ELECTRONIC INSTRUMENTATION

Reference Books• Measurement System : Ernest O Doebelin• Electronic Instrumentation : H.S Kalsi

Reference Books• Measurement System : Ernest O Doebelin• Electronic Instrumentation : H.S Kalsi

Electronic Instrumentation• Instrumentation is a branch of engineering

that deals with the measurement and controlof different parameters.

• Instrumentation is defined as "the artand science of measurement and control".

• Measuring is used to monitor a process oroperation

• Instrumentation is a branch of engineeringthat deals with the measurement and controlof different parameters.

• Instrumentation is defined as "the artand science of measurement and control".

• Measuring is used to monitor a process oroperation

UNIT 1

Objectives ofEngineering Measurement

Objectives ofEngineering Measurement

Objectives• At the end of this Unit

Basic measuring systemPerformance characteristics of

instrumentsErrors in measurementUnits-Dimensions Standards.Instrument calibration.

• At the end of this Unit

Basic measuring systemPerformance characteristics of

instrumentsErrors in measurementUnits-Dimensions Standards.Instrument calibration.

Objectives Of Engineering Measurements

1. Measurements of system parameterinformation.

2. Automatic control of a system.

3. Simulation.

4. Experimental design.

5. To perform various manipulation.

6. Testing of materials and quality control.

7. Verification of scientific theories.

1. Measurements of system parameterinformation.

2. Automatic control of a system.

3. Simulation.

4. Experimental design.

5. To perform various manipulation.

6. Testing of materials and quality control.

7. Verification of scientific theories.

Basic Measuring System• A measurement assigns a specific value to a

physical variable. The physical variable nowbecomes the measured variable.

• A measurement system is a tool used to measurethe physical variable.

• Methods of measurement can be classified in totwo

• Direct methods– Un known quantity is directly compared against a

standard– Result is expressed as a numerical number

• In direct methods– In engineering application measurement systems

uses this methods

• A measurement assigns a specific value to aphysical variable. The physical variable nowbecomes the measured variable.

• A measurement system is a tool used to measurethe physical variable.

• Methods of measurement can be classified in totwo

• Direct methods– Un known quantity is directly compared against a

standard– Result is expressed as a numerical number

• In direct methods– In engineering application measurement systems

uses this methods

Simple measuring systemSignal conditioningelement

Data transelement

Data processingelement

Primary sensingelement

Transducer

Data display

Transducer

Data recording

Basic Measuring System• Four Parts of Measurement System

– Sensor-Transducer Stage– Signal Conditioning Stage– Output Stage

Sensor• The sensor is a physical element that uses some

natural phenomenon to sense the variable beingmeasured.

• The transducer changes this sensed informationinto a detectable signal form (electrical,mechanical, optical, etc.)

• A Transducer is a device which converts one formof energy into some other form of energy

• It is also known as 'Pickup Element'.

• The sensor is a physical element that uses somenatural phenomenon to sense the variable beingmeasured.

• The transducer changes this sensed informationinto a detectable signal form (electrical,mechanical, optical, etc.)

• A Transducer is a device which converts one formof energy into some other form of energy

• It is also known as 'Pickup Element'.

Sensor• Mainly Transducers can be classified into two types on

the basis of power supply required• Active Transducers• Passive Transducers.• Active transducers are those which does not requires

external power supply for their operation.• For example: Photo Voltage Cell, Piezo Electric Crystal,

Generator etc.• Passive Transducers: Passive Transducers are those

transducers which requires external power supply fortheir operation.

• For Example: Resistive, Inductive and CapacitiveTransducers.

• Mainly Transducers can be classified into two types onthe basis of power supply required

• Active Transducers• Passive Transducers.• Active transducers are those which does not requires

external power supply for their operation.• For example: Photo Voltage Cell, Piezo Electric Crystal,

Generator etc.• Passive Transducers: Passive Transducers are those

transducers which requires external power supply fortheir operation.

• For Example: Resistive, Inductive and CapacitiveTransducers.

Signal Conditioner

• Its role comes into play when the output oftransducer or primary sensing element is verylow. It is used to amplify or modify the incomingsignal from transducer according to outputrequirement.

• When noise is present in signal, filters need to beused to eliminate it.

• If the processor operates only on digital signal,A/D and D/A converters must be used at theinput and output of the processor

• In other words Signal Conditioning is done toimprove the quality of output of measurementsystem.

• Its role comes into play when the output oftransducer or primary sensing element is verylow. It is used to amplify or modify the incomingsignal from transducer according to outputrequirement.

• When noise is present in signal, filters need to beused to eliminate it.

• If the processor operates only on digital signal,A/D and D/A converters must be used at theinput and output of the processor

• In other words Signal Conditioning is done toimprove the quality of output of measurementsystem.

Signal Conditioner• This optional intermediate stage can be used to

increase

– The magnitude of the signal throughamplification,

– Remove portions of the signal through somefiltering technique,

– Provide mechanical or optical linkage betweenthe transducer and the output range.

• This optional intermediate stage can be used toincrease

– The magnitude of the signal throughamplification,

– Remove portions of the signal through somefiltering technique,

– Provide mechanical or optical linkage betweenthe transducer and the output range.

O/P stage• The output unit of a measurement system is

consists of a display and storage unit

• It is used to display or analyze the final outputof the measurement system.

• The examples of Output unit can be anyoutput device like CRO (Cathode RayOscilloscope) or XY recorder.

• The output unit of a measurement system isconsists of a display and storage unit

• It is used to display or analyze the final outputof the measurement system.

• The examples of Output unit can be anyoutput device like CRO (Cathode RayOscilloscope) or XY recorder.

ComparisonDigital Signal Analog Signal• Data Storage can be

easily done• Processing of digital

information is very easy• Will not interfere with

other signals, so lessaffected with Noise. Datatransmission quality isgood

• Repeaters are requiredfor long distancecommunication

• Difficult to store thesignal/information

• Processing of signal isdifficult

• Will interfere with othersignals, so affected withnoise. Transmissionquality is comparativelypoor

• Repeaters are notrequired

• Data Storage can beeasily done

• Processing of digitalinformation is very easy

• Will not interfere withother signals, so lessaffected with Noise. Datatransmission quality isgood

• Repeaters are requiredfor long distancecommunication

• Difficult to store thesignal/information

• Processing of signal isdifficult

• Will interfere with othersignals, so affected withnoise. Transmissionquality is comparativelypoor

• Repeaters are notrequired

Performance characteristics ofinstruments

JOBY JOHN 15

Performance characteristics ofinstruments

Performance characteristics of instruments

• A knowledge of the performancecharacteristics of an instrument is essential forselecting the most suitable instrument forspecific measuring jobs.

• Performance characteristics of an instrumentare mainly divided into two.

• Static characteristics• Dynamic characteristics

• A knowledge of the performancecharacteristics of an instrument is essential forselecting the most suitable instrument forspecific measuring jobs.

• Performance characteristics of an instrumentare mainly divided into two.

• Static characteristics• Dynamic characteristics

STATIC CHARACTERISTICS

• The set of criteria defined for the instrumentwhich are used to measure the quantities thatare varying slowly with time or constant is calledstatic characteristics.

• OR• The static characteristics of an instrument are

considered for instruments which are usedto measure an unvarying process condition.

• Some criteria will be set to for the measurementof quantities that are either constant or varyslowly is called static characteristics

• The set of criteria defined for the instrumentwhich are used to measure the quantities thatare varying slowly with time or constant is calledstatic characteristics.

• OR• The static characteristics of an instrument are

considered for instruments which are usedto measure an unvarying process condition.

• Some criteria will be set to for the measurementof quantities that are either constant or varyslowly is called static characteristics

STATIC CHARACTERISTICS

• All the static performance characteristics areobtained by one form or another of a processcalled calibration.

• It provides a opportunity to check the instrumentagainst a known standard and to find the errorsand accuracy.

• Calibration involves comparison of an instrumentwith either primary standard or a secondarystandard or an instrument with known accuracy

• All the static performance characteristics areobtained by one form or another of a processcalled calibration.

• It provides a opportunity to check the instrumentagainst a known standard and to find the errorsand accuracy.

• Calibration involves comparison of an instrumentwith either primary standard or a secondarystandard or an instrument with known accuracy

STATIC CHARACTERISTICS

• There are a number of related definitions (orcharacteristics) such as

• Accuracy & Precision• Sensitivity• Linearity & Hysteresis• Repeatability and Reproducibility• Resolution,• Drift,• Span

• Threshold etc.

• There are a number of related definitions (orcharacteristics) such as

• Accuracy & Precision• Sensitivity• Linearity & Hysteresis• Repeatability and Reproducibility• Resolution,• Drift,• Span

• Threshold etc.

STATIC CHARACTERISTICS

• Accuracy: The degree of exactness (closeness) ofa measurement compared to the expected (true)value.– It is expressed in terms of errors

• Static error = measured value – true value• Precision: A measure of the consistency or

reproducibility of measurements, i.e. successivereadings does not differ.– (Precision is the consistency of the instrument output

for a given value of input).– Accuracy can be improved by calibration but not

precision

• Accuracy: The degree of exactness (closeness) ofa measurement compared to the expected (true)value.– It is expressed in terms of errors

• Static error = measured value – true value• Precision: A measure of the consistency or

reproducibility of measurements, i.e. successivereadings does not differ.– (Precision is the consistency of the instrument output

for a given value of input).– Accuracy can be improved by calibration but not

precision

STATIC CHARACTERISTICS• Resolution: The smallest change in a measured

variable to which an instrument will respond.

• Sensitivity: The ratio of the change in output(response) of the instrument to a change of inputor measured variable.

• Drift : Gradual shift in the meassured value ,overan extended period, when there is no change ininput.

• Threshold: The minimum value of input forwhich the device just starts to respond

• Range/Span: The minimum and maximum value of quantity so that thedevice is capable of measuring

• Resolution: The smallest change in a measuredvariable to which an instrument will respond.

• Sensitivity: The ratio of the change in output(response) of the instrument to a change of inputor measured variable.

• Drift : Gradual shift in the meassured value ,overan extended period, when there is no change ininput.

• Threshold: The minimum value of input forwhich the device just starts to respond

• Range/Span: The minimum and maximum value of quantity so that thedevice is capable of measuring

STATIC CHARACTERISTICS

Repeatability: A measure of how well the output returns to a given value when thesame precise input is applied several times.

OrThe ability of an instrument to reproduce a certain set of reading within a givenaccuracy.

Linearity

• Input output relationship of a device must be lineari.e, Y= mx +C

• But practical systems shows small deviations from thelinear shape ( allowed within the specified limits)

Hysteresis• Input is increased from

negative value, outputincreases as indicated bycurve 1

• Then the input is steadilydecreased , output does notfollow the same path , butlag by a certain value asindicated by curve 2

• The difference between thetwo curves is calledHysterisis

• Input is increased fromnegative value, outputincreases as indicated bycurve 1

• Then the input is steadilydecreased , output does notfollow the same path , butlag by a certain value asindicated by curve 2

• The difference between thetwo curves is calledHysterisis

JOBY JOHN 24

DYNAMIC CHARACTERISTICS• The response of instruments or systems to dynamic

I/P s are also functions of time.

• Instruments rarely respond instantaneously tochanges in the measured variables

• Instead, they exhibit slowness or sluggishness due tosuch things as mass, thermal capacitance, fluidcapacitance or electric capacitance

• The response of instruments or systems to dynamicI/P s are also functions of time.

• Instruments rarely respond instantaneously tochanges in the measured variables

• Instead, they exhibit slowness or sluggishness due tosuch things as mass, thermal capacitance, fluidcapacitance or electric capacitance

DYNAMIC CHARACTERISTICS

The dynamic characteristics of an instrument are

• Speed of response

• Fidelity

• Time delay or lag

• Dynamic error

The dynamic characteristics of an instrument are

• Speed of response

• Fidelity

• Time delay or lag

• Dynamic error

DYNAMIC CHARACTERISTICS

• Speed of Response:

It is the ability of a system to respond to a suddenchanges in the input signal/quantity

• Fidelity:

It is the degree to which an instrument indicatesthe changes in the measured variable withoutdynamic error ( Indication of how much faithfullysystem responds to the changes in input).

• Speed of Response:

It is the ability of a system to respond to a suddenchanges in the input signal/quantity

• Fidelity:

It is the degree to which an instrument indicatesthe changes in the measured variable withoutdynamic error ( Indication of how much faithfullysystem responds to the changes in input).

DYNAMIC CHARACTERISTICS• Lag:

It is the retardation or delay in the response of aninstrument to changes in the measured variable.

Two types : Process lag(process) and Control lag(Instrument)

• Dynamic Error:It is the difference between the true values of a

quantity changing with time and the value indicatedby the instrument, if no static error is assumed.

• NOTE : The dynamic and transient behavior ofthe instrument is as important as the staticbehavior.

• Lag:It is the retardation or delay in the response of an

instrument to changes in the measured variable.Two types : Process lag(process) and Control lag

(Instrument)

• Dynamic Error:It is the difference between the true values of a

quantity changing with time and the value indicatedby the instrument, if no static error is assumed.

• NOTE : The dynamic and transient behavior ofthe instrument is as important as the staticbehavior.

