsbetweentheinput/outputportsandinput/outputunits.

2.MemoryItistheareaoftheCPUinwhichdataandinformationarestoredandretrieved.Itistheretoholdthesystemsoftwareanduserprograms.AsshowninFigure16.4,thememoryisusedtostoredifferentfiles.Fileisthecollectionofwordsandawordhastwobytes,lowerbyteandhigherbyte.Eightbitsmakeaword.Bitisthesmallestunitofinformation,eitherhighor low.To store a bit, the smallest unit ofmemory is known as amemorycell. Aregisterisagroupofmemorycells.Forexample,eightmemorycellsconnectedinparallelformsaneight-bitregister.So,tostoreaword(2bytes),twosuchregistersaretobeused.To identifymemory locations, it is very essential to adopt an addressing schemewhichmaybeoctalorhexadecimal.

Figure16.4Bit,byte,word,filerelationships

APLCmemorysystemhasbothROMandRAM.PLCoperating-systemprogramsarestoredpermanentlyintoROM,whereasinformationcanbestoredandretrievedinto/fromthe RAM. The programs and data in RAM can be changed by the user. However, topreventthelossofprogramswhenthepowersupplyisswitchedoff,abatteryisusedinthePLCtomaintain theRAMcontentsforaperiodof time.Userprograms(say, ladderlogicprogram)canbewrittenintotheRAMandanewprogramcanoverwritepreviouslywritten programs in the same locations. Apart from these possibly, as a bolt-on extramodule,erasableandprogrammableread-only-memory(EPROM)isavailableanditcanbe programmed and then the program made permanent. After a program has beendevelopedinRAM,itmaybe loaded intoanEPROMmemoryandmadepermanent. Inaddition, thereare temporarybufferstoragefor input/outputmodules.Memorycapacity,oftenexpressedintermsofkilo-bytes,canvaryfromPLCtoPLC.

3.PowerSupplyItisasectionofCPUwhichconvertsaclinevoltagetovariousoperationaldcvalues.Thepowersupplymakesregulateddcvoltagewithproperfilteringcircuittoensurethesupplyof desired low dc voltage levels to the processor and circuits in the input and outputmodules.

16.5.2TheInput/Output(I/O)Modules

Theinput/outputmoduleprovidestheinterfacebetweenthesystemandtheoutsideworld,allowing for connections to bemade through input/output channels to input and outputdevices. The input module has terminals into which outside process electrical signals,generatedby sensorsor transducers, are fed.Theoutputmodulehas terminals towhichoutputsignalsaresent toactivate relays,solenoids,varioussolid-stateswitches,motors,indicators and displays.A very simple control scheme using a PLC has been shown inFigure16.5.

Figure16.5InputandoutputschemesinaPLC

It is also through the input/output module that programs are entered from aprogrammingterminal.Everyinput/outputpointhasauniqueaddresswhichcanbeusedby theCPU for identifying the device. The input/output channels provide isolation andsignal-conditioningfunctionssothatsensorsandactuatorscanoftenbedirectlyconnectedtothemwithouttheneedforothercircuitry.Electricalisolationfromtheexternalworldisusuallybymeansofopto-isolators(opto-coupler).

Anelectronic systemforconnecting I/Omodules to remote locationscanbeadded ifneeded.TheactualoperatingprocessunderPLCcontrolcanbehundredsofmetersfromtheCPUanditsI/Omodules.Inputandoutputdevicescanbeclassifiedasgivingsignalswhich are discrete or digital or analog as shown in Figure 16.6. Analog devices givesignals whose size is proportional to the size of the variable being monitored. Forexample, a variable potential divider has no definite on-state, i.e. signals coming fromthese typesofdevicesmayhaveanyvalue inbetweenofforzero(minimum)andonorone (maximum).Digitaldeviceshave twodistinctstatesonandoffand theycangiveasequenceofon-offsignals.

Outputsarespecifiedasbeingofrelaytype,transistortypeortriactype.

For faster switching operation or response, transistor-type output is preferred overrelay-typeoutput.OffRelay-typeoutputisolatesthePLCfromtheexternalcircuit.Butinthe transistor type, opto-isolators are used to provide isolation.Triac outputwith opto-isolator can be used to control external loadswhich are strictly connected to ac powersupply.

Figure16.6Digitalandanalogdevices

Outputs to actuators allow a PLC to cause something to happen in a process. Fewpopular actuators are solenoid, valves, lights/indicator (normally, to test designed logiccircuits),motorstarters, servomotors,etc.Typicalexamplesofsensorsusedas inputs to

PLCareswitches,potentiometers,LVDTs(LinearVariableDifferentialTransformers),etc.

ThewayinwhichdcdevicesareconnectedtoaPLCcanbedescribedwiththetermssourcingandsinking.Withsourcing,usingtheconventionalcurrent-flowdirectionasfrompositivetonegative,aninputdevicereceivescurrentfromtheinputmodule,i.e.theinputmodule acts as the source of the current (Figure16.7(a)). If the current flows from theoutputmodule toanoutputdeviceor load, theoutputmodule is referred toassourcing.[Figure 16.7(b)]. With sinking, using the conventional current-flow direction as frompositive to negative, an input device is the sink for the current [Figure 16.7(c)]. If thecurrentflowstotheoutputmodulefromanoutputdeviceorloadthentheoutputmoduleisreferredtoassinking[Figure16.7(d)].

Figure16.7SourcingandsinkingofI/Odevices

TherearetwocommontypesofmechanicaldesignforPLCsystems;asinglebox,andthemodular/racktypes.Thesingle-boxtype(sometimescalledbrick)iscommonlyusedfor small programmable controllers and is supplied as an integral compact packagecompletewithpowersupply,processor,memory,andinput/outputunits.Typically,suchaPLCmight have 6, 8, 12 or 24 inputs and 4, 8 or 16 outputs. Some box or brickPLCsystemshavetheoptionstoextendmoreinputandoutputbylinkinginput/outputboxes.

Systems with larger numbers of inputs and outputs are likely to be modular anddesignedtofitinracks.RackisanenclosurewithslotsonwhichtheCPU,powersupplyandI/Omodulesaremounted.Therack typecanbeusedforall sizesofprogrammablecontrollersandhasvariousfunctionalunitspackagedinindividualmoduleswhichcanbepluggedintoslotsaccordingtorequirement.Thus,itiscomparativelyeasytoexpandthenumberof inputs/outputsbyjustaddingmoreI/Omodulesor toexpandthememorybyaddingmorememoryunitsasshowninFigure16.8.

Figure16.8RackandI/Omodulearrangement

16.5.3PLCProgrammingTerminalTheprogrammingterminalconnectsPLCprogrammer/monitor(PM)toCPUbyacable.PLC programming equipment exists to allow the user to write, edit and monitor aprogram, as well as perform various diagnostic procedures. PLC programmingarrangementscanbeahand-helddevice,adesktopconsoleorapersonalcomputer.

Hand-held programming will normally contain enough memory to allow the unit toretainprogramswhilebeingcarriedfromoneplacetoanother.

Desktopconsolesarelikelytohaveavisualdisplayunitwithafullkeyboard.

Personalcomputersarewidelyconfiguredasprogramdevelopmentworkstations.SomePLCs only require the computer to have appropriate software; others require specialcommunicationcardstointerfacewiththePLC.

EverybrandofPLChasitsownprogramminghardware.Sometimes,itisasmallhand-helddevicethatresemblesanoversisedcalculatorwithaLiquidCrystalDisplay(LCD).Computer-basedprogrammerstypicallyuseaspecialcommunicationboard,installedinanindustrialterminalorpersonalcomputer,withtheappropriatesoftwareprograminstalled.Computer-based programming allows offline programming, where the programmerdevelopshisherlogic,storesitonadisk,andthendownloadstheprogramtotheCPUathis her convenience. In fact, it allowsmore than one programmer to develop differentmodulesoftheprogram.ProgrammingcanbedonedirectlytotheCPUifdesired.WhenconnectedtotheCPU,theprogrammercantestthesystem,andwatchthelogicoperateaseachelementis intensifiedinsequenceontheCRTwhenthesystemisrunning.SinceaPLCcanoperatewithouthavingtheprogrammingdeviceattached,andonedevicecanbeusedtoservicemanyseparatePLCsystems.Theprogrammercaneditorchangethelogiconlineinmanycases.

16.6 SYSTEMADDRESSING

TheknowledgeofaddressingsystemsorschemesisamusttoimplementandexecutieacontrolprograminaPLC.Inputdeviceslikepushbuttons,limitswitches,etc.,aretobeconnectedwith thecontroller to feed inputcommandsand thenexecutionof thecontrolprogrambrings theresultsout throughoutputdevices likemotorstarters,solenoids,andlight bulbs, etc., connected with the system. Inputs and outputs are wired to interfacemodules, installedinanI/Orack.Normally,eachrackhasa two-digitaddress,eachslothasitsownaddress,andeachterminalpointisnumbered.

16.6.1I/OAddressesAtthetimeofrelaylogicorladder-diagramimplementation,allinputandoutputdevicesconnected with the PLC are identified by unique addresses. As it has already beendiscussed,I/Omodulesarekeptintherack.InaPLCsystem,eachrackcanbeidentifiedbyatwo-digitaddress.Ineachrack,slotsaretheretoplaceinputandoutputcards.Again,theslotsarenumbered(say,0to7).Forexample,assuminganinputcardhaseightinputchannelswhicharenumbered(00to07).Now,asshowninFigure16.9,inatypicalPLC,toconnecttwoswitches(onepushbuttonandanothertemperatureswitch)withtheinputcard,placedinslot3ofrack01,twochannelsorterminalsofthatinputcardaretobeused(say,01and03).So,theassignedaddresstothepush-buttonswitchbecomesI:013/01andforthetemperaturesensor,isI:013/03.Moreprecisely,inaninput/outputdeviceaddress,the first alphabet indicates device type (‘I’ for input device or ‘O’ for output device)followedbyacolon(:)andthen,thenexttwodigitsindicatetheracknumberfollowedbytheslotnumberandafteraslant(/),theterminalnumberorbitnumber.

Figure16.9Aninputcardandladderlogic

16.6.2ImageTableAddressesAsshowninFigure16.10,inaPLCsystem,onefileisreservedasaninputimagetable.Everyword in that file has a three-digit octal address beginningwith 1:,which can beinterpretedastheletterIforinput.Thewordaddressesstartwithoctal1:000to1:017(orhigher).Thisnumberisalsofollowedbyaslant(/)andthe2-digitbitnumber.

Figure16.10Solutionofonelineoflogic

InFigure16.10,theinputaddressI:000/04,becomesmemoryaddressI:000/04,andtheoutput address 0:007/14 becomes memory address 0:007/14. In other words, type ofmodule,rackaddress,andslotpositionidentifythewordaddressinmemory.Theterminalnumberidentifiesthebitnumber.

16.6.3RemoteI/OSo far it has been assumed that a PLC consists of a CPU, power-supply unit, and acollectionofI/Ocardsmountedinthelocalrack.Intheearlydays,PLCsdidtendtobearrangedlikethis,butinalargeandscatteredplantwiththisarrangement,allsignalshaveto be brought back to some central point using expensivemulticore cables. Itwill alsomake commissioning and fault findingmore difficult, as signals can only bemonitoredeffectivelyatapointpossiblysomedistancefromthedevicebeingtested.

PLCmanufacturers, therefore,provide theability tomountI/Oracksremotefromtheprocessor,andlinktheserackswithsimpleandcheapscreenedpairoffibreopticcables.IfremoteI/Oisused,provisionshouldbemadeforaprogramterminal tobeconnectedlocaltoeachrack.RemoteI/Oallowscompleteunitstobebuilt,wiredtoabuilt-inrack,and tested offsite prior to delivery and installations. Figure 16.11 shows three remoteracks,andconnectstothecontrollingPLCmountedinasubstationfaraway,viaaremoteI/Ocable,plusafewpowersuppliesandhardwaresafetysignals.

Figure16.11RemoteI/Oracks

16.7 PLCOPERATIONANDPROGRAMSCAN

APLCprogramcanbe considered tobehaveas apermanent running loopas shown inFigure 16.12(a). The actions carried out by a PLC shown in Figure 16.12(a) is calledprogramscan,andtheperiodoftheloopiscalledprogramscantime.ThisdependsonthesizeofthePLCprogramandthespeedoftheprocessor.

Figure16.12ThreestepsinPLCoperation

Atstart,thePLCscansthestateofalltheconnectedinputsandstorestheirstatesinthePLCmemory.WhenPLCprogramaccessesaninput,itreadstheinputstateasitwasatthe start of the program scan.A zone of PLCmemory corresponding to the outputs ischanged by the execution of the program, and then, all the outputs are updatedsimultaneously at the endof the scan.The action is thus read inputs, execute program,update outputs. Therefore, a PLC does not communicate continuouslywith the outsideworld.

PLCmemorycanbeconsidered toconsistof fourzonesorareasas shown inFigure16.12(b).Theinputsarereadintotheinputmimicareaatthestartofthescancalledinputimageword(explainedearlier),andtheoutputupdatedfromtheoutputmimiczoneorareacalled output imageword at the end of the scan. Therewill be an area in thememoryreservedforinternalsignalswhichareusedbytheprogrambutarenotconnecteddirectlytotheoutsideworld(timers,counters,latches,etc.).Thesethreeareasareoftenreferredtoasdatatableordatabase.AsindicatedinFigure16.13,totalresponsetimeisthesumofinputresponsetime,programexecutiontimeandoutputresponsetime.

Figure16.13PLCresponsetime

16.8 IMPLEMENTATIONOFCONTROLPROGRAMSINPLC

PLCs from different manufacturers can be programmed in various ways. PopularprogramminglanguagesforPLCsareladderdiagrams,FunctionBlockDiagrams(FBD),andstatementlist.Withafewexceptions,aprogramwritteninoneformatcanbeviewedinanother.

16.8.1LadderDiagramsAsan introduction to ladderdiagram,consider thesimplerelaycircuitwhichcontainsacoilandcontactsasshowninFigure16.14.Whenavoltageisappliedtotheinputcoil,theresultingcurrentcreatesamagneticfield.Themagneticfieldpullsametalswitch(orreed)towardsitandthecontactstouch,closingtheswitch.Thecontactthatcloseswhenthecoilis energised is called normally open (NO). The Normally Closed (NC) contacts touchwhen the inputcoil isnotenergised.When the inputcoil isnotenergised, thenormallyclosed contacts will be closed (conducting). The relay shown in the figure has twocontacts; one NO another NC.When the relay coil is energised, contacts of the relaychange their state, i.e. NO contacts get closed and NC contacts get opened. The relayarrangementcanbeshownwiththehelpofdifferentschematiccircuitsasshowninFigure16.14.Relaysarenormallydrawninaschematicformusingacircletorepresenttheinputcoil.Theoutputcontactsareshownwithtwoparallellines.NOcontactsareshownastwolines,andwillbeopen(nonconducting)whentheinputisnotenergised.NCcontactsareshownwithtwolineswithadiagonallinethroughthem.Now,ifitisrequiredtooperateNO(C)contactofthisrelay,connectedtoanacsource,throughtwoinputrelaycontacts,A (NC) and B (NO) then the relay logic diagram shown in Figure 16.15 is the mostappropriateforatypicallogic.Accordingtotherelaylogicdiagramshowninthefigure,activationoftheinputrelaycoilcorrespondstothecontactB,makesC(output)closedandactivation of the input relay coil corresponds to the contactA,makesC (output) to getopened.Thissortofarrangementisnormallyemployedinconventionalhard-wiredrelaylogiccircuit.

Figure16.14Simplerelaylayoutsandschematics

ThesameschemecanbeimplementedfollowingladderlogicasshowninFigure16.15.Theladderlogic-diagramisthemostcommonlyusedmethodofprogrammingPLCs.Theladder diagram consists of two vertical lines representing the power rails. Circuitsconnected as horizontal lines between two rails are called rungs of the ladder. Fewsymbols used to denote ladder logic inputs and outputs are shown in Figure 16.16 and16.17respectively.Takingintoconsiderationtheseladderlogicsymbols,theladderlogicimplementedinFigure16.15mimicsthesamehard-wiredrelaylogic.Finally,thisladderlogicisinsertedasacontrolprogramtoaPLCwhere,inputdevices,andoutputdevicesarearrangedinafashionasillustratedinFigure16.18.So,theladder-logicprogramsareloadedintothePLC,theinputandoutputdevicesareconnectedtoI/Omodulesandthentheexecutionoftheprogramupdatesoutputsaccordingtothestatusofinputs.

Figure16.15Asimplerelaycontrollerandcorrespondingladder-logic

Figure16.16Ladderlogicinputs

Figure16.17LadderlogicNormalOutput

Figure16.18APLCillustratedwithrelays

Many relays alsohavemultipleoutputs and this allowsanoutput relay to alsobe aninput simultaneously.The circuit shown in Figure16.19 is an example of this and it iscalledaseal-incircuit. In this circuit, thecurrent can flow througheitherbranchof thecircuit,throughthecontactslabelledAorB.TheinputBwillonlybeonwhentheoutputBison.IfBisoff,andAisenergisedthenBwillturnon.IfBturnsonthentheinputBwillturnon,andkeepoutputBonevenifinputAgoesoff.AfterBisturnedon,theoutputBwillnotturnoff.

Figure16.19Aseal-incircuit

AnotherexampleofladderlogiccanbeseeninFigure16.20.Tointerpretthisdiagram,imaginethatthepowerisontheverticallineontheleft-handside,calledhotrail.Ontheright-handsideistheneutralrail.Inthefiguretherearetworungs,andoneachrungthereare combinations of inputs (two vertical lines) and outputs (circles). If the inputs areopenedorclosedintherightcombination,thepowercanflowfromthehotrail,throughtheinputs,topowertheoutputs,andfinallytotheneutralrail.Aninputcancomefromasensor,switch,oranyothertypeofsensor.AnoutputwillbesomedeviceoutsidethePLCthat is switched on or off, such as lights or motors. In the top rung, the contacts arenormallyopenandnormallyclosed,whichmeansifinputAisonandinputB isoffthenpowerwillflowthroughtheoutputandactivateit.AnyothercombinationofinputvalueswillresultintheoutputXbeingoff.

Figure16.20Asimpleladderlogicdiagram

Example16.1 Try to develop (without looking at the solution) a relay-basedcontrollerthatwillallowthreeswitchesinaroomtocontrolasinglelight.

SolutionThereare twopossibleapproaches to thisproblem.The firstassumes thatanyoneoftheswitchesonwillturnonthelight,butallthreeswitchesmustbeoffforthelighttobeoff.TheladderlogicisshowninFigure16.21.

Figure16.21Ladderlogictocontrollingonelightwiththreeswitches

Thesecondsolutionassumesthateachswitchcanturnthelightonoroff,regardlessofthe states of the other switches. This method is more complex and involves thinkingthrough all of the possible combinations of switch positions. Youmight recognise thisproblemasanexclusiveorproblem.TheladderlogicisasshowninFigure16.22.

Figure16.22Ladderlogictocontrollingonelightinadifferentwaywiththreeswitches

Note: It is important to get a clear understanding of how the controls are expected towork.Inthisexample,tworadicallydifferentsolutionswereobtainedbaseduponasimpledifferenceintheoperation.

16.8.2FunctionBlockDiagramFunctionBlockdiagram(FBD)isusedforPLCprogramsdescribedintermsofgraphical

blocks. It isdescribedasbeingagraphical language fordepictingsignalanddata flowsthrough Inputs blocks, these being reusable software elements. A function block is aprograminstructionunitwhich,whenexecuted,yieldsoneormoreoutputvalues.Thus,ablockisrepresentedinamannershowninFigure16.23withthefunctionnamewrittenintheblock.Functionalblockscanhavestandardfunctions,suchasthoseofthelogicgatesor counter or timers or have functions defined by the user, e.g. a block to obtain anaveragevalueofinputs.

Figure16.23Functionblock

16.8.3StatementListInstatement-listprogrammingapproach,an instructionset similar toassembly languagefor amicroprocessor is used. Statement lists, available on few brands of PLCs, are themostflexibleformofprogrammingfortheexperienceduserbutarebynomeansaseasytofollowasladderdiagramsorlogicsymbols.

Figure16.24showsasimpleoperationinladder-diagramformforaMistsubishiPLC.TheequivalentstatementlistwouldbeasshowninTable16.1.

Figure16.24Mitsubishiladderdiagram

Table16.1EquivalentstatementlistforFigure16.24

Line Instruction Comment

0 LDX405 LDstartsrungorbranch

1 ANDX406 Xnnnareinputs(AND-ingisforseriesconnection)

2 ANIX407 ANIisANDwithnot

3 LDY430 LDstartsanewbranchleg

4 ANIM100 Mnnnareinternalstorage

5 ORB ORthetwobranchlegs(OR-ingforparallelconnection)

6 ANDM101

7 OUTY430 Endofrungwithoutput

16.8.4LogicFunctionsThere are many control situations requiring actions to be initiated when a certaincombinationofconditionsisrealised.Thus,foranautomaticdrillingmachine,theremightbeaconditionthatthedrillmotoristobeactivatedwhenlimitswitchesareactivatedthatindicatethepresenceoftheworkpieceandthedrillpositionasbeingatthesurfaceoftheworkpiece.SuchsituationinvolvestheANDlogicfunction,conditionAandconditionB

havingbothtobesatisfiedforanoutputtooccur.Similarly,othersituationsmaydemandtoimplementlogicslikeOR,NOT,NAND,NOR,XOR.Theelectriccircuit,truthtable,ladder diagramand functional block diagram for different logics are presented inTable16.2.Table16.2Characteristicsfordifferentlogics

16.9 MOREINLADDERLOGIC

Combinationallogicaloneisnotenoughtoimplementcontrolprogramsformorecomplexsystems, especially, those with event-based devices. The example of such event-basedsystemisillustratedinFigure16.25witha timingdiagram.The input to thedevice isapushbutton.Whenthepushbuttonispushed,theinputtothedeviceturnson.Ifthepushbutton is then releasedand thedevice turnsoff, it is a logicaldevice. Ifwhen thepush

button is released and the device stays on, it will be a type of event-based device. Toreiterate, the device is event based if it can respond to one or more things that havehappenedbefore.Ifthedevicerespondsonlyonewaytotheimmediatesetofinputs,itislogical. To implement such event-based devices in ladder logic diagrams, somecomponentsareavailableinPLCprogrammingapproach.Latches,timers,countersarethemostfrequentlyusedcomponentsusedinladderdiagrams.

Figure16.25Aneventdrivendevice

16.9.1LatchesorSet-resetCoilsAnotherfunctionwhichisoftenavailableistheabilitytolatchandunlatch(setandreset)aninternalrelay.Alatchisjustlikeastickyswitch—whenpushed,itwillturnonandwillcontinuewithitson-state,itmustbepulledtoreleaseitandturnitoff.Alatchinladderlogicusesoneinstructiontolatch,andasecondinstructiontounlatch,asshowninFigure16.26.TheoutputwithanL insidewill turntheoutputDonwhen the inputAbecomestrue.DwillstayonevenifAturnsoffandthismakesCtoturnoff.OutputDwillturnoffifinputBbecomestrueandtheoutputwithaUinsidebecomestrue.Ifanoutputhasbeenlatchedon,itwillkeepitsvalue,evenifthepowerhasbeenturnedoff.

Figure16.26Aladderlogiclatch

16.9.2TimersThe most commonly used process-control device after coils and contacts is the timer.There are four fundamental types of timers as illustrated in Table 16.3. A single inputtimer,calledanon-retentivetimer,isusedinsomePLCs.AnexampleofsuchatimerisshowninFigure16.27.EnergisingIN001causesthetimertorunfor8seconds.Attheendof8seconds,theoutputgoeson.Anon-delaytimerwillwaitforasettimeafteralineofladderlogichasbeentruebeforeturningon,butitwillturnoffimmediately.Anoff-delaytimerwillturnonimmediatelywhenalineofladderlogicistrue,butitwilldelaybeforeturningoff.Anon-delaytimercanbeusedtoallowanoventoreachacertaintemperaturebeforestartingproduction.Anoff-delaytimercankeepcoolingfansonforasettimeafter

theovenhasbeenturnedoff.Table16.3Fourbasictimertypes

On-delay Off-delay

Non-retentive On-delaytimer(TON) Off-delaytimer(TOF)

Retentive Retentiveon-delaytimer(RTO) Retentiveoff-delaytimer(RTF)

Figure16.27Single-inputtimer

Aretentivetimerwillsumalloftheonorofftimeforatimer,evenifthetimerisneverfinished. A nonretentive timerwill start timing the delay from zero each time. Typicalapplicationsforretentivetimersincludetrackingthetimebeforemaintenanceisneeded.Anonretentivetimercanbeusedforastartbuttontogiveashortdelaybeforeaconveyorbeginsmoving.

