electrical measurements and instrumentation

8/13/2019 Electrical Measurements and Instrumentation

1/185

ELECTRICAL MEASUREMENTS AND

INSTRUMENTATION

EE204

LECTURER

ENG. G. KAPUNGU


2/185

INTRODUCTION

Formal definition:

Measurement (also called metrology) is the

science of determining values of physical

variables.

Instrumentation is the technology of

measurement.


3/185

Physical Variables

Temperature

Pressure

Light intensity

Displacement

Speed

LevelFlow-rate etc


4/185

Typical Applications of Measurements

1. Monitoring of a process or operation to

indicate its state or condition.

Examples:

i. Monitoring environmental conditions

ii. Water and electricity meters monitor

quantity used.iii. Patient monitoring in hospitals (blood

pressure, heart beat, temperature) etc.


5/185

Applications (contd)

iv. In vehicles various instruments areincorporated to indicate speed, fuel left intank, engine temperature etc.

2. Process control:automatic control systems incorporatemeasuring instruments at various stages of

the process.3. Data recordingthis is the recording of data

for storage and later use.


6/185

Contd

examples of recording media are magnetic

tape, paper chart cd etc.

Block diagram of an instrumentation system

measurement target

object object

Dataacquisition

Data

processing Datadistribution


7/185

Instrumentation system

1. Data acquisition

this is acquiring information about the

measurement object using suitable sensors

and conversion into electrical data

(transduction).

more than one variable can be measured orone variable can be measured at different

points simultaneously.


8/185

Contd

2. Data processing

This is manipulation of measurement data in

order to achieve some desired result.

3. Data distribution

This is the supplying of data to the target

object(s) This could be a monitor, controller or a

recorder.


9/185

Standards

1. International standards:

Defined by international agreements

2. Primary standards: Maintained at institutions around the world

Main function is checking accuracy of

secondary standards


10/185

Contd

3. Secondary standards

Employed in industry as references for

calibration and for verifying working

standards.

4. Working standards

Used as measurement references on a day

to day basis in all electronics labs.


11/185

Measurement errors

Measurement can thus be redefined as theprocess of comparing an unknown quantity withan expected (standard ) quantity

Usually, measurement gives a value that is notthe expected value.

The difference is measurement error.

Error is the measure of the degree that themeasured value conforms to the expected value.


12/185

Contd

That is where and are the

expected and the measured values

respectively.

Can be

Fractional error =

And % error is fractional error is fractional

error x100%

nn XYE nY nX

n

nn

Y

XY


13/185

Contd

Absolute fractional error = and is

always positiven

nn

Y

XY


14/185

Types of errors (3 types)

1. Gross errors or Human errors

these result from carelessness e.g.

misreading an instrument or incorrectly

recording a reading.

2. Systematic errors -

Instrumental errors due to friction and zero

positioning.


15/185

Contd

Environmental errorsdue to ambient

conditions i.e.

o Temperature

o Humidity

o Pressure

o Presence of electric and magnetic fields


16/185


17/185


18/185

Measurement error combinations

Used when quantities are calculated from

measurements made from two (or more)

instruments.

it is assumed that the errors combine in a

worst possible way.

i. Sum of quantities

which give

)()(2211

VVVVV

)()( 2121 VVVVV


19/185

Contd

ii. Difference of quantities

the error of the difference of two

measurements are again additive:

and

)()( 2211 VVVVV

)()( 2121 VVVVV


20/185


21/185

Contd

IV. Quotient of quantities:

% error in E/I = (%error in E) + (%error in I)

v. Quantity raised to a power:%error in = B(%error in A)

BA


22/185

Contd

Some more definitions :

i. Accuracythe degree of exactness of a

measurement compared with the expected

value.

ii. Relative accuracy, A = 1(absolute error)

iii. % accuracy = A x 100%

iv. Precisionis the consistency or repeatability

of a measurement.


