Text Book on Instrumentation Update Latest09

1.0 MEASUREMENT

Science and Engineering Technology depends on the

technique of measurement for a significant

achievement in research and production.

The human senses cannot provide exact quantitative

information about the events occuring in our

environment and thus scienctific instruments are

employed to enable human to observe and measure

aspects of physical universe beyond the range and

precision of an unaided human senses.

Instruments are the essential extensions of human

sensing and perception without which scientific

exploration of nature would be impossible. Basic to all

engineering is design and basic to all design is the

measurements. Whatever exists, exists in some

amounts and thus needs to be quantified. If an engineer

or scientist were to be deprived of his measuring

devices, his discorveries or intellectual works would be

reduced to guessing and speculation.

Measurement: can be defined as a means for

describing the various physical and chemical

parameters of materials in quantitative terms. It is the

process by which one can convert physical parameters

to meaningful number. The result of measurement is

expressed as:

1

For example; 10cm lenght implies that the object is 10

times as large as 1cm (standard). For consistence and

quantitative comparison of physical parameters, certain

standards of mass, length, time, temperature and

electrical quantities have been established.

1.1 Measurement Units

The standard measure of each kind of physical quantity

is the Unit; the number of times the unit occurs in any

given amount of the same quantity is the number of

measure. Without the unit, the number of measure has

no physical meaning.

The very first measurement units were those used in

barter trade to quantify the amounts being exchanged

and to establish clear rules about the relative values of

different commodities. The early establishment of

standards for the measurement of physical quantities

proceeded in several countries at broadly parallel times,

and in consequence, several sets of units emerged for

measuring the same physical variable. For instance,

length can be measured in yards, meters, or several

other units. Apart from the major units of length,

subdivisions of standard units exist such as feet, inches,

centimeters and millimeters, with a fixed relationship

between each fundamental unit and its subdivisions.

Yards, feet and inches belong to the Imperial System of

units, which is characterized by having varying and

2

Measurement and Instrumentation Measurement Units

cumbersome multiplication factors relating fundamental

units to subdivisions such as 1760 (miles to yards), 3

(yards to feet) and 12 (feet to inches). The metric

system is an alternative set of units, which includes for

instance the unit of the meter and its centimeter and

millimeter subdivisions for measuring length.

All multiples and subdivisions of basic metric units are

related to the base by factors of ten and such units are

therefore much easier to use than Imperial units.

However, in the case of derived units such as velocity,

the number of alternative ways in which these can be

expressed in the metric system can lead to confusion.

As a result of this, an internationally agreed set of

standard units (SI units or Syst`emes Internationals

d’Unit´es) has been defined, and strong efforts are

being made to encourage the adoption of this system

throughout the world. In support of this effort, the SI

system of units will be used exclusively in this book.

However, it should be noted that the Imperial system is

still widely used, particularly in America and Britain. The

European Union has just deferred planned legislation to

ban the use of Imperial units in Europe in the near

future, and the latest proposal is to introduce such

legislation to take effect from the year 2010

1.2 Fundamental and Derived Units

To measure an unknonwn we must have acceptable unit

standard for the property that is to be assessed. Since

there are virtually hundreds of different quantities that

3

Measurement and Instrumentation Fundamental and derived units

man is called upon to measure, it would seem that

hundreds of different standard units would be required.

Fortunately, this is not the case. By choosing a small

number of basic quantities as standards, we can define

all the other in terms of these few.

The basic units are called fundamentals, while all the

others which can be expressed in terms of fundamental

units are called derived units, and formed by multiplying

or dividing fundamental units. The primary fundamental

units which most commonly used are lenght, mass, and

time, while measurement of certain physical quantities

in thermal, electrical, and illumination discipline are also

represented by fundamental units. These units are used

only when these particular classes are involved, and

they may therefore be defined as auxiliary fundamental

units. Every derived unit originates from some physical

law defining that unit. For example, the voltage [volt]:

This is the basic S.I units of volt.

4


Table 1.1 below shows the six basic S.I quantity and

units of measurement, with their unit symbol:

Table 1.1 Fundamental and Derived Units

Quantity Standard Unit Symbol

Length Metre M

Mass Kilogram Kg

Time Second s

Electric Current Ampere A

Temperature kelvin K

Luminous intensity Candela cd

Matter mole mol

(b) Supplementary fundamental units

Quantity Standard unit Symbol

Plane angle radian rad

Solid angle steradian Sr

(c) Derived units

Quantity Standard unit Symbol

Derivation formula

Area Square metre m2

Volume cubic metre m3

Velocity metre per second m/s

Acceleration metre per second squared m/s2

Angular velocity radian per second rad/s

Angular acceleration radian per second squared rad/s2

Density kilogram per cubic meter kg/m3

Specific volume cubic metre per kilogram m3/kg

Mass flow rate Kilogram per second kg/s

Volume flow rate cubic metre per second m3/s

Force newton N Kgm/s2

Pressure newton per square metre N/m2

Torque newton meter Nm

5


Momentum kilogram meter per second kgm/s

Moment of inertia kilogram meter squared kgm2

Kinematic viscosity Square meter per second m2/s

Dynamic viscosity newton second per square

meter

Ns/m2

Work, energy, heat Joule J Nm

Specific energy Joule per cubic meter J/m3

Power Watt W J/s

Thermal conductivity Watt per meter kelvin W/mK

Electric charge Coulombs C As

Voltage, emf, p.d Volt V W/A

Electric field strength volt per meter V/m

Electric resistance Ohms V/A

Electric capacitance Farad F As/V

Electric inductance Henry H Vs/A

Electric conductance Siemen S A/V

Resistivity Ohm meter m

Permitivity farad per meter F/m

Permeability Henry per meter H/m

Current density Ampere per square metre A/m2

Magnetic flux Webber Wb Vs

Magnetic flux density Tesla T Wb/m2

Magnetic field strenght Ampere per metre A/m

Frequency Hertz Hz s-1

Luminous flux Lumen lm cdsr

Luminance candela per square metre cd/m2

Illumination Lux lx lm/m2

Molar volume Cubic metre per mole m3/mol

Molarity Mole per kilogram mol/kg

Molar energy joule per mole J/mol

A derived unit is recongnized by its dimensions, which

can be defined as the complete algebraic formula for

6


the derived unit. The dimentsional symbols for the

fundamental units of lenght, mass and time are L, M,

and

T, respectively. So the dimensional symbol for the

derived unit of voltage as analysed is:

.

1.3 Multiples and Submultiples of units

The units in actual use are divided into submultiples for

the purpose of measuring quantities smaller than the

unit itself. Futhermore, multiples of units are designated

and named so that measurement of quantities much

larger than the unit is facilitated. Table 1.1 lists the

decimal multiples and submultiples of units.

Table 1.1

Name Symbol Equivalent

Tetra T 1012

Giga G 109

Mega M 106

Kilo K 103

Milli m 10-3

Micro 10-6

Nano n 10-9

Pico p 10-12

1.4 Standards of Measurement

A standard of measurement is a physical representation

of a unit of measurement. A unit is realized by reference

7

Measurement and Instrumentation Multiples and Submultiples of Units

to an arbitrary material standard or to natural

phenonmena including physical and atomic constants.

Standard of measurement classified by their function

and application in the following categories:

1. International standards

2. Primary Standards

3. Secondary standards

4. working standards

The international standards are defined by

international agreement. They represent certain units of

measurements to the closest possible accuracy that

production and measurement technology allow. These

standards are maintained at the International Bureau of

weights and measures in America and not available to

the ordinary user of measuring instruments.

The primary (basic) standards are maintained by

national standards laboratories in different parts of the

world. The National Bureau of standards (NBS) in

America, National Physical Laboratory (NPL) in Britain,

and Physikalisch Technische in Germany. The primary

standards represent the fundamental units and some of

the derived mechanical and electrical units. Primary

standards are not available for use outside the national

laboratories. One of the main functions of primary

standards is the verification and calibration of

secondary standards.

8

Measurement and Instrumentation Standards for Measurement

Secondary standards are the basic reference

standards used in industrial measurement laboratories.

These standards are maintained by the particularly

involved industry and are generally sent to the national

standards

laboratories (primary) on a periodic basis for

caliberation and comparison.

Working standards are the principal tools of a

measurement laboratory. They are used to check and

caliberate general laboratory instrument for accuracy

and performance or to perform comparison

measurements in industrial applications. A

manufacturer of precision resistances, for example, may

use a standard resistor (a working standard) in the

quality control department of his plant to check his

testing equipment.

1.5 Scale

Every measuring instruments has a scale which has

been appropriately graduated to indicate the magnitude

of the variable or quantity under measurement. For

digital instrument the numerical value is indicated or

displayed straight away at the indicating unit of the

instrument but for analogue instruments we have

basically two types of scale – Linear scale and non-linear

scale.

Linear scale: Shown in figure 1.1 bellow, where the

divisions or graduation are evenly spaced. The

9

Measurement and Instrumentation Measurement Scale

voltmeter shown has a range 0-100V, i.e. a full-scale

deflection (f.s.d) of 100V.

Figure 1.1

A non-linear scale is shown below in figure 1.2 below.

The scale is cramped at the begining and the graduation

are uneven throughout the range. The ammeter shown

has a f.s.d. of 15A.

Figure 1.2

1.6 APPLICATIONS OF MEASUREMENT

Today, the techniques of measurement are of immense

importance in most facets of human civilization. Present

day applications of measuring instruments can be

classified into three major areas.

The first of these is their use in regulating trade,

applying instruments that measure physical quantities

such as length, volume and mass in terms of standard

units.

The second application area of measuring instruments

is in monitoring functions. These provide information

10

Measurement and Instrumentation Applications of Measurement

that enables human beings to take some prescribed

action

accordingly. For example, regular study of a barometer

allows us to decide whether we should take our

umbrellas if we are planning to go out for a few hours.

Whilst there are thus many uses of instrumentation in

our normal domestic lives. The majority of monitoring

functions of instrumentation exist to provide the

information necessary to allow a human being to control

some industrial operation or process. In a chemical

process for instance, the progress of chemical reactions

is indicated

by the measurement of temperatures and pressures at

various points, and such measurements allow the

operator to take correct decisions regarding the

electrical supply to heaters, cooling water flows, valve

positions etc.

The third application of measurement instrumentation is

in its use as part of automatic feedback control systems.

Figure 1.1 shows a functional block diagram of a simple

temperature control system in which the temperature Ta

of a room is maintained at a reference value Td. The

value of the controlled variable Ta, as determined by a

temperature-measuring device, is compared with the

reference value Td, and the difference e is applied as an

error signal to the heater. The heater then modifies the

room temperature until Ta = Td.