DYNAMIC CHARACTERISTICS

Inputs used to study characteristics of a system areImpulse signalStep SignalRamp signalExponential signal (sinusoidal signal)

Transient ResponseResponse exhibited by the system suddenly after an input change

Steady State responseResponse exhibited by the system at infinite time after an input change

Inputs used to study characteristics of a system areImpulse signalStep SignalRamp signalExponential signal (sinusoidal signal)

Transient ResponseResponse exhibited by the system suddenly after an input change

Steady State responseResponse exhibited by the system at infinite time after an input change

Time Response of a System

• Peak TimeTime taken to reach the maximum overshoot

•Delay TimeTime taken to reach 50% of the final expected value at the first time

Time constantTime required to for the output to reach 63.2% of its final value

• Settling TimeTime taken for the output oscillations are died out completely or diminished

within the allowed limits• Rise Time

Time taken by the system to reach the desired value first time in the transientstage, when the input is changed from one state to another• Over shoot

Maximum deviation of the output from input in the transient stage.Percentage of overshoot = (Max. Overshoot/ Final expected value)*100

• Peak TimeTime taken to reach the maximum overshoot

•Delay TimeTime taken to reach 50% of the final expected value at the first time

Time constantTime required to for the output to reach 63.2% of its final value

• Settling TimeTime taken for the output oscillations are died out completely or diminished

within the allowed limits• Rise Time

Time taken by the system to reach the desired value first time in the transientstage, when the input is changed from one state to another• Over shoot

Maximum deviation of the output from input in the transient stage.Percentage of overshoot = (Max. Overshoot/ Final expected value)*100

Time Response of a System

JOBY JOHN 31

Error

JOBY JOHN 32

Error• Error is the difference between the true value of

the variable and the measured value.• Errors are classified as

1. Gross error /Human error (human mistakesand instrument malfunctions)

2. Random errors (Noise/Interference)

3. Systematic errors (which may be eitherconstant or variable)-Due to shortcoming of theinstruments

• Error is the difference between the true value ofthe variable and the measured value.

• Errors are classified as

1. Gross error /Human error (human mistakesand instrument malfunctions)

2. Random errors (Noise/Interference)

3. Systematic errors (which may be eitherconstant or variable)-Due to shortcoming of theinstruments

Random Errors

Associated to any measurement or electronicsignal we find random, non-deterministicvariations as the result of different sources:

• Electronic noise (Johnson, shot,..)• Interference• Even though interference is systematic ,for

the easiness of modeling, it can be renderedas random.

All the random sources are independent.

Associated to any measurement or electronicsignal we find random, non-deterministicvariations as the result of different sources:

• Electronic noise (Johnson, shot,..)• Interference• Even though interference is systematic ,for

the easiness of modeling, it can be renderedas random.

All the random sources are independent.

JOBY JOHN 34

Gross error

• Instrumentation misuse, calculation errors andother human mistakes (mistakes in reading,recording )are the main source of Gross errors.

• Gross error mainly occur due to carelessness orlack of experience of a human being or incorrectadjustments of instruments

• These errors can be minimized by– 1.Taking great care while taking reading, recordings

and calculating results.– 2. Taking multiple readings preferably by different

persons.

• Instrumentation misuse, calculation errors andother human mistakes (mistakes in reading,recording )are the main source of Gross errors.

• Gross error mainly occur due to carelessness orlack of experience of a human being or incorrectadjustments of instruments

• These errors can be minimized by– 1.Taking great care while taking reading, recordings

and calculating results.– 2. Taking multiple readings preferably by different

persons.

Systematic errors

A constant uniform deviation in the operationof an instrument is known as systematicerror.

• There are three types of systematic errors as– Instrumental errors– Environmental errors– Observational errors

A constant uniform deviation in the operationof an instrument is known as systematicerror.

• There are three types of systematic errors as– Instrumental errors– Environmental errors– Observational errors

Systematic ErrorsInstrumental errorsThese errors are mainly due to following three

reasons• Short-comings of instrumentThese are because of the mechanical structure of

the instruments eg. Friction in the bearings ofvarious moving parts, irregular spring tensions,hysteresis, gear backlash, variation in air gap etc.

• Ellimination.– Selecting proper instrument and the transducer for

the measurement.– Recognize the effect of such errors and apply the

proper correction factors.– Calibrate the instrument carefully against standard.

Instrumental errorsThese errors are mainly due to following three

reasons• Short-comings of instrumentThese are because of the mechanical structure of

the instruments eg. Friction in the bearings ofvarious moving parts, irregular spring tensions,hysteresis, gear backlash, variation in air gap etc.

• Ellimination.– Selecting proper instrument and the transducer for

the measurement.– Recognize the effect of such errors and apply the

proper correction factors.– Calibrate the instrument carefully against standard.

Systematic errorsINSTRUMENTAL ERRORS

• Misuse of instrumentA good instrument if used in abnormal way givesmisleading results.

Poor initial adjustments,Improper zero setting,Using leads of high resistance.Elimination: Use the instrument intelligently & Correctly• Loading effects

Loading effects due toImproper way of using the instrumentElimination: Use the instrument intelligently & Correctly

INSTRUMENTAL ERRORS• Misuse of instrument

A good instrument if used in abnormal way givesmisleading results.

Poor initial adjustments,Improper zero setting,Using leads of high resistance.Elimination: Use the instrument intelligently & Correctly• Loading effects

Loading effects due toImproper way of using the instrumentElimination: Use the instrument intelligently & Correctly

Systematic ErrorsObservational ErrorsError introduced by the observerFew souces are:• Parallax error while reading the meter,• wrong scale selection,• habits of individual obsever• EliminationUse the• instrument with mirrors,• instrument with knife edge pointers,• Instrument having digital display

Observational ErrorsError introduced by the observerFew souces are:• Parallax error while reading the meter,• wrong scale selection,• habits of individual obsever• EliminationUse the• instrument with mirrors,• instrument with knife edge pointers,• Instrument having digital display

Systematic ErrorsEnvironmental Errors (due to the External Conditions)• The various factors : Temperature changes,

Pressure, vibratons, Thermal emf., straycapacitance, cross capacitance, effect of Externalfields, Aging of equipments and Frequencysensitivity of an instrument.

Elimination• Using proper correction factors and using the

instrument Catalogue• Using Temperature & Pressure control methods

etc.• Reducing the effect of dust, humidity on the

components in the instruments.• The effects of external fields can be minimized by

using the magnetic or electrostatic shields ofscreens.

Environmental Errors (due to the External Conditions)• The various factors : Temperature changes,

Pressure, vibratons, Thermal emf., straycapacitance, cross capacitance, effect of Externalfields, Aging of equipments and Frequencysensitivity of an instrument.

Elimination• Using proper correction factors and using the

instrument Catalogue• Using Temperature & Pressure control methods

etc.• Reducing the effect of dust, humidity on the

components in the instruments.• The effects of external fields can be minimized by

using the magnetic or electrostatic shields ofscreens.

Error due to Other Factors

• Effect of the Time on Instruments

– There is a possibility of change in calibration errorin the instrument with time. This may be calledageing of the instrument.

• Mechanical ErrorFriction between stationary and rotating parts and

residual torsion in suspension wire cause errors ininstruments. So, checking should be applied.Generally, these errors may be checked from timeto time.

• Effect of the Time on Instruments

– There is a possibility of change in calibration errorin the instrument with time. This may be calledageing of the instrument.

• Mechanical ErrorFriction between stationary and rotating parts and

residual torsion in suspension wire cause errors ininstruments. So, checking should be applied.Generally, these errors may be checked from timeto time.

spectrum Analyzer

SPECTRUM ANALYZERS The problems associated with non-real-time analysis in the

frequency domain can be eliminated by using a spectrumanalyzer. A spectrum analyzer is a real-time analyzer, whichmeans that it simultaneously displays the ampli­tude of all thesignals in the frequency range of the analyzer.

Spectrum analyzers, like wave analyzers, provide informationabout the voltage or energy of a signal as a function offrequency. Unlike wave analyzers. spectrum analyzersprovide a graphical display on a CRT. A block diagram of anaudio spectrum analyzer is shown in Fig.7.

The problems associated with non-real-time analysis in thefrequency domain can be eliminated by using a spectrumanalyzer. A spectrum analyzer is a real-time analyzer, whichmeans that it simultaneously displays the ampli­tude of all thesignals in the frequency range of the analyzer.

Spectrum analyzers, like wave analyzers, provide informationabout the voltage or energy of a signal as a function offrequency. Unlike wave analyzers. spectrum analyzersprovide a graphical display on a CRT. A block diagram of anaudio spectrum analyzer is shown in Fig.7.

SPECTRUM ANALYZERS The problems associated with non-real-time analysis in the

frequency domain can be eliminated by using a spectrumanalyzer. A spectrum analyzer is a real-time analyzer, whichmeans that it simultaneously displays the ampli­tude of all thesignals in the frequency range of the analyzer. Spectrum analyzers, like wave analyzers, provide information

about the voltage or energy of a signal as a function offrequency. Unlike wave analyzers. spectrum analyzersprovide a graphical display on a CRT. A block diagram of anaudio spectrum analyzer is shown in Fig. 7.

The problems associated with non-real-time analysis in thefrequency domain can be eliminated by using a spectrumanalyzer. A spectrum analyzer is a real-time analyzer, whichmeans that it simultaneously displays the ampli­tude of all thesignals in the frequency range of the analyzer. Spectrum analyzers, like wave analyzers, provide information

about the voltage or energy of a signal as a function offrequency. Unlike wave analyzers. spectrum analyzersprovide a graphical display on a CRT. A block diagram of anaudio spectrum analyzer is shown in Fig. 7.

SPECTRUM ANALYZERS The real-time, or multichannel. analyzer is basically a set of

stagger-tuned bandpass filters connected through anelectronic scan switch to a CRT. The composite amplitude ofthe signal within each filters bandwidth is displayed as afunction of the overall frequency range of the filter. Therefore, the frequency range of the instrument is limited

by the number of filters and their bandwidth. The electronicswitch sequentially connects the filter outputs to the CRT.

The real-time, or multichannel. analyzer is basically a set ofstagger-tuned bandpass filters connected through anelectronic scan switch to a CRT. The composite amplitude ofthe signal within each filters bandwidth is displayed as afunction of the overall frequency range of the filter. Therefore, the frequency range of the instrument is limited

by the number of filters and their bandwidth. The electronicswitch sequentially connects the filter outputs to the CRT.

SPECTRUM ANALYZERS Horizontal deflection is obtained from the scan generator,

which has a saw tooth output that is synchronized with theelectronic switch.

Horizontal deflection is obtained from the scan generator,which has a saw tooth output that is synchronized with theelectronic switch.

Fig. 7 Block diagram of an audio spectrum analyzer.

SPECTRUM ANALYZERS Such analyzers are usually restricted to audio-frequency

applications and may employ as many as 32 filters. Thebandwidth of each filter is generally made very narrow forgood resolution. The relationship between a time-domain presentation on the

CRT of an oscilloscope and a frequency-domain presentationon the CRT of a spectrum analyzer is shown in the three-dimensional drawing in Fig8.

Such analyzers are usually restricted to audio-frequencyapplications and may employ as many as 32 filters. Thebandwidth of each filter is generally made very narrow forgood resolution. The relationship between a time-domain presentation on the

CRT of an oscilloscope and a frequency-domain presentationon the CRT of a spectrum analyzer is shown in the three-dimensional drawing in Fig8.

SPECTRUM ANALYZERS Figure.8a shows a fundamental frequency f1 and its second

harmonic 2f1. An oscillo­scope used to display the signal inthe time-amplitude domain would display only onewaveform-the composite of f1 + 2f1 as shown in Fig. 8b. A spec­trum analyzer used to display the components of the

composite signal in the frequency-amplitude domain wouldclearly display the amplitude of both the fundamentalfrequency f1 and its second harmonic 2f1 as shown in Fig.8c.

Figure.8a shows a fundamental frequency f1 and its secondharmonic 2f1. An oscillo­scope used to display the signal inthe time-amplitude domain would display only onewaveform-the composite of f1 + 2f1 as shown in Fig. 8b. A spec­trum analyzer used to display the components of the

composite signal in the frequency-amplitude domain wouldclearly display the amplitude of both the fundamentalfrequency f1 and its second harmonic 2f1 as shown in Fig.8c.

SPECTRUM ANALYZERSSpectrum analyzers are used to obtain a wide variety of

information from various kinds of signals, including thefollowing. Spectral purity of continuous-wave (CW) signals. Percentage of modulation of amplitude-modulated (AM)

signals. Deviation of frequency-modulated (FM) signals. Noise such as impulse and random noise. Filter frequency response.

Spectrum analyzers are used to obtain a wide variety ofinformation from various kinds of signals, including thefollowing. Spectral purity of continuous-wave (CW) signals. Percentage of modulation of amplitude-modulated (AM)

signals. Deviation of frequency-modulated (FM) signals. Noise such as impulse and random noise. Filter frequency response.

SPECTRUM ANALYZERS

Fig.10 Three-dimensional relationship between time, frequency, and amplitude. (Courtesy Hewlett-Packard, Company.)

SPECTRUM ANALYZERS

Fig. 11 Test setup to measure the total harmonic distor­tion of an amplifies.

SPECTRUM ANALYZERS

waveform is applied to the amplifier. The output of the amplifier isapplied directly to the distortion analyzer which measures thetotal harmonic distortion.

In the field of microwave communications, in which pulsedoscillators are widely used. spectrum analyzers are an importanttool. They also find wide application in analyzing the performanceof AM and FM transmitters.

Spectrum analyzers and Fourier analyzers are widely used inapplications requiring very low frequencies in the fields ofbiomedical electronics, geolog­ical surveying. and oceanography.They are also used in analyzing air and water pollution.

waveform is applied to the amplifier. The output of the amplifier isapplied directly to the distortion analyzer which measures thetotal harmonic distortion.

In the field of microwave communications, in which pulsedoscillators are widely used. spectrum analyzers are an importanttool. They also find wide application in analyzing the performanceof AM and FM transmitters.