23/185

Contd

v. If i readings are taken and is the average ofthe readings, and is the reading, wedefine precision as:

vi. Instrument is a device used to indicate the presentvalue of a variable. (it can be analogue or digital)

iXiX

thi

i

ii

XXXP 1


24/185


25/185

Characteristics (response) of

instruments

These are divided into two types depending

on:

i. Type of input to the instrument

ii. The point in time the instrument is observed

iii. The type of output

Definition: - Plot of an instruments outputagainst time is a response curve.


26/185

Contd

a) Static response:

This describes the behavior of the instrument

when it attains steady state

( i.e. has been allowed enough time to settle

down to a steady reading)

Can also be response to a steady input.


27/185

Contd

b) Dynamic response:

This relates instrument behavior to a varying

input

Or instrument behavior after a sudden

change in input value e.g. application of a

step input or an impulse input).


28/185

Type of inputs

i. Ramp input

Signal amplitude changes linearly with time

time

amplituderamp f(t) = At; t > 0

= 0; t < 0


29/185

Inputs contd

ii. Step/steady input

A

amplitude

time

f(t) = Au(t)

u(t) = 1; t > 0

= 0; t < 0


30/185

Contd

iii. Impulse -

amplitude

time

0;0)( tt


31/185

Contd

iv. Step/ramp -

time

amplitude

f (t) = At; t > 0

= A ;t = 0


32/185

Contd

v. The sinusoid

Af(t) = Asint


33/185

Contd

vi. Random _

f(t) = ?


34/185

Static(steady state) characteristics

Listed on instrument data sheets

Apply only when instrument is used under

standard calibration conditions.

a) Accuracy and precision

b) Range or span

This is the maximum and minimum values

that an instrument is designed to measure.


35/185

Contd

c) Bias

This is a constant error that exists over the

full range of measurement.

i.e. a reading always appears before an input

is applied.

Can be removed by calibration.


36/185


37/185

Contd

e) Sensitivity

Change of in instrument output per unit

change in input.

i.e. sensitivity = scale deflection / value of

measurand causing the deflection.

(slope of output / input characteristic or

transfer function)


38/185

Contd

f) Sensitivity to disturbance

Instrument must be minimally sensitive to all

other conditions except the measurand.

ambient conditions are a source of this

disturbance and the effects are in three

forms:

i. Zero driftzero reading is modified by

ambient conditions.


39/185

Contd

E.g. in a voltmeter, zero drift coefficient

related to temperature changes is measured

in volts per degree.

An instrument can have several zero drift

coefficient related to other environmental

parameters.

Recalibration removes zero drift.


40/185

Contd

g) Sensitivity drift

This defines the amount by which is modified

by changes in ambient conditions.

h) Zone drift

Occurs only over a certain zone.


41/185

Illustration of drift

o/p

i/P

Nominal response

Zero drift

Sensitivity drift

both


42/185

Static characteristics (contd)

i) Hysteresis -

This is the non-coincidence of the loading

and the unloading calibration curves.

Associated with capability of memory since

reduction of input to zero results in a

remanance of the output quantity

This property is made use of in magnetic

recording.


43/185

Contd

j) Dead space

This is the range of input values where there

is no change in output

Also occurs in instruments which do not

exhibit hysteresis.

k) Threshold

The minimum value reached by the input

before instrument gives an output reading.


44/185

illustration

l) Resolutionsmallest change in input thatproduces an observable change in instrument

o/p

Input variable

threshold

Dead

band


45/185

Dynamic response

Lineartimeinvariant systems which are

asymptotically stable:

i. Linearobeys the principle of superposition

and the principle of frequency preservation.

ii. Time invariantsystem properties do not

vary with time.

iii. Asymptotically stablesystem stabilizes with

time.


46/185

Contd

For such a system, there exists an empirical

relationship between input and output which

is:

ii

m

im

mm

im

m

oo

n

on

nn

on

n

qbdt

dqbdt

qdbdt

qdb

qadt

dqa

dt

qda

dt

qda

011

1

1

011

1

1

.......

.......


47/185

Contd

The right hand side assumes use of known

inputs.

For a step input qi= x0for t > 0

= xrfor ramp input

= xssint

The qsare functions of time and the asandbsare constants.