11

Measurement and Instrumentation Applications of Measurement

Figure 1.1: Element of a simple controled loop system.

Excersice 1

1. Define Measurement and discuss its

importance in engineering and scientific

works.

2. Explain the term Unit of measurement.

3. Analyse the unit of the following Physical

quantities and write their basic S.I Units and

dimension; i. Pressure ii. Torque, iii. Density.

4. What do you understand by Standard of

measurement? Explain four types of Standards

that you know.

5. Discuss the application of measurement

techniqes in;

i. Trade regulation

12

Measurement and Instrumentation Chapter One

ii. Our day to day activities.

iii. Industrial process.

iv. Automatic feedback control system.

2.0 Introduction

There are certain characteristics of instruments that

influences the choice we make for our measurement.

Depending of the quantity or variable we want to

measure certain attribute like accuracy, cost, range,

sensitivity e.t.c of measuring instruments affects our

choice of choice of them. These influencial factors are

described in the following section.

13

2.1 Performance Characterisitcs of Measuring

Instrument.

2.2.1 Accuracy

It represent how closely an instrument reading

approaches the true value of the variable being

measured. The deviation of the measured value from

the true value is the indication of how accurate the

reading is. In practice, it is more usual to quote the

inaccuracy figure rather than the accuracy figure for an

instrument. Inaccuracy is the extent to which a reading

might be wrong, and is often quoted as a percentage of

the full-scale (f.s.) reading of an instrument. If, for

example, a pressure gauge of range 0–10 bar has a

quoted inaccuracy of 1.0% f.s. (1% of fullscale reading),

then the maximum error to be expected in any reading

is 0.1 bar. This means that when the instrument is

reading 1.0 bar,

the possible error is 10% of this value. The knowledge

of the accuracy figure of an instrument will provide us

the estimate of the expected error of measurement

using such instrument.

For example:

A 0 to 150V voltmeter has accuracy of 1% of full scale

reading. The theoretical (true) expected value we want

to measure is 83V. Determine the practical (measured)

value and the percentage of error.

Solution:

Tolerance= accuracy x VFSD

14

Measurement and Instrumentation Performance Characteristics of Instrument

Tolerance= 1% x 150 = 0.01 x 150 = 1.5V

Measured value= true ± tolerance

Measured value= 83 ± 1.5

Measured value= 84.5V or 81.5V

The percentage error is:

2.2.2 Range

It is defined as that region enclosed by the limits within

which a particular quantity is measured. Choice of range

is very important in measurement, if you choose a

range too small for the signal being measured, it may

damage the instrument and if the range chosen is too

large the percentage expected error is increased. Thus

the range

that will be chosen for a particular measurement should

be such that the indication is close to the full scale

deflection specification of the instrument.

For 60V the error is:

And for 30V

15


The range 0-150V is too large for the true value of the

measured voltage and thus the percentage error

increases as the measure value decreases. The the

choice of range should be such that the measured value

will be close to the full scale deflection of the range.

2.1.4 Span

It is algebraic difference of the upper and lower limits of

the range. For example The span of a (0 to10) voltmeter

is Span= 10-0=10 state. But the span for (-10 to +10)

voltmeter is Span= 10-(-10) =20 state

2.1.5 Loading effect

It’s the change of circuit parameter, characteristic, or

behaviour due to instrument operation without

maintainance.

2.1.6 Sensitivity

It represents the ratio of output signal to a change in

input, or it represent the response output of the

instrument to a change of its input. It is a measure of

the change in instrument output that occurs when the

quantity being measured changes by a given amount.

Thus if the value of the measured quantity is plotted

against the output value of an instrument, the

sensitivity of the instrument is given by the slope of the

straight line graph.

16

Measure Quantity

Output Reading

Gradient = Sensitivity of the instrument


Figure 2.1: Graphical representation of instrument

sensitivity.

2.1.7 Resolution

The smallest change in input that the instrument can

respond to, or the ratio of output to smallest change in

input.

2.1.8 Error

The deviation of the measured value from the true

value.

2.2 Measurement Error.

The complete statement of any measurement result has

three elements: the unit in terms of which the result is

stated; a numeric which states the magnitude of the

result in terms of the chosen unit; and its uncertainity,

the

experimenter’s estimate of the range within which the

result may differ from the actual value of the quantity.

Any physical measurement is uncertain to some extent,

and errors are present in all phases of the measurement

process.

No measurement can be made with perfect accuracy,

but its important to find out what the accuracy actually

is , and how different errors have entered to the

measurement. So study of error is a first steps in finding

17

Measurement and Instrumentation Measurement Error

ways to reduce them. Errors may come from different

sources and are usually classified under two main

heading:

2.2.1 Systematic Errors

These are types of errors that have known reasons, and

can be avoided, reduced or eliminated, and estimated.

These errors are subdivided into:

a) Gross (Human) Errors

i) Misreading of instruments and observation errors.

ii) Improper choice of instrument, or the range of

instrument.

iii) Incorrect adjustment or forgetting to zero.

iv) Erroneous calculations, computation mistakes, and

estimation errors.

v) Neglect of loading effects.

vi) Wrong positioning of the user.

b) Instrumentation (Equipment) Errors

i) Damaged equipment such as defective due to loading

effect or worn-out parts.

ii) Calibration errors.

iii) Bearing friction or loose gears.

iv) Component nonlinearities.

v) Loss during transmission.

vi) inproper position of equipment (vertical or

horizontal).

vii) error due to static charge.

c) Environmental Errors

i) Change in temperature, pressure and Humidity.