Spectrum analyzers and Fourier analyzers are widely used inapplications requiring very low frequencies in the fields ofbiomedical electronics, geolog­ical surveying. and oceanography.They are also used in analyzing air and water pollution.

SPECTRUM ANALYZERS

Another very important application of spectrum analyzers is themeasure­ment of intermodulation distortion. This phenomenonoccurs when two or more signals are applied to the input of anonlinear circuit such as an amplifier. particularly a poweramplifier. This problem is particularly trouble­some in thereproduction of music.

If these signals are applied to a completely linear circuit. eachpasses through the circuit unaffected by the other. However, ifthere is nonlinearity in the circuit. heterodyning of the signalsoccurs.

Another very important application of spectrum analyzers is themeasure­ment of intermodulation distortion. This phenomenonoccurs when two or more signals are applied to the input of anonlinear circuit such as an amplifier. particularly a poweramplifier. This problem is particularly trouble­some in thereproduction of music.

If these signals are applied to a completely linear circuit. eachpasses through the circuit unaffected by the other. However, ifthere is nonlinearity in the circuit. heterodyning of the signalsoccurs.

SPECTRUM ANALYZERS Limiting our discussion to two signals. we find that

heterodyning occurs because the lower-frequency signaltends to modulate the higher-frequency signal.

SPECTRUM ANALYZERS If f1, and f2 are the fundamental frequencies of the input

signals. the output spectrum may contain any or all of thefrequencies shown in Fig.12, as well as other harmonics.

Fig. 12 Some of the harmonics of f1 and f2 produced by amplifier nonlinearity.

SPECTRUM ANALYZERS

Fig. 13 Amplitude-modulated waveform pro­duced by intermodulation distortion.

SPECTRUM ANALYZERS If the nonlinearity of the circuit is significant. the modulation of

the higher-frequency signal by the lower-frequency signal willproduce the familiar amplitude modulation waveform as shown inFig13. The per­centage of intermodulation distortion is computedas

whereIMD = the intermodulation distortion expressed as a percentageM = the peak-to-peak modulated signalm = the minimum value of the modulated waveform

If the nonlinearity of the circuit is significant. the modulation ofthe higher-frequency signal by the lower-frequency signal willproduce the familiar amplitude modulation waveform as shown inFig13. The per­centage of intermodulation distortion is computedas

whereIMD = the intermodulation distortion expressed as a percentageM = the peak-to-peak modulated signalm = the minimum value of the modulated waveform

%100xmM

mMIMD

SPECTRUM ANALYZERS The spectrum analyzer can be used to measure the

intermodulation distor­tion, as shown in the circuit in Fig14.The frequency of the audio oscillator is generally set to

6 kHz.

Fig.14 Using the spectrum analyzer to measure intermodulation dis­tortion.

Chapter 14

Electronic InstrumentsDr.Debashis DeAssociate ProfessorWest Bengal University of Technology

Contents:

14-1 Introduction 14-2 Components of the Cathode-Ray Oscilloscope 14-3 Cathode-Ray Tube 14-4 Time-Base Generators 14-5 Measurements Using the Cathode-Ray Oscilloscope 14-6 Types of Cathode-Ray Oscilloscopes 14-7 Sweep Frequency Generator 14-8 Function Generator 14-9 Sine Wave Generator 14-10 Square Wave Generator 14-11 AF Signal Generator

14-1 Introduction 14-2 Components of the Cathode-Ray Oscilloscope 14-3 Cathode-Ray Tube 14-4 Time-Base Generators 14-5 Measurements Using the Cathode-Ray Oscilloscope 14-6 Types of Cathode-Ray Oscilloscopes 14-7 Sweep Frequency Generator 14-8 Function Generator 14-9 Sine Wave Generator 14-10 Square Wave Generator 14-11 AF Signal Generator

Objectives: This final chapter discusses the key instruments of electronic

measurement with special emphasis on the most versatile instrument ofelectronic measurement—the cathode-ray oscilloscope (CRO).

The objective of this book will remain unrealized without adiscussion on the CRO.

The chapter begins with the details of construction of theCRO, and proceeds to examine the active and passive mode input–outputwaveforms for filter circuits and lead-lag network delay.

This will be followed by a detailed study of the dual beamCRO and its uses in op-amp circuit integrator, differentiator, inverting andnon-inverting circuits, comparative waveform study, and accuratemeasurement with impeccable visual display.

In addition to the CRO, the chapter also examines the sweepfrequency generator, the function generator, the sine wave generator, thesquare wave generator and the AF signal generator.

This final chapter discusses the key instruments of electronicmeasurement with special emphasis on the most versatile instrument ofelectronic measurement—the cathode-ray oscilloscope (CRO).

The objective of this book will remain unrealized without adiscussion on the CRO.

The chapter begins with the details of construction of theCRO, and proceeds to examine the active and passive mode input–outputwaveforms for filter circuits and lead-lag network delay.

This will be followed by a detailed study of the dual beamCRO and its uses in op-amp circuit integrator, differentiator, inverting andnon-inverting circuits, comparative waveform study, and accuratemeasurement with impeccable visual display.

In addition to the CRO, the chapter also examines the sweepfrequency generator, the function generator, the sine wave generator, thesquare wave generator and the AF signal generator.

INTRODUCTION: The cathode-ray oscilloscope (CRO) is a

multipurpose display instrument used for the observation,measurement , and analysis of waveforms by plotting amplitude alongy-axis and time along x-axis.

CRO is generally an x-y plotter; on a single screen it candisplay different signals applied to different channels. It can measureamplitude, frequencies and phase shift of various signals. Manyphysical quantities like temperature, pressure

and strain can be converted into electrical signals by the use oftransducers, and the signals can be displayed on the CRO.

A moving luminous spot over the screen displays thesignal. CROs are used to study waveforms, and other time-varyingphenomena from very low to very high frequencies.

The central unit of the oscilloscope is the cathode-ray tube (CRT), and the remaining part of the CRO consists of thecircuitry required to operate the cathode-ray tube.

The cathode-ray oscilloscope (CRO) is amultipurpose display instrument used for the observation,measurement , and analysis of waveforms by plotting amplitude alongy-axis and time along x-axis.

CRO is generally an x-y plotter; on a single screen it candisplay different signals applied to different channels. It can measureamplitude, frequencies and phase shift of various signals. Manyphysical quantities like temperature, pressure

and strain can be converted into electrical signals by the use oftransducers, and the signals can be displayed on the CRO.

A moving luminous spot over the screen displays thesignal. CROs are used to study waveforms, and other time-varyingphenomena from very low to very high frequencies.

The central unit of the oscilloscope is the cathode-ray tube (CRT), and the remaining part of the CRO consists of thecircuitry required to operate the cathode-ray tube.

Block diagram of a cathode-rayoscilloscope:

COMPONENTS OF THE CATHODE-RAY OSCILLOSCOPE:

The CRO consists of the following: (i) CRT (ii) Vertical amplifier (iii) Delay line (iv) Horizontal amplifier (v) Time-base generator (vi) Triggering circuit (vii) Power supply

The CRO consists of the following: (i) CRT (ii) Vertical amplifier (iii) Delay line (iv) Horizontal amplifier (v) Time-base generator (vi) Triggering circuit (vii) Power supply

CATHODE-RAY TUBE: The electron gun or electron emitter, the deflecting system

and the fluorescent screen are the three major components of a generalpurpose CRT. A detailed diagram of the cathode-ray oscilloscope is given in Fig. 14-2.

Electron Gun:

In the electron gun of the CRT, electrons are emitted, converted into asharp beam and focused upon the fluorescent screen.

The electron beam consists of an indirectly heated cathode, a controlgrid, an accelerating electrode and a focusing anode.

The electrodes are connected to the base pins. The cathode emitting theelectrons is surrounded by a control grid with a fine hole at its centre.

The accelerated electron beam passes through the fine hole. The negative voltage at the control grid controls the flow of electrons

in the electron beam, and consequently, the brightness of the spot on the CROscreen is controlled.

In the electron gun of the CRT, electrons are emitted, converted into asharp beam and focused upon the fluorescent screen.

The electron beam consists of an indirectly heated cathode, a controlgrid, an accelerating electrode and a focusing anode.

The electrodes are connected to the base pins. The cathode emitting theelectrons is surrounded by a control grid with a fine hole at its centre.

The accelerated electron beam passes through the fine hole. The negative voltage at the control grid controls the flow of electrons

in the electron beam, and consequently, the brightness of the spot on the CROscreen is controlled.

Deflection Systems: Electrostatic deflection of an electron beam is used in a

general purpose oscilloscope. The deflecting system consists of apair of horizontal and vertical deflecting plates. Let us consider two parallel vertical deflecting plates

P1 and P2. The beam is focused at point O on the screen in the absenceof a deflecting plate voltage.

If a positive voltage is applied to plate P1 with respect toplate P2, the negatively charged electrons are attracted towards thepositive plate P1, and these electrons will come to focus at point Y1 onthe fluorescent screen.

Electrostatic deflection of an electron beam is used in ageneral purpose oscilloscope. The deflecting system consists of apair of horizontal and vertical deflecting plates. Let us consider two parallel vertical deflecting plates

P1 and P2. The beam is focused at point O on the screen in the absenceof a deflecting plate voltage.

If a positive voltage is applied to plate P1 with respect toplate P2, the negatively charged electrons are attracted towards thepositive plate P1, and these electrons will come to focus at point Y1 onthe fluorescent screen.

Deflection Systems:The deflection is proportional to the deflecting voltage between the plates. If the polarity

of the deflecting voltage is reversed, the spot appears at the point Y2, as shown in Fig. 14-3(a).

Deflection Systems:

To deflect the beam horizontally, an alternating voltage is applied to the horizontaldeflecting plates and the spot on the screen horizontally, as shown in Fig. 14-3(b).

The electrons will focus at point X2. By changing the polarity of voltage, the beam will focus atpoint X1. Thus, the horizontal movement is controlled along X1OX2 line.

Spot Beam Deflection Sensitivity:

Electrostatic Deflection:

Electrostatic Deflection:

Electrostatic Deflection:

Electrostatic Deflection:

Fluorescent Screen: Phosphor is used as screen material on the inner

surface of a CRT. Phosphor absorbs the energy of the incidentelectrons. The spot of light is produced on the screen where theelectron beam hits. The bombarding electrons striking the screen, release

secondary emission electrons. These electrons are collected ortrapped by an aqueous solution of graphite called “Aquadag”which is connected to the second anode. Collection of the secondary electrons is necessary to

keep the screen in a state of electrical equilibrium. The type of phosphor used, determines the color of

the light spot. The brightest available phosphor isotope, P31,produces yellow–green light with relative luminance of 99.99%.

Phosphor is used as screen material on the innersurface of a CRT. Phosphor absorbs the energy of the incidentelectrons. The spot of light is produced on the screen where theelectron beam hits. The bombarding electrons striking the screen, release

secondary emission electrons. These electrons are collected ortrapped by an aqueous solution of graphite called “Aquadag”which is connected to the second anode. Collection of the secondary electrons is necessary to

keep the screen in a state of electrical equilibrium. The type of phosphor used, determines the color of

the light spot. The brightest available phosphor isotope, P31,produces yellow–green light with relative luminance of 99.99%.

Display waveform on the screen:Figure 14-5(a) shows a sine wave applied to vertical deflecting plates and a repetitive ramp or

saw-tooth applied to the horizontal plates.

The ramp waveform at the horizontal plates causes the electron beam to be deflectedhorizontally across the screen.

If the waveforms are perfectly synchronized then the exact sine wave applied to the verticaldisplay appears on the CRO display screen.

Triangular waveform: Similarly the display of the triangular waveform is as shown in Fig. 14-5(b).

TIME-BASE GENERATORS: The CRO is used to display a waveform that varies as a function of time. If the wave form is to

be accurately reproduced, the beam should have a constant horizontal velocity.

As the beam velocity is a function of the deflecting voltage, the deflecting voltage must increaselinearly with time.

A voltage with such characteristics is called a ramp voltage. If the voltage decreases rapidly tozero—with the waveform repeatedly produced, as shown in Fig. 14-6—we observe a pattern which isgenerally called a saw-tooth waveform.

The time taken to return to its initial value is known as flyback or return time.

The CRO is used to display a waveform that varies as a function of time. If the wave form is tobe accurately reproduced, the beam should have a constant horizontal velocity.

As the beam velocity is a function of the deflecting voltage, the deflecting voltage must increaselinearly with time.

A voltage with such characteristics is called a ramp voltage. If the voltage decreases rapidly tozero—with the waveform repeatedly produced, as shown in Fig. 14-6—we observe a pattern which isgenerally called a saw-tooth waveform.

The time taken to return to its initial value is known as flyback or return time.

Simple saw-tooth generator &associated waveforms: The circuit shown in Fig. 14-7(a) is a simple sweep circuit, in which the capacitor C

charges through the resistor R.

The capacitor discharges periodically through the transistor T1, which causes the waveform shownin Fig. 14-7(b) to appear across the capacitor.

The signal voltage, Vi which must be applied to the base of the transistor to turn it ON forshort time intervals is also shown in Fig. 14-7(b).

Time-base generator using UJT: The continuous sweep CRO uses the UJT as a time-base generator. When power is first

applied to the UJT, it is in the OFF state and CT changes exponentially through RT .

The UJT emitter voltage VE rises towards VBB and VE reaches the plate voltage VP.

The emitter-to-base diode becomes forward biased and the UJT triggers ON. Thisprovides a low resistance discharge path and the capacitor discharges rapidly.

When the emitter voltage VE reaches the minimum value rapidly, the UJT goes OFF. Thecapacitor recharges and the cycles repeat.

