BETL 305 ELECTRONIC MEASUREMENT &

INSTRUMENTATION

BY PRASHANT KUMAR

ASST. PROFESSOR

MITS GWALIOR

UNIT II TRANSDUCERSTransducer Block Diagram

A transducer will have basically two main components.

They are

1. Sensing ElementThe physical quantity or its rate of change is sensed

and responded to by this part of the transistor.

2. Transduction ElementThe output of the sensing element is passed on to the

transduction element. This element is responsible for

converting the non-electrical signal into its proportional

electrical signal.

• There may be cases when the transduction element

performs the action of both transduction and

sensing. The best example of such a transducer is a

thermocouple.

• There are transducers which don’t require external

Excitation

• measurand=quantity under measurement

TRANSDUCER

Defnition of transducer: A transducer is a device, usually electrical, electronic, electro-mechanical, electromagnetic, photonic, or photovoltaic that converts one type of energy or physical attribute (egdisplacement, change in velocity) to another (generally electrical or mechanical) for various measurement purposes including measurement or information transfer (for example, pressure sensors).

STATIC CHARECTERISTICS OF TRANSDUCERS1. Linearity

Its input vs output characteristics should be linear and it should produce these characteristics in balanced way.

(Linearity–can be defined as the variation in the constant of proportionality between the input physical quantity and the output electrical signal. A sensor or a transducer is therefore said to be linear when the constant of proportionality has the same value within the whole measurand range (i.e. when the graph relating input to output is a straight line))

2. Ruggedness

A transducer should be capable of withstanding overload and some safety arrangements

must be provided with it for overload protection.

3. Repeatability

The device should reproduce the same output signal when the same input signal is applied again and again under unchanged environmental conditions, e.g., temperature, pressure,

humidity, etc.

4. High Reliability and Stability

The transducer should give minimum error in measurement for temperature variations,

vibrations and other various changes in surroundings.

CONTINUED.......5. High Output Signal Quality (High SNR)

The quality of output signal should be good, i.e., the ratio of the signal to the noise should be high and the amplitude of the output signal should be enough.

6. No Hysteresis

It should not give any hysteresis during measurement while input signal is varied from its low value to high value and vice versa.

7. Residual Reformation

There should not be any deformation on removal of input signal after long period of use.

Resolution is the minimal change of the input necessary to produce a detectable change at the outputPrecision: The capacity of a measuring instrument to give the same reading when repetitively measuring the same quantity under the same prescribed conditionsPrecision implies agreement between successive readings, NOT closeness to the true valueTwo terms closely related to precision Repeatability : The precision of a set of measurements taken over a short time

interval Reproducibility : The precision of a set of measurements BUT i) taken over a long time interval or ii) Performed by different operators or iii) with different instruments or iv) in different laboratories

Hystheresis: The difference between two output values that correspond to the same input depending on the trajectory followed by the sensor (i.e., magnetization in ferromagnetic materials)

The basic equation is y = mX + B, where X is the scaling or multiplier, and B is the offset. Using a little basic algebra we can apply this same set up to calculate scale and offset of any linear sensor or device with a linear output

CLASSIFICATION OF TRANSDUCERS

ACTIVE TRANSDUCERSActive transducers are those which do not require any power source for their operation. They work on the energy conversion principle.

ACTIVE TRANSDUCER PARAMETER

1.PEIZOELCTRIC TRANSDUCER Pressure/strain/displacement to Electric potential

2.THERMOCOUPLE Temperature to electrical potential (emf)

3. Electromagnetic Change in area/velocity /displacement to Induced Emf

EXAMPLE OF PRECISION & ACCURACY (SHOOTING DART)

STRAIN GAUGE

MECHANICAL STRAIN =

ELECTRICAL STRAIN

ELECTRICAL OUTPUT

=

STRAIN GAUGE

l

l

R

R

Wheatstone bridge

R

R

GENERAL WORKING OF STRAIN

GAUGE

STRAIN: It is defined as extension or reduction per

unit lengthl

Sl

STRESS STRAIN CURVE

The change in the value of resistance by the application of force can be explained by the normal dimensional changes of elastic material.

If a positive strain occurs, its longitudinal dimension (x-direction) will increase while there will be a reduction in the lateral dimension (y-direction).

The reverse happens for a negative strain.

Since the resistance of a conductor is directly proportional to its length and inversely proportional to its cross sectional area, the resistance changes.

The resistivity of a conductor is also changed when strained. This property is known as piezoresistive effect.

GAUGE FACTOR

2

resistance of unstrained gauge=R = .....( )

to find R we need to differentiate R w.r.t stress S

...............( )

both side by R = we get

1 1 1

Li

A

dR L L A Lii

dS A S A S A x

Ldividing

A

dR L A

R dS L S A S

1

...............( )iiix

As we observe it from eq(iii)

The effective change in resistance w.r.t strain is due

to three factors Per unit change in length Per unit change in area

Per unit change in resistivity

(Peizoresitivity)

The piezoresistiveeffect is a change in

the electrical resistivity of a

semiconductor or metal when

mechanical strain is applied

L

L

A

A

GAUGE FACTOR…..

