instrumentation measurements and
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Measurements andInstrumentationKTUNOTES.IN
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Linearity
• The linearity is defined as the maximum deviationfrom the linear characteristics as a percentage ofthe full scale output.
• is the closeness to a straight line of the relationship betweenthe true process variable and the measurement.
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Sensitivity of measurement
• measure of the change in instrument outputthat occurs when the quantity beingmeasured changes by a given amount.
• Static Sensitivity K = Change of Output Signal /Change in Input Signal
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Reliability• is the probability that a device will adequately
perform (as specified) for a period of time underspecified operating conditions.
Drift• The drift is defined as the gradual shift in the
indication over a period of time where in theinput variable does not change.
• Because of environment factors like strayelectric fields, stray magnetic fields, thermal e.m.fs, changes in temperature, mechanicalvibrations etc.
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Span• Span represents the algebraic
differences between the upper andlower range values of the instrument.
• An instrument which has a readingrange of –100°C to 100 °C span is200 °C.
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Hysteresis
• Hysteresis is defined as the magnitude of error caused in theoutput for a given value of input, when this value isapproached from opposite directions ; i.e. from ascendingorder & then descending order
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Backlash
• It is defined as the maximum distance orangle through which any part of mechanicalsystem may be moved in one directionwithout causing motion of next part.
• be minimized if components are made to veryclose tolerances
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DYNAMIC CHARACTERISTICS
• Dynamic characteristics of a measuringinstrument refer to the case where themeasured variable changes rapidly.
• The dynamic characteristics of anymeasurement system are:– (1) Speed of response and Response time – (2) Lag– (3) Fidelity– (4) Dynamic error
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Speed of Response
• It is the rapidity with which an instrument ormeasurement system responds to changes inmeasured quantity.
Response Time
• is the time required by instrument or systemto settle to its final steady position after theapplication of the input.
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Measuring Lag• The delay in the response of an instrument to a
change in the measured quantity is knownas measuring lag.
Measuring lag is of two types– i) Retardation type: In this the response begins
immediately after a change in measured quantity hasoccurred.
– ii) Time delay: In this the response of themeasurement system begins after a dead zone afterthe application of the input.
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Fidelity• Fidelity of a system is defined as the ability of
the system to reproduce the output in thesame form as the input.
Dynamic Error• It is the difference between the true value of
the quantity changing with time and thevalue indicated by the instrument if no staticerror is assumed.
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Sources of error
• Poor design
• Change in process parameters, irregulationsupsets etc.
• Poor maintenance
• Certain design limitations
• Insufficient knowledge of process parametersand design conditions
• Errors caused by the person operating instrument
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ERRORS IN MEASUREMENT
• errors are classified mainly into threecategories as follows:– (a) Gross errors
– (b) Systematic errors
– (c) Random errorsKTUNOTES.IN
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• Gross Errors– These errors are due to the gross blunder on the
part of the experimenters or observers.
– These errors are caused by mistake in usinginstruments, recording data and calculatingmeasurement results.
For example: A person may read a pressure guageindicating 1.01 N/m2 as 1.10 N/m2 .
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Systematic Errors
• These are inherent errors of apparatus ormethod.
• These errors always give a constant deviation.• Constructional Error– None of the apparatus can be constructed to
satisfy all specifications completely
• Determination Error– It is due to the indefiniteness in final adjustment
of measuring apparatus.
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Errors in Reading or Observation• (a) Construction of the Scale : There is a possibility of
error due to the division of the scale not being uniformand clear.
• (b) Fitness and Straightness of the Pointer : If thepointer is not fine and straight, then it always gives theerror in the reading.
• (c) Parallax : Without a mirror under the pointer theremay be parallax error in reading.
• (d) Efficiency or Skillness of the Observer : Error in thereading is largely dependent upon the skillness of theobserver by which reading is noted accurately.
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• Error due to Other Factors– Errors in Measurement Temperature Variation
– Effect of the Time on Instruments
– Effect of External Electrostatic and MagneticFields
– Mechanical ErrorKTUNOTES.IN
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Random Errors
• After corrections have been applied for all the parameterswhose influences are known, there is left a residue ofdeviation.
• These are random error and their magnitudes are notconstant.
• Persons performing the experiment have no control over theorigin of these errors.
• These errors are due to so many reasons such as noise andfatigue in the working persons.
• These errors may be either positive or negative.• To these errors the law of probability may be applied.• Generally, these errors may be minimized by taking average
of a large number of readings.
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Classification of MeasuringInstruments
• Measuring instruments may be broadlyclassified as follows
1. Absolute instruments
2. Secondary instruments
(a) Indicating instruments
(b) Integrating instruments
(c) Recording instruments
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Absolute instruments
• absolute instruments are those which gives the value of thequantity to be measured, in terms of the constants of theinstruments and their deflection only.
• Such instruments do not require any previous calibration orcomparison.
Example: Tangent galvanometer (is a very commonexample) and Rayleigh’s current balance instruments.
• Uses: These instruments used as standardizing instruments inlaboratories.
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Secondary instruments
• “secondary instruments are those in which thevalue of electrical quantity to be measured canbe determined from the deflection of theinstruments”.