48/185

Contd

In practical instruments, certain assumptions

can be made and certain restrictions can be

imposed.

1stassume only step input. The 1stand higher

order terms on the right hand side reduce to

zero.

i.e.:

iooo

n

on

n qbqadt

dqadt

qda 01.........


49/185

Zeroorder instrument

2ndassumption

Then

The expression describes a zeroorder

instrument and k is the static sensitivity.There is no dynamic error and output strictly

follows input.

arezerosaan 1,........,

iio

o

o kqqa

b

q


50/185

Contd

A linear displacement potentiometer is a

typical example of a zero order instrument.


51/185

Firstorder instrument

If all second and higher order terms are

assumed to be zero

and initial conditions are such that at t

= 0 (no bias)

Then:

Let D = d/dt

0o

q

ioooo qbqa

dt

dqa 1


52/185


53/185


54/185

Contd

The first part on the right hand side is the

particular integral and the second the

complementary function

The c.f. reduces to zero as t becomes large

resulting in the output assuming the value of

the p.i.


55/185

illustration

An instrument satisfying the above conditions

is a first - order instrument.

Final reading

o/p

time

90%

63%

90% lag

Dynamic error


56/185

Contd

A typical firstorder instrument (or part of an

instrument system) is a thermocouple.

The time it takes the output to reach 63% of

final value is the time constant.

The instruments are associated with lag

quoted as % of response.

Figures used are usually the time required for

output to rise to 90%, 95% and 98%.


57/185

Dynamic characteristics of importance

These are fidelity and speed of response:

a) Fidelity -

Quality of indication by the instrument for a

time-varying input.

Degree of closeness with which the output

reproduces the time-varying input.

Difference results in dynamic error.


58/185

Contd

b) Speed of response

Rapidity with which the instrument response

to changes in input.

The delay is called lag.

Both dynamic error and lag must be known

for each input in order to make correct

estimation of data.


59/185

Second - order instrument

Assumptions:

i. all third order coefficients and above are

zero.

ii. Initial conditions are such that output is zero

at t = 0.

iii. The original equation becomes:

ioo qbqaDaqDa 0012

2


60/185

Contd

Let static sensitivity

Let un-damped natural frequency

And damping ratio

0

0

abk

2

0

aa

2

1

2aa


61/185

Contd

then:

Any instrument which obeys the above

equation is a second-order instrument.

Dynamic behavior depends on the value of

the damping ratio

1/2/2

DD

k

q

q

i

o


62/185


63/185


64/185

Contd

The transducer must fulfill two major

functions:

i. To sense the presence, magnitude, change in

and frequency of some measurand.

ii. To provide an electrical output which when

processed and supplied to a readout device,

gives an accurate representation of theoriginal measurand.


65/185

Classification of transducers

These are classified as:

i. Genuine energy converters ( called active

transducers)

ii. Energy controllers (passive transducers)

Important considerations in transducer

selection:

i. Long term stability of input / output

relationships (transfer characteristic)


66/185

Contd

ii. Size, shape and weight of the device

iii. Response to rapid changes in measurand

iv. Electrical output impedance

v. Reliability, availability and cost.

vi. Response to interfering and modifying inputs

vii. Effects of ambient conditions(temperature,humidity, vibration and supply frequency in

the case of ac powered devices.


67/185

Interfering and modifying inputs

Transducer

Interfering i/p, Ii

Modifying i/p, Mi

Desired i/p, Di

o/p due to MI ii &

o/p

o/p due to MD ii &


68/185

Contd

Desired input refers to the quantity the

transducer is specifically intended to respond

to.

Interfering input represents those quantitiesthe transducer is unintentionally sensitive to.

Modifying input represents the quantity

whose effect is to modify the desired andinterfering inputs.


69/185

Contd

Common sources of modifying inputs are

ambient conditions and battery voltage.

Finally, transducer behavior can be affected by

self heating, vibration and supply frequency.

Note:

A device that convert the modified electrical

signal into a non-electrical signal is an output

transducer e.g. a radio speaker.