18

Measurement and Instrumentation Systematic Error

ii) Stray electric and magnetic fields.

iii) Mechanical vibration.

iv) Weather variations (day, night, and four seasons).

2.2.2Calibration Errors

Calibration is an act or process of making adjustments

or marking on an index scale so that the readings of a

measuring device conform to an accepted and certified

standard. Errors that can generate from these process

are classified as calibration error, types of which are

discussed as follows:

i. Zero Error: This occur when the pointer or indication

of the instrument does not read zero when no input

signal is applied to it. If the indicated reading from

instrument with Zero error is plotted compared with the

correct reading from a standard guage the graph will be

as shown in figure 2.2a.

ii. Range Error: In the effect of Range error, the

instrument may be correct at the minimum (i.e zero

reading, when there is no input signal), but it deviates

from the actual value in the range of the instrument.

The

graph of the indicated reading compared with the

correct reading from a standard guage is shown in

figure 2.2b.

(a) (b)

19

Measurement and Instrumentation Systematic Error

Figure 2.2

iii. Hysteresis: Hysteresis is produced when the

displayed values are too small for increasing signals and

too large for decreasing signals. This is commonly

caused in mechanical instruments by loose gears and

friction.

iv. Non-linear error: The calibration may be correct

at the maximum and minimum values of the range but

the graph joining them may not be a straight line (when

it ought to be). The graph of readings from an

instrument with Hysteresis and Non-linear error

compared with readings from a standard guage is

shown in figure 2.3a and 2.3b respectively.

(a) (b)

Figure 2.3 Hysteresis and Non-linear error.

2.2.3 Random Errors

These are errors due to causes that can not be directly

established because of unknown events that cause

small variation in measurement. They are quite random

and cannot be explained. We can reduce this type of

errors after addressing the systematic errors by taking

20

Measurement and Instrumentation Random Error

many readings and applying statistical methods to

determine the best true estimate of measurement

readings.

2.3 Statistical Estimations of error in

measurement These errors are due to unknown

causes and occur even when all systematic errors have

been accounted for. In well designed experiments few

random errors usually occur, but they become

important in high accuracy work. The only way to offset

these errors is by increasing the number of readings

and using statistical means to obtain the best

approximation of the true value of the quantity under

measurement.

2.3.1 Statistical Analysis of Data

To make statistical methods useful, the systematic

errors should be small compared with random errors

because statistical treatment can not improve the

accuracy of measurement.

1 Arithmetic Mean(X`):

It’s the value that lies in the medial number of

measured variable and represents the most accurate

measured value for the true value. Arithmetic mean is

given by:

, where Xi is the reading values taken, and Fi

is the number of times that each reading occur in the

measurements, or the frequency number of each

reading.

21

Measurement and Instrumentation Statistical Analysis of Data

2. Deviation from the Mean(di):

Deviation is the departure of a given reading from the

mean value. It’s given by:

The deviation from the mean may have a positive or a

negative value and the algebraic sum of all the

deviation must be zero in symmetrical curve.

3 Average Deviation (D):

The average deviation is the sum of the absolute values

of deviations divided by the number of readings.

where and n=number of all readings.

4. Standard Deviation(δ):

It is the root mean square deviation and the standard

deviation represents the variation of the reading from

the mean value, for a finite number of reading.

5. Variance (v):

It is defined as mean square standard deviation

6. Probable Error (r):

It is the maximum chance (50%) that any given

measurement will have a random error not greater than

r. Probable error r is given by

22


Example 1.1:

The following readings were recorded for voltage

measurement:

10.1, 9.7, 10.2, 9.6, 9.7, 10.1, 9.6, 9.7, 10.1

Calculate:

1. Arithmetic mean (X)

2. Deviation from the mean (d)

3. Average deviation (D)

4. standard deviation (σ)

5. Variance (V)

6. probable error (±r)

Solution:

Rearrange the reading in two colums with its frequency

or (number of reading), thus

Reading values No. Of reading Di(xi-x)

10.1 3 0.3

9.7 3 -0.1

9.6 2 -0.2

10.2 1 0.4

1.

2.

3.

23


4.

5.

6.

Excersice 2

1. Briefly describe eight (8) factors that affects the

choice of instrument to be used for a

measurment.

24

Measurement and Instrumentation Chapter two

2. A thermometer has a range from -20 to 1500C.

The accuracy is guaranteed to ±3% f.s.d. If the

true value under measurement is 900C, determine

the possible values that can be indicated by the

thermometer.

3. Defferentiate between the range and the span of

an instrument. Explain how the choice of range in

a measurement affects the readings from such

measurment.

4. A digital thermometer reads from -120 to + 300 0C. The accuracy is guaranteed to plus or minus

2% f.s.d. Determine the possible true values of

the measured temperature if the thermometer

reads 800C.

5. In an experiment involving temperature

mesurement, the following readings were

recorded in 0C: 20.1, 19.8, 20.3, 20.1, 19.7.

20.1,19.8, 19.6, 19.7, 20.1.

Calculate:

i. Arithmetic mean (X)

ii. Deviation from the mean (d)

iii. Average deviation (D)

iv. standard deviation (σ)

v. Variance (V)

vi. probable error (±r)

6. The table below shows the correponding change

in the resistance of a platinum resistance

thermometer to temperature. Plot the graph of

25

Measurement and Instrumentation Chapter two

Temperature against resistance and hence,

determine the measurement sensitivity of the

instrument in ohms/°C. If the temperature

changes by 3000C, what is the change in

resistance of the thermometer? Also determine

the temperature when the instruments reading is

295.