Figure16.28ExampleofTONtimer

AnexampleofaTONtimer isshowninFigure16.28.Therunghasasingle inputAandafunctionblockfortheTON.(Note:ThistimerblockwilllookdifferentfordifferentPLCs,but itwill contain the same information.)The information inside the timerblockdescribesthetimingparameters.ThefirstitemisthetimernumberT4:0(oraddress).ThisisalocationinthePLCmemorythatwillstorethetimerinformation.TheT4:indicatesthatitistimermemory,andthe0indicatesthatitisinthefirstlocation.Thetimebaseis1.0 indicating that the timer will work in 1.0 second intervals. Other time bases areavailableinfractionsandmultiplesofseconds.Thepresetisthedelayforthetimer,inthiscaseitis4.Tofindthedelaytime,multiplythetimebasebythepresetvalue4*1.0s=4.0s. The accumulator value gives the current value of the timer as 0.While the timer isrunning, theaccumulatedvaluewill increaseuntil it reaches thepresetvalue.Wheneverthe inputA is true, the EN output will be true. The DN output will be false until theaccumulator has reached the preset value. The EN andDN outputs cannot be changedwhenprogramming,buttheseareimportantwhendebuggingaladder-logicprogram.ThesecondlineofladderlogicusesthetimerDNoutputtocontrolanotheroutputB.

16.9.3CountersTherearetwobasiccountertypes:count-upandcount-down.Whentheinputtoacount-upcountergoes true, theaccumulatorvaluewill increaseby1 (nomatterhow long theinputistrue.)Iftheaccumulatorvaluereachesthepresetvalue,thecounterDNbitwillbe

set.Acount-downcounterwill decrease the accumulator value until the preset value isreached.A count-up (CTU) instruction is shown in Figure 16.29. The instruction requires

memoryinthePLCtostorevaluesandstatus, inthiscase, it isC4:0.TheC4:indicatesthatitiscountermemory,andthe0indicatesthatitisthefirstlocation.Thepresetvalueis4andthevalueintheaccumulatoris2.IftheinputAgoesfromfalsetotrue,thevalueinthe accumulatorwould increase to 3. IfA is turned off, then on again the accumulatorvaluewouldincreaseto4,andtheDNbitwouldturnon.Thecountcancontinueabovethepreset value. If inputB goes true thevalue in the counter accumulatorwill becomezero.

Figure16.29CTUcounter

16.9.4MasterControlRelays(MCRs)MasterControlRelay (MCR) function is a powerful programming tool.WhenMCR isenabled,theladderdiagramfunctionsnormally.Whenitisnotenabled,aspecificnumberofcoilsandfunctionsarefrozenintheoffposition.Coilsinthefrozensectionwillremainoffeveniftheircorrespondingenablelinesareturnedon.Inanelectricalcontrolsystem,amastercontrolrelayisusedtoshutdownasection.Asectionofladderlogiccanbeputbetween two lines containing MCRs. When the first MCR coil is active, all of theintermediateladderlogicisexecuteduptothelinewithanotherMCRcoil.WhenthefirstMCRcoilisinactive,theladderlogicisstillexamined,butalloftheoutputsorcoilsareforcedoff.

Take the example in Figure 16.30. If A is true then the ladder logic is executednormally.But, ifA is false, the following ladder logicwill be examined, but all of theoutputswillbeforcedoff.ThesecondMCRfunctionappearsonalinebyitselfandmarksthe end of the MCR block. After the second MCR, the program execution returns tonormalmode.Inthisexample,whileA is true,conditionofXwillequaltoB.AsY isalatch,itcanbeturnedonbyC,andcanbeturnedoffbyD.But,ifAbecomesfalse,Xwillbeforcedoff,andYwillcontinuewithitslaststate.UsingMCRblockstoremovesectionsof programswill not increase the speed of program execution significantly because thelogicisstillexamined.

Figure16.30MCRinstructions

16.9.5MoreExamplesonTimersandCounters

Example16.2 Develop the ladder logic thatwill turnonanoutput light,15secondsaftertheswitchAhasbeenturnedon.

Solution The ladder diagram for this problem is shown in Figure 16.31. An on-delaytimerblockwith15-secondsdelayhasbeenusedanditisbeingactivatedbytheswitchA,and the contact present in the second rung is closed to turn on the light when the 15-seconddelayiselapsed.

Figure16.31Asimpletimerexample

Example16.3Developtheladderlogicthatwillturnonalight,aftertheswitchAhasbeenclosed10times.PushbuttonBwillresetthecounters.

SolutionTheladderdiagramtoimplementthislogicisshowninFigure16.32wheretheup-counterblockkeeps thecountofpressing the switchA.When the count reaches thepreset value of the counter, the contact C5 in the second rung, corresponding to thecounter, is closed and the light is turned on. To reset the counter the reset coil of thecounterisenergisedbytheswitchBpresentinthirdrung.

Figure16.32Asimplecounterexample

EXERCISE

Objective-typeQuestions1.PLCsare___________designedforuseinthecontrolofawidevarietyofmanufacturingmachinesandsystems.

(a)special-purposeindustrialcomputers

(b)personalcomputers

(c)electromechanicalsystems

(d)alloftheabove

2.ThefirstcompanytobuildPLCswas

(a)generalmotors

(b)AllenBradley

(c)squareD

(d)Modicon

3.Whichofthefollowingstatementsisnotcorrect?

(a)ThePLCrungoutput[-()-]isadiscreteoutputinstructionorbitinmemory.

(b)Eachrungoftheladderlogicrepresentsalogicalstatementexecutedinsoftware—inputsontherightandoutputsontheleft.

(c)Inputandoutputinstructionsinladderlogicdonotdirectlyrepresenttheswitchesandactuators.

(d)PLCinputinstructionsarelogicalsymbolsassociatedwithvoltageattheinputmoduleterminals.

4.WhichofthefollowingstatementsisNOTcorrect?

(a)Thestatusofeachinputcanbecheckedfromonelocationandoutputscanbeforcedonandoff.

(b)AllsymbolsintheRLLrepresentactualcomponentsandcontactspresentinthecontrolsystem.

(c)PLCsarenotasreliableaselectromechanicalrelaysinRLL.

(d)Input(-||-)andoutput(-()-)instructionsymbolsintheladderlogicrepresentonlydatavaluesstoredinPLCmemory.

5.WhenarelayisNOTenergised,

(a)thereisanelectricalpaththroughtheNOcontacts

(b)thereisanelectricalpaththroughtheNCcontacts

(c)neithertheNOortheNCcontactshaveanelectricalpath

(d)boththeNOandtheNCcontactshaveanelectricalpath

Short-answerQuestions1.CanaPLCinputswitcharelaycoiltocontrolamotor?

2.DevelopasimpleladderlogicprogramthatwillturnonanoutputXifanyoneoftheinputsA,BandCison.

3.DevelopasimpleladderlogicprogramthatwillturnonamotoroperatedbytheoutputXiftheinputAisonandmotorwillturnoffiftheinputBison.

4.Whatarethebenefitsofinput/outputmodulesofaPLC?

5.HowdoinputandoutputcardsactasaninterfacebetweenthePLCandexternaldevices?

Long-answerQuestions1.GiveaconcisedescriptionofhardwareofaPLC.

2.DrawablockdiagramshowinginverygeneraltermsthemainunitsinaPLC.

3.WhywouldrelaysbeusedinplaceofPLCs?GiveanexampleofwhereaPLCcouldbeused.ListtheadvantagesofaPLCoverrelays.

4.Explainwhyladderlogicoutputsarecoils.DevelopasimpleladderlogicprogramthatwillturnonanoutputXifinputsAandB,orinputCison.

5.CanaPLCinputswitcharelaycoiltocontrolamotor?HowdoinputandoutputcardsactasaninterfacebetweenthePLCandexternaldevices?Whatarethebenefitsofinput/outputmodules?

6.Explainwhyastopbuttonmustbenormallyclosedandastartbuttonmustbenormallyopen.Explainthetrade-offsbetweenrelaysandPLCsforcontrolapplications.

17.1INTRODUCTIONTORFANDWIRELESSCOMMUNICATIONSYSTEM

Radio frequency (RF) is any frequencywithin the electromagnetic spectrum associatedwithradio-wavepropagation.WhenanRFcurrent(inputsignal)issuppliedtoanantenna,anelectromagneticfieldiscreatedthatis thenabletopropagatethroughspace.RFfieldpropagationtechnologyisusedinmanywirelesstechnologies.

Figure17.1DifferentformsofRFbasedwirelesscommunicationsystems

RF is similar to that of wireless and high-frequency signals. However, RF hasfrequenciesrangingfromafewkHztoroughly1GHz.Thisrangeextendsto300GHzbyconsideringmicrowavefrequenciesasradiofrequency.

Many of the wireless devices make use of RF fields, for example satellitecommunications systems,cordlessandcellular telephone, radioand televisionbroadcaststations,alloperate in theRFspectrum.Somewirelessdevicesoperateat IRorvisible-lightfrequencies,whoseelectromagneticwavelengthsareshorterthanthoseofRFfields.

Wirelesscommunicationcanbedefinedas the transferof informationoveradistancewithouttheuseofelectricalconductorsorwires.Thedistanceforwirelesscommunicationmay be small or large depending on the distance of communication. For example, atelevision remote control requires a shorter distance whereas radio communicationsrequiresalongerdistanceandmaybethousandsofkilometreslong.

In wireless communication systems, wider bandwidths, larger signal dynamics andhighercarrierfrequenciesareappliedinordertofulfillthedemandforhigherdatarates.SincetheRFtechnologyis,consequently,pushedtoitsoperationboundaries,theintrinsicimperfections of theRF IC technology aremore andmore about governing the systemperformanceofwirelessmodems.ForRFbasedwirelesscommunication,higherandevenhigher frequencies are alwaysdesired.This is due to the reason that higher frequenciesincludeefficiency inpropagation, immunity to some formsofnoiseand impairmentsaswellas thesizeof theantennarequired.Theheightof theantenna isdeterminedon thebasisofwavelengthofthesignalandisusuallyselectedasonefourthofthewavelengthofthesignal.

During transmittingof the signal, there are always lossesdue to spreadingof theRFenergyasitpropagatesthroughfreespace.Thisspacelosscanberepresentedas

where, Ptisthepoweroftransmitterantenna,

Pristhepowerofreceivingantenna

Risthedistancebetweentwoantennas.

Figure17.2Thesimplifiedblockdiagramofthewirelesscommunicationsystem

Thepurpose of using of high frequencies in communication is to reduce the antennasize, increaseefficiency inpropagationand improve thesignal-to-noise ratio.Accordingtothefollowingrelation,

Asfrequencyandwavelengthareinverselyproportional,werequirehighfrequenciestoreducetheantennasize.

17.2RADIOFREQUENCYANDMICROWAVESPECTRALANALYSIS

The display of electromagnetic radiation as a function of wavelength is termed aselectromagnetic spectrum. Based upon the wavelengths, the spectrum is divided intovariousfrequencybandsasshowninFigure17.3.

Figure17.3Differentelectromagneticwavespectra

FromFigure17.3,RadioFrequency(RF)areelectromagneticwaveswithwavelengthsof 100 km to 1 mm, which is a frequency of 300 Hz to 3000 GHz. The microwavefrequencies are electromagnetic waves with wavelengths ranging from as long as onemetretoasshortasonemillimetre,orwithfrequenciesbetween300MHz(0.3GHz)and300GHz.

Withtherapidadvanceofwirelesstechnologyandsatellitesensortechnology,thereisaneed for more andmore accurate fieldmeasurements to complement overhead data inproviding higher spectral resolution over progressively broader wavelength. In spectralanalysis,thefollowingfactorsareconsidered.

PowerinbandOccupiedbandwidthAdjacentchannelpowerResolutionbandwidthHarmonicdistortionNoisespecification

17.2.1PowerinBandItisthemeasurementoftotalpowerwithinanyspecifiedfrequencyrangeorband.Powerinbandiscalculatedbythefollowingequation:

Powerinband=

where,X is the inputpower spectrum froma specifiedband, fl is the lowboundof thefrequencyband,andfhisthehighboundofthefrequencyband.Thelowandhighboundsofthisbandcanbedeterminedfromthecentrefrequency.

17.2.2OccupiedBandwidthItisthemeasurementoffrequencybandorbandwidththatcontainsaspecifiedpercentageofthetotalpowerofthesignal.Occupiedbandwidthistheinverseofpowerinband.

For example, if the specified percentage is 99 then the occupied bandwidth is thebandwidththatcontains99%ofthetotalpowerofthesignal.Thatisthefrequencyrange

inbetweentheverticallines,asshowninFigure17.4.

Figure17.4SpectrumofanRFsignal

17.2.3AdjacentChannelPowerItbasicallymeasuresthewayaparticularchannelanditstwoadjacentchannelsdistributepower.Thismeasurementisperformedbycalculatingthetotalpowerinthechannelandalsothetotalpowerinthesurroundingupperandlowerchannels.

17.2.4ResolutionBandwidthItisdeterminedbythesmallestfrequencythatcanberesolved.InFourier-transform-basedspectrumanalysers, the resolutionbandwidth is inverselyproportional to thenumberofsamples acquired or the length of thewindow function.By takingmore samples in thetimedomainormaking theacquisition time longer,whilekeeping thesampling rate thesame,theRBWwillbelowered,meaninghigherfrequencyresolution.

17.2.5HarmonicDistortionIt is a measure of the amount of power contained in the harmonics of a fundamentalsignal. Harmonic distortion is inherent to devices and systems that possess nonlinearcharacteristics—themorenonlinearthedevice,thegreateritsharmonicdistortion.Whenasignal of a particular frequency f1 passes through a nonlinear system, the output of thesystem consists of f1 and its harmonics f2 and f3. Figure 17.5 demonstrates thisrelationship.

Harmonicdistortionisexpressedaseitherpoweroraspercentageratio,whereharmonicpowerdistortionisPHD,whichisobtainedfrom

where,PHDisthepoweroftheharmonicdistortionindBc,PfundisthefundamentalsignalpowerindBordBm,andPharmisthepoweroftheharmonicofinterestindBordBm.

Figure17.5Fundamentalfrequencyf1withsecondandthirdharmonics

Torepresentintheformofpercentageratio,itisconvertedintovoltage,andcalculatedusingthefollowingequation.

whereVharmandVfundaretheharmonicvoltageandfundamentalvoltagerespectively,

In some applications, the harmonic distortion is measured as a Total percentageHarmonicDistortion(THD).Thismeasurementrequires thepowersummationofall theharmonicsinthespectrumband,asdefinedinthefollowingequation:

17.2.6PhaseNoiseTherearevarioussourcesofnoise.Whenthecarriersignalcontainnoiseduetophaseandfrequencymodulationofthesignalthenthenoiseistermedphasenoise.Thespectrumofphasenoiseisnormallyclosetothecarrierspectrum,andismeasuredindecibelsrelativetothecarrierfrequency(dBc).

Noisefloor isaspecifiednoiselevelbelowwhichsignalscannotbedetected,underaspecificmeasurementconditions.

17.3 RADIOFREQUENCYSPECTRUMANALYSER

Analysingsignalsintermsoftheirfrequenciesiscalledspectrumanalysis.Thespectrumanalyser can measure the frequencies present in a complex signal or the frequenciesresultingfrommodulationonacarrier.

Thespectrumanalyserisameasuringinstrumentthatdisplaysfrequencycomponentsofasignal.Eachfrequencycomponentcontainedintheinputsignalisdisplayedasasignallevel corresponding to that frequency.Thevertical scale displays the amplitudeof eachcomponent,andthechosenfrequencybandisdisplayedhorizontally.

SpectrumAnalysers(SA)areusefulaselectronictestequipmentusedindesigntestandmaintenance of radio-frequency circuitry and equipment. A spectrum analyser works

similar to that of an oscilloscope, as a basic tool used for observing signals. The onlydifference between the two is that where an oscilloscope looks at signals in the timedomain,spectrumanalyserlooksatsignalsinthefrequencydomain.Acommonspectrumanalyserhasthefollowingfeatures:

Frequencytuningrange—Measurementrangeoftheanalysersothatallofthefrequencycomponentsofthesignalcanbemeasured.Frequencyaccuracyandstability—Tobemorestableandaccuratethanthesignaltobemeasured.Sweepwidth—Thefrequencybandoverwhichtheunitcansweepwithoutreadjustment.Resolutionbandwidth—Needtobestrongenoughtoresolvedifferentspectralcomponentsofthesignal.Sensitivityand/ornoisefigure—Toobserveverysmallsignalsorsmallpartsoflargesignals.Sweeprate—Maximumsweeprateisestablishedbythesettlingtimeofthefilterthatsetstheresolutionbandwidth.Dynamicrange—Thedifferencebetweenthelargestandsmallestsignaltheanalysercanmeasurewithoutreadjustment.Phasenoise—Asignalwithspectralpuritygreaterthanthatoftheanalyserconversion,oscillatorscannotbecharacterised.

There are basically two types of spectrum analysers—analog type and is digital-typespectrumanalysers:

Ananalogspectrumanalyser—useseitheravariableband-passfilterwhosemid-frequencyisautomaticallytuned(shifted,swept)throughtherangeoffrequenciesofwhichthespectrumistobemeasuredorasuper-heterodynereceiverwherethelocaloscillatorissweptthrougharangeoffrequencies.AdigitalspectrumanalysercomputestheDiscreteFourierTransform(DFT),amathematicalprocessthattransformsawaveformintothecomponentsofitsfrequencyspectrum.

Super-HeterodyneAnalyser(SPA)Theworkingprincipleofasuper-heterodynetypeanalyserisverysimilartoanAMorFMradio receiver. In SPA, the incomingRF signal is firstmoderately amplifiedwith user-adjustablegainfactorandthensenttotheoneinputofamixerwhichactslikeananalogmultiplier.Theoutputsignalofa localoscillatorasshowninFigure17.6,goes tootherinputof themixerand then theoutputof themixer is thesumanddifferencefrequencybetweenRFandlocaloscillator.ThissignalthengoestotheIntermediateFrequency(IF)port of themixer.This IF signal is subsequently band filtered, rectified and sent to thevertically deflecting plates of theCathodeRayTube (CRT) in the SPA.The functionalblockdiagramofasimpleSuper-HeterodyneAnalyser(SPA)isshowninFigure17.6.

Figure17.6Functionalblockdiagramofasimplesuper-heterodyne(SPA)analyser

17.4 RFSCALARANDVECTORNETWORKANALYSER

The RF network analyser is an active test instrument which generates a signal that isappliedtothedeviceundertest,andthenitmeasurestheresponse.

ThedifferentfunctionalelementsofacommonRFnetworkanalyzerarethefollowing:

(a)SignalSeparationThesignalseparationelementisoftencalledtestset.Itprovidestwofunctions:

Measureaportionofincidentsignalforrationing.Thismaybeaccomplishedusingasplitterordirectionalcoupler.Separatetheincident(forward)andreflected(reverse)travellingwavesattheinputofDUT.

(b)ReceiverandSignalDetectionWhenthesignalispassedthroughthedeviceundertestandseparated from the source signal, it is processed in theRFnetwork analyser so that theresults canbegained.The first stageconsistsof a radio receiverwithademodulatorordetector.Typically,atunedradioreceiverisusedtoprovidethebestsensitivity,dynamicrangeaswellasharmonic/spurioussignalrejection.

(c)ProcessorandDisplayTheprocessedRFsignalsfromthereceiveranddetectorsectionaredisplayedinaformatthatcanbeinterpreted.

17.4.1DifferentTypesofRFAnalysersTherearedifferenttypesofnetworkanalyserswhichareabletomeasuretheparametresoftheRFcomponentsanddevicesindifferentways.Basedonthisnetwork,analyserscanbeclassifiedas

1. Scalarnetworkanalyser2. Vectornetworkanalyser

1.ScalarNetworkAnalyser(SNA)TheScalarNetworkAnalyser(SNA)isusedtomeasurefrequencyresponseofanydeviceorasystem.Itbasicallyconsistsoftwocomponents:(i)sweepgenerator,and(ii)spectrumgenerator. The sweep generator generates constant amplitude sinusoid with varying

frequencystartingfromlowtohigh.Theminimum(low)andmaximum(high)valueofthe frequencyand the time to increase fromminimum tomaximumfrequencyareuser-configurable.Thespectrumanalyserplotsthefrequencycontentsoftheinputsignal.Now,iftheoutputofthesweepgeneratorisconnectedtotheinputofthespectrumanalyserthenthespectrumanalyserwillshowaconstanthorizontallineonthescreen.Astheamplitudeof all the harmonics of the sweep generator output signal are same, the line will shiftvertically if the amplitude of the sweep generator output signal is increased. Now if adeviceundertestwhosefrequencyresponsesaretobeobtainedisplacedinbetweenthesweepgeneratorandspectrumanalyser,meaningoutputofsweepgeneratorisconnectedto the input of the device and output of the device is connected to the input of thespectrumanalyser, thespectrumanalyserwilldirectlydisplay thefrequencyresponseofthe device. The straight line cannot be seen on the spectrum analyser screen if theresponseofthedevicechangesthesweepgeneratoroutputaccordingtothefrequencyandtheresponseofthedeviceatthatfrequency.

2.VectorNetworkAnalyser(VNA)A Vector Network Analyser ( VNA) works in similar fashion as the scalar networkanalyser, the difference being that it canmeasure amplitude aswell as phase of anRFsignal.ThatiswhyitiscalledVNA.Thesweepfrequencyrangecanbeadjustedbytheuser.TheVNAmeasuresthefrequencyresponseofthedeviceundertestovertheadjustedrangeofsweepfrequency.First,theVNAisusedtomeasuretheincidenttestsignalfromthesweepgenerator(whichisaconstantlineonthescreen),thenthereflectedsignalfromthe test device, byusingdirectional coupler as shown inFigure17.7, and after that thetransmitted signal from theRFdeviceunder test.Then theVNAautomatically reversestheconnectionstomeasurethesamequantitieslookingintothedevicefromtheoppositedirection.Aftercompletionoftheprocess,theVNAdisplaysthesemeasuredquantitiesasafunctionoffrequency.

Figure17.7FunctionalblockdiagramofaVectorNetworkAnalyser(VNA)

TheVNAisacommondevicerequiredforRFdesignapplications.ThedeviceisoftenusedtocharacteriseRFdeviceperformanceintermsofnetworkscatteringparametres,orSparametres.

17.5 MODULATION

Modulation isdefinedas theprocess inwhichsomecharacteristicparametresofahigh-frequencysignalisvariedaccordingtothemessagesignal.Thelowerfrequencysignaliscalled themodulating signal, the higher frequency signal is called the carrier, and theoutputsignaliscalledthemodulatedsignal.

Accordingto themodulationprocess,modulation isof twotypes—analogmodulationanddigitalmodulation,discussedinthefollowingsubsections

17.5.1AnalogModulationIn analog modulation, characteristic parametres of a high-frequency sinusoidal signal(calledcarriersignal)isvariedaccordingtothemessagesignal,calledanalogmodulation.Generally,thecarrierisrepresentedas

whereAcistheamplitude,fcisthefrequencyandjisthephase.