70/185

Temperature transducers

These employ pure metal wire such as pureplatinum, copper, nickel, etc.

Provide definite resistance value at each

temperature.Platinum is the preferred metal because:

i. It is stable under different environmental

conditionsii. Resistance / temperature characteristic is

linear over a wide temperature range.


71/185

Resistance temperature detectors

It is least sensitive to contamination

RTDs:

The resistance of metals increases with

temperature according to:

Platinum RTDs are either thick film or wirewound type.

The thick film type has a faster speed ofresponse.

)](1[ 1212 TTRRT


72/185

Contd

If the two are immersed in hot water whose

temperature is T at time t = 0, response curves

are shown below:

time

T

Thickfilm

Wire wound


73/185

Contd

Note the superior response of the thick film

type.

This transducer is a firstorder type and is an

example of a passive transducer.


74/185


75/185

Contd

Operating temperature -60C to 150C

The resistance / temperature characteristic is

given by:

Where is a material constant which ranges

from 3000K to 5000K.

The major advantages are:

)11(

00TTeRR


76/185

Contd

1. high sensitivity and

2. Small size.

3. Small mass (implying shorter time constant)

The small size makes them ideal for

measurement in confined places.

The major disadvantages are limited range (-

60C to 150C)

and non-linearity.


77/185

Contd

Linearizing networks are now available

When connected to microprocessors software

does the linearising.

They also find applications in temperature

control systems where linearity is not as

important as sensitivity.

f


78/185

Some applications of thermistors

a. Because of their negative temperaturecoefficients, they are used to compensate for

effects of temperature on circuit components.

It is mounted on or near the circuit element sothat it experiences the same temperature as the

circuit element.

It can be arranged that the equivalent resistancethat results is constant over a wide temperature

range.

d


79/185

Contd

b. Measurement of thermal conductivity:

Two thermistors are placed in two cavities

They are connected in a bridge arrangement

so that with air in both cavities, bridge isbalanced.

Air in one cavity is replaced by, say, carbon

dioxide which has lower conductivityThe amount of bridge unbalance represents

amount of gas.

d


80/185

Contd

c. Measurement of gas flow-rate:

One thermistor is sealed in brass and other is

placed in a hollow pipe and the two are

placed in a bridge circuit.

With no gas flow, the bridge is balance.

When gas flows, the thermistor is cooled and

its temperature is reduced and resistance

increased.

C d


81/185

Contd

The out of balance voltage is proportional to

the flow-rate.

The thermistor is a passive transducer and is a

firstorder device.

Typical flow-rates of the order of 0.001 cubic

cm per minute have been measured by this

method.


82/185

C d


83/185

Contd

This effect results from the diffusion ofelectrons across the interface between the

two metals.

The material giving the electrons becomemore positive and the one receiving more

negative.

This is an active transducer which is of the firstorder type.

F b i i


84/185

Fabrication

V

Referencejunction

Metal 2

Metal 1Sensing

junction

TTsV

C td


85/185

Contd

Another configuration:

DVM 1J

2J

Ice

Cu

Cuconstantan

JisTV

C td


86/185

Contd

The thermal contact (junction) can be madeby twisting, welding, soldering, pressing or

brazing.

A general two junction thermocouple:

Material 1

Material 2

C td


87/185

Contd

An alternative expression for the transfercharacteristic is:

Where the Cs are thermoelectric constants.

These depend on the two materials used.

)()( 2

212

2211 TTCTTCV

P i i l f th l b h i


88/185

Principles of thermocouple behavior

a) Must contain two dissimilar metals.

b) Output voltage depends only on the

difference between the two junction

temperatures

c) If a third metal is inserted into metal 1 or

metal 2, output voltage is not affected

provided the new junctions are at sametemperature.

t i l


89/185

materials

Thermocouples are made from:

i. Copper and iron

ii. Base metal alloys of alumel, chromel,

constantan, etc.

iii. The noble metals platinum and tungsten

iv. Noble metal alloysplatinum/rhodium,

tungsten/rhenium

Th th il


90/185

The thermopile

This consists of several thermocouplesconnected together in series.