Continued..

2

2

2. .4 4

1 1 2.2. . ......( )

4

4

this value of eq (iv) in (iii) we get

1 1 2 1

poisson's ratio

strain =

/

D A DArea D

S S

A D DD iv

DA S S D S

substituting

dR L D

R dS L S D S S

now from

Lateral

Longitudnal axia

starin

.

D

DLl

L

D L

D L

1 1 2 1

when 0 it can be approximated as

1 1 2 1

2........( )

factor = G

eq (v) both side by

get

1 2

1

f

f

f

R L L

R S L S L S S

S

R L L

R S L S L S S

R L Lv

R L L

R

RGaugeL

L

Ldividing

L

we

GL

L

G

2 ( )L

strainS L

Continued…..1 1 2 1

factor = G

eq (v) both side by

get

1

1 2 ( )

2

f

f

f

dR L LR dS L S L S S

RRGaugeL

LL

dividingL

we

GL

L

LG strain

S L

Desirable characteristics in a material for strain

Gauge1.High Gauge factor2.High resistivity3. Low temp. sensitivity (Low temp coefficient of resistance)4. Low Hysteresis5. Linearity (Strain Vs Resistance should be linear)6. High yield point

STRAIN GAUGE

A bonded strain gauge will be either a wire type or a foil type as shown in the figure

below. It is connected to a paper or a thick plastic film support. The measuring leads are

soldered or welded to the gauge wire. The bonded strain gauge with the paper backing is connected to the elastic member whose

strain is to be measured.

Unbonded Strain Gauge is used at places where the Gauge is to be

detached and used again and again

BASIC STRAIN GAUGE WORKING USING WHEATSTONE BRIDGE

A quarter bridge output corresponding to the application of a force is shown below. Initially, the circuit will be balanced

without the application of any force. When a downward force is applied, the length of the strain gauge increases and thus a

change in resistance occurs. Thus an output is produced in the bridge corresponding to the strain.

SEMICONDUCTOR STRAIN GAUGEFor Semiconductor strain gauge material used is either n-type S.C or P-type S.C

It is based on Principle of Piezo-resistivity

Advantages :

1. High Gauge factor (>>130)

2. Very Low hystresis (<<0.05%)

Disadvandage

1. Poor linearity

2. prone to error due to high sensitivity to temp.

COMPARISON BETWEEN SEMICONDUCTOR VS METALLIC GAUGEPARAMETERS METALLIC STRAIN GAUGE SEMICONDUCTOR STRAIN

GAUGE

GAUGE FACTOR LOW HIGH

HYSTRESIS HIGH LOW

LINEARITY HIGH POOR

COST LOW EXPENSIVE

STRAIN GAUGE

PRINCIPLE OF WORKING OF S.GAUGE: Resistance of a

conductor changes when it is strained. This property can be

used to measure Pressure, Force and Displacement.

APPLICATION OF STRAIN GAUGE:1.TO measure pressure

2. To measure Displacement3. To measure force

THERMISTORS

MATHEMATICAL EXPRESSSIONS

APPLICATION OF THERMISTORS

1. measurement of temp.(thermistors’s large change of resistance with temp. provides good accuracy and resolution)

2. temperature compensator in in electronic circuits (because of NTC)

3. measurement of power at high frequency

4. measurement of level of liquid/ flow of liquid

5. measurement of time delay

MATHEMATICAL ANALYSIS OF THERMISTOR

0

0

0 0

1 1R=R exp ..

eq

....( )

(

i)

R is the resistance of thermistor at the temperature T in K

R is the resistance at given temperature T in K

is the material specific constant

differentiat

iT T

wher

i g

e

n

2

0

0

w.r.t Temp. T

we get

log

ln ln

1 1

dR R

dT T

taking weget

R R

T T

2

1 dR

R dT

T

2

1 dR

R dT T

CAPACITIVE TRANSDUCERS

• PRINCIPLE OF WORKING : A capacitive transducer works on principle of Capacitance of Parallel plate capacitor.

• Capacitance of a parallel plate capacitor is given by

• Capacitive transducer works on the principle that capacitance is varied by variation in any one of following parameters

I. Change in effective plate area A /(overlapping area)II. Change in sepration between parallel platesIII. Variation in dielectric constant

0 r AC

d

r

Change in capacitance can be converted into required electrical format using capacitor equation

by capacitor eqution

Q=CV......(i)

differentiating both side we get

( )C C

dQ dV dCC V

dt dt dt

dV dC dQI C V I

dt dt dt

VARIABLE AREA BASED CAPACITOR TRANSDUCERCapacitance of parallel plate capacitor is directly proportional to effective overlapping area between two plates.