To improve the sweep linearity, twoseparate voltage supplies are used; a low voltagesupply for the UJT and a high voltage supply for theRTCT circuit. This circuit is as shown in Fig. 14-7(c).

RT is used for continuous control offrequency within a range and CT is varied orchanged in steps. They are sometimes known astiming resistor and timing capacitor.

Oscilloscope Amplifiers: The purpose of an oscilloscope is to produce a faithful representation of the signals applied to its

input terminals.

Considerable attention has to be paid to the design of these amplifiers for this purpose. Theoscillographic amplifiers can be classified into two major categories.

(i) AC-coupled amplifiers

(ii) DC-coupled amplifiers

The low-cost oscilloscopes generally use ac-coupled amplifiers. The ac amplifiers, used inoscilloscopes, are required for laboratory purposes. The dc-coupled amplifiers are quite expensive. They

offer the advantage of responding to dc voltages, so it is possible to measure dc voltages as pure signals

and ac signals superimposed upon the dc signals.

DC-coupled amplifiers have another advantage. They eliminate the problems of low-frequencyphase shift and waveform distortion while observing low-frequency pulse train.

The amplifiers can be classified according to bandwidth use also:

(i) Narrow-bandwidth amplifiers

(ii) Broad-bandwidth amplifiers

The purpose of an oscilloscope is to produce a faithful representation of the signals applied to itsinput terminals.

Considerable attention has to be paid to the design of these amplifiers for this purpose. Theoscillographic amplifiers can be classified into two major categories.

(i) AC-coupled amplifiers

(ii) DC-coupled amplifiers

The low-cost oscilloscopes generally use ac-coupled amplifiers. The ac amplifiers, used inoscilloscopes, are required for laboratory purposes. The dc-coupled amplifiers are quite expensive. They

offer the advantage of responding to dc voltages, so it is possible to measure dc voltages as pure signals

and ac signals superimposed upon the dc signals.

DC-coupled amplifiers have another advantage. They eliminate the problems of low-frequencyphase shift and waveform distortion while observing low-frequency pulse train.

The amplifiers can be classified according to bandwidth use also:

(i) Narrow-bandwidth amplifiers

(ii) Broad-bandwidth amplifiers

Vertical Amplifiers: Vertical amplifiers determines the sensitivity and bandwidth of an oscilloscope.

Sensitivity, which is expressed in terms of V/cm of vertical deflection at the mid-bandfrequency.

The gain of the vertical amplifier determines the smallest signal that theoscilloscope can satisfactorily measure by reproducing it on the CRT screen.

The sensitivity of an oscilloscope is directly proportional to the gain of the verticalamplifier. So, as the gain increases the sensitivity also increases.

The vertical sensitivity measures how much the electron beam will be deflectedfor a specified input signal. The CRT screen is covered with a plastic grid pattern called agraticule.

The spacing between the grids lines is typically 10 mm. Vertical sensitivity isgenerally expressed in volts per division.

The vertical sensitivity of an oscilloscope measures the smallest deflection factorthat can be selected with the rotary switch.

Vertical amplifiers determines the sensitivity and bandwidth of an oscilloscope.Sensitivity, which is expressed in terms of V/cm of vertical deflection at the mid-bandfrequency.

The gain of the vertical amplifier determines the smallest signal that theoscilloscope can satisfactorily measure by reproducing it on the CRT screen.

The sensitivity of an oscilloscope is directly proportional to the gain of the verticalamplifier. So, as the gain increases the sensitivity also increases.

The vertical sensitivity measures how much the electron beam will be deflectedfor a specified input signal. The CRT screen is covered with a plastic grid pattern called agraticule.

The spacing between the grids lines is typically 10 mm. Vertical sensitivity isgenerally expressed in volts per division.

The vertical sensitivity of an oscilloscope measures the smallest deflection factorthat can be selected with the rotary switch.

Frequency response: The bandwidth of an oscilloscope detects the range of frequencies that can be

accurately reproduced on the CRT screen. The greater the bandwidth, the wider is the range ofobserved frequencies.

The bandwidth of an oscilloscope is the range of frequencies over which the gainof the vertical amplifier stays within 3 db of the mid-band frequency gain, as shown in Fig. 14-8.

Rise time is defined as the time required for the edge to rise from 10–90% of itsmaximum amplitude. An approximate relation is given as follows:

MEASUREMENTS USING THE CATHODE-RAY OSCILLOSCOPE:

1) Measurement of Frequency:

MEASUREMENTS USING THE CATHODE-RAY OSCILLOSCOPE:

2) Measurement of Phase:

3 Measurement of Phase Using Lissajous Figures:

Measurement of Phase Using Lissajous Figures:

Measurement of Phase Using Lissajous Figures:

Measurement of Phase Using Lissajous Figures:

Measurement of Phase Using Lissajous Figures:

TYPES OF THE CATHODE-RAY OSCILLOSCOPES: The categorization of CROs is done on the basis of whether they are digital

or analog. Digital CROs can be further classified as storage oscilloscopes. 1. Analog CRO: In an analog CRO, the amplitude, phase and frequency are

measured from the displayed waveform, through direct manual reading. 2. Digital CRO: A digital CRO offers digital read-out of signal information, i.e., the

time, voltage or frequency along with signal display. It consists of an electronic counteralong with the main body of the CRO.

3. Storage CRO: A storage CRO retains the display up to a substantial amount oftime after the first trace has appeared on the screen. The storage CRO is also useful forthe display of waveforms of low-frequency signals.

4. Dual-Beam CRO: In the dual-beam CRO two electron beams fall on a single CRT.The dual-gun CRT generates two different beams.

These two beams produce two spots of light on the CRTscreen which make the simultaneous observation of two different signal waveformspossible. The comparison of input and its corresponding output becomes easier usingthe dual-beam CRO.

The categorization of CROs is done on the basis of whether they are digitalor analog. Digital CROs can be further classified as storage oscilloscopes.

1. Analog CRO: In an analog CRO, the amplitude, phase and frequency aremeasured from the displayed waveform, through direct manual reading.

2. Digital CRO: A digital CRO offers digital read-out of signal information, i.e., thetime, voltage or frequency along with signal display. It consists of an electronic counteralong with the main body of the CRO.

3. Storage CRO: A storage CRO retains the display up to a substantial amount oftime after the first trace has appeared on the screen. The storage CRO is also useful forthe display of waveforms of low-frequency signals.

4. Dual-Beam CRO: In the dual-beam CRO two electron beams fall on a single CRT.The dual-gun CRT generates two different beams.

These two beams produce two spots of light on the CRTscreen which make the simultaneous observation of two different signal waveformspossible. The comparison of input and its corresponding output becomes easier usingthe dual-beam CRO.

SWEEP FREQUENCY GENERATOR: A sweep frequency generator is a signal

generator which can automatically vary its frequencysmoothly and continuously over an entire frequencyrange. Figure 14-15 shows the basic block diagram of asweep frequency generator.

The sweep frequency generator has the rampgenerator and the voltage-tuned oscillator as its basiccomponents.

Applications of the Sweep Frequency Generator:

FUNCTION GENERATOR: The basic components of a function generator are:

(i) Integrator

(ii) Schmitt trigger circuit

(iii) Sine wave converter

(iv) Attenuator

SINE WAVE GENERATOR: A sine wave is produced by converting a triangular wave, applying proper circuits. The

triangular wave is produced by employing an integrator and a Schmitt trigger circuit.

This triangular wave is then converted to a sine wave using the diode loading circuit ,as shownin Fig. 14-19. Resistors R1 and R2 behave as the voltage divider. When VR2 exceeds V1, the diode D1 becomes forward-biased.

There is more attenuation of the output voltage levels above V1 than levels below V1. With thepresence of the diode D1 and resistor R3 in the circuit, the output voltage rises less steeply.

The output voltage falls below V1 and the diode stops conducting, as it is in reverse-bias. The circuitbehaves as a simple voltage-divider circuit. This is also true for the negative half-cycle of the input Vi . If R3 iscarefully chosen to be the same as R4 , the negative and the positive cycles of the output voltage will be the same. Theoutput is an approximate sine wave.

A sine wave is produced by converting a triangular wave, applying proper circuits. Thetriangular wave is produced by employing an integrator and a Schmitt trigger circuit.

This triangular wave is then converted to a sine wave using the diode loading circuit ,as shownin Fig. 14-19. Resistors R1 and R2 behave as the voltage divider. When VR2 exceeds V1, the diode D1 becomes forward-biased.

There is more attenuation of the output voltage levels above V1 than levels below V1. With thepresence of the diode D1 and resistor R3 in the circuit, the output voltage rises less steeply.

The output voltage falls below V1 and the diode stops conducting, as it is in reverse-bias. The circuitbehaves as a simple voltage-divider circuit. This is also true for the negative half-cycle of the input Vi . If R3 iscarefully chosen to be the same as R4 , the negative and the positive cycles of the output voltage will be the same. Theoutput is an approximate sine wave.

SINE WAVE GENERATOR:

The approximation may be further improved by employinga six-level diode loading circuit, as shown in Fig. 14-20(a).

SINE WAVE GENERATOR: The circuit is adjusted by comparing a 1 kHz sine wave and the output of the

triangular/sine wave converter on a dual-track CRO. R1, R2, R3 and the peak amplitude of Ei areadjusted in sequence for the best sinusoidal shape.

CIRCUIT DIAGRAM OF SINE WAVE GENERATOR:

SQUARE WAVE GENERATOR A square wave can be most easily obtained from an operational amplifier astable

multi-vibrator. An astable multi-vibrator has no stable state—the output oscillates continuouslybetween high and low states.

In Fig. 14-21, the block comprising the op-amp, resistors R2 and R3 constitutes aSchmitt trigger circuit. The capacitor C1 gets charged through the resistor R1. When the voltage of thecapacitor reaches the upper trigger point of the Schmitt trigger circuit, the output of the op-ampswitches to output low. This is because the Schmitt trigger is a non-inverting type. Now, when theop-amp output is low, the capacitor C1 starts getting discharged.

SQUARE WAVE GENERATOR: As the capacitor discharges and the capacitor voltage reaches the lower

trigger point of the Schmitt trigger, the output of the op-amp switches back to theoutput high state.

The capacitor charges through the resistor again and the next cyclebegins. The process is repetitive and produces a square wave at the output.

The frequency of the output square wave depends on the time taken bythe capacitor to get charged and discharged when the capacitor voltage varies fromUTP (upper trigger point) and LTP (lower trigger point).

As the capacitor discharges and the capacitor voltage reaches the lowertrigger point of the Schmitt trigger, the output of the op-amp switches back to theoutput high state.

The capacitor charges through the resistor again and the next cyclebegins. The process is repetitive and produces a square wave at the output.

The frequency of the output square wave depends on the time taken bythe capacitor to get charged and discharged when the capacitor voltage varies fromUTP (upper trigger point) and LTP (lower trigger point).

AF SIGNAL GENERATOR:

POINTS TO REMEMBER:

1. CRO is used to study waveforms.

2. CRT is the main component of a CRO.

3. Prosperous P31 is used for the fluorescent screen of a CRO.

4. A CRO has the following components:

(a) Electron gun

(b) Deflecting system

(c) Florescent screen

5. Lissajous figures are used to measure frequency and phase of the waves under study.

6. A time-base generator produces saw-tooth voltage.

7. An oscilloscope amplifier is used to provide a faithful representation of input signalapplied to its input terminals.

1. CRO is used to study waveforms.

2. CRT is the main component of a CRO.

3. Prosperous P31 is used for the fluorescent screen of a CRO.

4. A CRO has the following components:

(a) Electron gun

(b) Deflecting system

(c) Florescent screen

5. Lissajous figures are used to measure frequency and phase of the waves under study.

6. A time-base generator produces saw-tooth voltage.

7. An oscilloscope amplifier is used to provide a faithful representation of input signalapplied to its input terminals.

IMPORTANT FORMULAE:

TRANSDUCERSTRANSDUCERS

INTRODUCTION OF TRANSDUCERS

• A transducer is a device that convert one form of energyto other form. It converts the measurand to a usableelectrical signal.

• In other word it is a device that is capable of convertingthe physical quantity into a proportional electricalquantity such as voltage or current.

• A transducer is a device that convert one form of energyto other form. It converts the measurand to a usableelectrical signal.

• In other word it is a device that is capable of convertingthe physical quantity into a proportional electricalquantity such as voltage or current.

Pressure Voltage

BLOCK DIAGRAM OF TRANSDUCERS

• Transducer contains two parts that are closely related toeach other i.e. the sensing element and transductionelement.

• The sensing element is called as the sensor. It is deviceproducing measurable response to change in physicalconditions.

• The transduction element convert the sensor output tosuitable electrical form.

• Transducer contains two parts that are closely related toeach other i.e. the sensing element and transductionelement.

• The sensing element is called as the sensor. It is deviceproducing measurable response to change in physicalconditions.

• The transduction element convert the sensor output tosuitable electrical form.

CHARACTERISTICS OF TRANSDUCERS

1. Ruggedness2. Linearity3. Repeatability4. Accuracy5. High stability and reliability6. Speed of response7. Sensitivity8. Small size

1. Ruggedness2. Linearity3. Repeatability4. Accuracy5. High stability and reliability6. Speed of response7. Sensitivity8. Small size

TRANSDUCERS SELECTION FACTORS1. Operating Principle: The transducer are many times selected

on the basis of operating principle used by them. The operatingprinciple used may be resistive, inductive, capacitive ,optoelectronic, piezo electric etc.

2. Sensitivity: The transducer must be sensitive enough toproduce detectable output.

3. Operating Range: The transducer should maintain the rangerequirement and have a good resolution over the entire range.