Resistance () Temperature (°C)307 200314 230321 260328 290

26

3.1 Classification of Instruments

Electrical indicating and test instruments can be

classified under the following headings;

1 Electrical and Electronic Instruments

The measuring instrument that use mechanical

movement of electromagnetic meter to measure

voltage, current, power, etc. is called electrical

measuring instrument, so the heart of these

instruments was the d’Arsonval meter, while any

measurement system that uses d’Arsonval meter with

amplifiers to increase the sensitivity of measurements is

called electronic

instrument.

2 Analogue and Digital Instruments

An analogue instrument are the instrument that use

analogue signal (signal varying in continuous fashion

and take on an infinite number of values in any given

range) to display the magnitude of quantity under

measurement.

The digital instrument use digital signal (signal which

vary in discrete steps and take up only finite different

values in a given range, (like binary signal which take

only two levels zero and one) to indicate the results of

measurement in digital form.

3 Absolute and Secondary Instruments

27

In absolute instrument the measured value is given in

term of instrument constants and the deflection of one

part of the instrument e.g. tangent galvanometer, and

Rayliegh current balance. In these instruments no

calibrated scale is necessary. While in secondary

instruments, the quantity of the measured values is

obtained by observing the output indicated by these

instruments.

These classes of instruments are interweaven as a

digital instrument can be classified as an electronic

instrument, an analogue instrument can be classified

under electrical instrument both can be futher classified

as an absolute or secondary instrument. In the next

section we will discribe Measuring instrument in terms

of digital and analogue instrument and in the discussion

further classifications will be identified and discussed.

3.2 Digital Meters

All types of digital meter are basically modified forms of

the digital voltmeter (DVM), irrespective of the quantity

that they are designed to measure. Digital meters

designed to measure quantities other than voltage are

in fact digital voltmeters that contain appropriate

electrical circuits to convert the measured quantities

into voltage signals. Digital multimeters are also

essentially digital voltmeters that contain several

conversion circuits, thus allowing the measurement of

voltage, current and resistance within one instrument.

28

Measurement and Instrumentation Classification of Instruments

Digital meters have been developed to satisfy a need

for higher measurement accuracies and a faster speed

of response to voltage changes than can be achieved

with analogue instruments.

The binary nature of its output reading can be readily

applied to a display that is in the form of discrete

numerals. It also has a very high input impedance

(10MΩ compared with 1– 20 kΩ for analogue meters).

The ability to measure signals of frequency up to 1MHz

and the common inclusion of features such as automatic

ranging, which prevents overload and reverse polarity

connection etc. are the advantages of Digital meters

over analogue.

Moreover, the greater cost of digital meters due to the

higher manufacturing costs compared with analogue

meters makes the analogue meter preferable in a

situation where cost is of importance.

The block diagram of a simple digital meter is shown in

figure 3.1 below:

Figure 3.1 A block diagram of digital meter

29

Pulse

generator

AND gate NOT gate Counter Digital

readout

Input

voltage

Reset

Measurement and Instrumentation Digital Meter

As shown in Figure 2.14, a pulse generator generates a

pulse whose width is directly proportional to the input

signal. The output of the pulse generator is one of the

inputs of an AND gate circuit. The output of the pulse

generator is a train of pulses. The output of the AND

gate is, thus, a positive trigger train of duration T

second and the NOT circuit changes it into a negative

trigger train. The counter, then, starts counting the

number of triggers in T seconds which is proportional to

the magnitude of signal to be measured. The counter

can be calibrated according to the type of signal been

measured say voltage or current.

Thus, it can be observed from the above description

that the digital meter described above, is basically, an

analog-to digital converter (ADC) which converts an

analog signal into a train of pulses, the number of which

is proportional to the magnitude of the input signal.

With appropriate signal conditioning of the input signal,

digital meter can be used to measure many electrical

and physical quantities such as a.c. voltages, d.c. and

a.c. current, resistance, temperature, pressure, etc.

3.3 ANALOGUE METERS

Analogue meters are relatively simple and inexpensive

and are often used instead of digital instruments,

especially when cost is of particular concern.

Whilst digital instruments have the advantage of

greater accuracy and much higher input impedance,

analogue instruments suffer less from noise and

30

isolation problems. Because analogue instruments are

usually passive instruments that do not need a power

supply,

this is often very useful in measurement applications

where a suitable mains power supply is not readily

available.

Analogue meters are electromechanical devices that

drive a pointer against a scale. They are prone to

measurement errors from a number of sources that

include inaccurate scale marking during manufacture,

bearing friction, bent pointers and ambient temperature

variations. Inaccuracy figures are between (0.1% and

3%.)

All analogue electrical indicating instruments require

three essential devices:

(a) A deflecting or operating device. A mechanical

force is produced by the current or voltage which

causes the pointer to deflect from its zero position.

(b) A controlling device. The controlling force acts in

opposition to the deflecting force and ensures that the

deflection shown on the meter is always the same for a

given measured quantity. It also prevents the pointer

always going to the maximum deflection. There are two

main types of controlling device—spring control and

gravity control.