The three characteristic parametres of the carrier signal are amplitude, phase andfrequency,andthesecanbevariedaccordingtothemessagesignal.So,analogmodulationtechniquesareclassifiedintothreetypes.Theyare

AmplitudemodulationPhasemodulationFrequencymodulation

1.AmplitudeModulation(AM)Amplitudemodulationmeansmodulatingtheamplitudeofthegivensignal.Inamplitudemodulation,theamplitudeofthecarriersignalisvariedinaccordancetotheinstantaneousamplitudeofthemodulatingsignal.ThecomplexenvelopofanAMsignalisgivenby

where, the constant A has been included to specify the power level and m(t) is themodulatingsignal(maybeanalogordigital).Thisequationreduces to thefollowingforAMsignal:

Figure17.8(a)Originalmessagesignal(b)modulatingsignaland(c)thesignalafterAM

Figure17.8showsthemodulatingsignalandthesignalafterAM.

2.PhaseModulation(PM)Thephasemodulationisdefinedasaprocess inwhichthephaseof thecarrier isvariedlinearlyaccordingtothemessagesignal.Ifm(t)isthemessagesignal(orthemodulationsignal) tobe transmittedwith thehelpofacarriersignalofamplitudeac, frequencywCand phase angle fC, then the time domain equation of the phasemodulated signal willbecome

andthemessagesignal,carriersignalandmodulatedsignalareshowninFigure17.9.

Figure17.9Messagesignal,carriersignalandmodulatedsignal

3.FrequencyModulation(FM)Frequencymodulationmeansmodulatingthefrequencyofthesignal,bychangeincarrierfrequency. Frequency of carrier signal is varied by the amplitude of message signal.Frequencymodulation hasmany attractive improvements over amplitudemodulation. Itofferstheadvantageofalmosttotalim-munityfromnoiseinterferenceasiteliminatesthe

problemoffading,whichispronouncedinampli-tudemodulation.

Informationsignal=m(t)

Carriersignal=ACcos(2πct)

k is the frequency deviation constant (Hz/volt) that represents themaximum shift ofsignalfrequencyfromthecarrierfrequencyinonedirection

Figure 17.10 shows the time domain frequency modulated signal. The figuredemonstrateshowamessagesignalmodifiesthefrequencyofacarriersignalinFM.

AMmodulation requires less bandwidthwhen compared toFMmodulation.But FMmodulationrequireslesspowerwhencomparedtoAMmodulation.Figure17.10Carrierwavewithmessagesignal,(b)Frequencymodulatedsignal

17.5.2DigitalModulationThedigital-modulationprocessinvolvesswitchingorkeyingtheamplitude,frequencyorphaseofthecarrieraccordingtotheincomingdata.Theinputtothedigitalmodulatorsisinbinarydigitsbaseduponthekeyingthesetechniquesaredividedintothreetypes:

1. AmplitudeShiftKeying(ASK)2. FrequencyShiftKeying(FSK)3. PhaseShiftKeying(PSK)

By digital modulation, we can convey a large amount of information as compared toanalogmodulation and they also providemore information capacity, compatibilitywithdigital data services, higher data security, better quality communications, and quickersystemavailability.

1.AmplitudeShiftKeying(ASK)InASK, the amplitudeof the carrier is changedaccording to themodulatingwaveformwhichisadigitalsignal(bit).Thelevelofamplitudecanbeusedtorepresentbinarylogic0s and 1s. Here, two states of the carrier signal is considered, i.e. ON or OFF. In themodulatedsignal,logic0isrepresentedbytheabsenceofacarrier,thusitissaidtobean

OFF/ONkeyingoperation.ASKdemonstratespoorperformance,asitisheavilyaffectedbynoiseandinterference.Mathematicallyitcanberepresentedas;

Figure17.11ASKmodulatedsignal

2.FrequencyShiftKeying(FSK)In FSK, the frequency of the carrier is changed according to themodulatingwaveformwhichisadigitalsignal.ThesimplestFSKisbinaryFSK(BFSK).BFSKliterallyimpliesusingacoupleofdiscretefrequenciestotransmitbinary(0sand1s)information.Withthisscheme, the“1” is called themark frequency and the“0” is called thespace frequency.Mathematicallyitcanberepresentedas;

Early telephone-line modems used audio frequency-shift keying to send and receivedata,uptoratesofabout300bitspersecond.Figure17.12showstheFSKmessagesignal,carriersignalandmodulatedsignal

Figure17.12(a)Messagesignal(b)carriersignal(c)FSKmodulatedsignal

3.PhaseShiftKeying(PSK)InPSK,thephaseofthecarrierischangedaccordingtothemodulatingwaveformwhichisadigitalsignal.PSKusesafinitenumberofphases;eachassignedauniquepatternofbinary bits. Usually, each phase encodes an equal number of bits. Each pattern of bitsformsthesymbolthatisrepresentedbytheparticularphase.

Mathematicallyitcanberepresentedas;

where fc is the frequencyof the carrierwave, andEb andTb are energy per bit and bitdurationrespectively..Figure17.13showsthemessagesignalandPSKmodulatedsignal

PSKhasbetterpowerandfrequencyefficienciescomparedtoASKandFSK.PSKachievessmallBitErrorRate(BER)forthesameC/N(carrier-noiseratio).PSKhasconstantenvelope,andisrobusttotime-varyingfadingchannel.PSKispopularlyusedinmanycommunicationsystemssuchassatelliteandmobilecommunicationsystems.

Figure17.13MessagesignalandPSKmodulatedsigna

17.5.3ModulationMeasurementTwo different types of modulation measurements are developed in order to take intoaccount both the amplitude, and phase noise on the carrier. They areModulationErrorRatio(MER)andErrorVectorMagnitude(EVM).Errorvectormagnitudeandmodulationerrorratioexpresssamekindofinformationandarecloselyrelatedtoeachother.Inotherwords, we can say that there is a one-to-one relationship between the two types ofmeasurements.

In a digital system, Modulation Error Ratio (MER) is similar to Signal-to-Noise orCarrier-to-Noise used in analog systems. As compared to EVM, MER is easier tounderstandasitrelatesdirectlytotheS/N(signaltonoise).Theamountofthemarginthesystemhasbefore failurecanbedeterminedbydetermining theMER(modulationerrorratio) of a digital signal. At the time of system failure,MER ismore advantageous ascomparedtoanalogsystemsaspoorMERisnotnoticeableonthepicturerightup.Ontheotherhand,inanalogsystemsdegradationsincarriertonoiseperformancecanbeseen.

Inanalogsystems,carrier-to-noiseratioissimplyameasureoftheratioofpeakvideocarrierpoweroverthenoiseinthechannel,overthesystembandwidthexpressedindB.Forthistypeofmeasurement,wecanalsousedigitalchannels,butunfortunatelytheydonotprovidethecompletepictureandduetothisreason,wehavetogoforMERandEVM.

MERandEVMcanbedirectlycorrelatedwitheachothersincetheyareessentiallythesamemeasurement; the only difference is on specification and performance.MER andEVMcanbeconsidereda figureofmerit for theQAMsignal that includesall typesofimpairments,notjustnoiseasincarrier-to-noiseinanalogsystems.

Figure 17.14 shows the ideal and measured location, where, v is the ideal symbolvector,wisthemeasuredsymbolvector,qisthephaseerror,(e=w–v)isthemagnitude

errorvector,ande/vistheEVM.

This quantifies, but does not necessarily reveal, the nature of the impairment. Toremovethedependenceonsystemgaindistribution,EVMisnormalizedby |v|,which isexpressedasapercentage.Analytically,rmsvalueofEVMoverameasurementwindowofNsymbolsisdefinedas

Figure17.14Idealandmeasuredlocation

MERisdefinedasfollows:

MER=10log(rmserrormagnitude/averagesymbolmagnitude)measuredindB

17.6 COMMUNICATIONSYSTEMS

Communicationistheprocessoftransferringinformationfromoneplacetoanother.Theinformation generated at source is transferred to the receiver through communicationchannel.

ThebasicelectroniccommunicationsystemcanbeshowninFigure17.15asfollows;

Figure17.15Blockdiagramofabasiccommunicationsystem

On the source side, there is a transmitter device that makes the input electricalinformation suitable for efficient transmission over a given channel. In general, atransmitter modulates amplitude or frequency of a high-frequency carrier wave by anoriginal electrical information signal which is known as the baseband signal. On thedestinationside,thereceiveristhedevicethatreceivesinformationfromthechannelanddemodulates theelectricalsignal fromit.Thereceiveralsoamplifiesandremovesnoiseand distortion from the noise contaminated received signal. The output transducerconvertselectricalsignalfromthereceiveroutputtoaformofmessageasrequiredbytheuser. Communication can be made in two forms—analog communication and digitalcommunication.

RFCommunicationSystemComponentsThe RF communication system consists of various components and each performsdifferentfunctionsaslistedbelow:

PLO:GeneratestheRFcarrierattherequiredfrequencyModulator:Variesthefrequency,amplitude,orphaseofanIFcarriertoputinformationontoitUpconverter:ShiftsthemodulatedIFsignaltoRFsignalPoweramplifier:IncreasesthepowerlevelofthemodulatedRFcarrierTXantenna:TransmitstheRFcarrierinthedirectionofthereceiverRXantenna:CollectsthetransmittedRFsignalatthereceiverRFfilter:AllowsonlyaspecifiedrangeofRFfrequenciestopassandblocksallotherfrequenciesLNA:AmplifiestheweakreceivedRFcarrierMixerandIFamplifier:ShiftstheRFcarriertoalowerfrequencybelowtheRFbandandamplifiesittoalevelwhereitcanbedemodulatedDemodulator:Removestheinformationfromthelow-frequencycarrier

AnRFcommunicationsystemblockdiagramisshowninFigure17.16.

Figure17.16RFcommunicationsystem

It applies to any typeofwirelessRFcommunication system:cellularphone,wirelessLAN,satellitecommunicationssystem.AnyRFcommunicationsystemmustcontainallofthedevicesshownthoughperformancerequirementsofeachdevicevaryfromsystemtosystem.

17.7 RFVOLTAGEANDPOWERMEASUREMENT

Asystem’soutputpowerlevelisfrequentlythecriticalfactorinthedesign,andultimatelytheperformanceof almost all radio frequencyandmicrowaveequipment.Measurementuncertaintiescauseambiguitiesinrealisableperformanceofatransmitter.

Forthemeasurementofaveragepower,asensoralongwithacalibratedpowermetreisconnectedwiththeRFtransmitter.Initially,iftheoutputofthesensorisswitchedoff/notallowedtoenterintothepowermetre,thepointerofthepowermeterissettozero.Thenthe sensor is switched on and the indication on the power meter is observed, which

indicatestheaveragepowerofthetransmitter.

FordesignandapplicationofanRFandmicrowavesystem,itisnecessarytodeterminethe power. Average power is very popular and used in specifying almost all RF andmicrowave systems. It is necessary to determinepower level.Generally, there are threemethodsformeasuringpoweratRFandmicrowavefrequencies.Eachof thesemethodsusesdifferentkindsofdevices toconvertRFpower tomeasurabledcor low frequencysignal.Themethodsareasfollows:

1. Byusingathermistor2. Byusingathermocouple3. Byusingadiodedetector

17.7.1PowerMeasurementUsingaThermistorFrom early times, for the measurement of RF/microwave power, bolometer sensors,especially thermistors, are being used. Presently, thermocouple and diode technologieshavecapturedthebulkofthoseapplicationsbecauseoftheirincreasedsensitivities,widerdynamicrangesandhigherpowercapabilities.Forcertainapplications,athermistorisstillthesensorofchoiceduetoitspowersubstitutioncapability.

The bolometer is a temperature—sensitive resistive element, whose resistance variesdue tochange in temperature.Thechange in temperature results fromconvertingRFormicrowave energy into heat within the bolometric element. Basically, two types ofbolometersareused—oneisthebarretterandtheotheristhethermistor.Abarretterisathinwirethathasapositivetemperaturecoefficientofresistance,whichisnotcommonlyusednow.Thermistorsaresemiconductorswithnegativetemperaturecoefficient.

17.7.2PowerMeasurementUsingaThermocoupleThermocouplesworkontheprinciplebasedondissimilarmetalsgeneratingavoltageduetotemperaturedifferencesathotandacoldjunctionofthetwometals.

Thetwomainreasonsforevolutionofthermocouplesare

1. Theyexhibithighersensitivitythanpreviousthermistortechnology2. Theyfeatureaninherentsquare-lawdetectioncharacteristic(inputRFpoweris

proportionaltodcvoltageout).

Since thermocouplesareheat-basedsensors, theyare true“averagingdetectors.”Thisrecommends them for all types of signal formats from CW to complex digital-phasemodulations.Theyaremoreruggedthanthermistors,makeuseablepowermeasurementsdownto0.3mW(–30dBm,fullscale),andhavelowermeasurementuncertaintybecauseofbetterSWR.

17.7.3PowerMeasurementUsingaDiodeDetectorDiodesconverthigh-frequencyenergytodcbywayoftheirrectificationproperties,whicharisefromtheirnonlinearcurrent-voltage(I-V)characteristic.

Rectifyingdiodeshavebeenusedasdetectorsandforrelativepowermeasurementsatmicrowavefrequencies.Forabsolutepowermeasurement,however,diodetechnologyhadbeenlimitedmainlytoRFandlowmicrowavefrequencies.

17.7.4MeasuringRFVoltageswithaVoltmeterTo measure RF voltages ranging from few hundred millivolts to several hundredmillivolts, a voltmeter uses diode detectors. Generally diode detectors fallow inversesquarelawbelow100V.Sobytakingtheadvantageofinversesquarelaw,powerdetectorsorvoltagedetectorsaredesigned.

Toachievebestsensitivity,adiodeshouldbematchedascloselyaspossibletosourceimpedance. Simple diode detectors are used for designing RF voltmeter to measurevoltagesfrom100mVtoseveralhundredmV.In thedesignofvoltmeter , twotypesofdiodedetectorsareused.

1. Seriesdetector2. Shuntdetector

Out of these, shunt detectors are mostly suitable for measuring RF and microwavevoltages.Inthiscase,diodesaredirectlyconnectedtogroundasshowninFigure17.17.

Figure17.17Circuitdiagramofashunttypedetector

InFigure17.17(shuntdetector),thediodeisconnectedinshuntanditisgrounded.Thedesigncomponentsshouldhaveshortleadstoavoidanyerrorreadingsandaterminationresisterisconnectedacrosstheinputtomeasureoutputofamplifierandsignalsources.Asmall silicon diode is readily available but germanium diodes will give low offsetvoltages. In order to remove these offset voltages, a battery and resister (high value) isconnectedinthecircuit.

EXERCISE

Objective-typeQuestions1.ThebandwidthofRFincludingmicrowaveisapproximately

(a)20Hzto20kHz

(b)1kHzto300GHz

(c)3GHzto3000GHz

(d)3Hzto300MHz

2.Identifythewrongstatement.

(a)Powerinbandisthemeasureoftotalpowerwithinaspecifiedfrequencyrange.

(b)Occupiedbandwidthmeasuresbandwidththatcontainstotalpowerofthesignal.

(c)Adjacentchannelpowermeasuresthewayaparticularchannelanditstwoadjacentchannelsdistributepower.

(d)Resolutionbandwidthmeasuresthesmallestfrequencythatcanberesolved.

3.InFouriertransform-basedspectrumanalysers,theresolutionbandwidthis

(a)proportiontothelengthofwindowfunction

(b)inverselyproportionaltothesamplingfrequency

(c)inverselyproportionaltothelengthofthewindowfunction

(d)proportionaltothesamplingfrequency

4.Phasenoisesaredueto

(a)modulationofthesignalwithcarriersignal

(b)noisefromothersignals

(c)noiseduetochangeofphaseduringreflection

(d)noiseduetochangeofphaseduringtransmissionindifferentmedium

5.Inthesweepgenerator,iftheoutputisconnectedtotheinputofaspectrumanalyserthen

(a)asingleverticalcanbeobserved

(b)asinglehorizontallinecanbeobserved

(c)asawtoothwavecanbeobserved

(d)lotofrandomlinescanbeobserved

6.Identifythecorrectstatement.

(a)CarrierfrequenciesofFMsignalsarerelativelylowerthanAMsignals.

(b)AntennasforFMsignalsarelargerinsizethanAMantennas.

(c)FMsignalscantravellongerdistancethanAMsignals

(d)FMsignalsaremoreimmunetonoisethanAMsignals

7.Thisisnotadigitalmodulationtechnique:

(a)Amplitudeshiftkeying

(b)Phaseshiftkeying

(c)Frequencyshiftkeying

(d)Pulseshiftkeying

8.ThesensorusedforRFpowermeasurement

(a)Thermocouple

(b)Microphone

(c)Straingauge

(d)Photodiode

Short-answerQuestions1. Why is spectral analysis important in RF communication system?What are themain different factors being

measured?Defineeachfactor.

2.Howarethepowerinbandandoccupiedbandwidthinterrelated?Explaininbrief.Howistheadjacentchannelpowermeasured?

3.Howistheharmonicdistortioncalculated?Statethepossiblesourcesofphasenoise.

4. What are different features a typical spectrum analysermust have?What are the different types of spectrumanalyserbeingused?

5.Statetheworkingprincipleofasuper-heterodyne-typespectrumanalyser.

6.Howdoesavectornetworkanalyserwork?Writedownsomeofitsapplications

7. Whatare thedifferentanalog-modulation techniquesused incommunication?Compareeachof themwithoneanother.

8. Whatare thedifferentdigital-modulation techniquesused incommunication?Compareeachof themwithoneanother.

9. HowcanadiodebeusedformeasurementofRFpower?ComparethebolometerwiththermocouplebasedRFpower.metre

10.ExplaintheRFvoltagemeasurementtechniqueswithapropercircuitdiagram.

18.1 INTRODUCTION

Kaolfirstsuggestedthepossibilitythatlow-lossopticalfibrescouldbecompetitivewithcoaxial cable and metal waveguides for telecommunications applications. It was not,however,until1970whenCorningGlassWorksannouncedanopticalfibrewithlosslessthan thebenchmark levelof10dB/km.After that, commercial applicationsbegan toberealised. The revolutionary concept which Corning incorporated and which eventuallydrove the rapid development of optical fibre communicationswas primarily amaterialsone—itwas the realisation that low doping levels and very small index changes couldsuccessfully guide light for tens of kilometres before reaching the detection limit. Theensuingdemandforopticalfibresinengineeringandresearchapplicationsspurredfurtherapplications. Today, we see a tremendous variety of commercial and laboratoryapplicationsofopticalfibretechnology.

18.2 HOWDOESANOPTICALFIBREWORK?

The optical fibre works on principles similar to other waveguides, with the importantinclusionofacylindricalaxisofsymmetry.

Whenlightistravellingfromonemedium(n0)intoamediumofdifferentdensity(n1),acertainamountofincidentlightisreflected.Thiseffectismoreprominentwherethelightistravellingfromahigh-densitymediumintoalower-densitymedium.Theexactamountof light that is reflecteddependson thedegreeofchangeof refractive indexandon theangle of incidence. If the angle of incidence is increased, the angle of refraction isincreasedatagreaterrate.Atacertainincidentangle(qC),therefractedraywillhaveanangleofrefractionthathasreached90°(thatis, therefractedrayemergesparalleltotheinterface). This is referred to as the critical angle. For rays that have incident anglesgreaterthanthecriticalangle,therayisinternallyreflectedtotally.Intheory,totalinternalreflectionisconsideredtoreflect100%ofthelightenergybutinpractice,itreflectsabout99.9%oftheincidentray.

Figure18.1showsthegenericopticalfibredesign,withacoreofhighrefractiveindexsurroundedbyalow-indexcladding.Thisindexdifferencerequiresthatlightfrominsidethefibrewhichis incidentatananglegreater thanthecriticalanglebetotallyinternallyreflectedattheinterface.

Asimplegeometricalpictureappearstoallowacontinuousrangeofinternallyreflectedraysinsidethestructure;infact, thelight(beingawave)mustsatisfyaself-interferenceconditioninordertobetrappedinthewaveguide.Thereareonlyafinitenumberofpathswhich satisfy this condition; these are analogous to the propagating electromagneticmodesofthestructure.Fibreswhichsupportalargenumberofmodes(thesearefibresoflarge core and large numerical aperture) are calledmultimode fibres, whereas a fibresallowingonlyonemodeofpropagationarecalledsingle-modefibres.

Figure18.1(a)Genericopticalfibredesign(cross-sectionview)(b)Pathofaraypropagatingatthegeometricanglefortotalinternalreflection

18.3 SOURCESANDDETECTORS

This section will examine the operation of the optical sources and their associateddetectorsusedwithfibreopticsystems.

18.3.1OpticalSourcesEffectiveopticalsourcesforfibreopticsystemsneedthefollowingfeatures:

Tobeabletoeffectivelycouplelightintosmallfibrecore,assmallas8.5micrometresforsingle-modefibresEasilymodulatedbyelectricalsignalstoconveydata,withgoodlinearitytopreventharmonicsandinter-modulationdistortionProvidehighopticaloutputpowerHavehighreliabilitySmallsizeandweightLowcost

Light emitting junction diodes (LED) and laser diodes (LD) fulfill many of theserequirementsandwewillnowexaminetheirpropertiesindetail.

1.LightEmittingDiodes(LEDs)LEDisbasicallyaspeciallydesignedp-njunctiondiode.LEDscanprovidelightoutputinthe visible spectrum as well as in the 850 nm, 1350 nm and the 1500 nm windows.Comparedwiththelaser,theLEDhasaloweroutputpower,slowerswitchingspeedand

greaterspectralwidth,hencethereismoredispersion.Thesedeficienciesmakeitinferiorforusewithhigh-speeddatalinksandtelecommunications.However,itiswidelyusedforshort-andmedium-rangesystemsusingbothglassandplasticfibresbecauseitissimple,cheap,reliableandislesstemperaturedependent.ItisalsounaffectedbyincominglightenergyfromFresnelreflections,etc.Althoughthelowerpowermakesitsafertouse,itcanstill be dangerouswhen the light is concentrated through a viewing instrument.TypicalLEDisshowninwiresFigure18.2.

Figure18.2LightEmittingDiode(LED)

BasicLEDOperatingPrinciplesWhenapositivevoltageisappliedtothep-regionandanegativevoltageappliedtothen-region, electrons and holes flow towards the junction of the two regions where theycombine.Whenanelectroncombineswithahole,theatomreturnstoitsneutralstateandenergyisreleased,havingbeenconvertedintoopticalenergyintheformofphotons.Initssimplest form, the radiatedenergy from theLED is causedby the recombinationof theelectrons and holes, which are injected into the junction by the forward bias voltage.Figure18.3illustratesthisprocess.

Figure18.3BasicLEDOperation

The size of the band gap determines the energy of the emitted photon. Differentsemiconductor materials have different band-gap energies and the gap energy (W) inelectronvolts(eV)canberelatedtothewavelength(l)bytheequation:

The usual LEDs applied in fibre optic systems use gallium aluminum arsenide(GaAlAs)for800to900nmwavelengthsandgalliumarsenide(GaAs)for930nm.LEDsforusewithplasticfibresneedtooperateatabout660nmandareproducedwithgalliumarsenide phosphide (GaAsP) compounds. Various indium gallium arsenide phosphide(InGaAsP)compoundsareusedforlongerwavelengthsof1300and1550nm.

2.LasersAnotherformofLEDisthelaserdiode.ThemostcommonformoflaserdiodeiscalledanInjectionLaserDiode(ILD)orjustInjectionDiode(ID).Thewordinjectionisnotofinterest—it merely refers to part of the process occurring inside the semiconductormaterial.Alaserprovidesalightoffixedwavelengthwhichcanbeinthevisibleregionaround635nmorinanyoneofthethreeinfraredwindows.Thelighthasaverynarrowbandwidth,typicallyonlyafewnanometreswide.Thisensuresthatchromaticdispersioniskepttoalowvalueandthis,togetherwithfastswitching,allowshighdata-transmissionrates.Asthelaserdeviceitselfisbarelyvisibletotheunaidedeye,itmustbecontainedinsomeformofpackage.TwotypicalexamplesareshowninFigure18.4.