• Such instruments are need to be pre-calibratedby comparison with an absolute instrument.
• Without calibration, the deflection of suchinstruments is meaningless.Example: An ammeter, voltmeter, a glass
thermometer, and a pressure gauge instruments.
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Indicating Instruments:
• The value of the electrical quantity is indicatedby these instruments at the time when it isbeing measured.
• Pointers moving over the scale give theindication.E.g., Ammeters, Voltmeters and watt metersKTUNOTES.IN
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Recording Instruments:
• A continuous record of variations of the electrical quantityover a long period of time is given by these instruments.
• It has a moving system which carries an inked pen whichrests tightly on a graph chart.
E.g., Graphic recorders and galvanometer recorders are theexamples of these instruments.
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Integrating instruments:
• The total amount of either electricity or electrical energysupplied over a period of time is measured by theseinstruments.E.g., Ampere hour meters, watt-hour meters, energy metersare the few examples of these instruments.KTUNOTES.IN
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Essentials of Indicating Instruments
The moving system is subjected to the following3 torques/forces:
1) Deflecting torque or operating torque
2) Controlling torque or restoring torque
3) Damping torqueKTUNOTES.IN
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Deflecting torque/Deflecting force Td
• a deflecting system converts an electricalsignal to a mechanical force
• The deflecting torque is produced by(magnetic effect, induction effect, thermaleffect, hall effect) of electric current orvoltage
• The deflecting torque causes the movingsystem to move from its zero position.
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Controlling torque (Tc)
• It is the torque which controls the movementof the pointer
• In indicating instruments, the controllingtorque, also called restoring or balancingtorque, is obtained by two methods which are– Spring control
– Gravity control
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Spring Control
• In the spring control method, a hair spring usually of
phosphor bronze, attached to the moving system isused.
• With the deflection of the pointer, the spring istwisted in the opposite direction.
• This twist in the spring produces restoring torquewhich is directly proportional to the angle ofdeflection of the moving system.
• The pointer comes to a position of rest (orequilibrium) when the deflecting torque (Td) and thecontrolling torque (Tc) are equal.
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• the deflection torque is proportional to the current passingthrough them.
• Td ∝ I And for spring control Tc ∝ θ• As Tc = Td, θ ∝ I
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Gravity Control
• Gravity control is obtained by attaching a small adjustableweight to some part of the moving system such that the twoexert torques in the opposite directions.
• the controlling or restoring torque is proportional to the sineof the angle of deflection, i.e., Tc ∝ Sinθ
• The degree of control is adjusted by screwing the weight upor down the carrying system.
• If Td ∝ I
• Then for position of rest,Td = Tc Or I ∝ Sin θ
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• Hence in gravity control instruments, the scales are notuniform but are cramped or crowded at their lower ends.
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Damping torque/Stabilising force• Damping torque is one which acts on the moving system of
the instrument only when it is moving and always opposes itsmotion.
• It is necessary to avoid oscillations of moving system about itsfinal deflected position
• The function of damping is to absorb the energy fromoscillating system and to bring it to rest in its equilibriumposition
• The damping force can be produced by
i) air friction,
ii) eddy currents,
iii) fluid friction.
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Air-friction damping
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Eddy current damping
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Ammeter
• Ammeters are connected in the series withthe circuit whose current is to be measured.
• The power loss in an ammeter is (I2Ra) whereI is the current to be measured Ra is theresistance of the ammeter
• ammeter should have low electricalresistance so that they cause a small voltagedrop and consequently absorb small power
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Voltmeter
• Voltmeters are connected in parallel with thecircuit whose voltage is to be measured
• the power loss in voltmeter is (V2/Rv), whereV is the voltage to be measured and Rv is theresistance of the voltmeter.
• Therefore voltmeters should have a highelectrical resistance, in order that the currentdrawn by them is small and consequently thepower consumed is small
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Permanent Magnet Moving Coil (PMMC)instrument (Only for DC measurement)
• One of the most accurate type of instrumentused for D.C.
• Material used for magnet in PMMC is Alnicoand Alcomax .
• The field strength in PMMC varies from 0.1Wb/m2 to 1Wb/m2
• Damping: Eddy current damping is used. Thisis produced by aluminum former.
• Control: Spring control is used.
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construction
• A permanent magnet is used in this typeinstrument.
• Aluminum former is provided in thecylindrical in between two poles of thepermanent magnet .
• Coils are wound on the aluminum formerwhich is connected with the spindle.
• This spindle is supported with jeweledbearing.
• Two springs are attached on either end ofthe spindle.
• The terminals of the moving coils areconnected to the spring.
• Therefore the current flows throughupper spring , moving coil and lowerspring
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Principle of operation
• When D.C. supply is given to the moving coil, D.C. current flowsthrough it.
• When the current carrying coil is kept in the magnetic field, itexperiences a force. This force produces a torqueband the formerrotates.
• The pointer is attached with the spindle. When the formerrotates, the pointer moves over the calibrated scale.
• When the polarity is reversed a torque is produced in theopposite direction.
• The mechanical stopper does not allow the deflection in theopposite direction.