4. Accuracy: High accuracy is assured.5. Cross sensitivity: It has to be taken into account when

measuring mechanical quantities. There are situation where theactual quantity is being measured is in one plane and thetransducer is subjected to variation in another plan.

6. Errors: The transducer should maintain the expected input-output relationship as described by the transfer function so asto avoid errors.

1. Operating Principle: The transducer are many times selectedon the basis of operating principle used by them. The operatingprinciple used may be resistive, inductive, capacitive ,optoelectronic, piezo electric etc.

2. Sensitivity: The transducer must be sensitive enough toproduce detectable output.

3. Operating Range: The transducer should maintain the rangerequirement and have a good resolution over the entire range.

4. Accuracy: High accuracy is assured.5. Cross sensitivity: It has to be taken into account when

measuring mechanical quantities. There are situation where theactual quantity is being measured is in one plane and thetransducer is subjected to variation in another plan.

6. Errors: The transducer should maintain the expected input-output relationship as described by the transfer function so asto avoid errors.

Contd.7. Transient and frequency response : The transducer should meet

the desired time domain specification like peak overshoot, risetime, setting time and small dynamic error.

8. Loading Effects: The transducer should have a high inputimpedance and low output impedance to avoid loading effects.

9. Environmental Compatibility: It should be assured that thetransducer selected to work under specified environmentalconditions maintains its input- output relationship and does notbreak down.

10. Insensitivity to unwanted signals: The transducer should beminimally sensitive to unwanted signals and highly sensitive todesired signals.

7. Transient and frequency response : The transducer should meetthe desired time domain specification like peak overshoot, risetime, setting time and small dynamic error.

8. Loading Effects: The transducer should have a high inputimpedance and low output impedance to avoid loading effects.

9. Environmental Compatibility: It should be assured that thetransducer selected to work under specified environmentalconditions maintains its input- output relationship and does notbreak down.

10. Insensitivity to unwanted signals: The transducer should beminimally sensitive to unwanted signals and highly sensitive todesired signals.

CLASSIFICATION OF TRANSDUCERS

The transducers can be classified as:

I. Active and passive transducers.II. Analog and digital transducers.III. On the basis of transduction principle used.IV. Primary and secondary transducerV. Transducers and inverse transducers.

The transducers can be classified as:

I. Active and passive transducers.II. Analog and digital transducers.III. On the basis of transduction principle used.IV. Primary and secondary transducerV. Transducers and inverse transducers.

• Active transducers :

• These transducers do not need any external source of powerfor their operation. Therefore they are also called as selfgenerating type transducers.

I. The active transducer are self generating devices whichoperate under the energy conversion principle.

II. As the output of active transducers we get an equivalentelectrical output signal e.g. temperature or strain to electricpotential, without any external source of energy being used.

ACTIVE AND PASSIVE TRANSDUCERS

• Active transducers :

• These transducers do not need any external source of powerfor their operation. Therefore they are also called as selfgenerating type transducers.

I. The active transducer are self generating devices whichoperate under the energy conversion principle.

II. As the output of active transducers we get an equivalentelectrical output signal e.g. temperature or strain to electricpotential, without any external source of energy being used.

Piezoelectric Transducer

CLASSIFICATION OF ACTIVE TRANSDUCERS

• Passive Transducers :

I. These transducers need external sourceof power for their operation. So they arenot self generating type transducers.

II. A DC power supply or an audiofrequency generator is used as anexternal power source.

III. These transducers produce the outputsignal in the form of variation inresistance, capacitance, inductance orsome other electrical parameter inresponse to the quantity to be measured.

ACTIVE AND PASSIVE TRANSDUCERS

• Passive Transducers :

I. These transducers need external sourceof power for their operation. So they arenot self generating type transducers.

II. A DC power supply or an audiofrequency generator is used as anexternal power source.

III. These transducers produce the outputsignal in the form of variation inresistance, capacitance, inductance orsome other electrical parameter inresponse to the quantity to be measured.

CLASSIFICATION OF PASSIVETRANSDUCERS

PRIMARY AND SECONDARYTRANSDUCERS

• Some transducers contain the mechanical as well as electricaldevice. The mechanical device converts the physical quantityto be measured into a mechanical signal. Such mechanicaldevice are called as the primary transducers, because they dealwith the physical quantity to be measured.

•The electrical device then convert this mechanical signal intoa corresponding electrical signal. Such electrical device areknown as secondary transducers.

• Some transducers contain the mechanical as well as electricaldevice. The mechanical device converts the physical quantityto be measured into a mechanical signal. Such mechanicaldevice are called as the primary transducers, because they dealwith the physical quantity to be measured.

•The electrical device then convert this mechanical signal intoa corresponding electrical signal. Such electrical device areknown as secondary transducers.

CONTD

•Ref fig in which the diaphragm act as primarytransducer. It convert pressure (the quantity to bemeasured) into displacement(the mechanical signal).•The displacement is then converted into change inresistance using strain gauge. Hence strain gauge acts asthe secondary transducer.

•Ref fig in which the diaphragm act as primarytransducer. It convert pressure (the quantity to bemeasured) into displacement(the mechanical signal).•The displacement is then converted into change inresistance using strain gauge. Hence strain gauge acts asthe secondary transducer.

CLASSIFICATION OF TRANSDUCERSAccording to Transduction Principle

CAPACITIVE TRANSDUCER:•In capacitive transduction transducers the measurand is converted toa change in the capacitance.• A typical capacitor is comprised of two parallel plates ofconducting material separated by an electrical insulating materialcalled a dielectric. The plates and the dielectric may be eitherflattened or rolled.• The purpose of the dielectric is to help the two parallel platesmaintain their stored electrical charges.• The relationship between the capacitance and the size of capacitorplate, amount of plate separation, and the dielectric is given byC = ε0 εr A / dd is the separation distance of plates (m)C is the capacitance (F, Farad)ε0 : absolute permittivity of vacuumεr : relative permittivityA is the effective (overlapping) area of capacitor plates (m2)

CLASSIFICATION OF TRANSDUCERSAccording to Transduction Principle

d

Area=A

CAPACITIVE TRANSDUCER:•In capacitive transduction transducers the measurand is converted toa change in the capacitance.• A typical capacitor is comprised of two parallel plates ofconducting material separated by an electrical insulating materialcalled a dielectric. The plates and the dielectric may be eitherflattened or rolled.• The purpose of the dielectric is to help the two parallel platesmaintain their stored electrical charges.• The relationship between the capacitance and the size of capacitorplate, amount of plate separation, and the dielectric is given byC = ε0 εr A / dd is the separation distance of plates (m)C is the capacitance (F, Farad)ε0 : absolute permittivity of vacuumεr : relative permittivityA is the effective (overlapping) area of capacitor plates (m2)

Area=A

Either A, d or ε can be varied.

ELECTROMAGNETIC TRANSDUCTION:•In electromagnetic transduction, the measurand isconverted to voltage induced in conductor by change inthe magnetic flux, in absence of excitation.•The electromagnetic transducer are self generating activetransducers•The motion between a piece of magnet and anelectromagnet is responsible for the change in flux

CLASSIFICATION OF TRANSDUCERSAccording to Transduction Principle

ELECTROMAGNETIC TRANSDUCTION:•In electromagnetic transduction, the measurand isconverted to voltage induced in conductor by change inthe magnetic flux, in absence of excitation.•The electromagnetic transducer are self generating activetransducers•The motion between a piece of magnet and anelectromagnet is responsible for the change in flux

Current induced in a coil.

INDUCTIVE TRANSDUCER:

•In inductive transduction, the measurand is convertedinto a change in the self inductance of a single coil. It isachieved by displacing the core of the coil that isattached to a mechanical sensing element

CLASSIFICATION OF TRANSDUCERSAccording to Transduction Principle

INDUCTIVE TRANSDUCER:

•In inductive transduction, the measurand is convertedinto a change in the self inductance of a single coil. It isachieved by displacing the core of the coil that isattached to a mechanical sensing element

CLASSIFICATION OF TRANSDUCERSAccording to Transduction Principle

PIEZO ELECTRIC INDUCTION :

•In piezoelectric induction the measurand is convertedinto a change in electrostatic charge q or voltage Vgenerated by crystals when mechanically it is stressedas shown in fig.

PIEZO ELECTRIC INDUCTION :

•In piezoelectric induction the measurand is convertedinto a change in electrostatic charge q or voltage Vgenerated by crystals when mechanically it is stressedas shown in fig.

CLASSIFICATION OF TRANSDUCERSAccording to Transduction Principle

PHOTOVOLTAIC TRANSDUCTION :

•In photovoltaic transduction the measurand isconverted to voltage generated when the junctionbetween dissimilar material is illuminated as shown infig.

PHOTOVOLTAIC TRANSDUCTION :

•In photovoltaic transduction the measurand isconverted to voltage generated when the junctionbetween dissimilar material is illuminated as shown infig.

n-typesemiconductor

Physics of Photovoltaic Generation

n-typesemiconductor

p-typesemiconductor

+ + + + + + + + + + + + + + +- - - - - - - - - - - - - - - - - - Depletion Zone

CLASSIFICATION OF TRANSDUCERSAccording to Transduction Principle

PHOTO CONDUCTIVE TRANSDUCTION :

•In photoconductive transduction the measurand isconverted to change in resistance of semiconductormaterial by the change in light incident on the material.

CLASSIFICATION OF TRANSDUCERSTransducer and Inverse Transducer

TRANSDUCER:

•Transducers convert non electrical quantity toelectrical quantity.

INVERSE TRANSDUCER:

• Inverse transducers convert electrical quantity to anon electrical quantity

TRANSDUCER:

•Transducers convert non electrical quantity toelectrical quantity.

INVERSE TRANSDUCER:

• Inverse transducers convert electrical quantity to anon electrical quantity

PASSIVE TRANSDUCERS

• Resistive transducers :– Resistive transducers are those transducers in which the

resistance change due to the change in some physicalphenomenon.

– The resistance of a metal conductor is expressed by asimple equation.

– R = ρL/A– Where R = resistance of conductor in Ω

L = length of conductor in mA = cross sectional area of conductor in m2

ρ = resistivity of conductor material in Ω-m.

• Resistive transducers :– Resistive transducers are those transducers in which the

resistance change due to the change in some physicalphenomenon.

– The resistance of a metal conductor is expressed by asimple equation.

– R = ρL/A– Where R = resistance of conductor in Ω

L = length of conductor in mA = cross sectional area of conductor in m2

ρ = resistivity of conductor material in Ω-m.

RESISTIVE TRANSDUCER

There are 4 type of resistive transducers.

1. Potentiometers (POT)2. Strain gauge3. Thermistors4. Resistance thermometer

There are 4 type of resistive transducers.

1. Potentiometers (POT)2. Strain gauge3. Thermistors4. Resistance thermometer

POTENTIOMETER

• The potentiometer are used for voltage division. They consist of aresistive element provided with a sliding contact. The sliding contactis called as wiper.

• The contact motion may be linear or rotational or combination of thetwo. The combinational potentiometer have their resistive element inhelix form and are called helipots.

• Fig shows a linear pot and a rotary pot.

• The potentiometer are used for voltage division. They consist of aresistive element provided with a sliding contact. The sliding contactis called as wiper.

• The contact motion may be linear or rotational or combination of thetwo. The combinational potentiometer have their resistive element inhelix form and are called helipots.

• Fig shows a linear pot and a rotary pot.

STRAIN GAUGE

• The strain gauge is a passive, resistive transducer whichconverts the mechanical elongation and compression into aresistance change.

• This change in resistance takes place due to variation in lengthand cross sectional area of the gauge wire, when an externalforce acts on it.

• The strain gauge is a passive, resistive transducer whichconverts the mechanical elongation and compression into aresistance change.

• This change in resistance takes place due to variation in lengthand cross sectional area of the gauge wire, when an externalforce acts on it.

TYPES OF STRAIN GAUGE

• The type of strain gauge are as

1. Wire gauge

a) Unbonded

b) Bonded

c) Foil type

2. Semiconductor gauge

• The type of strain gauge are as

1. Wire gauge

a) Unbonded

b) Bonded

c) Foil type

2. Semiconductor gauge

UNBONDED STRAIN GAUGE• An unbonded meter strain gauge is shown in fig• This gauge consist of a wire stretched between

two point in an insulating medium such as air.The wires may be made of various copper, nickel,crome nickle or nickle iron alloys.

• In fig the element is connected via a rod todiaphragm which is used for sensing the pressure.The wire are tensioned to avoid buckling whenthey experience the compressive force.

• An unbonded meter strain gauge is shown in fig• This gauge consist of a wire stretched between

two point in an insulating medium such as air.The wires may be made of various copper, nickel,crome nickle or nickle iron alloys.

• In fig the element is connected via a rod todiaphragm which is used for sensing the pressure.The wire are tensioned to avoid buckling whenthey experience the compressive force.

• The unbounded meter wire gauges used almost exclusively intransducer application employ preloaded resistance wireconnected in Wheatstone bridge as shown in fig.

• At initial preload the strain and resistance of the four arms arenominally equal with the result the output voltage of the bridgeis equal to zero.

• Application of pressure produces a small displacement , thedisplacement increases a tension in two wire and decreases itin the other two thereby increase the resistance of two wirewhich are in tension and decreasing the resistance of theremaining two wire .

• This causes an unbalance of the bridge producing an outputvoltage which is proportional to the input displacement andhence to the applied pressure .

• The unbounded meter wire gauges used almost exclusively intransducer application employ preloaded resistance wireconnected in Wheatstone bridge as shown in fig.

• At initial preload the strain and resistance of the four arms arenominally equal with the result the output voltage of the bridgeis equal to zero.

• Application of pressure produces a small displacement , thedisplacement increases a tension in two wire and decreases itin the other two thereby increase the resistance of two wirewhich are in tension and decreasing the resistance of theremaining two wire .