All the reference junctions are at the same

temperature and all the hot junctions areexposed to the temperature being measured

The effect of connecting together n

thermocouples is to increase the sensitivity bya factor, n.

ill t ti


91/185

illustration

Reference junction

V

Force transducer


92/185

Force transducer

The strain gauge:

This is a resistive input transducer whose

resistance change is related to changes in

length.

Increase in length from L to L +

Results in increase in resistance from R to R +

Sensitivity of the gauge (or gauge factor) is

given by:

L

R

Contd


93/185

Contd

RR

LLRRG ///

Where: R = resistance

L = length

= mechanical strain

Hookes Law: S = E

Where: E = Youngs modulusS = mechanical stress


94/185

Contd


95/185

Cont d

Strain gauges are used in the measurement offorce, pressure, acceleration and dc bridges

are used as conditioners.

Main source of error is resistance change dueto temperature.

Bridge methods which make use of dummy

gauges compensate for these errors.

Force measurement (Contd)


96/185

Force measurement (Cont d)

The Piezoelectric transducer:

These are also used in the measurement of

force, acceleration and pressure

They are made from crystalline materials like

quartz, Rochelle salt and ceramics like barium

titanate

These materials generate a voltage whendeformed.

Contd


97/185

Cont d

The crystals contain molecules withasymmetrical charge distribution

When pressure is applied, crystal deforms and

there is relative displacement of +ve andvecharges within the crystal.

This produces external charges of opposite

sign.

Contd


98/185

Cont d

The associated output voltage is given by:

Where C is the capacitance of the crystal

The surface charge is related to the applied

pressure by:

Recall : for a parallel plate cap.

substituting for C:

Cvq o

ApSq q

d

AC ro

ro

qo

dpSv

Contd


99/185

Cont d

Letting the voltage sensitivity =

The output voltage becomes:

Reverse Piezoelectric effect:

When an ac voltage is applied across the

piezoelectric crystal, it vibrates at a frequency

determined by its geometry and size.

This reverse effect finds applications in sound

ro

qS

dpSv vo

Contd


100/185

Cont d

Generators found in toys, watches, electroniccalculators, electronic games, etc.

The piezo crystal can be cut to dimensions

which give it a desired natural frequency.

The frequency is very stable and is used to

stabilize oscillators in radio transmitters ,

clocks, computers, etc.

Step response of the piezoelectric


101/185

crystal

63%

time

o/p

Applied step

Contd


102/185

Cont d

This is a firstorder linear device.

Equivalent circuit:

pC

pR

Charge amplifier


103/185

Charge amplifier

Output of the piezo crystal is very small andhas to be amplified.

A charge amplifier is used for this purpose.

ovpC

fC

R

Op amp


104/185

Contd


105/185

Cont d

And

i.e. the output is independent of the crystal

and lead capacitances.

Example:

A piezoelectric transducer has a sensitivity of

28pC/N. it is connected to a charge amplifier

with a feedback capacitor of 22nF.

f

oC

qv

Example contd


106/185

Example cont d

Calculate the output of the at the instant astep input of 5kN is applied.

Solution:

A force of 5kN produces a charge ofq = 28 x 5000 coulomb = 140nC

= 6.36V6

9

1022

10140

x

x

C

qv

f

o

Example 2


107/185

Example 2

A system of piezo and amplifier has a timeconstant of 90 sec. how long will it take to lose

the first 5 sec of the step input?

Solution:

The output voltage is an exponential delay of

the form:

And

5% of step is 0.95V.

/t

o Vev

sec90

Contd


108/185

Cont d

90/95.0 tVeV

= 4.6 sec.


109/185

Contd


110/185

Cont d

For static or low frequency applications,

For frequencies of the order of 100kHz

Piezoresistive transducer:

This is change in crystal resistance with

pressure.