Figure18.4Typicallaserdiode

Basic Principles of Laser Operation LASER stands for Light Amplification by theStimulated Emission of Radiation. LEDs and lasers use very similar principles ofoperation.IntheearliersectionofLED,ithasbeendiscussedthatlightisemittedfromanLEDwhenanelectrondropsfromahighenergylevel toalowerone.Whenthisoccurswithout outside influence, it is known as spontaneous emission. This occurs in someradioactive material. With the LED discussed in the previous section, a forward-biasvoltagewasusedtostimulatetheemission.Anelectronsittingat theupperenergylevelcan alsobe stimulated to drop to the lower level by a photonwith the right amount ofenergy.Inthisway,theexternalphotoncanstimulatetheemissionofasecondphotonatthe same wavelength. Laser action takes place through optical resonance. The laserstructure is very similar to an edge LED, having a thin, narrow active regionwith theaddition of reflective-end facets and reflective sides as shown in Figure 18.5. In thisresonator, the light is confined and reflected backward and forward through the excitedmedium. The laser is biased to begin the emission of photons. The photons reflectbackwardandforwardandstimulatefurtheremissionofphotonsfromelectronswaitingtorecombine.The light travellingbackand forthalong theaxisof the resonatorcontinuesthis action and builds up in strength until it is strong enough to break through the

reflectiveendandthus,alaserbeamisformed.

Figure18.5LASERsource

18.3.2OpticalDetectorsThe function of the optical detector is to efficiently convert the small amount of lightenergyreceivedfromthefibre,asphotons,intoelectricalsignals.Thedetectorneedstobea low inherent noise device, incorporating appropriate amplification to generate usefuloutput signals from low level inputs. Twomain types of devices are used for practicaldetectors:PINdiodesandavalanchephotodiodes.

1.PINDiodesThePINdiodeisverywidelyusedasadetectorforconvertinglightenergyreceivedfromtheopticalfibreintoanelectronicsignal.ThePINdiodeslooklikeLEDs.Thedifferenceis in its construction. The name ‘PIN’ stands as ‘P’ for p-type semiconductor, ‘I’ forintrinsicsemiconductorand‘N’standsforn-typesemiconductor.Inthiscase,theintrinsiclayerisinthemiddlepositionandonesidecoversthep-typesemiconductorwhereastheothersidecoversthen-typesemiconductor.Hence,itiscalledP-I-NorPINdiode.

TheTheory of itsOperation The PIN photodiode has awide intrinsic semiconductorlayerseparatingthep-andn-regions,asshowninFigure18.6.Thediodeisreversebiased(4.5–18volts)andthishelpsdrawthecurrentcarriersawayfromtheintrinsicregion.Thewidthof the intrinsic layer ensures that there is a highprobabilityof incomingphotonsbeing absorbed in it rather than in the p- or n-regions. The intrinsic layer has a highresistance because it has no free charges. This results in most of the diode voltageappearingacrossit,andtheresultantelectricalfieldraisestheresponsespeedandreducesnoise.Whenlightofsuitableenergystrikestheintrinsiclayer,itcreateselectron-holepairsby raisinganelectron from thevalenceband to theconductionbandand leavingaholebehind in the process. The bias voltage causes these current carriers (electrons in theconduction band) to quickly drift away from the junction region, producing a currentproportionaltotheincidentlight,asshowninFigure18.6.

Figure18.6Theoryofoperation,PINphotodiode

2.AvalancheDiode/AvalanchePhotoDiode(APD)Avalanchephotodiodesareusedwhereveryweaklightsignalshavetobeamplified,andconvertedintoastrongelectricalsignal.Thesediodesworkonhigheroperatingvoltages,i.e.reverse-biasvoltageisveryhigh,nowwheneverasmallamountoflightenergyfallsontheintrinsicregion,avalanchebreakdownoccursandhencelargereversebiascurrentflowsthroughthecircuit.ThemainadvantagesofAPDaregoodoutputatlowlightlevelsandawidedynamicrange—itcanhandlehighandlowlightlevels.ThedisadvantagesofAPDs are higher noise levels, higher cost, requires higher operating voltages and itsdecreesofgainwithanincreasingtemperature.

OperatingPrinciplesAvalanchephotodiodesusesemiconductor junctiondetectorswithinternal gain through avalanche currentmultiplication.Averyhigh reversebias voltage(50–300volts)isappliedtoap-njunction.Aphotonisabsorbedinthedepletionregion,creating a free electron and a free hole. These charges accelerate in the strong electricfield.Whenthey

collidewithneutralatomsinthecrystallattice,theirkineticenergyissufficienttoraiseelectronsacross thebandgapandcreateadditionalelectron-holepairs.Thesesecondarychargesalsoacceleratecreatingmoreelectron-holepairs.Inthisway,thecurrentproducedbyonephotonismultiplied.

Thep+andn+layersarehighlydopedregionswithverysmallvoltagedropsasshowninFigure18.7.Thedepletionregionislightlydoped,almostintrinsic.Mostofthephotonsareabsorbedinthisarea,formingelectron-holepairs.Theelectronsmovetothep–regionthathasbeendepletedoffreechargebythelargereversevoltage.Thedepletionregionatthep+n+junctioneffectivelyreachesrightthroughthep-layer.Thestrongelectricfieldsacross the p-layer cause avalanche multiplication of the electrons. The holes produceddriftacrosstheplayertothep+electrodebutdonotcausefurthermultiplication.Becausethisstructurelimits thechargecarriermultiplicationtoelectronsonly, ithasbetternoiseperformance.

Figure18.7Theoryofoperation,avalanchephotodiode

18.4 FIBREOPTICPOWERMEASUREMENT

18.4.1OpticalPowerThe fundamental unit of measure used in fibre optics is light power. As with electricpower,opticpowerismeasuredinwatts.

Forlight,thetotalenergyQisgivenby

Q=NQpwhere,QpistheenergyofasinglephotonandNisthenumberofphotons

Therefore,

PowerMeterPower in a fibre optic system is like voltage in an electrical circuit—it’s what makesthingshappen.It is important tohaveenoughpower,butnot toomuch.Toolittlepowerand the receivermay not be able to distinguish the signal fromnoise; toomuch poweroverloadsthereceiverandcauseserrorstoo.

Measuringpowerrequiresonlyapowermetre(mostcomewithascrew-onadapterthatmatchestheconnectorbeingtested)andalittlehelpfromthenetworkelectronicstoturnonthetransmitter.Duringthemeasurementofpower,themetremustbesettotheproperrange(usuallydBm,sometimesmicrowatts,butnever“dB”a relativepowerrangeusedonlyfortestingloss)andtheproperwavelengthsmatchingthesourcebeingused.Figure18.8showsthetechniqueusedinthemeasurementofopticalpower.

Figure18.8Measurementofopticalpower

To measure power, attach the metre to the cable that has the output you want tomeasure.Thatcanbeatthereceivertomeasurereceiverpower,ortoareferencetestcable

(testedandknowntobegood)thatisattachedtothetransmitter,actingasthe“source”,tomeasure transmitterpower.A typicalpowermetre is shown inFigure18.9.Turnon thetransmitter/source and note the power themetremeasures. Compare it to the specifiedpowerforthesystemandmakesureithasenoughpowerbutnottoomuch.For the powermetre as shown in Figure 18.9, thewavelength is adjustable over the

threewindowsandsomeoffera facility tostepupanddownbysmall increments.Thisallows the fibre characteristics tobequoted at any requiredwavelength. It is a ‘nice tohave’ rather than an essential feature. The power levels can be indicated in mW or indecibelsasdBm,relativetoonemilliwattorasdBr,relativetoapreviouslynotedvalue.Theyareavailablewithinternalmemoriestostoretheday’sworkandathermalprinterforhardcopies.

IfthelightsourceandpowermetrearetobeusedtoMeasuredpowercheckaninstallationorrepaironacommercialbasis,thecustomerwillneedassurancethatreadingofthepowermetre is correct. The proof of this is provided by a calibration certificate for eachinstrumentwhichmustberenewedatintervals,usuallyannually.Thecalibrationmustbecarriedoutbyanauthorisedcompanywhoseinstrumentsthemselvesarecalibratedagainstthe appropriate national standards. In this way, we can trace the accuracy back to itssource.

Figure18.9Typicalpowermetre

18.4.2MeasurementofLossIt isbasically thedifferencebetweenthepowercoupled into thecableat the transmitterendandwhatcomesoutatthereceiverend.Testingforlossrequiresmeasuringtheopticalpower lost in a cable (including connectors, splices, etc.)with a fibre optic source andpowermetrebyconnectingthecablebeingtestedtoaknowngoodreferencecable.

For loss measurement, a power metre along with a test source is required. The testsourceshouldmatchthetypeofsource(LEDorlaser)andwavelength(850,1300,1550nm).

Therearetwomethodsthatareusedtomeasureloss,whichwecall“single-endedloss”and“doubleendedloss”.Single-endedlossusesonlythelaunchcable,whiledouble-endedlossusesareceivecableattachedtothemetre.

Single-ended loss ismeasuredbymating the cableunder test to the reference launchcableandmeasuringthepoweroutputat thefarendwiththemetre.Bydoingthis, totallossisbeingmeasuredthatislossoftheconnectormatedtothelaunchcableandthelossofanyfibre,splicesorotherconnectorsinthecableundertest.Thismethodisdescribed

inFigure18.10.Reversethecabletotesttheconnectorontheotherend.

For the measurement of double-ended loss attach the cable to test between tworeference cables, one attached to the source and one to the metre. In this way, twoconnectors’ lossesarebeingmeasuredoneoneachend,plus the lossofall thecableorcablesinbetween.ThismethodisshowninFigure18.11.

Wealsoneedoneor tworeferencecables,dependingonthetest.Theaccuracyof themeasurementwilldependonthequalityofyourreferencecables.Referencecablesalwaysneed tobe testedby the single-endedmethoddiscussedearlier, to ensure theyaregoodbeforestartingthetestofothercables.

Figure18.10Singleendedlossmeasurement

Figure18.11Doubleendedlossmeasurement

Example18.1 Calculate theapproximate lossatwavelengthsof1300nmand 1550 nm for a optical system having 2 connectors, 2splicesandasingle-modeoptical fibrewithalengthof10km.

Solution

Foreachconnector,lossis0.5dB.Foreachsplice,lossis0.2dBForthesingle-modefibre,thelossisabout0.5dBperkmfor1300nmsources,and0.4dBperkmfor1550nm.

Soapproximatelossis

(0.5×2+0.2×2+10×0.5)dBfor1300nmwavelength

=6.4dB

and

(0.5×2+0.2×2+10×0.4)dBfor1550nmwavelength

=5.4dB

18.4.3OpticalTimeDomainReflectometre(OTDR)Themost commonly used and best recognisedmethod of analysing the state of a fibreoptic link is to test itwithanOpticalTimedomainReflectometre (OTDR).TheOTDRuses backscattered light of the fibre to imply loss. The OTDR works like RADAR,sendingahighpowerlaserlightpulsedownthefibreandlookingforreturnsignalsfrombackscattered light in the fibre itself or reflected light from the connector or spliceinterfaces.Bymeasuringthetimeittakesforthereflectedlighttoreturntothesourceandknowing the refractive index of the fibre, it is possible to calculate the distance to thereflectionpoint.

Whenthisinstrumentisconnectedtooneendofanyfibreopticsystemupto250kminlength,withinafewseconds,itisabletomeasuretheoverallloss,orthelossofanypartofasystem,theoveralllengthofthefibreandthedistancebetweenanypointsofinterest.

1.OperatingPrincipleAslighttravelsalongthefibre,asmallproportionofitislostbyRayleighscattering.Asthelightisscatteredinalldirections,someofitjusthappenstoreturnbackalongthefibretowardsthelightsource.Thisreturnedlightiscalledbackscatter.Thebackscatterpoweris a fixed proportion of the incoming power and as the losses take their toll on theincomingpower,thereturnedpoweralsodiminishesasshowninFigure18.12.

Figure18.12LossduetoRayleighscattering

TheOTDRcancontinuouslymeasure the returnedpower level andhencededuce thelosses encountered on the fibre. Any additional losses such as connectors and fusionspliceshavetheeffectofsuddenlyreducingthetransmittedpoweronthefibreandhencecausingacorrespondingchangeinbackscatterpower.Thepositionandthedegreeofthelossescanbeascertained.

Example18.2Anopticalfibrehasacoreofrefractiveindexof1.5.Whenthe fibre is being testedwithanOTDRsystem, it showsasharpfaultpeakafterwithdelayof1.4μs.Findthepossibledistanceoffault.

SolutionTravellingspeedoflightthroughthecoreis

Thismeansthatitwilltake5nstotravelthedistanceof1m.

IftheOTDRmeasuresatimedelayof1.4msthenthedistancetravelledbythelightis

The280metresisthetotaldistancetravelledbythelightandisthe‘onwardsandreturn’distance.Thefaultlocationisthereforeonly140m.

2.InsidetheOTDRIngeneral,anOTDRsystemhasthefollowinginsidecomponents:

(a)TimerThetimerproducesavoltagepulsewhichisusedtostartthetimingprocessinthedisplayatthesamemomentasthelaserisactivated.

(b) Pulsed Laser The laser is switched on for a brief moment, the ‘on’ time beingbetween1nsand10ms.Thewavelengthofthelasercanbeswitchedtosuitthesystemtobeinvestigated.

(c)DirectiveCouplerThedirectivecouplerallowsthelaserlighttopassstraightthroughintothefibreundertest.Thebackscatterfromthewholelengthofthefibreapproachesthedirectivecouplerfromtheoppositedirection.Inthiscase, themirrorsurfacereflects thelightintotheavalanchephotodiode(anAPD).Thelighthasnowbeenconvertedintoanelectricalsignal.

(d)AmplifyingandAveraging The electrical signal from theAPD is veryweak andrequiresamplificationbeforeitcanbedisplayed.Theaveragingfeatureisquiteinterestingandwewilllookatitseparatelytowardstheendofthischapter.

(e)Display Theamplified signals arepassedon to thedisplay.Thedisplay is either aCathodeRayTube(CRT)likeanoscilloscopeoracomputermonitor,oraliquidcrystalasincalculatorsandlaptopcomputers.TheydisplaythereturnedsignalsonasimpleXYplotwiththerangeacrossthebottomandthepowerlevelindecibelsuptheside.

(f)DataHandlingAninternalmemoryorafloppydiskdrivecanstorethedataforlateranalysis.TheoutputisalsoavailableviaanRS232linkfordownloadingtoacomputer.Inaddition,manyOTDRshaveanonboardprintertoprovidehardcopiesoftheinformationonthescreen.Thisprovidesuseful‘beforeandafter’imagesforfaultrepairaswellasarecordoftheinitialinstallation.InsidecomponentsofatypicalOTDRsystemareshowninFigure18.13.

Figure18.13FunctionalblockdiagramofanOTDRsystem

3.MeasurementUsingOTDRImpurities in the glass will cause a continuous low level reflection as the light travels

throughtheglassfibre.Thisisreferredtoasbackscatter.Thecorrecttechnicaltermofthisis Rayleigh scattering. The strength of the backscatter signal received at the sourcegraduallydrops,asthepulsemovesawayfromthesource.ThisisseenonanOTDRasanear linear drop in the received reflected signal and the slope of this linear drop is theattenuationofthefibre(dBperkm).Figure18.14illustratesatypicalreflectioncurveforan OTDR and notes the backscatter. Generally, an OTDR will not provide accuratereadings of irregularities and losses in the fibre for the first 15m of the cable. This isbecausethepulselengthanditsrisetimefromtheOTDRarecomparativelylargewhencompared to the time it takes for the pulse to travel the short distance to the point ofreflectionwithinthis15mandback.Toovercomethisproblem,areelofcableisinsertedbetween theOTDRand the link tobe tested.When reading theOTDRscreen, the firstlengthofcableisignoredandisreferredtoasthedeadband.WithreferencetotheOTDRplotinFigure18.14,theY-axisoftheplotshowstherelativeamplitudeofthelightsignalthatisreflectedbacktothesourceandtheX-axisrepresentstime.ThetimebaseisdirectlytranslatedanddisplayedasdistancebytheOTDR.

The sudden peaks that appear along the slope are the points where reflections haveoccurredandthelightthathasreflectedbacktothesourceisstrongerthanthebackscatter.There are five main reflection points illustrated in Figure 18.14. In their order ofdecreasingmagnitude,theyare

1. Reflectionfromtheunterminatedendofthefibre2. Reflectionfromaconnector3. Reflectionfromasplice4. Reflectionfromahairlinecrackinthefibre5. Backscatter

After each of the reflections, the slope of the attenuation curve drops suddenly.Thisdroprepresents the loss introducedby theconnector, spliceor imperfection in the fibre.Point (6) noted in Figure 18.14 illustrates a splice where the cores of fibres are wellmatched for light travelling in the direction away from the source. This splice has noreflectionbutjustalossintroducedbythesplice.Thetypeofdropatthepoint(6)intheattenuationcurvecouldalsobecausedbyasharpbendinthefibrewherelightescapesoutofthefibreatthebendandisnotreflectedback.Sometypesoffaultsinthefibrewillalsocausesimilarresults.

Point (7) noted in Figure 18.14 shows the noise floor of the instrument. This is thelowest sensitivity of a received signal that the device can accept.Measurements madeclose to this level are not very accurate.OTDR testing can provide very accurate faultanalysisoveralmostanylengthoffibre.ItisimportantthatthedeadbandrollofcableisalwaysinsertedbetweentheOTDRandthelinkbeforemakingthemeasurement.Onthebetter quality instruments, a resolution of 1m for fault location and .01 dB for in-linelossescanbeobtained.Someinstrumentswilloperatewitharangeofupto400km.

Figure18.14TracefromanOTDR

EXERCISE

Objective-typeQuestions1.Lightpassesthroughthefibreduetophenomenaof

(a)totalinternalreflection

(b)reflectionfromtheinterfaceoftwomedium

(c)transmissiontothesecondmedium

(d)bothtransmissionandreflectionattheinterfaceoftwomedium

2.LEDsoperatinginthewavelengthof800–900nmaremainlymadeof

(a)GaAs

(b)GaAlAs

(c)GaAsP

(d)InGaAsP

3.ThewidthofactiveregionofLASERdiodeiscomparatively

(a)widerthatLEDs

(b)almostequaltoLEDs

(c)muchwiderthatLEDs

(d)narrowerthanLEDs

4.PINphotodiodesarekeptin

(a)forwordbias

(b)reversebias

(c)connectedcircuitandnobiasvoltagesaregiven

(d)initiallyforwordbiasedandthenreversebiased

5.Avalanchephotodiodeshaveoutputvoltagecomparatively

(a)lowerthatPINphotodiode

(b)higherthanPINphotodiode

(c)higherthannormalphotodiode

(d)higherthannormalandPINphotodiode

6.InOTDRresponse,thepeaksofthereflectedwaveformdonotoccurdueto

(a)reflectionfromtheunterminatedendofthefibre

(b)reflectionfromaconnector

(c)backscatter

(d)reflectionfromtheinterfaceofcoreandcladding

Short-answerQuestions1.Howdolightwavestravelthroughanopticalfibre?Explainwithaproperdiagram.

2.Statetheworkingprincipleofap-njunctionphotodiode.

3.HowareLASERdiodesdifferentfromLEDs?HowdoLASERdiodesgenerateLASERlight?

4.HowdoPINdiodeswork?Whatarethebenefitsofavalanchediodesandhowdotheywork?

5.Howistheopticalpowerinafibreopticnetworkmeasured?Explaininbrief.

6.Statetheproceduresadoptedduringthemeasurementoffibreloss.

7.HowdoestheOTDRwork?Explaininbriefwithadiagram.

8.DrawthefunctionalblockdiagramofatypicalOTDRsystemandexplaininbriefabouteachelement.

9.HowaredifferentreflectivecomponentsmeasuredusinganOTDRsystem?

10.Calculatetheapproximatelossatwavelengthsof800nmand900nmforanopticalsystemhaving1connector,4splicesandasingle-modeopticalfibrewithalengthof10km.

TableI.BasicunitsTableII.DerivedunitswithassignednamesTableIIIa.SIUnitsprefixesTableIIIb.BinaryprefixesforbytesTableIV.Acceptednon-SIunitsTableV.Acceptednon-SIunitswithexperimentalvaluesTableVI.UnitsdeprecatedbytheSI

TableIBasicUnits

TableIIDerivedunitswithassignednames

TableIIIaSIUnitsprefixes

TableIIIbBinaryprefixesforbytes

TableIVAcceptednon-SIunits

TableVAcceptednon-SIunitswithexperimentalvalues

TableVIUnitsdeprecatedbytheSI

UNITCONVERSIONTABLE

HOWTOREADTHISTABLE:ThetableprovidesconversionfactorstoSIunits.Thesefactorscanbeconsideredasunitymultipliers.Forexample:

Length:m/X

0.0254in0.3048ft

meansthat

1=0.0254(m/in)

1=0.3048m/ft

TheSIunitsarelistedimmediatelyafterthequantity;inthiscase:Length:m/X.Themstands formetre, and the “X” designates the non-SI units for the same quantity. Thesenon-SIunitsfollowthenumericalconversionfactors.

ExampleA.1 To calculate how many metres are in 10 ft, the tableprovidestheconversionfactoras0.3048m/ft.

Hence,multiply

10ftX0.3048m/ft=3.048m

ExampleA.2 Convertthermalconductivityof10kcal/h-m-°CtoSIunits.Selecttheappropriateconversionfactorfortheseunits,

10(kcal/h-m-°C)X1.163(w/m-K)/(kcal/h-m-°C)=11.63w/m-KLength:m/X

Mass:kg/X

Time:s/X

Temperature:K/X(difference)

Area:m2/X

Volume:m3/X

FlowRate,Volume:(m/s)/X

SpecificVolume:(m3/kg)/X

Velocity:(m/s)/X

Acceleration:(m/s2)/X

Momentum:(kg-m/s)/X

AngularVelocity:(rad/s)/X

AngularAcceleration:(rad/s2)/X

Momentum,Angular:(kg-m2/s)/X

MassMomentofInertia:(kg-m)/X

FlowRate,Mass:(kg/s)/X

Density:(kg/m3)/X

FlowRate,Mass/Volume:(kg/m-s)/X

SpecificVolume:(m3/kg)/X

Force:N/X

SurfaceTension:(N/m)/X

Pressure,Stress:(N/m2)/X

Torque:N-m/X

DynamicViscosity:(Kg/m-s)/X

DynamicViscosity:(g/cm-s)/X

Energy:J/X

Power:W/X

SpecificHeat,GasConstant:(J/kg-K)/X

ThermalConductivity:(W/m-K)/X

HeatTransferCoefficient:(W/m2-K)/X

B.1 INTRODUCTION

Althoughmany students know the decimal (base 10) system, and are very comfortablewith performingoperations using this system, it is important for students to understandthatthedecimalsystemisnottheonlysystem.Bystudyingothernumbersystemssuchasbinary (base 2), octal (base 8), and hexadecimal (base 16), students will gain a betterunderstandingofhownumbersystemsworkingeneral.Whendiscussinghowacomputerstores information, the binary number system becomes very important since this is thesystem that computersuse. It is important that studentsunderstand that computers storeandtransmitdatausingelectricalpulses,andthesepulsescantaketwoforms:“on”(1)or“off”(0).

Thefollowingtopicstreatthemanipulationofnumbersrepresentedindifferentbasesaswellasthebinaryrepresentationofnegativeintegersandfloating-pointnumbers.

B.2 DIFFERENTBASES

Thefollowingareaseriesofexamplesthatshouldhelpstudentsunderstandhownumbersarerepresentedusingdifferentbases.