• the polarity should be maintained with PMMC instrument.• If A.C. is supplied, a reversing torque is produced. This cannot
produce a continuous deflection. Therefore this instrumentcannot be used in A.C.
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Torque developed by PMMC
Let Td =deflecting torqueTC = controlling torqueθ = angle of deflectionK=spring constantb=width of the coil B=Flux density l=height of
the coil or length of coilN=No. of turnsI=currentB=Flux densityA=area of the coil
The force produced in thecoil is given by
F = BIL sinθWhenθ= 900
For N turns, F = NBILTorque produced Td = F×
⊥r distanceTd= NBIL b =BINATd = BANITd ∝ I
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Advantages• _ Torque/weight is high• _ Power consumption is less• _ Scale is uniform• _ Damping is very effective• _ Since operating field is very strong, the effect of stray field is
negligible• _ Range of instrument can be extendedDisadvantages• _ Use only for D.C.• _ Cost is high• _ Error is produced due to ageing effect of PMMC• _ Friction and temperature error are present
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Dynamometer (or) Electromagneticmoving coil instrument (EMMC)
• This instrument can be used for themeasurement of voltage, current and power.
• The difference between the PMMC anddynamometer type instrument is that thepermanent magnet is replaced by anelectromagnet.
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Construction
• A fixed coil is divided into two equal half.
• The moving coil isplaced between thetwo half of the fixedcoil.
• Both the fixed andmoving coils are aircored.
• So that the hysteresiseffect will be zero. T
• he pointer is attachedwith the spindle.
• In a non metallic formerthe moving coil iswounded.
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Torque developed by EMMC
• Let• L1=Self inductance of fixed coil• L2= Self inductance of moving coil• M=mutual inductance between fixed coil
and moving coil• i1=current through fixed coil• i2=current through moving coil• Total inductance of system
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• Hence the deflection of pointer is proportional to the currentpassing through fixed coil and moving coil.
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Advantages• _ It can be used for voltmeter, ammeter and wattmeter• _ Hysteresis error is nill• _ Eddy current error is nill• _ Damping is effective• _ It can be measure correctively and accurately the rms value of
the voltageDisadvantages• _ Scale is not uniform• _ Power consumption is high(because of high resistance )• _ Cost is more• _ Error is produced due to frequency, temperature and stray field.• _ Torque/weight is low.(Because field strength is very low)
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Moving Iron (MI) instruments
• One of the most accurate instrument used forboth AC and DC measurement
There are two types of moving iron instrument.– Attraction type
– Repulsion typeKTUNOTES.IN
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Attraction type M.I. instrumentConstruction
• It consists of a coil wound on ahollow cylindrical bobbin.
• A small piece of soft iron iseccentrically pivoted just outside thecoil.
• A pointer is attached to the spindle .• The spindle is pivoted to jewel
bearings.• Air friction damping may be used.• A piston, attsached to the spindle,
moves inside an air chamber andgives the necessary damping.
• Spring control is almost universallyused.
• A hair spring made of phosphorbronze, is attached to the spindleturns.
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Torque developed by M.I
• Let ‘θ ’ be the deflection corresponding to a current of‘i’ amp
• Let the current increases by di, the correspondingdeflection is ‘θ + dθ ’
• There is change in inductance since the position ofmoving iron change w.r.t the fixed electromagnets.
• Let the new inductance value be ‘L+dL’. The currentchange by ‘di’ is dt seconds.
• Let the emf induced in the coil be ‘e’ volt.
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• Eqn gives the energy is used in to two forms. Part ofenergy is stored in the inductance.
• Remaining energy is converted in to mechanical energywhich produces deflection.
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REPULSION TYPE MOVING IRONINSTRUMENT
Construction:• It consists of a hollow cylindrical
bobbin carrying a coil.• Two soft iron pieces A & Bare fixed
inside the bobbin.• One piece (A) is fixed to the spindle
and the other piece (B)is fixed onthe bobbin wall.
• A pointer is attached to the spindle.• Air friction damping may be used.
Spring control arrangement isprovided on spindle.
• The spindle is pivoted to jewelbearings. Pointer moves over agraduated scale.
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Extension of range of PMMC instrument
Case-I: Shunt
• A low shunt resistance connected in parallel with theammeter to extent the range of current.
• Large current can be measured using low current ratedammeter by using a shunt.– Let Rm =Resistance of meter
– Rsh=Resistance of shunt
– Im = Current through meter
– Ish =current through shunt
– I= current to be measure
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• Shunt resistance is made ofmanganin.
• This has leastthermoelectric emf.
• The change is resistance,due to change intemperature is negligible.KTUNOTES.IN
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Multiplier
• A large resistance is connected in series withvoltmeter is called multiplier .
• A large voltage can be measured using avoltmeter of small rating with a multiplier.– Let Rm =resistance of meter– Rse =resistance of multiplier– Vm =Voltage across meter– Vse= Voltage across series resistance– V= voltage to be measured
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Functional Elements of aMeasurement System
• Primary sensing element
• Variable conversion element
• Variable manipulation element
• Signal conditioning element
• Data transmission element
• Data presentation element.
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