• This causes an unbalance of the bridge producing an outputvoltage which is proportional to the input displacement andhence to the applied pressure .

BONDED STRAIN GAUGE• The bonded metal wire strain gauge are used for both stress

analysis and for construction of transducer.• A resistance wire strain gauge consist of a grid of fine

resistance wire. The grid is cemented to carrier which may bea thin sheet of paper bakelite or teflon.

• The wire is covered on top with a thin sheet of material so asto prevent it from any mechanical demage.

• The carrier is bonded with an adhesive material to thespecimen which permit a good transfer of strain from carrier togrid of wires.

• The bonded metal wire strain gauge are used for both stressanalysis and for construction of transducer.

• A resistance wire strain gauge consist of a grid of fineresistance wire. The grid is cemented to carrier which may bea thin sheet of paper bakelite or teflon.

• The wire is covered on top with a thin sheet of material so asto prevent it from any mechanical demage.

• The carrier is bonded with an adhesive material to thespecimen which permit a good transfer of strain from carrier togrid of wires.

BONDED METAL FOIL STRAIN GAUGE

• It consist of following parts:1. Base (carrier) Materials: several types of base material are used to

support the wires. Impregnated paper is used for room temp. applications.2. Adhesive: The adhesive acts as bonding materials. Like other bonding

operation, successful starain gauge bonding depends upon careful surfacepreparation and use of the correct bonding agent.

In order that the strain be faithfully transferred on to the strain gauge, thebond has to be formed between the surface to be strained and the plasticbacking material on which the gauge is mounted .

.

• It consist of following parts:1. Base (carrier) Materials: several types of base material are used to

support the wires. Impregnated paper is used for room temp. applications.2. Adhesive: The adhesive acts as bonding materials. Like other bonding

operation, successful starain gauge bonding depends upon careful surfacepreparation and use of the correct bonding agent.

In order that the strain be faithfully transferred on to the strain gauge, thebond has to be formed between the surface to be strained and the plasticbacking material on which the gauge is mounted .

.

It is important that the adhesive should be suited to thisbacking and adhesive material should be quickdrying type and also insensitive to moisture.

3. Leads: The leads should be of such materials whichhave low and stable resistivity and also a lowresistance temperature coefficent

It is important that the adhesive should be suited to thisbacking and adhesive material should be quickdrying type and also insensitive to moisture.

3. Leads: The leads should be of such materials whichhave low and stable resistivity and also a lowresistance temperature coefficent

Contd.

• This class of strain gauge is only an extension of thebonded metal wire strain gauges.

• The bonded metal wire starin gauge have been completelysuperseded by bonded metal foil strain gauges.

• Metal foil strain gauge use identical material to wirestrain gauge and are used for most general purpose stressanalysis application and for many transducers.

• This class of strain gauge is only an extension of thebonded metal wire strain gauges.

• The bonded metal wire starin gauge have been completelysuperseded by bonded metal foil strain gauges.

• Metal foil strain gauge use identical material to wirestrain gauge and are used for most general purpose stressanalysis application and for many transducers.

SEMICONDUCTOR GAUGE• Semiconductor gauge are used in application where a high gauge

factor is desired. A high gauge factor means relatively higher changein resistance that can be measured with good accuracy.

• The resistance of the semiconductor gauge change as strain isapplied to it. The semiconductor gauge depends for their action uponthe piezo-resistive effect i.e. change in value of resistance due tochange in resistivity.

• Silicon and germanium are used as resistive material forsemiconductor gauges.

• Semiconductor gauge are used in application where a high gaugefactor is desired. A high gauge factor means relatively higher changein resistance that can be measured with good accuracy.

• The resistance of the semiconductor gauge change as strain isapplied to it. The semiconductor gauge depends for their action uponthe piezo-resistive effect i.e. change in value of resistance due tochange in resistivity.

• Silicon and germanium are used as resistive material forsemiconductor gauges.

RESISTANCE THERMOMETER• Resistance of metal increase with increases in

temperature. Therefore metals are said to have apositive temperature coefficient of resistivity.

• Fig shows the simplest type of open wire constructionof platinum résistance thermometer. The platinumwire is wound in the form of spirals on an insulatingmaterial such as mica or ceramic.

• This assembly is then placed at the tip of probe• This wire is in direct contact with the gas or liquid

whose temperature is to be measured.

• Resistance of metal increase with increases intemperature. Therefore metals are said to have apositive temperature coefficient of resistivity.

• Fig shows the simplest type of open wire constructionof platinum résistance thermometer. The platinumwire is wound in the form of spirals on an insulatingmaterial such as mica or ceramic.

• This assembly is then placed at the tip of probe• This wire is in direct contact with the gas or liquid

whose temperature is to be measured.

• The resistance of the platinum wire changes with thechange in temperature of the gas or liquid

• This type of sensor have a positive temperaturecoefficient of resistivity as they are made from metalsthey are also known as resistance temperaturedetector

• Resistance thermometer are generally of probe typefor immersion in medium whose temperature is to bemeasured or controlled.

• The resistance of the platinum wire changes with thechange in temperature of the gas or liquid

• This type of sensor have a positive temperaturecoefficient of resistivity as they are made from metalsthey are also known as resistance temperaturedetector

• Resistance thermometer are generally of probe typefor immersion in medium whose temperature is to bemeasured or controlled.

THERMISTOR

•Thermistor is a contraction of a term “thermal resistor”.•Thermistor are temperature dependent resistors. They aremade of semiconductor material which have negativetemperature coefficient of resistivity i.e. their resistancedecreases with increase of temperature.•Thermistor are widely used in application which involvemeasurement in the range of 0-60º Thermistor are composedof sintered mixture of metallic oxides such as magnese,nickle, cobalt, copper, iron and uranium

•Thermistor is a contraction of a term “thermal resistor”.•Thermistor are temperature dependent resistors. They aremade of semiconductor material which have negativetemperature coefficient of resistivity i.e. their resistancedecreases with increase of temperature.•Thermistor are widely used in application which involvemeasurement in the range of 0-60º Thermistor are composedof sintered mixture of metallic oxides such as magnese,nickle, cobalt, copper, iron and uranium

Contd.

•The thermistor may be in the form of beads, rods anddiscs.•The thermistor provide a large change in resistance forsmall change in temperature. In some cases theresistance of themistor at room temperature maydecreases as much as 6% for each 1ºC rise intemperature.

•The thermistor may be in the form of beads, rods anddiscs.•The thermistor provide a large change in resistance forsmall change in temperature. In some cases theresistance of themistor at room temperature maydecreases as much as 6% for each 1ºC rise intemperature.

Thermocouples

See beck Effect

When a pair of dissimilar metals are joined at one end, and there is atemperature difference between the joined ends and the open ends,thermal emf is generated, which can be measured in the open ends.

This forms the basis of thermocouples.

VARIABLE-INDUCTANCETRANSDUCERS

• An inductive electromechanicaltransducer is a transducer which convertsthe physical motion into the change ininductance.

• Inductive transducers are mainly usedfor displacement measurement.

• An inductive electromechanicaltransducer is a transducer which convertsthe physical motion into the change ininductance.

• Inductive transducers are mainly usedfor displacement measurement.

• The inductive transducers are of the self generatingor the passive type. The self generating inductivetransducers use the basic generator principle i.e. themotion between a conductor and magnetic fieldinduces a voltage in the conductor.

• The variable inductance transducers work on thefollowing principles.

• Variation in self inductance• Variation in mutual inductance

• The inductive transducers are of the self generatingor the passive type. The self generating inductivetransducers use the basic generator principle i.e. themotion between a conductor and magnetic fieldinduces a voltage in the conductor.

• The variable inductance transducers work on thefollowing principles.

• Variation in self inductance• Variation in mutual inductance

PRINCIPLE OF VARIATION OF SELFINDUCTANCE

• Let us consider an inductive transducer havingN turns and reluctance R. when current I ispassed through the transducer, the fluxproduced is

• Φ = Ni / R• Differentiating w.r.t. to t,• dΦ/dt = N/R * di/dt• The e.m.f. induced in a coil is given by• e = N * dΦ/dt

• Let us consider an inductive transducer havingN turns and reluctance R. when current I ispassed through the transducer, the fluxproduced is

• Φ = Ni / R• Differentiating w.r.t. to t,• dΦ/dt = N/R * di/dt• The e.m.f. induced in a coil is given by• e = N * dΦ/dt

• e = N * N/R * di/dt• e = N2 / R * di/dt• Self inductance is given by• L = e/di/dt = N2 / R• The reluctance of the magnetic circuit is R = Ɩ/μA• Therefore L = N2 / Ɩ/μA = N2 μA / Ɩ• From eqn we can see that the self inductance may

vary due toi. Change in number of turns Nii. Change in geometric configurationiii. Change in permeability of magnetic circuit

• e = N * N/R * di/dt• e = N2 / R * di/dt• Self inductance is given by• L = e/di/dt = N2 / R• The reluctance of the magnetic circuit is R = Ɩ/μA• Therefore L = N2 / Ɩ/μA = N2 μA / Ɩ• From eqn we can see that the self inductance may

vary due toi. Change in number of turns Nii. Change in geometric configurationiii. Change in permeability of magnetic circuit

CHANGE IN SELF INDUCTANCE WITHCHANGE IN NUMBER OF TURNS N

• From eqn we can see the output may vary with thevariation in the number of turns. As inductivetransducers are mainly used for displacementmeasurement, with change in number of turns theself inductance of the coil changes in-turn changingthe displacement

• Fig shows transducers used for linear and angulardisplacement fig a shows an air cored transducer forthe measurement of linear displacement and fig bshows an iron cored transducer used for angulardisplacement measurement.

• From eqn we can see the output may vary with thevariation in the number of turns. As inductivetransducers are mainly used for displacementmeasurement, with change in number of turns theself inductance of the coil changes in-turn changingthe displacement

• Fig shows transducers used for linear and angulardisplacement fig a shows an air cored transducer forthe measurement of linear displacement and fig bshows an iron cored transducer used for angulardisplacement measurement.

CHANGE IN SELF INDUCTANCE WITHCHANGE IN PERMEABILITY

• An inductive transducer that works on the principle of changein self inductance of coil due to change in the permeability isshown in fig

• As shown in fig the iron core is surrounded by a winding. Ifthe iron core is inside the winding then the permeabilityincreases otherwise permeability decreases. This cause the selfinductance of the coil to increase or decrease depending on thepermeability.

• The displacement can be measured using this transducer

• An inductive transducer that works on the principle of changein self inductance of coil due to change in the permeability isshown in fig

• As shown in fig the iron core is surrounded by a winding. Ifthe iron core is inside the winding then the permeabilityincreases otherwise permeability decreases. This cause the selfinductance of the coil to increase or decrease depending on thepermeability.

• The displacement can be measured using this transducer

displacement

Ferromagneticformer

coil

VARIABLE RELUCTANCE INDUCTIVETRANSDUCER

• Fig shows a variable reluctance inductive transducer.• As shown in fig the coil is wound on the ferromagnetic iron. The

target and core are not in direct contact with each other. They areseparated by an air gap.

• The displacement has to be measured is applied to the ferromagneticcore

• The reluctance of the magnetic path is found by the size of the airgap.

• The self inductance of coil is given by• L = N2 / R = N2 / Ri + Ra• N : number of turns• R : reluctance of coil• Ri : reluctance of iron path• Ra : reluctance of air gap

• Fig shows a variable reluctance inductive transducer.• As shown in fig the coil is wound on the ferromagnetic iron. The

target and core are not in direct contact with each other. They areseparated by an air gap.

• The displacement has to be measured is applied to the ferromagneticcore

• The reluctance of the magnetic path is found by the size of the airgap.

• The self inductance of coil is given by• L = N2 / R = N2 / Ri + Ra• N : number of turns• R : reluctance of coil• Ri : reluctance of iron path• Ra : reluctance of air gap

CONTD.

• The reluctance of iron path is negligible

• L = N2 / Ra

• Ra = la / μoA

• Therefore L œ 1 / la i.e. self inductance of the coil is inverselyproportional to the air gap la.

• When the target is near the core, the length is small. Hence theself inductance is large. But when the target is away from thecore, the length is large. So reluctance is also large. This resultin decrease in self inductance i.e. small self inductance.

• Thus inductance is function of the distance of the target fromthe core. Displacement changes with the length of the air gap,the self inductance is a function of the displacement.

• The reluctance of iron path is negligible

• L = N2 / Ra

• Ra = la / μoA

• Therefore L œ 1 / la i.e. self inductance of the coil is inverselyproportional to the air gap la.

• When the target is near the core, the length is small. Hence theself inductance is large. But when the target is away from thecore, the length is large. So reluctance is also large. This resultin decrease in self inductance i.e. small self inductance.

• Thus inductance is function of the distance of the target fromthe core. Displacement changes with the length of the air gap,the self inductance is a function of the displacement.

PRINCIPLE OF CHANGE IN MUTUALINDUCTANCE

• Multiple coils are required for inductive transducersthat operate on the principle of change in mutualinductance.

• The mutual inductance between two coils is given by• M = KsqrtL1L2• Where M : mutual inductance• K : coefficient of coupling• L1:self inductance of coil 1• L2 : self inductance of coil 2• By varying the self inductance or the coefficient of

coupling the mutual inductance can be varied

• Multiple coils are required for inductive transducersthat operate on the principle of change in mutualinductance.

• The mutual inductance between two coils is given by• M = KsqrtL1L2• Where M : mutual inductance• K : coefficient of coupling• L1:self inductance of coil 1• L2 : self inductance of coil 2• By varying the self inductance or the coefficient of

coupling the mutual inductance can be varied

DIFFERENTIAL OUTPUTTRANSDUCERS

• Usually the change in self inductance ΔL forinductive transducers is insufficient for the detectionof stages of an instrumentation system.