(c) A damping device. The damping force ensures that

the pointer comes to rest in its final position quickly and

without undue oscillation. There are three main types of

31

Measurement and Instrumentation Analogue Meters

damping used—eddy-current damping, air-friction

damping and fluid-friction damping.

Analogue meter can be designed using two basic types

of instruments namely, Moving-coil instruments and

Moving-iron instruments. The principle of operation of

these instrument are discussed in detail in the following

section.

3.4 MOVING-COIL INSTRUMENTS

A moving-coil meter is a very commonly used form of

analogue voltmeter because of its sensitivity, accuracy

and linear scale, although it only responds to d.c.

signals.

Moving-coil instruments also called Parmanent

Magnet Moving coil (PMMC) meter or (D’Arsonval)

meter or galvanometer all are the same instrument, a

coil of fine wire is suspended in a magnetic field

produced by permanet magnet. According to the

fundamental law of electromagnetic force, the coil will

rotate in the magnetic field when it carries an electric

current by electromagnetic (EM) torque effect. A pointer

which is attached to the movable coil will deflect

according to the amount of current to be measured

which is applied to the coil. The (EM) torque is counter

balanced by the mechanical torque of control springs

attached to the movable coil also. When the torques are

balanced the moving coil will stop and its angular

deflection represent the amount of electrical current to

be measured against a fixed reference, called scale. If

32

Measurement and Instrumentation Moving-coil Instruments

the permanent magnet field is uniform and the spring

linear, then the pointer deflection is also linear.

If a current I is being carried by the coil, the force F

applied to the conductor by the magnetic field of flux B

is given by:

F = BIL.

If the flux density B is made constant (by using

parmanent magnets) and the conductor is a fixed lenght

(say, a coil) then the force will depend only on the

current flowing in the conductor.

In the design of a moving-coil instrument a coil is placed

centrally in the gap between shaped pole pieces. The

coil is supported by steel pivots, resting in jewel

bearings, on a cylindrical iron core. Current is led into

and out of the coil by two phosphor broze spiral

hairsprings which are wound in opposite directions to

minimize the effect of temperature change and to limit

the coil swing (i.e to control the movement) and return

the movement to zero position when no current flows.

Current flowing in the coil produces forces, the direction

being obtained by Fleming’s left-hand-rule. The two

forces, FA and FB, produce a torque which will move the

coil in a clockwise direction, i.e move the pointer from

the left to right. Since the force produced is proportional

to the input current, then the scale is linear (see figure

2.0).

33 FB

FA

Torque

Current input

Pointer

Fixed iron core

Moving coil

SN

Measurement and Instrumentation Moving-coil Instruments

(a) (b)

Figure 3.2 Moving-coil Instrument

3.5 MOVING-IRON INSTRUMENT

As well as measuring d.c. signals, the moving-iron meter

can also measure a.c. signals at frequencies up to

125Hz. It is the cheapest form of meter available and,

consequently, this type of meter is also commonly used

for measuring voltage signals. The signal to be

measured is applied to a stationary coil, and the

associated field produced is often amplified by the

presence of an iron structure associated with the fixed

coil. The moving element in the instrument consists of

an iron vane that is suspended within the field of the

fixed coil. When the fixed coil is excited, the iron vane

turns in a direction that increases the flux through it.

The majority of moving-iron instruments are either of

the attraction type or of the repulsion type.

An attraction type of moving-iron instrument is shown in

Figure 3.9a below. When current flows in the solenoid, it

becomes magnetic and a pivoted soft-iron disc is

attracted towards the solenoid and the movement

cause a pointer to move across a scale.

34

Measurement and Instrumentation Moving-iron Instruments

In the repulsion type moving-iron instrument as shown

in Figure 3.9b, two pieces of iron are placed inside the

solenoid, one being fixed, and the other attached to the

spindle carrying the pointer. When current passes

through the solenoid, the two pieces of iron are

magnetized in the same direction and therefore repel

each other. The pointer thus move across the scale.

For an excitation current I, the torque produced that

causes the vane to turn is given by:

where M is the mutual inductance and is the angular

deflection. Rotation is opposed by the controlling spring

as shown in figure 3.9, that produces a backwards

torque given by:

At equilibrium, T = Ts, and is therefore given by:

The instrument thus has a square-law response where

the deflection is proportional to the square of the signal

being measured, i.e. the output reading is a root-mean

squared (r.m.s.) quantity.

The instrument can typically measure voltages in the

range of 0 to 30 volts.

However, it can be modified to measure higher voltages

by placing a resistance in series with it, as in the case of

moving-coil meters. The scale, however, is non linear.

35

Scale

Pivot and controlling spring

Air-piston damping

Soft iron discSolenoid

Pointerinput current


(a) Attraction type

(b) Repulsion Type

Figure 3.9 Moving-iron instrument

3.6 ELECTRODYNAMIC METERS

This instrument is suitable for the measurement of

direct and alternating current up to frequency 2kHz, it

can also measure voltage and power.

The instrument has a moving circular coil that is

mounted in the magnetic field produced by two

separately wound, series-connected, circular stator

coils.

The torque is dependent upon the mutual inductance

between the coils and is given by:

36

Scale

Solenoid

Pivot and Controlling SpringFixed piece of iron

Moveable piece of iron

Pointer


where I1 and I2 are the currents flowing in the fixed and

moving coils, M is the mutual inductance and

represents the angular displacement between the coils.