1.TheDecimalSystemIneverydaylife,weuseasystembasedondecimaldigits(0,1,2,3,4,5,6,7,8,9) torepresent numbers and refer to the system as the decimal system. Consider what thenumber83means.Itmeanseighttensplusthree:

83=(8×10)+3

Thenumber4728meansfourthousands,sevenhundreds,twotens,pluseight:

4728=(4×1000)+(7×100)+(2×10)+8

Thedecimalsystemissaidtohaveabase,orradix,of10.Thismeansthateachdigitinthenumberismultipliedby10raisedtoapowercorrespondingtothatdigit’sposition:

83=(8×101)+(3×100)

4728=(4×103)+(7×102)+(2×101)+(8×100)

The same principle holds for decimal fractions but negative powers of 10 are used.Thus,thedecimalfraction0.256standsfor2tenthsplus5hundredthsplus6thousandths:

0.256=(2×10–1)+(5×10–2)+(6×10–3)

Anumberwithbothanintegerandfractionalparthasdigitsraisedtobothpositiveandnegativepowersof10:

472.256=(4×102)+(7×101)+(2×100)+(2×10–1)+(5×10–2)+(6×10–3)

Ingeneral,forthedecimalrepresentationofX=…d2d1d0.d–1d–2d–3…,thevalueofXis

2.TheBinarySystemInthedecimalsystem,10differentdigitsareusedtorepresentnumberswithabaseof10.In the binary system, we have only two digits, 1 and 0. Thus, numbers in the binarysystemarerepresentedtothebase2.

Toavoidconfusion,wewillsometimesputasubscriptonanumbertoindicateitsbase.For example, 8310 and 472810 are numbers represented in decimal notation, or morebriefly,decimalnumbers.Thedigits1and0inbinarynotationhavethesamemeaningasindecimalnotation:

02=01012=110

Torepresentlargernumbers,aswithdecimalnotation,eachdigitinabinarynumberhasavaluedependingonitsposition:

102=(1×21)+(0×20)=210

112=(1×21)+(1×20)=310

1002=(1×22)+(0×21)+(0×20)=410andsoon.Again,fractionalvaluesarerepresentedwithnegativepowersoftheradix:

1001.1012=23+20+2–1+2–3=9.62510Ingeneral,forthebinaryrepresentationofY=…b2b1b0.b–1b–2b–3…,thevalueofY

is

3.ConvertingbetweenBinaryandDecimalItisasimplemattertoconvertanumberfrombinarynotationtodecimalnotation.Infact,weshowedseveralexamplesintheprevioussubsection.Allthatisrequiredistomultiplyeachbinarydigitbytheappropriatepowerof2andaddtheresults.

(a)BinarytoDecimalFortheintegerpart,recallthatinbinarynotation,anintegerrepresentedby

bm–1bm–2…b2b1b0bi=0or1

hasthevalue

(bm–1×2m–1)+(bm–2×2m–2)+…+(b1×21)+b0

(b)DecimaltoBinarySupposeitisrequiredtoconvertadecimalintegerNintobinaryform.IfwedivideNby2,inthedecimalsystem,andobtainaquotientN1andaremainderR0,wemaywrite

To find b–2, we repeat the process. Therefore, the conversion algorithm involvesrepeated multiplication by 2. At each step, the fractional part of the number from thepreviousstepismultipliedby2.Thedigit totheleftofthedecimalpointintheproductwill be 0 or 1 and contributes to the binary representation, starting with the mostsignificantdigit.Thefractionalpartoftheproductisusedasthemultiplicandinthenextstep.

Thisprocessisnotnecessarilyexact;thatis,adecimalfractionwithafinitenumberofdigitsmayrequireabinaryfractionwithan infinitenumberofdigits. Insuchcases, theconversionalgorithmisusuallyhaltedafterapre-specifiednumberofsteps,dependingonthedesiredaccuracy.

4.HexadecimalNotationBecauseof the inherentbinarynatureofdigitalcomputercomponents,all formsofdatawithin computers are represented by various binary codes. However, no matter howconvenient thebinarysystemisforcomputers, it isexceedinglycumbersomeforhumanbeings.Consequently,most computer professionalswhomust spend timeworkingwiththeactualrawdatainthecomputerpreferamorecompactnotation.

What notation to use?One possibility is the decimal notation.This is certainlymorecompactthanbinarynotation,butitisawkwardbecauseofthetediousnessofconvertingbetweenbase2andbase10.

Instead,anotationknownashexadecimalhasbeenadopted.Binarydigitsaregroupedinto sets of four.Each possible combination of four binary digits is given a symbol, asfollows:

Because16symbolsareused, thenotation iscalledhexadecimal,and the16symbolsarethehexadecimaldigits.

Asequenceofhexadecimaldigitscanbethoughtofasrepresentinganintegerinbase16.

Inhexadecimalsystem,thepossibledigitsare0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

(Note:Inbase10,A=10,B=11,C=12,D=13,E=14,F=15)

Thus,

Hexadecimal notation is used not only for representing integers. It is also used as aconcise notation for representing any sequence of binary digits, whether they representtext,numbers,orsomeothertypeofdata.Thereasonsforusinghexadecimalnotationarethefollowing:

1. Itismorecompactthanbinarynotation.2. Inmostcomputers,binarydataoccupysomemultipleof4bits,andhencesome

multipleofasinglehexadecimaldigit.3. Itisextremelyeasytoconvertbetweenbinaryandhexadecimal.

As an example of the last point, consider the binary string 110111100001. This isequivalentto

This process is performed so naturally that an experienced programmer canmentallyconvert visual representations of binary data to their hexadecimal equivalent withoutwritteneffort

5.HexadecimaltoBinaryConversionSinceonehexadecimaldigitcanberepresentedusingfourbinarydigits,wecanconverteachhexadecimaldigitintoagroupoffourbinarydigits.

2A4E

2A4E16=0010101001001110

=101010010011102

Asthenamesuggests,theWestonfrequencymeterisaninstrumentusingwhichunknownfrequency of a signal can be measured. It is basically a moving-iron-type instrumentwhich works on the principle that whenever the frequency changes, the currentdistributionchangesbetweentwoparallelcircuits,oneofwhichisinductiveandtheothernon-inductive.Anychangeinfrequencychangestheinductiveimpedanceoftheinductivearm causing current distribution to change between the two parallel paths. Figure C.1showstheconstructionaldetailsofaWestonfrequencymeter.

FigureC.1WestonFrequencymeter

The axes of the two coilsA1–A2 andB1–B2 are mutually perpendicular. A soft ironneedle that carries a pointer is placed at the central locationwithin the coils.CoilA isconnectedinserieswithaninductanceLAacrossanon-inductiveresistanceRA.CoilB isconnectedinserieswithanon-inductiveresistanceRBacrossaninductanceLB.TheotherinductorLactsasafiltertoremoveanyharmonicsthatmaybepresentinthesignal.

Assupplyisgiventothesystem,themagneticfieldsdevelopedbythetwocoilsareatright angles to each other. Depending on the strength of these two magnetic fields, adeflectingtorqueisdevelopedthatmovesthesoftironneedleandhencethepointeronacalibratedscale.Thedeflectingtorqueandhencetheamountofdeflectionofthepointerthusdependsonthemagnitudeofcurrentsinthetwocoils.

Oncethefrequencydeviatesfromacertainpresentvalue,theinductancevaluesLAandLB change, but the resistances RA and RB remain the same. This makes the currentdistributionin the twocoils tochangefromtheir initialpresetvalues.Dependingonthefrequency, one coil becomes stronger than the other. Thus, the deflecting torque undersuchconditionwillbedifferentfromthatinthenormalcaseandthepointerwilldeviateeither towards left or to the right indicating lower or higher frequency than the presetvaluerespectively.

SolvedSampleQuestionPapersSOLVEDQUESTIONPAPER-1

1.Answerthefollowingquestions:

(2×10)

(a)Givetwoexamplesofeach:(i)Absoluteinstrument(ii)Secondaryinstrument

(i)Absoluteinstruments—Tangentgalvanometer,Absoluteelectrometer

(ii)Secondaryinstruments—Moving-coilinstrument,Moving-ironinstrument

(b)Awattmeterhasacurrentcoilof0.03Ωresistanceandapressurecoilof6000Ωresistance.Calculatethepercentageerrorifthewattmeterissoconnectedthat(i)thecurrentcoilisontheloadside,and(ii)thepressurecoilisontheloadside.Theloadtakes20Aatavoltageof220Vand0.6powerfactorineachside.

Loadspecifiedis20Aat250Vwith0.6powerfactor.

(i)CurrentCoil(CC)onloadside

Figure1

Truepower =VIcosφ=250×20×0.6=3000W

PowerlostinCC =I2×rC(whererCistheresistanceofCC)

=202×0.03=12W

Thewattmeterwillthusreadtotalpower=3000+12=3012W12

Hence,errorinmeasurement

(ii)PressureCoil(CC)onloadside

Figure2

Truepower =3000WPowerlostinPC =V2/RP(whereRPistheresistanceofPC)

=2502/6000=10.42W

Thewattmeterwillthusreadtotalpower=3000+10.42=3010.42W

Hence,errorinmeasurement

(c) What is creep and how are creep adjustments made in a single-phaseinduction-typeenergymeter?

ReferSection8.3.3inChapter8onMeasurementofEnergy.

(d)Whataretheadvantagesofaninstrumenttransformer?

ReferSection3.2inChapter3onInstrumentTransformers.

(e)If‘J’istheinertiaconstant,‘D’isthedampingconstantand‘K’isthecontrolconstant of a D’arsonaval galvanometer, write down the condition forunderdamped,criticallydampedandoverdampedcases.

Underdamped:D2<4kJ

Criticallydamped:D2=4kJ

Overdamped:D2>4kJ

(f) A simple slide-wire is used for measurement of current in a circuit. Thevoltagedropacrossastandardresistorof0.1Ωisbalancedat75cm.Findthemagnitudeofcurrentifthestandardcellemfof1.45Visbalancedat50cm.

ReferExample5.3inChapter5onPotentiometers.

(g)Writedownfourapplicationsofadcpotentiometer.

ReferSection5.4inChapter5onPotentiometers.

(h)DrawthecircuitdiagramofOwen’sbridge.Whatdoesitmeasure?

ReferSection6.4.5inChapter6onACBridges.

(i)WritedowntheexpressionforthegaugefactorofastraingaugeintermsofPoisson’sratio(µ).

[ReferEquation(11.6)inSection11.4ofChapter11onSensorsandTransducers]

Thegaugefactorisdefinedastheratioofper-unitchangeinresistancetoper-unitchangeinlength.

where =strain,ρistheresistivityofthewire,andµisthePoisson’sratio.

(j)Whatarethedifferentformsofthermistorsavailable?Drawthem.

Thermistors are ceramic semiconductors and have either large positivetemperaturecoefficientofresistance(PTCdevices)orlargenegativetemperaturecoefficientofresistance(NTCdevices).

NTCThermistors

Beadtype

•Barebeads

•Glasscoatedbeads

•Ruggedisedbeads

•Miniatureglassprobes

•Glassprobes

•Glassrods

•Bead-in-glassenclosures

Metallisedsurface-contacttype

•Disks

•Chips(wafers)

•Surfacemounts

•Flakes

•Rods

•Washers

Figure5

2. (a) What are the different forces acting on an indicating type of instrument?Discussthem.

(6)

ReferSection2.4inChapter2onAnalogMeters.

(b) A weight of 5 g is used as the controlling weight in a gravity-controlledinstrument. Find its distance from spindle if the deflecting torquecorrespondingtoadefectionof60°is1.13×10–3Nm.

(4)

Forgravitycontrol,thecontroltorqueisgivenby

Tc=Wlsinθ=mglsinθ

Thus,asperthegivendata,1.13×10–3=5×10–3×9.81×l×sin60°

Hence,distanceofweightfromspindlel=26.6mm

3.ConstructthedifferentpartsofanElectrodynamometerwattmeterandexplainitstheoryformeasurementofpower.Discusstheshapeofscalealso.

(10)

ReferSections7.4.1,7.4.2,and7.4.3inChapter7onPowerMeasurement.

4.(a)Derivethesteady–statedeflectionofa‘D’arsonavalgalvanometer.Whatareintrinsicconstantsofagalvanometer?Explainthese.

(6)

Let,

l,d =dimensionsofverticalandhorizontalsidesofthecoil(m)N =numberofturnsinthecoilB =air-gapfluxdensityI =moving-coilcurrentk =suspensionspringconstantθF =finalsteady-statedeflectionofthegalvanometercoil

Figure7

Forceoneachsideofcoil=NBIlsinα

whereαistheanglebetweentheconductorandthedirectionofmagneticfield.

Sincethemagneticfieldisradial(duetothestationerycore),α=90°

Hence,forceoneachsideofcoil=NBIl

Thus,deflectingtorqueTd=Force×Distance=NBIld

=NBAI

whereA=ld=areaofcoil

ThequantitiesN,B,andAareconstantforagivengalvanometer.

Hence,deflectingtorqueTd=GI

whereG=NBA=Displacementconstantofthegalvanometer

The controlling torque is provided by the suspension. At a deflection of θF, thedeflectingtorqueisgivenbyTc=kθFForfinalsteadydeflection,Td=Tcor,kθF=GI

Hence,finalsteadydeflectionθF=GI/k

TheintrinsicconstantsofaD’arsonavalgalvanometerare

1. DisplacementConstant: The deflecting torque is given byTd =GI, thisG iscalledthedisplacementconstantandithasavalueG=NBA

2.InertiaConstant:Whilethemovingsystemmovesinthespacebetweenthetwomagnets,aretardingtorqueisproducedduetoinertiaofthemovingsystem.ThevalueofthistorqueisgivenbyTj=J(d2θ/dt2);J is themomentofinertiaofthemovingsystemandθ is thedeflectionat time t.Themomentof inertiaJ isalsocalledtheinertiaconstant.

3.DampingConstant:Dampingtorqueisprovidedonthemovingsystemeitherbyairfrictionorbytheactionofeddycurrent.Ineithercase,thedampingtorqueisgivenbyTD=D(dθ/dt);thisDiscalleddampingconstant.

4.ControlConstant:Thecontroltorqueprovidedbythesuspension,thattendstocontrolthemovementofthemovingsystemandalsotriestorestorethesystemtoitsinitialpositionisgivenbyTc=kθ;thiskiscalledthecontrolconstant.

(b)AD’arsonavalgalvanometerhasthefollowingdata:Fluxdensity=8×10–3,Wb/m2.Numberofturns=300,Lengthofcoil=15mm.Widthofcoil=30mm, Spring constant = 2.5 × 10–3 Nm/rad. Calculate (a) the deflection ofgalvanometer foracurrentof1μA,and (b)currentsensitivity inmm/μA ifthescaleiskept1mawayfromthemirror.

(4)

(i)Displacementconstant=G=NBld=300×8×10–3×15×10–3×30×10–3

=1.08×10–3Nm/A

Deflectionofgalvanometer

(ii)Deflectioninmmwhenthescaleiskeptatadistanceof1mmfromthemirror

=2000θF=864mm

Hence,currentsensitivityS=864mm/μA

5.Drawtheequivalentcircuitandphasordiagramofacurrenttransformer.Derivetheexpressionforratioandphaseangleerror.

(10)

Refer Sections 3.4, 3.4.1, 3.4.2, 3.5.1, and 3.5.2 in Chapter 3 on InstrumentTransformers.

6. Describe the working of Maxwell’s inductance-capacitance bridge formeasurementofinductance.Derivetheequationforbalanceanddrawthephasordiagramunderbalancecondition.Whataretheadvantagesanddisadvantagesofthisbridgecircuit?

(10)

ReferSection6.4.1inChapter6onACBridges.

7.(a)Explainthefunctionofatime-basegeneratorinaCRO.

(5)

ReferSection9.4inChapter9onCathodeRayOscilloscope.

(b)ExplainhowvoltageandcurrentaremeasuredwiththehelpofCRO?

(5)

ReferSection9.7inChapter9onCathodeRayOscilloscope.

8.Writeshortnotesonanytwoofthefollowing:

(5×2)

(a)ElectricalResonancetypeFrequencyMeter

In an electrical resonance–type frequency meter, an unknown frequency ismeasuredwiththehelpofanR-L-Cresonatingcircuit.

Figure8

Theunknownfrequencyacsource,whosefrequencyistobemeasuredisusedasthevoltagesourceinthedrivingcircuitasshowninthefigure.Voltagesupplytothe resonatingcircuit isgivenbycoupling thecoilLwith theoutput coilof thesignal ac source. Resonance in the RLC circuit is obtained by varying thecapacitance.AnelectronicvoltmeterconnectedacrossthecapacitorisusedastheprimarydetectorforcheckingresonanceconditionintheRLCcircuit.WithcertainvalueofR,L,andC,whenresonance isobtainedat theunknownfrequency, thevoltage indicated by the electronic voltmeter will be maximum. The unknownfrequencycanbecalculatedbyusingthemathematicalconditionforresonanceinaseriesRLCcircuit.

(b)Slide-wiredcPotentiometer

ReferSection5.2inChapter2onPotentiometers.

(c)LVDT

ReferSection11.3inChapter11onSensorsandTransducers.

CapacitiveTransducer

(d)ReferSection11.7.4inChapter11onSensorsandTransducers

SOLVEDQUESTIONPAPER-21.Attemptanyfourpartsofthefollowing:

(4×4=16)

(a)Defineandexplainbrieflythestaticperformanceparametersofinstruments.

ReferSection1.7inChapter1onConceptsofMeasurementSystems.

(b)Asourcehavinganopencircuitvoltageof20Vandanoutputimpedanceof(1.5 j4)Ω isconnected througha transmissionnetworkof impedance (0.5+j1)Ω.Whatshouldbetheloadimpedancesothatthemaximumpowerwillbedeliveredtoit?Calculatethemaximumdeliverablepower.

For maximum power transfer, load impedance must be equal to the complexconjugateofSourceimpedance

Thus,loadimpedance=(2–j5)Ω

Maximumdeliverablepower=202/(4×2)=50W

(c) Derivetheequationsforcapacitanceanddissipationfactorofalow-voltageScheringbridge.Drawthephasordiagramofthebridgeunderconditionsofbalance.

ReferSection6.5.2inChapter6onScheringBridge.

(d)ExplainthefunctionandworkingofaWagnerearthDevice.

ReferSection6.7inChapter6onScheringBridge

(e)Describethephenomenonofsynchronizationofverticalinputsignal-to-sweepgeneratorinCRO.

ReferSection9.5inChapter9onCathodeRayOscilloscope.

(f)DiscussdelaysweepinCRO.

When short-durationpulses aredisplayed in theCRO,proper synchronisation isachievedbyinternaltriggeringintheactriggermode.However,duetothefinitedelayofthetriggeramplifiersusedinternally,theinitialbuild-upofthepulsemaynot be observable in the display.To avoid this, a delay line producing a typicaldelayintherangeof100nsto1msisoftenincorporatedintheYamplifier.

The “delayed sweep” is an additional facility available in someoscilloscopes,enablingenhancedresolutionintimemeasurements.The“delayingsweep”allowstheoperatortoselectanyspecificdelaytimebymeansofa10-turncalibrateddial.This delay is generated by applying a sweep ramp to a voltage comparator thatproducesa triggerpulse at a laterpoint in time.Thedelayed sweep starts at theselectedtime,andisusuallyadecadeortwofasterthanthedelayingsweep.Usingaveryhighspeedforthedelayedsweep,considerablemagnificationisachievedsothat shortdurationphenomenaoccurringafter adelayperiod followinga triggercanbeconvenientlyobserved.

Figure1

2.Attemptanyfourpartsofthefollowing:

(4×4=16)

(a)Writeatechnicalnoteonloadingeffectsofinstruments

ReferSection1.9inChapter1onConceptsofMeasurementSystems.

(b)Explainwiththehelpofablockdiagram,thevariouspartsofanelectronicmultimeter.

ReferSection10.4inChapter10onElectronicInstruments.

(c) Describe the methods of measurement of voltage and power a radiofrequencies.

ReferSection17.7inChapter17onMicrowaveandRFMeasurement.

(d) What are the various factors taken into consideration while selecting anelectronictypeanalogvoltmeter.

ReferSection10.3inChapter10onElectronicInstruments.

(e)Asawtoothvoltagehasapeakvalueof40Vandatimeperiodof5.0secondsasshowninFigure2.

Figure2

Calculate the error when measuring this voltage with an average readingvoltmeter,calibratedintermsofrmsvalueofsinusoidalwaves.

Error=(Truevalue–Actualvalue)/Actualvalue=

(f) Describethecircuitdiagramandoperationofadcvoltmeterusingadirectcoupledamplifier.

dcvoltmeterusingdirectcoupledamplifier

Figure3DirectcoupledamplifierDCvoltmeterusingcascadetransistor

This typeofvoltmeter isverycommonbecauseof its lowcost.This instrumentcanbeusedonly tomeasurevoltagesof theorderofmillivoltsowing to limitedamplifier gain. The circuit diagram for a direct coupled amplifier dc voltmeterusing cascaded transistors is shown in Figure 3. An attenuator is used in inputstage to select voltage range. A transistor is a current-controlled device; soresistanceisinsertedinserieswiththetransistorQ1toselectthevoltagerange.Itcanbeseenfromthefigurethatsensitivityofthevoltmeteris200kiloohms/volt,neglectingthesmallresistanceofferedbythetransistorQ1.Othervaluesofrange-selecting resistors are also so chosen that sensitivity remains the same for allranges.Socurrentdrawnfromthecircuitisonly5microamperes.

Two transistors in cascadedconnections areused insteadof a single transistorforamplificationinordertokeepthesensitivityofthecircuithigh.TransistorsQ1and Q2 are taken complementary to each other and are directly coupled tominimise the number of components in the circuit. They form a direct coupledamplifier.Avariable resistanceR is put in the circuit for zero adjustment of thePMMC.ItcontrolsthebuckingcurrentfromthesupplyEtobuckoutthequiescentcurrent.Thedrawbackof suchavoltmeter is that ithas toworkunder specifiedambient temperature to get the required accuracy; otherwise excessive driftproblemoccursduringoperation.

Figure4DirectcoupledamplifiertransistoriseddcvoltmeterusingFET

DCVoltmeterusingFET

AnothercircuitdiagramofadirectcoupledamplifierdcvoltmeterusingFET ininputstageisshowninFigure4.Inthisvoltmeter,thevoltagetobemeasuredisfirst attenuated with the range selector switch to keep the input voltage of theamplifierwithinitslevel.AFETisusedintheinputstageofamplifierbecauseofitshighinputimpedancesothatitdoesnotloadthecircuitofwhichthevoltageistobemeasuredanditalsokeepsthesensitivityofthevoltmeterveryhigh.AstheFETisavoltagecontrolleddevice,sotheresistancenetworkofattenuatorisputinshunt in the circuit.TransistorsQ2 andQ3 form the direct coupled dc amplifierwhose output is finally supplied to the PMMC meter. When transistors workwithin their dynamic region, the deflectionof themeter remains proportional totheappliedinputvoltage.Thisvoltmetercanbeusedformeasurementofvoltagesoftheorderofmillivoltsbecauseofsufficientgainoftheamplifier.

Apart from the high input impedance, this circuit has another advantage thatwheninputvoltageexceedsitslimit,theamplifiergetssaturatedwhichlimitsthecurrentpassingthroughthePMMCmeter.Sothemeterdoesnotburnout.

3.Attemptanytwopartsofthefollowing:

(4.5×2=9)

(a)Describetheworkingofaninter-modulationdistortionmeterwiththehelpofablockdiagram.

ReferSection13.17inChapter13onSignalGeneratorsandAnalysers.

(b)Whataredifferenttypesofdistortionscausedbyamplifiers?

Frequency distortion, phase distortion, amplitude distortion, intermodulationdistortion,crossoverdistortion,totalharmonicdistortion.

(c)Describethebasiccircuitofaspectrumanalyser.

ReferSection13.18inChapter13onSignalGeneratorsandAnalysers.

4.Attemptanytwopartsofthefollowing:

(4.5×2=9)

(a) Explain frequency measurement using Schmitt trigger with the help of adiagram.

ReferSection10.5inChapter10onElectronicInstruments.

(b)Sketchtheblockdiagramfortime-intervalmeasurementmodeofoperationusingDDAsandDCAs.

Readerscanrefertoreferencematerial.

(c)Explaintheoperationofdigitalphasemeterswiththehelpofblockdiagram.

Readerscanrefertoreferencematerial.

SOLVEDQUESTIONPAPER-31.(a)Comparebetweenspringandgravity-controlmethods.

ReferSection2.5.2inChapter2onAnalogMeters.

(b) The deflecting torque of an ammeter varies as the square of the currentpassing through it. If a current of 5A produces a deflection of 90 degrees,whatwillbethedeflectionforacurrentof10Awhentheinstrumentis

i.Springcontrolled?

ii.Gravitycontrolled?