• The differential arrangement comprises of a coil thatis divided in two parts as shown in fig a and b.

• In response to displacement, the inductance of onepart increases from L to L+ΔL while the inductanceof the other part decreases from L to L- ΔL. Thedifference of two is measured so to get output 2 ΔL.This will increase the sensitivity and minimize error.

• .

• Usually the change in self inductance ΔL forinductive transducers is insufficient for the detectionof stages of an instrumentation system.

• The differential arrangement comprises of a coil thatis divided in two parts as shown in fig a and b.

• In response to displacement, the inductance of onepart increases from L to L+ΔL while the inductanceof the other part decreases from L to L- ΔL. Thedifference of two is measured so to get output 2 ΔL.This will increase the sensitivity and minimize error.

• .

• Fig c shows an inductive transducer that providesdifferential output. Due to variation in the reluctance,the self inductance of the coil changes. This is theprinciple of operation of differential output inductivetransducer

• Fig c shows an inductive transducer that providesdifferential output. Due to variation in the reluctance,the self inductance of the coil changes. This is theprinciple of operation of differential output inductivetransducer

LINEAR VARIABLE DIFFERENTIALTRANSFORMER(LVDT)

• AN LVDT transducercomprises a coil former on towhich three coils are wound.

• The primary coil is excitedwith an AC current, thesecondary coils are woundsuch that when a ferrite coreis in the central linearposition, an equal voltage isinduced in to each coil.

• The secondary are connectedin opposite so that in thecentral position the outputsof the secondary cancelseach other out.

• AN LVDT transducercomprises a coil former on towhich three coils are wound.

• The primary coil is excitedwith an AC current, thesecondary coils are woundsuch that when a ferrite coreis in the central linearposition, an equal voltage isinduced in to each coil.

• The secondary are connectedin opposite so that in thecentral position the outputsof the secondary cancelseach other out.

LVDT contd…

• The excitation is applied to the primarywinding and the armature assists theinduction of current in to secondarycoils.

• When the core is exactly at the centerof the coil then the flux linked to boththe secondary winding will be equal.Due to equal flux linkage thesecondary induced voltages (eo1 &eo2) are equal but they have oppositepolarities. Output voltage eo istherefore zero. This position is called“null position”

• The excitation is applied to the primarywinding and the armature assists theinduction of current in to secondarycoils.

• When the core is exactly at the centerof the coil then the flux linked to boththe secondary winding will be equal.Due to equal flux linkage thesecondary induced voltages (eo1 &eo2) are equal but they have oppositepolarities. Output voltage eo istherefore zero. This position is called“null position”

• Now if the core is displaced from its nullposition toward sec1 then flux linked to sec1increases and flux linked to sec2 decreases.Therefore eo1 > eo2 and the output voltage ofLVDT eo will be positive

• Similarly if the core is displaced toward sec2then the eo2 > eo1 and the output voltage ofLVDT eo will be negative.

• Now if the core is displaced from its nullposition toward sec1 then flux linked to sec1increases and flux linked to sec2 decreases.Therefore eo1 > eo2 and the output voltage ofLVDT eo will be positive

• Similarly if the core is displaced toward sec2then the eo2 > eo1 and the output voltage ofLVDT eo will be negative.

Bridge circuits (DC & AC) are an instrument to measureresistance, inductance, capacitance and impedance.

Operate on a null-indication principle. This means theindication is independent of the calibration of theindicating device or any characteristics of it.

# Very high degrees of accuracy can be achieved usingthe bridges.

Used in control circuits.# One arm of the bridge contains a resistive element

that is sensitive to the physical parameter(temperature, pressure, etc.) being controlled.

Bridge circuits (DC & AC) are an instrument to measureresistance, inductance, capacitance and impedance.

Operate on a null-indication principle. This means theindication is independent of the calibration of theindicating device or any characteristics of it.

# Very high degrees of accuracy can be achieved usingthe bridges.

Used in control circuits.# One arm of the bridge contains a resistive element

that is sensitive to the physical parameter(temperature, pressure, etc.) being controlled.

Bridge circuits (DC & AC) are an instrument to measureresistance, inductance, capacitance and impedance.

Operate on a null-indication principle. This means theindication is independent of the calibration of theindicating device or any characteristics of it.

# Very high degrees of accuracy can be achieved usingthe bridges.

Used in control circuits.# One arm of the bridge contains a resistive element

that is sensitive to the physical parameter(temperature, pressure, etc.) being controlled.

Bridge circuits (DC & AC) are an instrument to measureresistance, inductance, capacitance and impedance.

Operate on a null-indication principle. This means theindication is independent of the calibration of theindicating device or any characteristics of it.

# Very high degrees of accuracy can be achieved usingthe bridges.

Used in control circuits.# One arm of the bridge contains a resistive element

that is sensitive to the physical parameter(temperature, pressure, etc.) being controlled.

Bridge circuits (DC & AC) are an instrument to measureresistance, inductance, capacitance and impedance.

Operate on a null-indication principle. This means theindication is independent of the calibration of theindicating device or any characteristics of it.

# Very high degrees of accuracy can be achieved usingthe bridges.

Used in control circuits.# One arm of the bridge contains a resistive element

that is sensitive to the physical parameter(temperature, pressure, etc.) being controlled.

Bridge circuits (DC & AC) are an instrument to measureresistance, inductance, capacitance and impedance.

Operate on a null-indication principle. This means theindication is independent of the calibration of theindicating device or any characteristics of it.

# Very high degrees of accuracy can be achieved usingthe bridges.

Used in control circuits.# One arm of the bridge contains a resistive element

that is sensitive to the physical parameter(temperature, pressure, etc.) being controlled.

TWO (2) TYPES of bridge circuits are used inmeasurement:

1) DC bridge:a) Wheatstone Bridgeb) Kelvin Bridge

2) AC bridge:a) Similar Angle Bridgeb) Opposite Angle Bridge/Hay Bridgec) Maxwell Bridged) Wein Bridgee) Radio Frequency Bridgef) Schering Bridge

TWO (2) TYPES of bridge circuits are used inmeasurement:

1) DC bridge:a) Wheatstone Bridgeb) Kelvin Bridge

2) AC bridge:a) Similar Angle Bridgeb) Opposite Angle Bridge/Hay Bridgec) Maxwell Bridged) Wein Bridgee) Radio Frequency Bridgef) Schering Bridge

TWO (2) TYPES of bridge circuits are used inmeasurement:

1) DC bridge:a) Wheatstone Bridgeb) Kelvin Bridge

2) AC bridge:a) Similar Angle Bridgeb) Opposite Angle Bridge/Hay Bridgec) Maxwell Bridged) Wein Bridgee) Radio Frequency Bridgef) Schering Bridge

TWO (2) TYPES of bridge circuits are used inmeasurement:

1) DC bridge:a) Wheatstone Bridgeb) Kelvin Bridge

2) AC bridge:a) Similar Angle Bridgeb) Opposite Angle Bridge/Hay Bridgec) Maxwell Bridged) Wein Bridgee) Radio Frequency Bridgef) Schering Bridge

TWO (2) TYPES of bridge circuits are used inmeasurement:

1) DC bridge:a) Wheatstone Bridgeb) Kelvin Bridge

2) AC bridge:a) Similar Angle Bridgeb) Opposite Angle Bridge/Hay Bridgec) Maxwell Bridged) Wein Bridgee) Radio Frequency Bridgef) Schering Bridge

TWO (2) TYPES of bridge circuits are used inmeasurement:

1) DC bridge:a) Wheatstone Bridgeb) Kelvin Bridge

2) AC bridge:a) Similar Angle Bridgeb) Opposite Angle Bridge/Hay Bridgec) Maxwell Bridged) Wein Bridgee) Radio Frequency Bridgef) Schering Bridge

The Wheatstone bridge is anelectrical bridge circuit usedto measure resistance.

It consists of a voltage sourceand a galvanometer thatconnects two parallel branches,containing four resistors. Figure 5.1: Wheatstone Bridge Circuit

The Wheatstone bridge is anelectrical bridge circuit usedto measure resistance.

It consists of a voltage sourceand a galvanometer thatconnects two parallel branches,containing four resistors.

One parallel branch contains one known resistance and oneunknown; the other parallel branch contains resistors of knownresistances.

Figure 5.1: Wheatstone Bridge Circuit

One parallel branch contains one known resistance and oneunknown; the other parallel branch contains resistors of knownresistances.

In the circuit at right, R4 is theunknown resistance; R1, R2 and R3are resistors of known resistancewhere the resistance of R3 isadjustable.

How to determine the resistanceof the unknown resistor, R4?

“The resistances of the other threeare adjusted and balanced untilthe current passing through thegalvanometer decreases to zero”.

In the circuit at right, R4 is theunknown resistance; R1, R2 and R3are resistors of known resistancewhere the resistance of R3 isadjustable.

How to determine the resistanceof the unknown resistor, R4?

“The resistances of the other threeare adjusted and balanced untilthe current passing through thegalvanometer decreases to zero”.

Figure 5.1: Wheatstone Bridge Circuit

In the circuit at right, R4 is theunknown resistance; R1, R2 and R3are resistors of known resistancewhere the resistance of R3 isadjustable.

How to determine the resistanceof the unknown resistor, R4?

“The resistances of the other threeare adjusted and balanced untilthe current passing through thegalvanometer decreases to zero”.

In the circuit at right, R4 is theunknown resistance; R1, R2 and R3are resistors of known resistancewhere the resistance of R3 isadjustable.

How to determine the resistanceof the unknown resistor, R4?

“The resistances of the other threeare adjusted and balanced untilthe current passing through thegalvanometer decreases to zero”.

In the circuit at right, R4 is theunknown resistance; R1, R2 and R3are resistors of known resistancewhere the resistance of R3 isadjustable.

How to determine the resistanceof the unknown resistor, R4?

“The resistances of the other threeare adjusted and balanced untilthe current passing through thegalvanometer decreases to zero”.

Figure 5.1: Wheatstone Bridge Circuit

In the circuit at right, R4 is theunknown resistance; R1, R2 and R3are resistors of known resistancewhere the resistance of R3 isadjustable.

How to determine the resistanceof the unknown resistor, R4?

“The resistances of the other threeare adjusted and balanced untilthe current passing through thegalvanometer decreases to zero”.

R3 is varied until voltage between the two midpoints (B and D) will bezero and no current will flow through the galvanometer.

A

BD

Figure 5.1: Wheatstone Bridge Circuit

C

R3 is varied until voltage between the two midpoints (B and D) will bezero and no current will flow through the galvanometer.

Figure 5.2: A variable resistor; theamount of resistance between theconnection terminals could be varied.

When the bridge is in balancecondition (no current flows throughgalvanometer G), we obtain;

voltage drop across R1 and R2 isequal,

I1R1 = I2R2

voltage drop across R3 and R4 isequal,

I3R3 = I4R4

When the bridge is in balancecondition (no current flows throughgalvanometer G), we obtain;

voltage drop across R1 and R2 isequal,

I1R1 = I2R2

voltage drop across R3 and R4 isequal,

I3R3 = I4R4

When the bridge is in balancecondition (no current flows throughgalvanometer G), we obtain;

voltage drop across R1 and R2 isequal,

I1R1 = I2R2

voltage drop across R3 and R4 isequal,

I3R3 = I4R4

AWhen the bridge is in balancecondition (no current flows throughgalvanometer G), we obtain;

voltage drop across R1 and R2 isequal,

I1R1 = I2R2

voltage drop across R3 and R4 isequal,

I3R3 = I4R4

Figure 5.1: Wheatstone Bridge Circuit

B

C

D

When the bridge is in balancecondition (no current flows throughgalvanometer G), we obtain;

voltage drop across R1 and R2 isequal,

I1R1 = I2R2

voltage drop across R3 and R4 isequal,

I3R3 = I4R4

When the bridge is in balancecondition (no current flows throughgalvanometer G), we obtain;

voltage drop across R1 and R2 isequal,

I1R1 = I2R2

voltage drop across R3 and R4 isequal,

I3R3 = I4R4

In this point of balance, we alsoobtain;

I1 = I3 and I2 = I4

Therefore, the ratio of two resistancesin the known leg is equal to the ratioof the two in the unknown leg;

2

4

1

3

R

R

R

R

In this point of balance, we alsoobtain;

I1 = I3 and I2 = I4

Therefore, the ratio of two resistancesin the known leg is equal to the ratioof the two in the unknown leg;

2

4

1

3

R

R

R

R

1

234 R

RRR

A In this point of balance, we also

obtain;

I1 = I3 and I2 = I4

Therefore, the ratio of two resistancesin the known leg is equal to the ratioof the two in the unknown leg;

Figure 5.1: Wheatstone Bridge Circuit

B

C

D

In this point of balance, we alsoobtain;

I1 = I3 and I2 = I4

Therefore, the ratio of two resistancesin the known leg is equal to the ratioof the two in the unknown leg;

Example 1

Find Rx?

Figure 5.3

Example 1

Figure 5.3

Sensitivity of the Wheatstone Bridge

When the pointer of a bridgegalvanometer deflects to rightor to left direction, this meansthat current is flowing throughthe galvanometer and thebridge is called in anunbalanced condition.

The amount of deflection is afunction of the sensitivity of thegalvanometer. For the samecurrent, greater deflection ofpointer indicates moresensitive a galvanometer.

When the pointer of a bridgegalvanometer deflects to rightor to left direction, this meansthat current is flowing throughthe galvanometer and thebridge is called in anunbalanced condition.