0 r AC

d

C A

C A

C A

Used to measure Linear displacementUsed to measure angular displacement

LINEAR DISPLACEMENT MEASUREMENT USNGVARIABLE AREA BASED CAPACITOR

0 0

0

of overlapping part of plates

of overlapping part of plates

Sensitivity= F/m

r r

r

A wlC C

d d

l length

w width

wC

l d

ANGULAR DISPLACEMENT MEASUREMENT USNGVARIABLE AREA BASED CAPACITOR

0

2

2

0

2

0

2

2

F/radian2

r

r

r

AC

d

rA

rC

d

C rSensitivity C

d

VARIABLE DISTANCE BASED CAPACITOR TRANSDUCER

It is used for linear displacement/pressure measurement.

0

0

2

1

F/meter

r

r

AC

d

Cd

ACsensitivity S

d d

VARIABLE DIELECTRIC CAPACITIVE TRANSDUCER

Liquid level measuremen

t using dielectric variation

Displacement measurement

ADVANTAGE OF CAPACITIVE TRANSDUCER

1) High sensitivity

2) Very small power requirement

3) Good frequency response

4) High input impedence so minimum loading effect

DISADVANTAGE OF CAPACITIVE TRANSDUCER

1. Proper insulation of metallic parts required

2. Non linear behaviour due due to edge effect

3. Stray capacitance between metallic wires affect performance

Applications:

Measurement of i) force, ii) angular and linear displacement ,iii) moisture, iv) pressure v) water level indicator

THERMOCOUPLE

It is temperature to electrical (emf) energy conversion based transducer.WORKING PRINCIPLE:Themocouple is based on three effects i) Seeback effectii) Peltier effectiii) Thompson effectSeeback effect: when the temperature difference exists between junctions of two dissimilar metals the the thermo emf is generated across terminals.

Peltier effect when electric current passes junction of two dissimilar metals heat is absorbed at one junction and liberated at another junction

Thompson effects: when a homogeneous electrical conductor is subjected to a temperature gradient then a corresponding voltage gradient is generated along the conductor.

Materials used in thermocouple

POSITIVE WIRE

NEGATIVE WIRE

Temp (degree centigrade)

COPPER CONSTANTAN -253 to 400

Iron CONSTANTAN -200 to 850

platinum Platinum(87%)+Rhodium(13%)

0-1400

2

emf generated

( ) ( )

thermal

E a T b T

Adavantage:High temperature measurement rangeEasy calibrationFast responseLow costDisadvantage1. Reference junction is

necessary2. Non linearity

LVDT (LINEAR VARIABLE DIFFERENTIAL AMPLIFIER)WORKING PRINCIPLE:

LVDT is based on variation in inductance with differential output.

Inductance can be varied by variation in these three quantities

I. Magnetic permeability of material

II. Number of turns

III. Geometric configuration

Secondary winding are connected with opposite polarity to provide differential output

0 r AL

l

CONSTRUCTIONLVDT consists of a cylindrical transformer where it is surrounded by one primary winding (P1) on one side and two secondary windings (S1and S2 ) on the other side

The number of turns in both secondary windings are equal, but they are connected such that both have opposite polarity.

The primary winding is connected to an AC source.

A soft iron core moves within the hollow cylindrical core and changes the magnetic flux linked with the primary and two secondary windings.

WORKINGCase 1: when iron core is at centre( null position) E0=0, (Es1=Es2) because the flux linking with both secondary windings is equal, hence equal emf are induced in them. (Es1 = Es2 ) ( E0=Es1-Es2)

Case 2: When the core is moved to the left of null position (O - A) more flux links with winding S1 and less with winding S2.

Hence, output voltage is Es1 is greater than Es2. The output voltage is positive and in phase with input signal.

Case 3: When the core is moved to the right of null position (O- B) more flux links with winding S2 and less with winding S1

Hence, output voltage Es2 is greater than Es1.The output voltage is negative and 180o out of phase with input signal.

Equivalent

Circuit of LVDT

WORKING AND CHARECTERISTICS

..

Adavntage of LVDT

1. high linearity

2. high sensitivity

3. very low hystresis

4. low power consumption

Disadvantages

1.large offset(threshold)

2. easily affected by stray magnetic field

Applications:

1. Linear displacement measurement

2. Measurement of pressure, tension,

PEIZOELECTRIC TRANSDUCER

Working principle:

The main principle of a piezoelectric transducer is that a force, when applied on the quartz crystal, produces electric charges on the crystal surface.

The charge thus produced can be called as piezoelectricity. Piezo electricity can be defined as the electrical polarization produced by mechanical strain on certain class of crystals.

The rate of charge produced will be proportional to the rate of change of force applied as input. As the charge produced is very small, a charge amplifier is needed so as to produce an output voltage big enough to be measured