(8+8)

Deflectingtorquevariesasthesquareofthecurrent,thusTd=KdI2

(i)Forspringcontrol,thecontrollingtorque(TC)isrelatedtotheangleofdeflection(θ)bytherelationTC=kθ

Understeadydeflectioncondition,Td=TC

KdI2 =kθ

θ =(Kd/k)I2=K1I2

Giventhatthedeflectionis90°whenthecurrentis5A.

Thus,90=K1.52

K1=3.6

Hence,foracurrentof10A,thedeflectionisθ=K1I2=3.6×102=360°

(ii)Forgravitycontrol,thecontrollingtorque(TC)isrelatedtotheangleofdeflection(θ)bythe

relationTC=kg.sinθ

Understeadydeflectioncondition,Td=TC

KdI2 =kg.sinθ

θ =sin–1[(Kd/kg)I2]=sin–1[K2I2]

Giventhatthedeflectionis90°whenthecurrentis5A.

Thus,90=sin–1[K2.52]

K2=1/25

Hence,foracurrentof10A,thedeflectionis

θ=K2I2=sin–1[(1/25)×102]=sin–1[4]

[Note:Thereisamathematicalerrorinthisquestion]

2. (a) Drawand explain the equivalent circuit andphasordiagramof a currenttransformer.

ReferSection3.4inChapter3onInstrumentTransformers.

(b)A1000/5Acurrenttransformer,barprimarytype,hasthelosscomponentofexcitingcurrentequalto0.7%oftheprimarycurrent.Findtheratioerror

i.Whenturnratioisequaltonominalratio

ii.Whenthesecondaryturnisreducedby0.5%

(8+8)

ForaCT,Percentageratioerror

Given,nominalration=1000/5=20

(i)Whenturnsratio(T)isequaltothenominalratio(n),

T=n

When the loss component of exciting current primary current, and secondarycurrentarerepresentedbyIC,IP,andISrespectively,then

Actualratio

Hence,percentageratioerror

(ii) Whensecondary turns is reducedby0.5% then thenewmodified turns ratio isgivenbyT1=0.995×n

Actualratio

Hence,percentageratioerror

3. (a) With a neat figure, explain the construction andworking principle of anelectricalresonancefrequencymeter.

In an electrical resonance-type frequency meter, an unknown frequency ismeasuredwiththehelpofanR-L-Cresonatingcircuit.

Figure1

Theunknownfrequencyacsource,whosefrequencyistobemeasuredisusedas

thevoltagesourceinthedrivingcircuitasshowninFigure1.VoltagesupplytotheresonatingcircuitisgivenbycouplingthecoilLwiththeoutputcoilofthesignalacsource.ResonanceintheRLCcircuitisobtainedbyvaryingthecapacitance.AnelectronicvoltmeterconnectedacrossthecapacitorisusedastheprimarydetectorforcheckingresonanceconditionintheRLCcircuit.WithcertainvaluesofR,L,and C, when resonance is obtained at the unknown frequency, the voltageindicatedby theelectronicvoltmeterwillbemaximum.Theunknownfrequencycan be calculated by using themathematical condition for resonance in a seriesRLCcircuit.

(b)Explaintheworkingofasingle-phasedynamometer-typepower-factormeter.

(8+8)

Single-phase dynamometer-type power factor meter is schematically shown inFigure2.

Figure2

Ithastwofixedcoilsthatareconnectedinserieswiththeloadandthusactasthecurrentcoils.Currentcoils,thus,carrythesamecurrentastheload.TwoidenticalcoilsAandBthatareconnectedtothespindleandplacedinthespacebetweenthetwo fixed coils are the moving coils. Coil A has a high value non-inductiveresistanceRconnectedwithitandthecoilBhasahighlyinductivechokecoilLconnectedtoit.BoththecoilsalongwiththeirrespectiveseriesconnectedRandLareconnectedparalleltothesupply,andarecalledthepressurecoils,sincecurrentthroughthesetwocoils,AandBareproportionaltothesupplyvoltage.ValuesofRandLaresoselectedthatatnormalfrequency,theirimpedancesbecomeequal(R=ωL)andhencethetwocoils,AandBcarry thesamecurrent.CoilAbeinghighlyresistive,itscurrentisalmostinphasewiththesupplyvoltageB.Similarly,thecoilBbeinghighlyinductive,itscurrentisalmostatanangleδ≈90°withthesupplyvoltageV.TheaxesofthecoilsAandBarealsokeptatthesameangleδ≈90°withrespecttoeachother.

Therewillbetwodeflectingtorques,oneactingonthecoilAandtheotheronB. These two coil windings are so arranged that they experience torque in theopposite direction. The pointerwhich is attached to these two coils jointly,will

thusattainasteadydeflectionwhenthesetwooppositetorquesoncoilsAandBareequal.Letusconsideralaggingpowerfactorcosφoftheload.

DeflectingtorqueonthecoilA,

whereθ=angulardeflectionfromthereferencehorizontalplane

M=mutualinductancebetweenthefixedcoilsandcoilA

DeflectingtorqueonthecoilB

Atequilibrium,TA=TB

Therefore,thedeflection(θ)oftheinstrumentisameasureofthepower-factorangle.By proper calibration, the scale can bemade to show the value of the power factordirectly.

4.(a)Whatisenergy-metertesting?Explainphantomloadtesting.

ReferSections8.4,and8.4.1inChapter8onMeasurementofEnergy.

(b)A220,5A,dcenergymeteristestedatitsmarkedratings.Theresistanceofthe pressure circuit is 8800 ohms and that of the current coil is 0.1 ohm.Calculatethepowerconsumedwhentestingthemeterwithphantomloadingwithacurrentcircuitexcitedbya6-voltbattery.

(8+8)

FollowtheproceduresimilartoExample8.5inChapter8onEnergyMeters.

5.Acurrentof10A,atafrequencyof50Hz,waspassedthroughtheprimaryofamutual inductor having a negligible phase defect, the voltage of primary andsecondaryterminalsweremeasuredonaco-ordinatepotentiometerandaregivenbelow:

Withsecondaryopencircuited;secondaryvoltageIq=–2.72+j1.57volts.

Primaryvoltage=–0.211+j0.352volts.

Withsecondaryshort-circuited:primaryvoltage=–0.051+j0.329volts.

Thephaseprimarycurrentrelativetothepotentiometercurrentwassameinboththetests.Determinetheresistancesandself-inductancesofthetwowindings.Findalsothemutualinductance.

(16)

Thevoltageequationsinthephasorformcanbewrittenas

E1=I1(R1+jX1)+I2(jXm) E2=I2(R2+jX2)+I1(jXm)where

E1=Voltageofprimarywinding, E2=Voltageofsecondarywinding,

I1=Currentofprimarywinding, I2=Currentofsecondarywinding,R1=Resistanceofprimarywinding, R2=Resistanceofsecondarywinding,X1=Self-reactanceofprimarywinding,

X2=Self-reactanceofsecondarywinding,

and Xm=Mutualreactance.

Underopen-circuitconditions:I2=0 E2=I1(jxm).

LetI1=Ip+jIq’whereIpandIqarethephaseandquadraturecomponentsofI1.

Therefore,wecanwriteE2=(Ip+jIq)(jXm)=(–Iq+jIp)XmFromthedatagiven,wehave–2.72+j1.57=–IqX+jIpX

Atopencircuit,E1=I1(R1+jX1)=j(Ip+jIq)(R1+jX1)

=(IpR1–IqX1)+j(IpX1+IqR1).

Puttingthenumericalvalues,weget–0.211+j0.352=(5R1–8.66X1)+j(5X1+8.66R1).

Equatingrealandtheimaginaryterms,wehave5R1–8.66X1=–0.211

(i)

and5X1+8.66R1=0.352

(ii)

Solving(i)and(ii),wegetR1=0.02Ω,andX1=0.0359Ω.

Self-inductanceofprimarywinding

AtshortcircuitofsecondarywindingE2=0,

E2–I2(R2+jX2)+I1(jXm)=0

Nowatshortcircuit,E1=0.051+j0.329

Self-reactanceofsecondarywinding

ResistanceofsecondarywindingR2=2.27W.

6.(a)Describeanyonemethodofmeasuringaveryhighvalueofresistance.

ReferSection4.4.4inChapter4onMeasurementofResistance

(b) A Lissajous pattern on the oscilloscope is stationary and has 6 verticalmaximum values and 5 horizontal maximum values. The frequency ofhorizontalinputis1500Hz.

Determinethefrequencyofverticalinput.

(8+8)

InaLissajouspatternonanoscilloscope,

where fv and fh are frequencies of the signals applied in vertical and horizontalplatesrespectively.

Given,fh=1500Hz

Thus,frequencyofverticalinput

7. Describe how an unknown capacitance can be measured with the help ofD’Sauty’s bridge. What are the limitations of the bridge and how are theyovercomebyusingamodifiedformofD’Sauty’sbridge.

(16)

ReferSection6.5.1inChapter6onACbridges.

8. (a) Explain the double-barmethod of measuring the flux density of an ironspecimen.

ReferSection12.11.2inChapter12onMagneticMeasurements.

(b)Asolenoidis60cmlongand2.5cmindiameter.Itisuniformlywoundwith600 turns of wire. Find the magnetic field strength at the centre of thesolenoidwhencarryingacurrentof2A.Ifthesecondarycoiliswouldroundthecentralpartofthesolenoid,calculatethefluxpassingthroughit.

(8+8)

ForthegivensolenoidasshowninFigure3.

Figure3

Themagneticfieldstrengthatanypointxonthecentralaxisofthesolenoidisgivenby

Given

L=60cm=0.6m

R=2.5/2=1.25cm=0.0125m

N=600

I=2A

Similarly,

Thus,

FluxdensityB=µ0×H=4 ×10-7×1998=2.51mWb/m2

Hence,fluxpassingthroughthecentralpartofthesolenoidisgivenby

φ=B×A=2.51×4 (0.0125)2=4.93mWb

SOLVEDQUESTIONPAPER-4PARTA(10×2=20)

1.Asetofindependentcurrentmeasurementswererecordedas10.03,10.10,10.11and10.08A.Calculatetherangeofanerror.

Rangeoferror=Imax–Imin=10.11–10.03=0.08A

2.Howistheinternationalstandardoflengthdefined?

Themetre(ormeter),isthefundamentalunitoflengthintheInternationalSystemofUnits(SI).Originallyintendedtobeoneten-millionthofthedistancefromtheearth’sequatortotheNorthPole(atsealevel),itsdefinitionhasbeenperiodicallyrefinedtoreflect growing knowledge of metrology. Since 1983, it has been defined as “thelength of the path travelled by light in vacuum during a time interval of1/299,792,458ofasecond.”

3.Compareandcontrastanaloganddigitalstorageoscilloscope.

ReferSection9.11inChapter9onCathodeRayOscilloscope.

4.Distributedcapacitanceofacoilismeasuredbychangingthecapacitanceoftheturning capacitor. The values of the tuning capacitors areC1 andC2 for theresonantfrequenciesf1and2f1.Whatisthevalueofthedistributedcapacitance?

Readermayrefertoreferencematerials

5. Inasweepfrequencygenerator,twooscillators,onewithfrequencyrangeof3GHzto5GHzisheterodynedwithasecondoscillatorshavingafixedfrequencyoutputof3GHz.Howdoestheoutputfrequencyvary?

Outputfrequencyvariesbetween0to8GHz.

6.Whatisintermodulationdistortion?

Intermodulationdistortionresultswhentwodifferentfrequenciesaresimultaneouslypassed through an amplifier (or other audio component).Twonew frequencies arecreatedfromthesumanddifferenceoftheoriginalfrequencies.Ifa100Hzand150Hztonearepassedthroughanamplifier,thesumoftheoriginalfrequencies(150+100=250Hz)andthedifference(150–100=50Hz)willbegenerated,resultinginintermodulationdistortion.IMdistortionismeasuredasapercentageoftheoriginalfrequenciesandalowerspecificationisbetter.

7.WhyisaSchmitttriggerusedinadigitalfrequencymeter?

Schmitttriggerisusedinadigitalfrequencymetertoconverttheinputsignal(whosefrequencyistobemeasured)toasquare-wavesignalofsamefrequency.Thissquare-wave signal isTTL compatible and can be used directly as one input to the countgate.

8.DrawtheblockdiagramofintegratingtypeDVM.

ReferSection10.6.3inChapter10onElectronicInstruments.

9.Listtheelementsofadigitaldataacquisitionsystem.

Thebasicelementsofadataacquisitionsystemareasfollows:

(a)Sensorsandtransducers

(b)Fieldwiring

(c)Signalconditioning

(d)Dataacquisitionhardware

(e)PC(operatingsystem)

(f)Dataacquisitionsoftware

10.Whatistheneedfordataloggers?

ReferSection15.3.1inChapter15onRecording,StorageandDisplayDevices.

PARTB(5×16=80)

11.(a)(i)HowcanyouconvertthePMMCmeterintoavoltmeterandammeter?Howcanyouextendtherangeofthesemeters?

(8)

ReferSection2.7inChapter2onAnalogMeters.

(ii)Explainthetypesoferrorswithanexample?

(8)

ReferSection1.8.1inChapter1onConceptsofMeasurementSystems.

OR

(b)(i)Whataretheconditionsforbridgebalance?

(8)

RefertoSection6.3inChapter6onACBridges.

(ii) How can you measure the unknown inductance usingMaxwell’s LCBridge?Drawthephasordiagramalso.

(8)

RefertoSection6.4.2inChapter6onACBridges.

12. (a) (i) Draw the block diagram of a sampling oscilloscope. How does thesampling oscilloscope increase the apparent frequency response of anoscilloscope?

(8)

ReferSection9.10inChapter9onCathodeRayOscilloscope

(ii)HowcanyoumeasurelargecapacitorsandsmallcoilsusingQ-meters?

(8)

Readermayrefertoreferencematerials

OR

(b)(i)Explainthevectorimpedancemeterwithaneatblockdiagram.

(8)

Readermayrefertoreferencematerials

(ii) How can you measure the RF voltage and power using RFmillivoltmeter?

(8)

ReferSection17.7inChapter17onMicrowaveandRFMeasurement.

13. (a) (i) Draw the block diagram of the frequency divider type of signalgeneratorwithfrequencymodulationandexplain.

(8)

ReferSection13.14inChapter13onSignalGeneratorsandAnalysers.

(ii) What are the basic elements of a function generator?Explain how togeneratethesquarewave,triangularwaveandsinewaveusingfunctiongenerator.

(8)

ReferSection13.13inChapter13onSignalGeneratorsandAnalysers.

OR

(b) (i) Explain theworkingof frequency-selectivewaveanalyzerwithaneatblockdiagram.

(8)

ReferSection13.16inChapter13onSignalGeneratorsandAnalysers.

(ii) How is the fundamental frequency suppressed using the fundamentalsuppressiondistortionanalyser.

(8)

ReferSection13.17inChapter13onSignalGeneratorsandAnalysers.

14. (a) (i) Drawtheblockdiagramofamultiplexeddisplayused inafrequencycounterandexplain.

(8)

(ii)Explainhowcanyouextendthefrequencyrangeofthecounter.

(8)

OR

(b)(i)Howcanyoumakeautomaticpolarityindicationandautomaticranginginadigitalinstrument?

(8)

(ii)Explaintheneedforvirtualinstrumentwithanexample.

(8)

Readermayrefertoreferencematerials.

15.(a)(i)Drawtheschematicofanisolationamplifierandexplaintheneedforanisolationamplifierininterfacingtransducers.

(8)

(ii)Withneatdiagramsexplaindigitaltoanalogmultiplexing.

(8)

Readermayrefertoreferencematerials.

OR

(b)(i)ExplaintheIEEE488electricalinterfacesystem.

(8)

ReferSection14.7inChapter14onDataAcquisitionSystems.

(ii) How can youmeasure the power using optical instrument?Draw theauto-rangingpowermeterandexplain.

(8)

ReferSection18.4inChapter18onFibreOpticMeasurements.

SOLVEDQUESTIONPAPER-5PART-A(10×2=20)

1.Answerthefollowing

(a)Sketchasimplediagramofanelectronicdcvoltmeter.

ReferSection10.6inChapter10onElectronicInstruments.

(b)EnumerateapplicationofCROformeasurementofelectricalquantities.

ReferSection9.7inChapter9onCathodeRayOscilloscope.

(c)Howmanycyclesofa6kHzsinusoidalsignalappearontheCROscreenifthesweepfrequencyis3kHz?

Twocycles.

(d)ForwhatmeasurementisanLCRmeterused?

Self-inductance,capacitance,losstangent,resistance.

(e)Awaveanalyserisusedforwhattypeofanalysis?

A wave analyser is an instrument designed to measure relative amplitude ofsingle frequencycomponents inacomplexwaveform.Basically, the instrumentacts as a frequency-selectivevoltmeterwhich is turned to the frequencyofonesignal while rejecting all other signal components. The desired frequency isselectedbyafrequency-calibrateddialtothepointofmaximumamplitude.TheamplitudeisindicatedeitherbyasuitablevoltmeteroraCRO.

(f)ForwhatapplicationscanCTandPTbeused?

Reducing high current and voltage to smaller values measurable with easilyavailablelow-rangeammetersandvoltmeters.

(g)Defineatransduceranddistinguishbetweenactiveandpassivetransducers.

A transducer is a device, usually electrical, electronic, electro-mechanical,electromagnetic, photonic, or photovoltaic that converts one type of energy orphysical attribute to another (generally electrical or mechanical) for variousmeasurement purposes including measurement or information transfer (forexample,pressuresensors).Anactivetransducerisatransducerwhoseoutputisdependent upon sources of power, apart from that supplied by any of theactuating signals, which power is controlled by one or more of these signals.Passive transducers are those which do not need an external source. Passivetransducersdirectlyproduceelectricsignalswithoutanexternalenergysource.

(h)Whatarenecessitiesofrecorders?

After collecting information about the state of some process, the nextconsideration is how to present it in a form where it can be readily used andanalysed.Thereare techniquesavailable toeitherdisplaymeasurementdata forcurrentuseorrecorditforfutureuse.Followingthis,standardsofgoodpractice

forpresentingdataineithergraphicalortabularformareavailable,usingeitherpaperoracomputermonitorscreenasthedisplaymedium.

(i)HowareLDCdisplaysadvantageousoverLEDdisplays?

SummariseSections15.4.2.and15.4.3inChapter15onRecording,StorageandDisplayDevices.

(j)Listvarioustypesoftelemetrysystems.

Readerscanrefertoreferencematerial.

PART-B(4×5=20)

2.Withthehelpofthecircuitdiagramofanelectronicmultimeter,listtheessentialelementsofthemeteranddiscussitsprincipleofworking.

(10)

ReferSection10.4inChapter10onElectronicInstruments.

3. Why is a CRO considered very useful instrument?With the aid of a blockdiagram representation, discuss working of a CRO. How is it used foreasurementofphaseangleofawave?

(10)

ReferSections9.2and9.9inChapter9onCathodeRayOscilloscope.

4.Describeaharmonicdistortionanalyserwiththehelpofablockdiagram.Howdoesacommercialharmonicdistortionanalyzerdifferfromtheidealone?

ReferSection13.17inChapter13onSignalGeneratorsandAnalysers.

5. Discussworkingofastraingaugeandderiveexpressionforthe“gaugefactor(G)”.Whyisthefactorabout2formostofthemetallicstraingauges?Astraingaugehasaresistanceof100Ωandthegaugefactorof2.1,ofstrainis2×10−3.Obtainthechangeinresistance.

ReferSection11.4.1inChapter11onSensorsandTransducers.

Given,R=100Ω,gaugefactor=2.1andstrain=2×10−3

Thus, change in resistance ΔR = Gauge factor ×R×Strain = 2.1×100×2×10 −3=0.42Ω

6.Describetheworkingprincipleofadigitaltaperecorder.Whatareitsareasofapplications?

ReferSection15.3.2inChapter15onRecording,StorageandDisplayDevices

PART-C(2×10=20)

7. (a) Explain theprincipleofworkingandoperationofaCurrentTransformer(CT)andderiveexpressionsfortheratioandphase-angleerrors.

(2×10)

ReferSections3.3,3.4,and3.5inChapter3onInstrumentTransformers.

(b)A1000/5,50Hzbarprimary-typecurrenttransformerhassecondaryburdenof1.5Ω(non-inductive).CalculatethefluxinthecoreandtheratioerroratratedconditionoftheCT.Assumeironlossinthecoretobe1.5watts.Neglectleakagefluxandthemagnetizingcurrent.

FollowExample3.3inChapter3onInstrumentTransformers.

8. (a) What is telemetry andwhat are its basic components? Sketch the block-diagramrepresentationofatypicaltelemetrysystemandexplainthemethodofdatatransmission.

(b)List typesof telemetrysystemsanddistinguishbetweendcandactelemetrysystems.

(10)

Readerscanrefertoreferencematerial.

9.Writeshortnoteson

(a)ApplicationsofTelemetrysystems

Readerscanrefertoreferencematerial

(b)Spectrumanalysisand

ReferSection13.18inChapter13onSignalGeneratorsandAnalysers.

(c)Special-purposeoscilloscope

Summarise sections 9.10, 9.11 and 9.12 in Chapter 9 on Cathode RayOscilloscope.

SOLVEDQUESTIONPAPER-6PARTA

1.(a)Explainindetailtheclassificationofmeasuringinstruments.

(8)

ReferSection1.6inChapter1onConceptsofMeasurementSystems.

(b) With a neat sketch, describe the construction and working of PMMCinstrument. Derive the torque equation for this instrument. Comment onshapeofscale.

(10)

ReferSections2.6and2.6.1inChapter2onAnalogMeters.

2. (a) Which three forces are required for satisfactory operation of an analogindicatinginstrument?Statethefunctionofeachforce.

(6)

ReferSection2.4inChapter2onAnalogMeters.

(b)Whatareshuntsandmultipliers?Whatarethedisadvantagesofashunt?

ReferSections2.7.1and2.7.2inChapter2onAnalogMeters.

Disadvantages of shunt—Refer Section 3.2 in Chapter 3 on InstrumentTransformers.

(c)Theinductanceofamoving-ironammeterisgivenbytheexpressionL=(12+5θ–2θ2)µH,whereθistheangulardeflectioninradiansfromzeroposition.Determine

(i)thespringconstant

(ii)theangulardeflectioninradiansforacurrentof10A,ifthedeflectionforacurrentof5Ais30°

(6)

FollowExample2.11inChapter2onAnalogMeters.

3.(a)DrawthecircuitdiagramofKelvin’sdoublebridge.Derivetheexpressionforunknownresistancewithusualnotations.

(8)

ReferSection4.3.2inChapter4onMeasurementofResistance.

Figure1

(b) InaMaxwell’s inductancecomparisonbridge, thearmab consistsofacoilwithinductanceL1andresistancer1inserieswithanon-inductiveresistanceR. Arm bc and cd are each a non-inductive resistance of 100 Ω. Arm adconsists of standard variable inductor L of 32.7 Ω resistance. Balance isobtained when L2 = 47.8 mH and R = 1.36 Ω. Find the resistance andinductanceofthecoilinthearmab.

(4)

ReferSection6.4.1inChapter6onacBridgesandthendothefollowing:

(c)ThefourimpedancesofanbridgeareZ1=400Ω 50°,Z2=200Ω 30°,Z3=800Ω –50°,Z4=400Ω –40°.Findoutwhetherthebridgeisbalancedundertheseconditions.

GivenR=1.36Ω

Hence,r1=32.7–1.36=31.34Ω

Figure2

Forthebridgetobebalanced,weneedtosatisfytwoconditions(referSection6.3inChapter6onacbridges).

Inmagnitudeonly,Z1Z4=Z2Z3

WeseethatZ1Z4=400×400=1600

AndZ2Z3=200×800=1600

Thus,amagnitudecriterionforbalanceismet.

Inphaseangle,weneedtohave (θ1+θ4)= (θ2+θ3)

Wehave (θ1+θ4)=50°–40°=10°

But, (θ2+θ3)=30°–50°=–20°

Thus, the angle criterion for balance is not satisfied. Hence, the bridge is notbalanced.