The amount of deflection is afunction of the sensitivity of thegalvanometer. For the samecurrent, greater deflection ofpointer indicates moresensitive a galvanometer.

When the pointer of a bridgegalvanometer deflects to rightor to left direction, this meansthat current is flowing throughthe galvanometer and thebridge is called in anunbalanced condition.

The amount of deflection is afunction of the sensitivity of thegalvanometer. For the samecurrent, greater deflection ofpointer indicates moresensitive a galvanometer.

Sensitivity of the Wheatstone Bridge

Figure 5.4.

Sensitivity of the Wheatstone Bridge (Cont…)Sensitivity S can be expressed in units of:

A

radiansS

orA

reesS

orA

etersmilS

I

D

Current

DeflectionS

;deg

;lim

A

radiansS

orA

reesS

orA

etersmilS

I

D

Current

DeflectionS

;deg

;lim

How to find the currentvalue?

Sensitivity of the Wheatstone Bridge (Cont…)Sensitivity S can be expressed in units of:

Figure 5.4.

Thevenin’s TheoremThevenin’s theorem is a approach usedto determine the current flowingthrough the galvanometer.

Thevenin’s equivalent voltage isfound by removing the galvanometerfrom the bridge circuit and computingthe open-circuit voltage betweenterminals a and b.

Thevenin’s theorem is a approach usedto determine the current flowingthrough the galvanometer.

Thevenin’s equivalent voltage isfound by removing the galvanometerfrom the bridge circuit and computingthe open-circuit voltage betweenterminals a and b.

Applying the voltage divider equation, we express the voltage at point aand b, respectively, as

31

3

RR

REVa

Applying the voltage divider equation, we express the voltage at point aand b, respectively, as

Thevenin’s theorem is a approach usedto determine the current flowingthrough the galvanometer.

Thevenin’s equivalent voltage isfound by removing the galvanometerfrom the bridge circuit and computingthe open-circuit voltage betweenterminals a and b.

Fig. 5.5: Thevenin’s equivalent voltage

Thevenin’s theorem is a approach usedto determine the current flowingthrough the galvanometer.

Thevenin’s equivalent voltage isfound by removing the galvanometerfrom the bridge circuit and computingthe open-circuit voltage betweenterminals a and b.

Applying the voltage divider equation, we express the voltage at point aand b, respectively, asApplying the voltage divider equation, we express the voltage at point aand b, respectively, as

42

4

RR

REVb

Thevenin’s Theorem (Cont…)

The difference in Va and Vb representsThevenin’s equivalent voltage. That is,

42

4

31

3

RR

R

RR

REVVV baTh

The difference in Va and Vb representsThevenin’s equivalent voltage. That is,

Thevenin’s equivalent resistance is foundby replacing the voltage source with itsinternal resistance, Rb. Since Rb isassumed to be very low (Rb ≈ 0 Ω), wecan redraw the bridge as shown in Fig.5.6 to facilitate computation of theequivalent resistance as follows:

Thevenin’s equivalent resistance is foundby replacing the voltage source with itsinternal resistance, Rb. Since Rb isassumed to be very low (Rb ≈ 0 Ω), wecan redraw the bridge as shown in Fig.5.6 to facilitate computation of theequivalent resistance as follows:

Thevenin’s Theorem (Cont…)

The difference in Va and Vb representsThevenin’s equivalent voltage. That is,

42

4

31

3

RR

R

RR

REVVV baTh

The difference in Va and Vb representsThevenin’s equivalent voltage. That is,

Fig. 5.5: Wheatstone bridgewith the galvanometer removed

Thevenin’s equivalent resistance is foundby replacing the voltage source with itsinternal resistance, Rb. Since Rb isassumed to be very low (Rb ≈ 0 Ω), wecan redraw the bridge as shown in Fig.5.6 to facilitate computation of theequivalent resistance as follows:

Fig. 5.6: Thevenin’s resistance

Thevenin’s equivalent resistance is foundby replacing the voltage source with itsinternal resistance, Rb. Since Rb isassumed to be very low (Rb ≈ 0 Ω), wecan redraw the bridge as shown in Fig.5.6 to facilitate computation of theequivalent resistance as follows:

Thevenin’s Theorem (Cont…)

4231 //// RRRRRTh 4231 //// RRRRRTh

42

42

31

31

RR

RR

RR

RRRTh

If the values of Thevenin’s equivalent voltage and resistance have been known,the Wheatstone bridge circuit in Fig. 5.5 can be changed with Thevenin’sequivalent circuit as shown in Fig. 5.7,

Fig. 5.5: Wheatstone bridge circuit

Thevenin’s Theorem (Cont…)

Fig. 5.6: Thevenin’s resistance42

42

31

31

RR

RR

RR

RRRTh

If the values of Thevenin’s equivalent voltage and resistance have been known,the Wheatstone bridge circuit in Fig. 5.5 can be changed with Thevenin’sequivalent circuit as shown in Fig. 5.7,

Fig. 5.7: Thevenin’s equivalent circuit

Thevenin’s Theorem (Cont…)

If a galvanometer is connected toterminal a and b, the deflection currentin the galvanometer is

If a galvanometer is connected toterminal a and b, the deflection currentin the galvanometer is

gTh

Thg RR

VI

where Rg = the internal resistance in the galvanometer

Thevenin’s Theorem (Cont…)

If a galvanometer is connected toterminal a and b, the deflection currentin the galvanometer is

Fig. 5.7: Thevenin’s equivalent circuit

If a galvanometer is connected toterminal a and b, the deflection currentin the galvanometer is

where Rg = the internal resistance in the galvanometer

R1 = 1.5 kΩ

Example 2

R3 = 3 kΩ

E= 6 V

Figure 5.8 : Unbalance Wheatstone Bridge

Calculate the current through the galvanometer ?

R2 = 1.5kΩ

R1 = 1.5 kΩ

Example 2R2 = 1.5kΩ

R3 = 3 kΩR4 = 7.8 kΩ

Rg = 150 Ω

R4 = 7.8 kΩ

Figure 5.8 : Unbalance Wheatstone Bridge

Calculate the current through the galvanometer ?

Slightly Unbalanced Wheatstone Bridge

If three of the four resistors in a bridge are equal to R and the fourthdiffers by 5% or less, we can develop an approximate but accurateexpression for Thevenin’s equivalent voltage and resistance. Considerthe circuit in Fig- 5.9, the voltage at point a is given as

22

E

R

RE

RR

REVa

If three of the four resistors in a bridge are equal to R and the fourthdiffers by 5% or less, we can develop an approximate but accurateexpression for Thevenin’s equivalent voltage and resistance. Considerthe circuit in Fig- 5.9, the voltage at point a is given as

The voltage at point b is expressed as

rRR

rREVb

Slightly Unbalanced Wheatstone Bridge

If three of the four resistors in a bridge are equal to R and the fourthdiffers by 5% or less, we can develop an approximate but accurateexpression for Thevenin’s equivalent voltage and resistance. Considerthe circuit in Fig- 5.9, the voltage at point a is given as

22

E

R

RE

RR

REVa

If three of the four resistors in a bridge are equal to R and the fourthdiffers by 5% or less, we can develop an approximate but accurateexpression for Thevenin’s equivalent voltage and resistance. Considerthe circuit in Fig- 5.9, the voltage at point a is given as

The voltage at point b is expressed as

Figure 5.9: Wheatstone Bridge withthree equal arms

Thevenin’s equivalent voltage is the difference in this voltage

Slightly Unbalanced Wheatstone Bridge (Cont…)

Thevenin’s equivalent voltage is the difference in this voltage

rR

rE

rRR

rREVVV abth 242

1

If ∆r is 5% of R or less, Thevenin equivalent voltage can be simplified tobeIf ∆r is 5% of R or less, Thevenin equivalent voltage can be simplified tobe

R

rEVth 4

Thevenin’s equivalent voltage is the difference in this voltage

Slightly Unbalanced Wheatstone Bridge (Cont…)

Thevenin’s equivalent voltage is the difference in this voltage

rR

rE

rRR

rREVVV abth 242

1

If ∆r is 5% of R or less, Thevenin equivalent voltage can be simplified tobeIf ∆r is 5% of R or less, Thevenin equivalent voltage can be simplified tobe

R

rEVth 4

Thevenin’s equivalent resistance can be calculated by replacing thevoltage source with its internal resistance and redrawing the circuit asshown in Figure 5.10. Thevenin’s equivalent resistance is now given as

Slightly Unbalanced Wheatstone Bridge (Cont…)

rRR

rRRRRTh

))((

2

Thevenin’s equivalent resistance can be calculated by replacing thevoltage source with its internal resistance and redrawing the circuit asshown in Figure 5.10. Thevenin’s equivalent resistance is now given as

o

If ∆r is small compared to R,the equation simplifies to

22

RRRth RRth or

Thevenin’s equivalent resistance can be calculated by replacing thevoltage source with its internal resistance and redrawing the circuit asshown in Figure 5.10. Thevenin’s equivalent resistance is now given as

Slightly Unbalanced Wheatstone Bridge (Cont…)

Thevenin’s equivalent resistance can be calculated by replacing thevoltage source with its internal resistance and redrawing the circuit asshown in Figure 5.10. Thevenin’s equivalent resistance is now given as

o o

R R

RRth

R R + Δr

Figure 5.10: Resistance of a Wheatstone.

We can draw the Thevenin equivalent circuit as shown in Figure 5.11

Slightly Unbalanced Wheatstone Bridge (Cont…)

We can draw the Thevenin equivalent circuit as shown in Figure 5.11

Figure 5.11: Approximate Thevenin’s equivalent circuit for a Wheatstonebridge containing three equal resistors and a fourth resistor differing by 5%or less

We can draw the Thevenin equivalent circuit as shown in Figure 5.11

Slightly Unbalanced Wheatstone Bridge (Cont…)

We can draw the Thevenin equivalent circuit as shown in Figure 5.11

Figure 5.11: Approximate Thevenin’s equivalent circuit for a Wheatstonebridge containing three equal resistors and a fourth resistor differing by 5%or less

Kelvin bridge is a modifiedversion of the Wheatstone bridge.The purpose of the modification isto eliminate the effects of contactand lead resistance whenmeasuring unknown lowresistances.

The measurement with a highdegree of accuracy can be doneusing the Kelvin bridge forresistors in the range of 1 Ω toapproximately 1 µΩ.

Kelvin bridge is a modifiedversion of the Wheatstone bridge.The purpose of the modification isto eliminate the effects of contactand lead resistance whenmeasuring unknown lowresistances.

The measurement with a highdegree of accuracy can be doneusing the Kelvin bridge forresistors in the range of 1 Ω toapproximately 1 µΩ.

Kelvin bridge is a modifiedversion of the Wheatstone bridge.The purpose of the modification isto eliminate the effects of contactand lead resistance whenmeasuring unknown lowresistances.

The measurement with a highdegree of accuracy can be doneusing the Kelvin bridge forresistors in the range of 1 Ω toapproximately 1 µΩ.

Since the Kelvin bridge uses a second set of ratio arms (Ra and Rb, it issometimes referred to as the Kelvin double bridge.

Kelvin bridge is a modifiedversion of the Wheatstone bridge.The purpose of the modification isto eliminate the effects of contactand lead resistance whenmeasuring unknown lowresistances.

The measurement with a highdegree of accuracy can be doneusing the Kelvin bridge forresistors in the range of 1 Ω toapproximately 1 µΩ.

Kelvin bridge is a modifiedversion of the Wheatstone bridge.The purpose of the modification isto eliminate the effects of contactand lead resistance whenmeasuring unknown lowresistances.

The measurement with a highdegree of accuracy can be doneusing the Kelvin bridge forresistors in the range of 1 Ω toapproximately 1 µΩ.

Kelvin bridge is a modifiedversion of the Wheatstone bridge.The purpose of the modification isto eliminate the effects of contactand lead resistance whenmeasuring unknown lowresistances.

The measurement with a highdegree of accuracy can be doneusing the Kelvin bridge forresistors in the range of 1 Ω toapproximately 1 µΩ.

Fig. 5.12: Basic Kelvin Bridge showinga second set of ratio arms

Since the Kelvin bridge uses a second set of ratio arms (Ra and Rb, it issometimes referred to as the Kelvin double bridge.

Fig. 5.12: Basic Kelvin Bridge showing a second set of ratio armsFig. 5.12: Basic Kelvin Bridge showing a second set of ratio arms

The resistor Rlc represents the lead and contact resistancepresent in the Wheatstone bridge.

The second set of ratio arms (Ra and Rb in figure) compensatesfor this relatively low lead-contact resistance.

Fig. 5.12: Basic Kelvin Bridge showing a second set of ratio armsFig. 5.12: Basic Kelvin Bridge showing a second set of ratio arms

The resistor Rlc represents the lead and contact resistancepresent in the Wheatstone bridge.

The second set of ratio arms (Ra and Rb in figure) compensatesfor this relatively low lead-contact resistance.

When a null exists, the value for Rx is the same as that for theWheatstone bridge, which is

At balance the ratio of Rb to Ra must be equal to the ratio of R3 to R1.Therefore,

1

32

R

RRRx

1

3

2 R

R

R

Rx or

At balance the ratio of Rb to Ra must be equal to the ratio of R3 to R1.Therefore,

a

bx

R

R

R

R

R

R

1

3

2

When a null exists, the value for Rx is the same as that for theWheatstone bridge, which is

At balance the ratio of Rb to Ra must be equal to the ratio of R3 to R1.Therefore,

1

3

2 R

R

R

Rx

At balance the ratio of Rb to Ra must be equal to the ratio of R3 to R1.Therefore,

a

bx

R

R

R

R

R

R

1

3

2