They are fabricated from semiconductor

materials e.g. silicon with boron as trace

impurity for p-type.

cZ

kZc 10


111/185

Displacement transducers using


112/185

resistive elements

The simplest type of displacement transduceris the a potentiometer

It consists of a resistive element with a moving

contactMotion of the contact can be translational,

rotational or a combination of the two (i.e.

helical).This is a passive device of the 0order type.

Displacement transducers (contd)


113/185

Displacement transducers (cont d)

The resistance element is driven by a dc or anac voltage and output voltage is a linear

function of input displacement

Materials usedi. wire wound on an insulating cylindrical core,

ii. carbon film or

iii. conduct plastics.

iv. Widely used are wirewound elements

Contd


114/185

Cont d

Major limitation is resolution (typically 40micro-meter for translational devices and 0.1for rotational pot of 5cm diameter).

Resolution is improved by use of carbon filmor conductive plastic.

Another limitation is linearity which dependson the uniformity of resistance along the

resistive element.Other major problems :

Contd


115/185

Cont d

Spurious output voltages associated with:

i. slider contact bounce

ii. Dirt

iii. Contact wear

iv. Friction and

v. Inertia of the moving parts

Displacement transducers using

l


116/185

capacitive elements

By definition, capacitance of a parallel platecapacitor is given by:

Any variation in any of the parameters in theexpression causes a variation in C.

Examples:

a. Variation in plate separation -

Faradsd

AC r

0

Contd.


117/185

Cont d.

fixed plate movable plate

displacement

Use of a capacitive transducer to


118/185

measure pressure

This uses a diaphragm and a static ( fixed)plate.

diaphragm

pressureStatic plate

Variation in area


119/185

Variation in area

This is made of a fixed semi-circular plate arotatable semi-circular plate.

As the plate rotates, the area between the

two changes thus changing the capacitance.Illustration:


120/185

Contd


121/185

Cont d

It can be shown that:

ss v

d

x

CC

C

CC

Cvv

][

21

1

21

2

Contd


122/185

Cont d

In this arrangement, P and Q are fixed andplate M moves between them.

assume M moves a displacement x towards P

we have:.

xd

andC

xd

C rr

0

20

1

Inductive transducers


123/185

By definition, self inductance of a coil is givenby:

Where N is the number of turns and S is thereluctance of the magnetic circuit and is given

by:

Where are

S

NL

2

A

lS

r0

r &0

Contd


124/185

The permeability of free space and therelative permeability of the material inside the

coil.

Any variation of the above parameters (usuallydue displacement ) alters the inductance.

Examples of inductance type transducers:

a. The simplest case is the change in thenumber of turns.

Contd


125/185

A sliding contact is used to alter the numberof turns.

b. Change in permeability (or reluctance) where

a soft iron plunger is used to alterpermeability.

Linear Variable DifferentialTransformer


126/185

This consists of a primary coil and twosecondary coils wound in opposition.

A ferromagnetic core (plunger) moves along

the axis of the three coils.since the two secondary coils are wound in

opposition,

When the core is at its central position,

In practice this condition is not met due tomismatches in the secondary coils.

21 vvvo

0ov

Contd


127/185

When the core is moved away from thecentre, the output voltage rises.

ov

x-x0

0180

Contd


128/185

This is a passive 0-order device whose outputdepends on both magnitude and direction of

displacement

Sensitivity ranges from 0.1V/cm to 50 mV/mThe complete displacement measurement

system based on the LVDT:

LVDT


129/185

oscillator LVDT

Phase

Sensitivedetector

Low-pass

filter ov

Contd


130/185

The phase sensitive detector produces anunsmoothed full-wave rectified signal which is

either +ve or -ve

This smoothed by the low-pass filter to giveThe oscillator supplies the primary coil a

reference to the phase sensitive detector.

ov

Photo-electric transducers


131/185

These can be divided into three types:i. Photo-conductive

ii. Photo-emissive and

iii. Photo-voltaic

Photo-conductive transducer (cell):

These are elements or compounds whose

conductivity increases with intensity of

electromagnetic radiation.

Contd


132/185

The radiation is usually in the visible or nearvisible part of the spectrum.