4.(a)Writeashortnoteonmeggerandearthtester.

(8)

ReferSection4.4.4inChapter4onMeasurementofResistance.

(b) Draw the circuit diagram of Anderson’s bridge. Derive the equation forunknowninductanceanddrawthephasordiagram.

(8)

ReferSection6.4.4inChapter6onacBridges.

5.(a)Explaintwo-wattmetermethodformeasuringpowerinan(R+L)load.Drawthephasordiagram.

(8)

ReferSection7.7.2(3)andFigure7.23inChapter7onPowerMeasurement.

(b)Writeashortnoteondigitalmulti-meter.

(8)

ReferSection10.4inChapter10onElectronicInstruments.

6.(a)Awattmeterreads5kWwhenitscurrentcoilisconnectedinredphaseanditsvoltagecoil isconnectedbetweenneutralandredphaseofasymmetrical3-phaesystemsupplyingabalancedthree-phaseinductiveloadof25Aat440V.Whatwillbethereadingofthewattmeteriftheconnectionsofcurrentcoilremain unchanged and voltage coil be connected between blue and yellowphase? Hence determine the total reactive power in the circuit. Draw thediagraminboththecases.

(8)

Figure3

Inthefirstcase,currentinCCofwattmeterIR=Iph=25A

VoltageinPCofwattmeter=VRN=VPh=440/√3=254V

Hence,wattmeterreadingP1=VPh×Iph×cosφ=5000Ω

or, 254×25×cosφ=5000

or, cosφ=0.787

or, φ=38°

Inthesecondcircuit,

Figure4

Inthesecondcircuit,thephasordiagramwithinductiveloadcanbedrawnas

Figure5

Inthiscase,currentinCCofwattmeterIR=Iph=25A

VoltageinPCofwattmeter=VBY=VLL=440V

AngledifferentbetweenCCcurrentandPCvoltageφ‘=(90°–φ)=(90°–38°)=52°

Hence,wattmeterreadingP1=VLL×Iph×cosφ‘=440×25×cos52°=6.77kW

Totalreactivepower=√3×6.77=11.73kVAR(b)WriteashortnoteonLPFtypewattmeter.

(4)

LowPowerFactorElectro-dynamometerTypeWattmeters

An ordinary electro-dynamometer wattmeter is not suitable formeasurement ofpower in low-power factor circuits owing to (i) small deflecting torque on themovingsystemevenwhenthecurrentandpressurecoilsarefullyexcited,and(ii)introductionoflargeerrorduetoinductanceofpressurecoilatlowpowerfactor.The special features incorporated in an electro-dynamometer type wattmeter tomakeitsuitableformeasurementofpowerinlow-power-factorcircuitsaregivenbelow.

(i)PressurecoilCircuitThepressurecoilcircuitismadeoflowresistanceinordertomakethepressurecoilcurrentlargeresultinginincreasedoperatingtorque.Thepressurecoilcurrentinalowpfwattmetermaybeasmuchas10timesthevalueusedforordinarywattmeters.

(ii) CompensationforInductanceofPressureCoilTheerrorcausedbypressurecoilinductanceisduetodifferenceinphasebetweenpressureCoilcurrentanditsvoltage.Nowwithlowpf,thevalueoftheerrorislarge.Theerrorcausedbyinductanceofpressurecoil iscompensatedbyconnectingacapacitoracrossapartofseriesresistanceinthepressurecoilcircuit.

(c)Whataretheerrorsinadynamometer-typewattmeter?Howaretheseerrorscompensated?

(4)

ReferSection7.4.4(andsummarise)inChapter7onPowerMeasurement.

PARTB

7. (a) An energymeter has a constant of 3200 imp/kWh rated for 220 V, 5 A.Calculate the total number of impulses in oneminute for full load at unitypower factor. In a test run at half load, the meter takes 59.5 second tocomplete30impulses,calculateerrorofmeter.

(6)

ReferExample8.1inChapter8onMeasurementofEnergy.

(b)Derivetorqueequationofsingle-phaseinduction-typeenergymeterwiththehelpofphasordiagram.

(8)

ReferSection8.2.3inChapter8onMeasurementofEnergy.

(c) Show a neat connection diagram of a three-phase energy meter used formeasurementofenergyincorporatingCTandPT.

(4)

ReferSection7.9inChapter7andapplyexactlythesameconceptforconnectionofenergy-metercoils.

OR

8.(a)A230Vsingle-phaseenergymeterhasconstantloadof5Apassingthroughitfor 8 hours at 0.9P.F. If themeterLEDmakes 26500 impulses during thisperiod,findthemeterconstantinimp/kWh.Calculatethepowerfactoroftheloadifthenumberofimpulsesare11230whenoperatingat230Vand6Afor5hours.

(6)

Energyconsumed

Theenergymetermakes26500impulsesduringthistime

Hence,meterconstantis26500/8.28=3200imp/kWh

Whenthenumberofimpulsesare11230,thenenergyconsumedis3.5kWh

Withapowerfactorx,

(b) Which are the possible errors in an induction-type single-phase energymeter?Explainandgivecompensationfortheerrors?

(4×2)

ReferSection8.3inChapter8onMeasurementofEnergyandSummarise.

(c) What is creeping error in an induction-type energy meter? How is itovercome?

ReferSection8.3.3Chapter8onMeasurementofEnergy.

9.(a)Describelow-pressuremeasurementbyMcLeodgauge.

(8)

Readerscanrefertoreferencematerial

(b)Inanexperiment,thevoltageacrossa10kΩresistorisappliedtoaCR).Thescreen shows a sinusoidal signal of 3 cm total vertical occupancy and 2 cmtotalhorizontaloccupancy.ThefrontpanelcontrolsofV/divandtime/divareon2V/divand2ms/divrespectively.Calculate thermsvalueof thevoltageacrosstheresistoranditsfrequency.Alsofindrumsvalueofcurrent.

(6)

Peakvalueofthesinusoidalvoltagebeingmeasured=3×2=6V

Hence,rmsvalue=6/ =4.24V

Onetimeperiodofthesinusoidalsignalbeingmeasured=2×2=4ms

Hence,frequencyofthesignal=1/4ms=250Hz

(c)Explainvacuumpressure.

(2)

Readerscanrefertoreferencematerial.

OR

10. (a) Explain pressure capacitance transducer with a neat diagram. Writeadvantagesanddisadvantagesofacapacitivetransducer.

(8)

ReferSection11.7.4inChapter11onSensorsandTransducers.

(b)ExplainfrontpanelcontrolsofCRO:

(8)

1.Time/div

2.Volt/div

3.Dualch.

4.invert

5.x-position

6.y-position

7.xy-mode

8.CH1CH2.

ReferSections9.2and9.3inChapter9onCathodeRayOscilloscope.

11.(a)Explainanytwotypesofhead-typeflowmeters.

(8)

Readerscanrefertoreferencematerial.

(b)Explainlevelmeasurementbymechanicalmethod.

Readerscanrefertoreferencematerial.

(8)

12. (a) Explain construction, working and application of load cell with a neatdiagram.

(8)

Readerscanrefertoreferencematerial.

(b)DescirbedisplacementmeasurementbyLVDTindetail.

Combine Sections 11.3, 11.3.1 and 11.3.2 in Chapter 11 on Sensors andTransducers.

(8)

SOLVEDQUESTIONPAPER-7PART-A

1. (a) Withusualnotations,prove that [1/(με )1/2]has thedimensionsofvelocity,whereμ=permeabilityandε=permittivity.

(5)

Readerscanrefertoreferencematerial.

(b)Theexpressionforeddycurrentsproducedinametallicformermovinginthefieldofapermanentmagnetisfoundas,

whereB=fluxdensity,l=lengthofformer,b=widthofformer,A=Areaofformer,ρ=resistivityofconductingformerandK=aconstant.

Check for dimensional correctness of the expression and incorporatenecessarycorrectionsusingLMTIsystemofunits.

RefertoSection2.5.3(3)inChapter2onAnalogMeters

(c) Definebridge sensitivityofagalvanometerandhenceobtainanexpressionforWheatstone’sbridgesensitivity(SB)intermsofvoltagesensitivity.WhenwillbeSBmaximum?

(8)

Voltage sensitivity Sv of a galvanometer is defined as the deflection in scaledivisionsperunitvoltageimpressedonthegalvanometer.

FortheWheatstonebridgeconfigurationshownbelow,thesensitivitytounbalancecanbecomputedbysolvingthebridgecircuitforasmallunbalance.Thesolutionisapproachedbyconverting theWheatstonebridgeofFigure1 to its“TheveninEquivalent’circuit.AssumethatthebridgeisbalancedwhenthebranchresistanceareP,Q,R,SsothatP/Q=R/S.SupposetheresistanceRischangedtoR+ΔRcreating an unbalance. This will to cause an emf e to appear across thegalvanometerbranch.Withgalvanometerbranchopen, thevoltagedropbetweenpointsaandbis:

Therefore,voltagedifferencebetweenpointsdandbis

LetSvbethevoltagesensitivityofgalvanometer.ESR

Therefore,deflectionofgalvanometeris

ThebridgesensitivitySBisdefinedasthedeflectionofthegalvanometerperunitfractionalchangeinunknownresistance.

Itisclearthatthesensitivityofthebridgeisdependentuponbridgevoltage,bridgeparametersandthevoltagesensitivityofthegalvanometer.

Rearrangingthetermsintheexpressionforsensitivity

ItisapparentthatmaximumsensitivityoccurswhereR/S=1.

2. (a) Derive theequationofbalance foranAndersonbridge.Alsodrawthephasordiagram

(10)

ReferSection6.4.4inChapter6onacBridges.

(b)WriteashortnoteonWagnerearthingdevice.

(4)

ReferSection6.7inChapter6onacBridges.

(C) An ac bridge is balanced at 2 kHzwith the following components in eacharm:ArmAB=10kΩArmAB=100µFinserieswith100kΩArmAD=50kΩFindtheunknownimpedanceR±jXinthearmDC,ifthedetectorisbetweenBD.

(6)

Usingthegeneralbridgebalanceequation,wehave

or,(R±jX)=(500k−j39.8)

Thus,R=500k,X=39.8

3. (a) What are shunts and multipliers? Derive an expression for both, withreferencetometersusedinelectricalcircuits.

(6)

ReferSection2.7inChapter2onAnalogMeters.

(b)WriteanoteonturnscompensationusedinCTandPT.

(4)

ReferSection3.5.4(3)inChapter3onInstrumentTransformers.

(c) A current transformer with a bar primary has 300 turns in its secondarywinding.Theresistanceandreactanceofthesecondarycircuitare1.5uand1.0 u respectively, including the transformerwinding.With 5A following inthesecondarywinding,themagnetisingmmfis100ATandthecorelossis1.2W.Determinetheratioandphaseangleerrors.

(10)

FollowExample3.4inChapter3onInstrumentTransformers.

4. (a) Discuss with a block diagram, the principle of operations of an electronicenergymeters.

(6)

Readerscanrefertoreferencematerial.

(b) Mention different errors present in an induction-type energy meter andsuggestmethodstominimisethem.

(6)

ReferSection8.3inChapter8onMeasurementofEnergy.

(c)Anenergymeterisdesignedtomake100revolutionsofthediscforoneunitofenergycalculate thenumberofrevolutionsmadeby it,whenconnectedtoaload carrying40Aat 230Vand0.4pf for 1hour. If it actuallymakes 360revolutions,findthepercentageerror.

(6)

FollowExample8.3inChapter8onMeasurementofEnergy.

PARTB

5.(a)Withablockdiagram,explaintheprincipleoftruermsrespondingvoltmeter.

(6)

ReferSection2.15inChapter2onAnalogMeters.

(b)ExplaintheoperationsofRAMPtypedigitalvoltmeter.

(6)

(b)CombineSections10.6and10.6.1inChapter10onElectronicInstruments.

(c)ExplaintheconstructionandoperationsofWestonfrequencymeter.

(6)

WestonFrequencyMeter:Asthenamesuggests,Westonfrequencymeterisaninstrument using which unknown frequency of a signal can be measured. It isbasically a moving-iron-type instrument which works on the principle thatwhenever the frequency change the current distribution changes between twoparallelcircuitsoneofwhichisinductiveandtheothernon-inductive.Anychangeinfrequencychangestheinductiveimpedanceoftheinductivearmcausingcurrentdistribution to change between the two parallel paths. Figure 2 shows theconstructionaldetailsofaWestonfrequencymeter.

TheaxesofthetwocoilsA1−A2andB1−B2aremutuallyperpendicular.Asoftironneedlethatcarriesapointerisplacedatthecentrallocationwithinthecoils.Coil A is connected in series with an inductance LA across a non-inductiveresistanceRA . CoilB is connected in serieswith a non-inductive resistanceRBacross an inductance LB . The other inductor L acts as a filter to remove anyharmonicsthatmaybepresentinthesignal.

Figure2WestonFrequencymeter

Assupplyisgiventothesystem,themagneticfieldsdevelopedbythetwocoilsareatrightanglestoeachother.Dependingonthestrengthofthesetwomagneticfields,adeflectingtorqueisdevelopedthatmovesthesoft-ironneedleandhencethepointeronacalibratedscale.Thedeflectingtorqueand,hence,theamountofdeflection of the pointer thus depends on the magnitude of currents in the two

coils.

Oncethefrequencydeviatesfromacertainpresentvalue,theinductancevaluesLAandLBchange,buttheresistanceRAandRB remainthesame.Thismakesthecurrent distribution in the two coils change from their initial preset values.Dependingon thefrequency,onecoilbecomesstronger than theother.Thus, thedeflecting torque under such conditionwill be different from that in the normalcaseandthepointerwilldeviateeithertowardsleftortotherightindicatinglowerorhigherfrequencythanthepresetvaluerespectively.

6. (a) What is a transducer? Briefly explain the procedure for selecting atransducer.

(6)

Refer Sections 11.1 and 11.2 in Chapter 11 on Sensors and Transducers andsummarize.

(b)Explainwithaneatsketch,theconstructionandworkingofalinearvariabledifferentialtransformer.

(6)

ReferSection11.3inChapter11onSensorsandTransducers.

(c)DeriveanexpressionforgaugefactorintermsofPoisson’sratio.

(6)

ReferSection11.4.1inChapter11onSensorsandTransducers.

7.(a)Withablockdiagram,explaintheworkingofadigitalstorageoscilloscope.

(6)

ReferSection9.11.2inChapter9onCathodeRayOscilloscope.

(b)ExplainthefrontpaneldetailsofadualtraceOscilloscope.

(6)

ReferSection9.112.1inChapter9onCathodeRayOscilloscope.

(c)Brieflyexplainphotoconductiveandphotovoltaiccells.

(6)

Readerscanrefertoreferencematerial.

8.(a)Explainwithablockdiagram,theessentialfunctionaloperationsofadigitaldataacquisitionsystem.

(6)

ReferSection14.2inChapter14onDataAcquisitionSystem.

(b)Withaneatsketch,explaintheworkingofanX-Yrecorder.

(06)

ReferSection15.2.1(3)inChapter15onRecording,StorageandDisplayDevices.

(c)WriteanoteonLEDandLCDdisplay.

(06)

ReferSections15.4.2and15.4.3inChapter15onRecording,StorageandDisplayDevices.

SOLVEDQUESTIONPAPER-81.(a)Thefollowing10observationswererecordedwhenmeasuringavoltage:31.6,

31.0,31.7,31.0,32.1,31.9,31.0,31.9,32.5and31.8volt.Find

(i)Probableerrorofonereading

(ii)Probableerrorofmean

(8)

x d d2

31.6 −0.05 0.002531 −0.65 0.422531.7 0.05 0.002531 −0.65 0.422532.1 0.45 0.202531.9 0.25 0.062531 −0.65 0.422531.9 0.25 0.062532.5 0.85 0.722531.8 0.15 0.0225

∑x=316.5 ∑d2=2.345

Mean=∑x/n=316.5/10=31.65

(i)Probableerrorofonereading=0.6745

(ii)Probableerrorofmean=0.6745

(b)DefinethefollowingforGaussiandistributionofdata:

(i)Precisionindex

(ii)Probableerror

(iii)Standarddeviationofmean

(iv)Standarddeviationofstandardofdeviation.

(8)

ReferSection1.7inChapter1onConceptsofMeasurementSystems.

OR

OR

(a)AcircuitwastunedforresonancebyeightdifferentstudentandthevaluesofresonantfrequencyinkHzwererecordedas432,447,444,435,446,444,436

and441.Calculate

(i)Standarddeviation

(ii)Variance

(8)

x d d2

432 −8.635 74.390625447 6.375 40.640625444 3.375 11.390625435 −5.625 31.640625446 5.375 28.890625444 3.375 11.390625436 −4.625 21.390625441 0.375 0.140625

∑x=3525 ∑d2=219.875

(i)Standarddeviation

(ii)Variance=(standarddeviation)2=10.48

(b)Definethefollowingwithsuitableexamples.

(i)Precision

(ii)Accuracy

(iii)Repeatability

(iv)Driftrelatedtotheinstruments

(8)

ReferSection1.7inChapter1onConceptsofMeasurementSystems.

2. (a) Explaintheblockdiagramofadcvoltmeterwithdirectcoupledamplifier.DCVoltmeterusingDirectCoupledAmplifier

(8)

Thistypeofvoltmeterisverycommonbecauseofitslowcost.Thisinstrumentcanbe used only to measure voltages of the order of millivolts owing to limitedamplifier gain.Anattenuator is used in the input stage to select voltage range.Atransistor isacurrent-controlleddevice;soresistance is inserted inserieswith thetransistorQ1toselectthevoltagerange.ItcanbeseenfromFig.1thatsensitivityofthevoltmeter is200kilo-ohms/volt,neglecting thesmall resistanceofferedby thetransistor Q1. Other values of range-selecting resistors are also so chosen thatsensitivityremainsthesameforallranges.Socurrentdrawnfromthecircuitisonly5micro-amperes.

Twotransistorsincascadedconnectionsareusedinsteadofasingletransistorforamplificationinordertokeepthesensitivityofthecircuithigh.TransistorsQ1andQ2aretakencomplementarytoeachotherandaredirectlycoupledtominimisethenumber of components in the circuit. They form a direct coupled amplifier. Avariable resistance R is put in the circuit for zero adjustment of the PMMC. Itcontrols thebuckingcurrent from the supplyE to buckout thequiescent current.The drawback of such a voltmeter is that it has towork under specified ambienttemperature toget the requiredaccuracyotherwiseexcessivedriftproblemoccursduringoperation.

Figure1Directcoupledamplifierdcvoltmeterusingcascadeshowsatransistor

(b)Explaintheworkingprincipleofvectorimpedancemeterwithneatsketch.

(8)

Readerscanrefertoreferencematerial

OR

(a)Whatdoyoumeanbytheterm‘Q-factor’.ExplaintheworkingofQ-meter.

(8)

Readerscanrefertoreferencematerial

(b)WriteshortnotesonRFpowerandvoltagemeasurements.

(8)

ReferSection17.7inChapter17onMicrowaveandRFMeasurement.

3. (a) Calculate thevelocityof theelectronbeaminanoscilloscope if thevoltageapplied to its vertical deflection plates is 2200 V. Also calculate the cut-offfrequency if the maximum transit time is 1/4 of a cycle. The length ofhorizontalplatesis65mm.

(8)

Velocityoftheelectronbeam=

[ReferExample9.1inChapter9onCathodeRayOscilloscope.]

Cut-offfrequency=

(b)ExplainthefollowingtermsofCRO:

(i)Blankingcircuit

(ii)Astimationcontrol

(8)

(i) Blankingcircuit Thepurpose of a sawtooth signal applied to the horizontaldeflectingplateofaCROistomovethebeamacrosstheCRTfromlefttorightalongthehorizontaldirection.Ifthisrateisslowthenthemovingpointwillbevisible, and if this rate is very fast then a solid line is visible.After the spotreachestherightmostpoint,ithastocomebackswiftlytotheinitialpoint,i.e.the leftmost point.This ‘fly-back’ time should be as fast as possible. Ideally,thisfly-backtimeshouldbezerosothatretraceofthespotisnotvisible.Inapractical circuit, to eliminate this retrace, a ‘blanking circuit’ is used thatapplies a high negative potential to the grid during the fly-back period thatpushesbackthespotrapidlytoitsstartingpoint.

(ii)AstigmatismcontrolInthehumaneye,astigmatismcauseslighttobefocusedaway from its intended target, the retina. Astigmatism is mainly due tocurvatureofthecornea.AsimilarcasemaybeobservedinaCROwhereduetocurvatureofthescreen,theelectronbeammaynotbefocusedproperlyonthescreenandmayappearblurred.Inmodernoscilloscopes,anadditionalfocusingcontrol marked as astigmatism is provided. To focus the spot correctly, it ismade tostopnear thecentreof thescreenbyswitchingoff the timebaseandadjusting theXandYpositioningcontrols.Thespot is thenmadeassharpaspossibleatthecentreofthescreenbyrepeatedadjustmentsofthefocusingandastigmatismcontrols.

OR

(a)ExplainthedifferenttypesofsweepusedinaCRO.

(8)

ReferSection9.5inChapter9onCathodeRayOscilloscope.

(b)ExplainthefollowingtermsofCRO:

(i)Z-axismodulation

(ii)Sourcesofsynchronization

(8)

(i)Z-axismodulationisactuallyintensitycontrol.Itisdonebyinsertingacontrolsignal between the cathode and ground or between the control grid and theground.Itisusedforcontrollingthebrightnessofdisplay.Aseriesofnegativepulsesareappliedtothecathodetomakethedisplaybrighterduringitssweepperiod. Alternatively, a series of positive pulses can also be applied to thecontrolgridtoachievethesamefunctionofbrighteningthedisplay.

(ii) There are normally three sources of synchronisation—internal, external andline. In internal synchronisation, the trigger isobtained from the signalbeingmeasured itself, through theverticalamplifier. In theexternalsynchronisationmethod,anexternaltriggersourceisusedtotriggerorinitiatethesignaltobemeasured. In the line synchronisation method, the trigger signal is obtainedfromthepowersupplylinetotheCRO.

4. (a) Explain theworking of frequency synthesised signal generatorswith a neatsketch.

(8)

ReferSection13.15inChapter13onSignalGeneratorsandAnalysers.

(b)Explaintheblockdiagramoffrequency-selectivewaveanalyzer.(8)

ReferSection13.16.1inChapter13onSignalGeneratorsandAnalysers.

OR

(a)Explaintheconstructionandworkingofaheterodynewaveanalyzer.

(8)

ReferSection13.16.21inChapter13onSignalGeneratorsandAnalysers.

(b)Explaintheblockdiagramofspectrumanalyseranditsapplications.

(8)

ReferSection13.18inChapter13onSignalGeneratorsandAnalysers.

Unit-V

5.Writeshortnotesonthefollowing:

(a)Seismicaccelerometers

(8)

Readerscanrefertoreferencematerial.

(b)RVDT

(8)

Readerscanrefertoreferencematerial.

OR

Writeshortsnotesonthefollowing:

(a)Ultrasonicflowmeters

(8)

Readerscanrefertoreferencematerial.

(b)Thermocouples.

(8)

ReferSection11.6.2inChapter11onSensorsandTransducers.

SOLVEDQUESTIONPAPER-91.AnsweranyFour:

(20)

(a) Define sensitivity of an analog instrument. For a PMMC instrumentwithFSD=100mA,findthesensitivity.

Sensitivity of a voltmeter is defined as Total voltmeter resistance in ohm 1 S==W/V

ForFSD=100mA,sensitivityS=1/(100×10–3)=10

(b)WhatisMeggar?Explainitsworking.

ReferSection4.4.4inChapter4onMeasurementofResistance.

(c)ForADC,defineresolution.Givenasuitableexample.

ReferSection10.3(a)inChapter10onElectronicInstruments.

(d)Explaintheworkingprincipleofadcmotor.

Readerscanrefertoreference.

(e)Explainthefunctionofdelaylineinoscilloscope.Whatarethetypesofdelaylines?