When used as an ammeter, the measured current is

applied to both coils. The torque is thus proportional to

I2. By suitable drawing of the scale, the position of the

pointer shows the squared root of this value, i.e. the

r.m.s. current.

Electrodynamic meters are typically expensive but have

the advantage of being more accurate than moving-coil

and moving-iron instruments. Voltage, current and

power can all be measured if the fixed and moving-coils

are connected appropriately.

Figure 3.10: Electrodynamic Meter

3.7 Moving-coil Rectifier instruments

37

Measurement and Instrumentation Electrodynamic Instruments

One major limitation in using analogue meters for a.c.

voltage measurement is that the maximum frequency

measurable directly is low, 2kHz for the dynamometer

voltmeter and only 100 Hz in the case of the moving-

iron instrument. A partial solution to this limitation is to

rectify the voltage signal and then apply it to a moving-

coil meter, as shown in Figure 3.12. This extends the

upper measurable frequency limit to 20 kHz.

Figure 3.12: Moving-coil rectifier instrument

3.8 Comparing Moving-Coil, Moving-iron and

Moving-coil rectifier instruments.

Types of instrument

Moving-coil Moving-iron Moving-coil rectifier

Frequency limits

- 20-200Hz 20-100kHz

Advantages 1. Linear scale.2. High sensitivity3. Well shielded from stray magnetic fields.4. Lower power consumption.

1. Robust construction.2. Relatively cheap 3. Measures dc and ac4. In frequency range 20-

1. Linear scale2. High sensitivity 3. Well shielded from stray magnetic fields4. Low power consumption5. Good

38

Measurement and Instrumentation Comparing Analogue Instruments

100Hz reads rms correctly regardless of supply wave-form.

frequency range.

Disadvantages

1. Only suitable for dc2. More expensive then moving iron type3 Easily damaged

1. Non-linear scale2. Affected by stray magnetic fields3. Hysteresis errors in dc circuits4 Liable to temperature errors5. Due to the inductance of the solenoid, readings can be affected by variation of frequency.

1. More expensive that moving iron type2. Errors caused when supply is non-sinusoidal

3.8 Applications of analogue instruments

Due to its non linear scale, moving-iron instrument and

applied in more specialised measurement and its scale

graduation and caliberation involves more complex

calculation than moving-coil instrument, thus the latter

is often employed as an ammeter, voltmeter, ohmeter,

multirange meters and multimeters. The application of

moving-coil meters as mentioned are discussed in the

following sections. However, moving-iron instrument

can also be used in all the applications discussed below.

3.8.1 Applications of Moving-coil instruments.

39

Measurement and Instrumentation Applications of Analogue Instruments

Moving coil instrument operates at low current levels of

one milliamp or so, it is only suitable for measuring low

current arround 1-2mA. If there is a requirement to

measure higher currents, the measuring range of the

instrument can be increased by placing a resistance in

parallel with the coil, so that only a fraction of the total

current will pass through the meter. In this situation the

added resistance is known as a shunt resistor.

Also, a moving coil instrument can be designed to

measure voltage signal, in this case a resistance is

connected in series with the instrument. This series

resistance should be much larger than the impedance of

the circuit being measured and also usually much larger

than the internal resistance of the moving coil

instrument. Resistor used in this situation is called a

Multiplier.

3.8.1 Moving-coil instument as an ammeter and

Calculation of Shunt Resistor.

In figure 3.3 below, a moving coil instrument with an

internal resistance ra, designed as an ammeter to

measure a full-Scale-deflection current of Ia. Its range of

measurement is increased to measure a higher current

of I, by connecting a shunt, Rs. Is is the value of the

diverted current by the shunt resistor Rs. The value of

the resistor Rs for any desired current I, can be

calculated by equation 3.1.

40

RS

R

IS

I Ia QIaP

S

A

ra

Measurement and Instrumentation Multiplier and Shunt

Figure 3.3

VPQ = VRS

Iara = ISRS

............................ equation 3.1

ra = Internal resistance of the ammeter.

Rs = The shunt resistor.

Example 3.1:

1. A moving-coil instrument gives a f.s.d when the

current is 40mA and its resistance is 25Ω. Calculate the

value of the shunt to be connected in paralled with the

meter to enable it to be used as an ammeter for

measuring currents up to 50A.

The circuit is shown below:

Where ra = resistance of instrument = 25Ω.

Rs = resistance of shunt,

Ia = maximum permissible current flowing in instrument

= 40mA = 0.04A,

Is = current flowing in shunt

41

RS

A

V

Ia = 40mA50A

ra

Is

Measurement and Instrumentation Calculating Multiplier and Shunt

I = total circuit current required to give f.s.d = 50A

Since I = Ia + Is then Is = I – Ia = 50 – 0.04 = 49.96A

V = Iara = IsRs

Hence,

Thus for the moving-coil instrument to be used as an

ammeter with a range 0-50A, a resistance of value

20.02mΩ needs to be connected in paralled with the

instrument.

3.8.2 Moving-coil instrument as a voltmeter and

Calculation Involving Multiplier

When using a moving-coil instrument as a voltmeter it

is always connected in parallel with the element being

measured, and measures the voltage between the

points across which it is connected. A moving coil

instrument (galvanometer) can be converted into a

voltmeter by connecting a high value resitance (called

multiplier) in series with it as shown in figure 3.4

below.