Examples of materials are:

Cadmium sulfide Cadmium selenide

Lead sulfide

Germanium and silicon

Contd


133/185

The material in deposited on a ceramicsubstrate in a zig-zag fashion.

Applications:

Automatic daylight switches

Automatic street lights control

Product counting on a production line.

Sorting of objects by size etc.

Contd


134/185

Advantages include: Inexpensive

Rugged

Will withstand shock and vibration

Operates at low voltage with a high enough

output to drive a relay.

Disadvantagescan be destroyed by strong

light and heat. Response is rather slow.

Examples of photo-conductive

transducer circuits


135/185

transducer circuits

Simple circuits:

Photo cell

relay

Photo-emissive transducers


136/185

Photo-emissive effect is the emission ofelectrons in a vacuum from metal orsemiconductor surfaces

This is as a result of absorption ofelectromagnetic energy by these materials.

The e.m. energy is in the visible or near visiblepart of the spectrum.

Electrons absorb enough energy from incidentphotons to escape from these surfaces.

Illustration


137/185

e

Incident photon

Evacuated glass tube

Semi-transparent

photocathode

e

anode

+-

Contd


138/185

Typical circuit used to measure photo-electriccurrent:

V

cellLR

pi

Lpo Riv

Contd


139/185

Photo-emissive materials are usuallycompounds of alkali metals.

Used in conjunction with a photomultiplier,

this transducer finds applications in atomicabsorption spectro-photometry.

for chemical identification of elements.

Photo-multiplier


140/185

Lightwindow

Photo

cathode

photon

Dynode 1 Dynode 3

Dynode 2

final

+700V

+100V +300V

+200V +600V

Contd


141/185

The released electrons are effectivelymultiplied by the process of secondary

emission at various stages of dynodes.

The gain of the tube is given by:Where: ksare constants for a given tube.

n is number of stages

vs is voltage between stages

nk

svkG 21

Semiconductor photo-diode


142/185

Depending on the external circuitry, thephoto-diode can be made to operate as aphoto-conductor or a photo-voltaic device (i.e.generates electrical energy.

These are fabricated from silicon and theyincorporate a p-n junction.

When reverse biased it operates as a

photoconductor and with no bias it is selfgenerating.

Contd


143/185

-V

fR

ov

Photovoltaic

configuration

Photoconductive

configuration

Signal conditioning


144/185

Transducers produce energy which is verysmall and often masked by noise signals.

The purpose of signal conditioning is to bring

the transducer output to a level and form thatis suitable for:

Signal conversion

Signal processing Indicating or recording

Contd


145/185

In passive transducers excitation andamplification are necessary

In active transducers, amplification is

required. Filtering may also be required in both cases.

Excitation may be ac or dc


146/185

Ac system


147/185

Ac carrier system:

transdu

cer

Ac

bridge

Calibration

& zeroing

Ac

amp

PhaseSensitive

detector

Carrier

oscillator

Power

supply

LowPass

filter

Signal conditioning


148/185

Note in each configuration, the presence of abridge after the transducer.

A bridge is used with passive transducers to

produce a change in voltage that isproportional to a parameter change (e.g. R,

C, or L)

The null indication principle is utilized.Bridges achieve a very high degree of accuracy


149/185

The Wheatstone Bridge


150/185

1R2R

3R 4R

1I 2I

A

B

C

D

Bridge analysis


151/185

In the bridge circuit, constitute theratio arms

is the standard arm and is the unknown

To measure the unknown resistor, theresistance in one or both ratio arms is

adjusted until balance is achieved.

At balance,

It can then be shown that

21&RR

3R 4R

2143 & RRRR VVVV

1

324

R

RRR

Example


152/185

Application of the Wheatstone bridge in strainmeasurement:

Assume ( strain gauge

resistance with no strain) = RAssume also that with no strain the bridge is

balanced.

Problem - assume gauge suffers a strain whichresults in a resistance change, R

4321 RRRR


153/185

Contd


154/185

Assume that 2R


155/185

i.e. strain is directly proportional to thebridges out of balance voltage and the meter

can be calibrated to read strain.