Thedelaylineisusedtodelaytheincomingverticalsignalandsynchroniseitwiththehorizontalsignal.OldscopesusedaseriesofLCcombinationstunedtogetagoodwaveform representation.Modern oscilloscopes use two types of delayingmethods,namelyfreerunningsweepandtriggeredsweep.

[Fortheremainingpartoftheanswer,referSections9.5.1and9.5.2inChapter9onCathoderayOscilloscopes]

2.(a) Whatisintensitymodulation?Forwhatpurposeisitused?Canphaseandfrequencybemeasuredusingintensitymodulation?

10

Readerscanrefertoreference.

(b)WhatisQmeter?ExplainanyoneofthetypesofQ-meterwiththehelpofcircuitdiagram.

(10)

Inmostradiofrequencywork,itisimportanttoobtainalargeratioofreactancetoresistanceinthereactiveelementsof thecircuit.ThisratioiscalledtheQofthecircuit.

AhighQisrequiredtoobtaingoodefficiency,goodwaveform,goodfrequencystability,highgain,etc.

TheQ-meter is required to obtained good efficiency theQ of a reactanceelementdirectly.Itmayalsobeusedtomeasure

•thereactanceandresistanceofacircuit,

•thedistributedcapacityofacircuit,and

•theresonantfrequencyofatunedcircuit,etc.

Figure1

Figure1showsthefundamentalcircuitofQ-meter.

TheoscillatorsuppliesacurrentItoRʹandtheunknownandC.SinceRʹisverysmallcomparedwiththeimpedanceoftheexternalcircuit,thevoltageEisequalto IRʹ.Hence, the reading I gives an indication of the voltage impressed on thecircuit.

IftheunknownandCaretunedtoresonance(i.e.CadjusteduntilEc=Max.),

whereRistheeffectiveseriesresistanceoftheunknownandC.Also,

Hence,ifEisheldconstantbyholdingIconstant,EcreadsdirectlyproportionaltoQandthismetermaybecalibrateddirectlyintermsofQ.SinceEcisproportionaltoE,ImaybecalibratedintermsofamultiplyingfactorforextendingtheQrangeoftheinstrument.

3.(a)DrawandexplainKelvin’sBridge.

(10)

ReferSection4.3.2inChapter4onMeasurementofResistance.

(b)Explaintheoperatingprincipleof3-phaseinductionmotor.

(10)

Readerscanrefertoreferencematerial.

4.(a)Drawandexplaintheblockdiagramofdigitalstorageoscilloscope.

(10)

ReferSection9.11.2inChapter9oncathodeRayOscilloscope.

(b)ExplainR–2Rladdertechniqueofdigitaltoanalogueconverter.

(10)

Readerscanrefertoreferencematerial.

5.(a)Drawandexplainanyoneofthetypesofelectronicvoltmeters.Stateitstwoadvantagesoveranalogvoltmeter.

(10)

ReferSections10.6and10.6.1inChapter10onElectronicInstruments.

(b)Explaindigitalphasemeterusingflip-flop.Drawrelevantwaveformsateachpointinablockdiagramtoillustrate.

(10)

Readerscanrefertoreferencematerial.

6.(a)ExplainScheringbridgeformeasurementofcapacitance.Derivetheequationofunknowncapacitanceatbalancedcondition.

(10)

ReferSection6.5.2inChapter6onacBridge.

(b)Whatisenergymeter?Drawitsconstructionalviewandexplain.

10

ReferSection8.2.2inChapter8onMeasurementofEnergy.

7.Writeshortnoteson(anytwo):

20

(a)Variablereluctancesteppermotor.

Readerscanrefertoreferencematerial.

(b)A.F.signalgenerator

Refer either Section 13.5 or 13.6 on Chapter 6 on Signal Generators andAnalysers.

(c)Digitalfrequencymeter.

ReferSection10.5inChapter10onElectronicInstruments.

AAbsoluteerror1.17

Absoluteinstruments2.1

Acceleratingvoltage9.5

Accuracy1.16,10.4,10.3

ACpotentiometers5.13,12.29

Actualtransformationratio3.31

A/DConversion14.14

AdjacentChannelPower17.4

AdvantagesandDisadvantagesofLVDT11.4

Advantagesofelectricaltransducers11.2

AdvantagesofElectromagneticFlowMeter11.10

Airfriction2.3

Air-frictiondamping2.8

Aliasing14.14

Aluminumdisc7.22

Aluminumspindle7.9

Aluminumvanes7.10

Ammetershunts2.18

Ampere1.4

Amplification14.10

Amplitudedistortion13.36

AmplitudeModulation(AM)17.9

AmplitudeShiftKeying(ASK)17.11

Analoginputsubsystems14.4

Analoginstruments2.1,2.2,1.13

Analogmodulation17.9

AnalogOutputSubsystem14.4,14.19

AnalogRecorders15.2

Analogsensors14.5

AnalogStorageOscilloscope9.18

Analog-to-DigitalConverter(DACsandADCs)9.20

Analysers13.1

Anderson’sBridge6.11

Angleofincidence18.1

Angleofrefraction18.1

ANSI/IEEEStandard488.1-198714.26

Antennasize17.2

ApplicationSoftware14.13

Aquadog9.1

Arbitrarywaveformgenerator10.14

Astatic7.18

Astaticelectrodynamometerinstruments7.18

AvalancheDiode18.6

Averagedeflectingtorque7.11

BBallisticgalvanometer12.1

Band-Pass(selective)Filter14.8

Band-stop(Notch)Filter14.9

BarkhausenCriteria13.3

Barretter17.16

Bar-typeCT3.15

Basebandsignal17.15

BasicRequirementsofaTransducer11.2

BasicTransistorLCOscillatorCircuit13.5

Bearings2.5

BFSK17.12

BinaryWeightedDAC14.20

Blondel’sTheorem7.25

Bolometer17.16

Brakemagnet8.5

BridgeandacPotentiometerMethods12.27

Burden3.2

BurrowsPermeameter12.23

Bushing-typeCT3.16

ButterworthFilter14.10

CCalibrationofammeter5.6,5.18

CalibrationofAmmeterbyPotentiometer5.10

CalibrationoftheBallisticGalvanometer12.5

Calibrationofvoltmeter5.5,5.18

CalibrationofVoltmeterbyPotentiometer5.9

Calibrationofwattmeter5.6,5.19

CalibrationofWattmeterbyPotentiometer5.10

Capacitancestandards1.3

CapacitiveTransducers11.23

CathodeRayOscilloscope(CRO)9.1

CathodeRayTube(CRT)9.1,15.18

CentralProcessingUnit(CPU)16.4

Characteristicfrequency13.15

CircularChartRecorder15.6

ClampontypeCTs3.16

ColdCathodeDisplay15.19

Coldjunction11.15

ColpittsCrystalOscillator13.16

ColpittsOscillators13.9

CommunicationSystems17.14

Comparisonbetweendifferenttypesofinstruments2.47

Comparisonmethods1.8

Compensatingcoil7.17

Compensationforpressurecoilinductance7.15

Compensationforvoltagevariation8.14

Conductivemesh9.19

Contactsandleadresistances4.20

Controller14.26

Controllingsystem2.3

Controllingtorque2.2,2.3,7.11

ControlProgram16.2

CoordinatePotentiometer5.14

Counters16.3

Counter/TimerandPulseI/O14.26

Counter/TimersSubsystems14.4

Countingsystem8.6

CreepingError8.12

Creeptest8.14

Criticalangle18.1

Criticallydamped2.3

Crompton’sdcpotentiometer5.2

Cross-overDistortion13.36

CrystalOscillators13.14

CTtransformation8.5

Currentcoil1.3,2.32,2.33,7.5

Currentstandards4.19

Currentterminals3.2

Currenttransformer7.35,14.6

DD/AConversion14.19

DACPerformance14.22

Dampingforce2.3

Dampingtorque2.2

DAQ14.3

DAQHardware14.3

Dataacquisition14.1

DataLogger15.15

Deadzone1.16

Deflectingplates9.1

Deflectingsystem2.3

Deflectingtorque2.2,2.14

Deflectionfactor9.5

Deflectionmethods1.8

Deflectionsensitivity9.5

Deflection-typeinstrument1.15

Delta-sigmamodulation14.20

Derivedunits1.2

DeSauty’sbridge6.17

DetectionofLowLevelSignals10.2

DeterminationofHysteresisLoop12.17

DeterminationofMagnetisingCurve12.15

Dielectriclosses6.18

Differentialtransformers11.22

Digitalfrequencymeter10.7

Digitalinput/outputsubsystems14.4

Digitalinputs14.24

Digitalinstruments1.13

Digitalmodulation17.11

Digitalmultimeter10.5

Digitalpatterngenerator10.14

Digitalrecorders15.15

Digitalsensors14.5

Digitalstorageoscilloscope9.19

Digitaltaperecording15.17

DigitaltoAnalog(D/A)converter10.4

DigitalVoltmeter(DVM)10.9

Diodedetector17.17

Directcomparisonmethods1.8

Directdeflectionmethodforhighresistancemeasurement4.26

Displaysystem15.18

Dissipationfactor6.19

DotMatrixDisplay15.22

DriverSoftware14.13

Drysdalepolarpotentiometer5.14

DSO9.19

DualBeamOscilloscopes9.23

Dual-SlopeIntegrating-TypeDVM10.11

Dualtraceoscilloscopes9.21

Dynamicrange14.22

Dynamometer7.5

Dynamometer-typewattmeter7.5

EEddy-currentdamping2.8,2.10

Eddy-currentErrors7.17

Eddycurrentlosses3.18

Eddycurrents2.3

Effectofpowerfactoronwattmeterreadings7.29

Electricalinstruments1.14

Electrodynamicammeter2.32

Electrodynamicvoltmeter2.32

Electrodynamicwattmeter2.33

ElectromagneticFlowmeter11.7

Electromagneticspectrum17.1

Electromagneticwavespectra17.3

Electrongun9.1

Electronicinstruments1.14,10.1

Electronicvoltmeter(EVM)10.2

Electrostaticinstruments2.37

Electrothermalinstruments2.41

Environmentalerrors1.21

Errorcausedbyvibrationofthemovingsystem7.19

Errorduetoconnection7.16

Errorduetooverload8.13

Errorduetopressurecoilcapacitance7.15

Errorduetopressure-coilinductance7.13

Errorduetovoltagevariations8.14

ErrorsinaWheatstonebridge4.16

ErrorsinElectrodynamometer-typeWattmeter7.13

ErrorsoccurringduringtheMeasurementusingthermocouple11.16

ErrorVectorMagnitude(EVM)17.13

EwingDoubleBarPermeameter12.21

ExtensionofrangeofPMMCInstruments2.18

Extensionofrangeofrectifierinstrument2.45

Externalmagneticfields7.18

F

Fibreopticpowermeasurement18.7

Fictitiousloading7.9

Fieldcoils2.28

Filtering14.5

Fixedcoils2.29

Flash/Parallel14.15

Flatpaneldisplay15.26

Flowmeters2.3

Fluidfriction2.8

Fluid-frictiondamping2.9,11.19

Fluxmeter12.8

FMrecording15.13

Forcesummingdevices4.19

Fourterminals9.7

Freerunning9.7

Freerunningsweep10.6

Frequencycounter10.7

Frequencydistortion13.35

Frequencygenerator9.24

FrequencyModulation(FM)17.10

Frequencyrangeofoscilloscope2.17

FrequencySelectiveWaveAnalyser13.33

FrequencyShiftKeying(FSK)17.12

Full-scaledeflection2.18

FunctionBlockDiagrams(FBD)16.12,16.16

Functiongenerator1.2,13.26

GGallCoordinatePotentiometer5.15

Galvanometer4.17

GeneralPurposeInterfaceBus(GPIB)14.26

GraphicRecorders15.2

GravityControl2.7

Grosserror1.19

Guaranteeerrors1.17

Guardarrangement4.25

Guardcircuits4.25

HHair-spring2.6

Hand-heldprogramming16.8

Hardbeam9.5

Harmonicdistortion17.5

Harmonicdistortionanalysers13.35

HartleyOscillator13.6

Hay’sbridge6.9

HeterodyneSweepGenerator13.31

HeterodyneWaveAnalyser13.33

HighOutputSignalQuality11.2

High-PassFilter14.7

HighQinductors6.9

HighReliabilityandStability11.2

HighResistances4.1

HopkinsonPermeameter12.19

Hot-wireInstrument2.41

HybridDAC14.21

HybridRecorders15.9

Hysteresis3.18,11.2

IIEEE488Interface14.26

IllioviciPermeameter12.22

ImageTableAddresses16.9

Indicatinginstruments1.13

Indirectcomparisonmethods1.8

Indirectmeasurementmethods1.8

Induction-typeinstruments2.39

Induction-typewattmeter7.22

Inductivetransducer11.3,11.20

In-phase’potentiometer5.15

Input/Output(I/O)Modules16.6

InputRelays16.3

Inputresistance10.2

Insertionerrors7.2

Instantaneouspower7.6

Instantaneoustorque7.11

Instrumentalerrors1.21

Insulationresistance4.30

Integratinginstruments1.13

Integrating-TypeDVM(VoltagetoFrequencyConversion)10.13

Inter-modulationDistortion13.36

Internallyreflected18.1

InternalTriggering(INT)9.8

InternalUtilityRelays16.3

Internationalampere1.4

Internationalstandards1.2

Inter-turncapacitance7.15

I/OAddresses16.9

Ionisationtransducers11.26

JJewelbearings7.9

Jewels2.5

KKelvin’sDouble-BridgeMethodforMeasuringLowResistance4.20

Kilowatt-hour(kWh)8.1

LLadderdiagrams16.12

LASER18.4

LCD15.23

LCoscillator10.16

LCOscillatoryCircuit13.3

Leakageflux12.25

LED15.19

LightEmittingDiode(LED)15.19,18.3

Limitingerror1.17

LinearError10.4

Linearisation14.11

Linearity11.2

LinearVariabledifferentialTransformer(LVDT)11.3

LiquidCrystalDisplay(LCD)15.23

Lissajouspatterns9.12

Listener14.26

Loadingeffect1.22,10.2

Localisationofcablefaults4.33

Looptests4.33

Lossangles6.20

Lossofchargemethodforhighresistancemeasurement4.29

Low-passfilter14.6

Lowresistances4.1

Luminosity9.5

MMagneticdiskandtapetyperecorder15.11

Magneticflowmeters11.7

Magneticmeasurements12.1

Magneticmeter(Magmeter)11.8

Magneticshielding12.30

Magneticshunt8.14

Magnetictape15.11

Magnetictesting12.26

Manualinstruments1.15

Markfrequency17.12

Maximumsamplingfrequency14.22

Maxwell’sbridgemethod12.28

Maxwell’sinductancebridge6.4

Maxwell’sinductance-capacitancebridge6.6

Measurementofcurrentbypotentiometer5.6

Measurementofenergy8.1

Measurementoffluxdensity12.11

Measurementoffrequency9.12

Measurementofhighvoltagebypotentiometer5.6

Measurementofloss18.8

Measurementoflowresistances4.19

MeasurementofmagneticfluxbyBallisticgalvanometer12.4

Measurementofmagneticleakage12.25

Measurementofmagnetisingforce(H)12.13

Measurementofpowerbypotentiometer5.8

Measurementofresistancebypotentiometer5.7

MeasuringRFvoltageswithavoltmeter17.17

Mechanicalinstruments1.14

Mediumresistances4.1

Meggar4.30

Megohmmeter4.30

Meritsanddemeritsofdigitalinstrumentsoveranalog10.2

Meterconstant8.1

Microprocessorclocks13.17

Microwave17.3

ModifiedDeSauty’sbridge6.18

Modulatedsignal17.9

Modulatingsignal17.9

Modulation17.9

ModulationErrorRatio(MER)17.13

Modulationoscillator10.16

Monoshot13.19

Monostablemultivibratorcircuits10.3

Monotonicity10.4

Movingcoil2.28,2.29

MovingIronorMI4.6

Multimodefibres18.2

Multi-rangeseriesohmmeter7.12

MurrayLoopTest4.34

NNetworkanalyser17.7

Networkscatteringparametres17.9

Nixietube15.27

Noisefloor17.5

Noiseshaping14.20

Nominalratio3.7

Non-inductiveresistance7.9

Non-sinusoidalOscillators13.2

Null-typeinstruments1.15

NyquistCriterion14.13

OOccupiedbandwidth17.4

Ohmmeter4.2

One-shot13.22

OP-AMPastablemultivibrator13.19

Opticaldetectors18.5

Opticalfibre18.1

Opticalpower18.7

Opticalsources18.2

OpticalTimeDomainReflectometre(OTDR)18.9

Oscillationtransducers11.27

Oscillator13.1

Oscillographicrecorders15.15

Over-compensationforfriction8.12

Overdamped2.3

OversamplingDACsorInterpolatingDACs14.20

Owen’sbridge6.13

PPaperlessrecorders15.9

PC-baseddataacquisitionsystem14.3

PDMrecording15.14

PDP15.26

Percentageofdistortion17.5

Percentageratioerror3.8

Permanentmagnetisation3.18

Permanentmagnetmovingcoilinstrument2.12

PermanentMagnetMovingCoil(PMMC)2.12

Permeameters12.19

Phantomloading8.15

Phase-angleerror3.32,8.9

Phasedistortion13.36

PhaseModulation(PM)17.10

Phasenoise17.5

PhaseShiftKeying(PSK)17.12

Phosphor-bronzesprings7.9

Phosphors15.18

Phosphorscreen9.1

Photoelectrictransducers11.24

Pierceoscillator13.16

Piezoelectrictransducers11.26

PINDiodes18.5

Pivotandjewelbearings2.4

PlasmaDisplayPanel(PDP)15.26

PLCprogrammingterminal16.8

Polarpotentiometer5.13

Portable-typeCT3.16

Positivefeedback13.1

Potentialterminals4.19

PotentialtransformersorPTs3.26,7.35

Potentiometer5.1

Potentiometermethodformeasuringlowresistance4.23

Poweramplifier9.7

Powerinband17.3

PowermeasurementinACCircuits7.6

PowermeasurementinDCCircuits7.1

Powermeasurementinpolyphasesystems7.25

Powermeasurementusingthermistor17.16

Powermeasurementwithinstrumenttransformers7.35

Powermeter18.7

Powersupply16.6

Precision1.16

Pressurecoil2.33,7.9

Pressuremeasurement11.19

Price’sguard-wiremethod4.28

Primarystandards1.2

Primarytransducer11.19

ProgrammableLogicControllers(PLCs)16.1

Programscantime16.11

Pulsegenerators13.18

Pulsewidthmodulator14.20

QQfactor6.8

Qualityfactor14.6

Quantisation14.14

Quantisationlevels14.14

Quartzcrystaloscillator10.16

RR-2RLadderDAC14.21

Radiofrequency17.1

RadiofrequencySpectrumAnalyser17.5

Ramp/Counter14.16

Ramp-TypeDVM10.10

Rampvoltage9.6

Randomerror1.19,1.21

Range14.19

Ratioarms4.16

Ratioerror3.7,3.32

RCOscillator13.10

ReactivePowerMeasurements7.33

Read-OnlyMemory(ROM)9.20

Recordinginstruments1.13

Rectifier-typeinstruments2.43

Referencecell5.2

Referencejunction11.15

Relativeerror3.18

RemoteI/O16.10

Repeatability11.2

Residualmagnetism1.3

Residualreformation11.2

Resistancestandards1.16

Resistancestraingauges11.5

Resistancetemperaturedetectors11.11

Resistancethermometers11.11

Resistivetransducers11.20

Resolution2.5

ResolutionBandwidth17.4

Resonance13.3,13.4

RFAnalysers17.7

RFcommunicationsystem17.15

RFnetworkanalyser17.7

RFsignalgenerator13.28

RFVoltageandPowerMeasurement17.16

Ribbonsuspension11.2

RollOff14.6

SSample-and-hold(S/H)9.20

Sampling14.14

Samplingoscilloscope9.17

Sawtoothwaveform9.6

ScalarNetworkAnalyser(SNA)17.7

Scheringbridges6.20

Schmitttrigger13.24

Secondaryemissionelectrons9.19

Secondaryinstruments1.13,2.1

Secondarystandards1.2

Secondarytransducer11.19

Seebeckvoltage11.14

Self-inductance6.4

Self-operatedinstruments1.15

Sensitivity1.16,2.20

Sensitivityofafull-waverectifiercircuit2.44

Sensitivityofahalf-waverectifiercircuit2.44

Sensitivityofrectifier-typeinstrument2.43

Sensor11.1

Sensorsandtransducers14.5

Seriesmagnet7.22

Series-typeohmmeter4.2

Settlingtime10.4,8.5

SevenSegmentDisplay15.20

Shadingbands8.5

Shadingcoil8.9

Shadingloop8.12

Shadingvaneforfrictioncompensation8.12

Shapeofscaleinelectrodynamometer-typewattmeter7.12

Shapeofscaleinseriesohmmeters4.4

Shapeofscaleinshuntohmmeters4.7

Shields7.18

Shunt2.18

Shuntmagnet7.22

Shuntsandmultipliers3.1

Signalconditioning14.5

Signalgenerators10.14

Sinewavegenerator13.24

Single-pointandmulti-pointrecorders15.5

Sinusoidaloscillators13.2

Spacefrequency17.12

Spaceloss17.2

Spectrumanalyser13.37,17.6

Spectrumanalysis17.5

Speedofresponse1.17

Spindle2.5

Spiralspring2.3,7.9

Spontaneousemission18.4

Springcontrol2.6

Squarewavegenerator13.18

Standardarm4.16

Standardcell1.4

Standardisation5.2

Standardizethepotentiometer5.2

Standardofmeasurement1.2

Standardresistor5.7

Standardvariableresistance4.14

Statementlist16.12,16.16

Storage10.3

Straingauges11.5

Straycapacitance7.16

Stripchartrecorder15.2

Substitutionmethodformeasuringresistance4.14

Successiveapproximation14.15

Super-Heterodyneanalyser17.6

Surfaceleakage4.24

Suspension2.4,7.9

SwampingResistance2.15

Sweepfrequencygenerator13.29

Sweepgenerator9.7,13.29

Synchronisation9.7

Systematicerror1.19,1.21

TTalker14.26

Tautsuspension2.4

Temperaturecoefficientofresistance11.11

Temperatureeffects8.13

Temperatureerrors7.19

Temperaturesensitivity10.4

Temperaturetransducers11.11

Testingofspecimens12.18

THD13.36

THD+N14.22

ThermalDotArrayRecorders15.10

Thermalemfs11.17

Thermistors11.14,17.16

Thermocouple2.39,17.16

Thermocoupleinstrument2.41

ThermometerCodedDAC14.21

Three-WattmeterMethod7.27

Timeandfrequencystandards9.1

Timebase10.14

Timers16.3

Tonegenerator2.6

Torque/weightratio2.6,11.1

Totalharmonicdistortion13.36

Totalinternalreflection18.1

TotalpercentageHarmonicDistortion(THD)17.5

Transducer10.1

TransistorisedVoltmeter(TVM)9.8

Triangularwavegenerator13.22

Triggercircuit9.8

TriggeredSweep6.1

TrueRMSvoltmeter2.46

Tuneddetector3.31

Turnsratio7.27

UUltravioletRecorders15.9

Underdamped2.3

Unitofenergy8.1

VVacuumTubeVoltmeter(VTVM)10.1

Vane8.12

VarleyLoopTest4.35

Verticaldeflectionplates9.2

Vibrationgalvanometers6.1

VNA17.8

Voltagecoil7.5

Voltage-controlled-oscillator13.27

VoltageControlledOscillator(VCO)13.29

Voltagestability14.17

Voltagestandards1.3

Voltmeter-ammetermethodformeasuringlowresistance4.19

Voltmeter-ammetermethodformeasuringresistance4.11

Voltmetermultipliers2.19

WWagnerearthdevice6.26

Waveanalyser13.33

Waveguides18.1

WestonfrequencymeterC.1Wheatstonebridge4.15,9.7

Widebandpreamplifier13.13

WienBridgeOscillators6.20

Wien’sbridge6.22

Wirelesscommunication17.2

Wirelesscommunicationsystem17.1

Workingstandards3.14

XX-YRecorder15.7