This configuration is referred to as a quarterbridge

Temperature compensation:

Change in strain gauge resistance alsodepends on changes in temperature

Temperature compensation


156/185

It becomes difficult to say whether R hasresulted exclusively from L or a contribution

from T.

In practice a second identical gauge is placedin an adjacent arm of the bridge.

Conditions:

Must be kept unstrained Must be identical to the active gauge

Contd


157/185

Must be kept under the same temperatureconditions as the active gauge.

can be the dummy gauge

Let R be resistance change due to T then:

Therefore the out of balance voltage due to

T is zero.

32orRR

222

)(&

2

V

RR

VRRV

VV CA

Contd


158/185

This is a temperaturecompensated quarterbridge.

The Half bridge:

To increase sensitivity, a half bridge is used.This consists of two identical active gauges in

adjacent arms.

These are mounted on opposite sides of thebeam.

The half bridge


159/185

1R active

3R active

1I 2I

A

B

C

D

Contd


160/185

Analysis of the half bridge:

Therefore the half bridge has twice the

sensitivity of the quarter bridge.

RRRR

VRRV

VV CA

)(

&2

R

RV

R

RV

R

VRVVAC2222


161/185

Contd


162/185

It can be shown that:Which is four times the sensitivity of the

quarter bridge.

Practical balancing arrangement

R

RVVAC

Summarydc bridges


163/185

The bridge can be used in a method called thenull method

Here, one or two resistors are manually

adjusted to achieve balance. An unknown resistor can be calculated.

It can also be used in the deflection mode

where change in any resistor value by Rresults in a proportional voltage ACV

Limitations of the Wheatstone bridge


164/185

It can measure resistances from a few ohms toseveral mega ohms.

The upper limit is set by reduction insensitivity

The lower limit is set by resistance ofconnecting leads and contact resistance.

To overcome the lower limitation, a modified

Wheatstone bridge is used. This is the Kelvinbridge

Ac Bridges


165/185

These are similar to dc brides butconsist of:

four impedance arms,

an ac source and

an ac detector

The impedances can be combinations of

resistors, capacitors and inductors.

Contd


166/185

They are not restricted to measuringimpedances only.

They are also very useful in:

Shifting phases Providing feedback networks for oscillators

and amplifiers

Filtering out undesirable signals

And measuring frequencies of audio signals

Analysis


167/185

In the diagram for the dc bridge, replace allresistors by impedance equivalents so that atbalance;

This is a general bridge equation

Is applicable to all bridges at balanceregardless of the actual components in thearms.

In general the impedances are complex anddepend on the frequency of the ac signal.

3241 ZZZZ

Contd


168/185

For balance, two conditions must be satisfiedsimultaneously:

a. Products of opposite arms of the bridge must

be equal.b. The sums of angles of opposite arms must be

equal.

c. i.e. 32413241 & ZZZZ

11 Z

Some practical ac bridges


169/185

1. Maxwell bridge: For this bridge,

Arm AB consists of

Arm BC consists of

Arm AD consists of

Arm CD consists of

Question: find -

11parlCR

2R

3R

xxseriesLR

xx LR &

solution


170/185

The impedances of the arms are written as:

xxx LjRZ

RZ

RZ

CRj

RZ

33

22

11

11

1

Contd


171/185

At balance:

Equating real and imaginary parts on the left

hand and right sides:

321 ZZZZ x

32

11

1 )(1

RRLRRCj

Rxx

321

1

32 RRCjRRRLjR xx

132

1

32 & CRRLR

RRR xx

Contd


172/185

Note that solutions to the Maxwell bridge arefrequency independent.

In general, ac bridge solutions are frequency

dependent.2. Similar angle bridge:

This bridge consists of

Arm AB =

Arm BC =

1R

2R


173/185


174/185

Bridges with frequency dependent

solutions


175/185

3. Opposite angle bridge This is used in the measurement of inductors

with high Q (Q >10)

Maxwell bridge is suitable for coils with Q

electrical measurements and instrumentation

Documents