Figure 3.4

42

A

Va Vm

Rm

V

ra


The Voltage range desired to be measured by the

instrument is given as V, Ia is the f.s.d current of the

moving coil instrument, ra is the internal resistance of

the instrument, Rm is the required multiplier for the

instrument the measure the desired voltage range,

while the Im is the curent that passes through the

resistor Rm. In this case the resistor Rm is in series with

the moving coil instrument, therefore Ia = Im, the shunt

resistor Rm can thus be calculated by equation 3.2

V = Va + Vm

= Iara + ImRm

Ia = Im (since and ra and Rm are in series)

V = Iara + IaRm

V = Ia (ra + Rm)

.............................. equation 3.2

Example 3.2: A moving-coil instrument having a

resistance of 10Ω, gives a f.s.d when the current is 8mA.

Calculate the value of multiplier to be connected in

series with the instrument so that it can be used as a

voltmeter for measuring p.d up to 100V.

The circuit diagram is shown below:

Where ra = resistance of instrument = 10Ω

RM = resistance of mutiplier.

43

V=100V

VMVa

ra

ARmI = 8mA


I = toal permissible instrument current = 8mA =

0.008A.

V = total p.d required to give f.s.d = 100V

V = Va + Vm = Ira + IRM

i.e. 100 = (0.008) (10) + (0.008)RM

thus RM =

Hence for the moving-coil instrument to be used as a

voltmeter with a range 0 – 100 V, a resistance of value

12.49kΩ needs to be connected in series with the

instrument.

3.8.3 Multirange D.C Meter

A moving coil instrument (or galvanometer) can be

designed to measure D.C Signals like current

(ammeter), Voltage (voltmeter), Resistance (ohmeter)

etc., of different ranges, by connecting different values

of shunt or multiplier as the case may be. The sections

below describes how these can be achieved.

1. Multirange DC Ammeter

The current range of d.c ammeter can be further

extended by a number of shunts selected by a range

switch; such ammeter is called a multirange ammeter.

This can be designed by Direct or Indirect Method.

a. Direct method:

44

Measurement and Instrumentation Multirange DC Meter

In direct method, the circuit design is shown in figure

3.5 below, the shunt resistors Rs1, Rs2 and Rs3 are

connected parallel to the galvanometer an also parallel

to one another. When one is connected the other two

are disconnected, and thus each of the three resistor

presents different ranges of current measurements Is1,

Is2 and Is3 in the instrument.

The value of each of the shunt resistors Rs1, Rs2 and Rs3

can be calculated independently using equation 3.3.

Figure 3.5

...................... equation 3.3

b. Indirect Method

An example of indirect method of multirange ammeter

design is shown in figure 3.6 below; the resistors Ra, Rb

and Rc are connected in series with one another and

they are all connected in parallel with the

galvanometer. In this case the shunt value at any given

range I1, I2 and I3 can be a resultant of one, two or the

three of the resistors Ra, Rb and Rc, depending on the

range value on which the range switch is on. For the

example in figure 3.6, when the range switch is on the

45

ra

IaIs3

Rs3 Rs2

Is2

Rs1

Is1


current range I1, the value of the shunt Rs1, is equal to

the sum of Ra+Rb+Rc, when the switch is on range I2, the

shunt value Rs2, is equal to Rb+Rc, while Ra is

disconneted and when the switch is on range I3, the

shunt value Rs3, is only equal to Rc, while the other two

resistors Ra and Rb is disconneted. Rs1, Rs2 and Rs3 can

be calculated using equation 3.3 above. Ra and Rb is

calculated using equation 3.4 and 3.5 respectively,

while Rc is equal to Rs3

Figure 3.6

For Range I1:

Rs1 = Ra + Rb +Rc

For Range I2:

Rs2 = Rb +Rc

i.e; Ra = Rs1 – Rs2 ...................................... (3.4)

For Range I3:

Rs3 = Rc

Rb = Rs2 – Rs3 ....................................... (3.5)

Example 3.3:

Design a multirange ammeter by using direct method

to give the following ranges 10mA, 100mA, 1A, 10A, and

46

I1

I2

I3

Ia

ra


100A. If d’Arsonval meter have internal resistance of

10 and full scale current of 1mA.

Solution:

The circuit design is shown below.

Example 3.4:

Design an ammeter by indirect method to provide an

ammeter with current ranges 1A, 5A, and 10A, with a

PMMC meter of internal resistance 50 and full scale

current of 1mA.

Solution

47

Ia

ra


The circuit is designed as shown above.

ra=50 Ia=1mA

For Range 1A:

Shunt resistor Rs1 = Ra + Rb + Rc

For range 5A:

For Range 10A:

48


2. Multirange D.C Voltmeter

a. Direct method

In this method each series resistance of multirange

voltmeter is connected directly with Moving-coil meter

to give the desired Voltage range as shown in figure 3.7.

The various multipliers can be calculated using equation

3.6.

Figure 3.7

.............................. equation 3.6

b. Indirect method

In this method one or more series resistance of

multirange voltmeter is connected with Moving-coil

meter to give the desired range as shown in figure 3.8.

The series resistance can be calculated using equation

3.7, 3.8 and 3.9 eliminatively.

49

Ra Rb Rc

Ia

ra

Rm1

Rm2

Rm3

ra

Ia


Figure 3.8

At range V1:

....................... (3.7)

At range V2:

........................ (3.8)

At range V3:

............... (3.9)

3.9 ANALOGUE MULTIMETER

The analogue multimeter is a multi-function instrument

that can measure current and resistance as well as d.c.

and a.c. voltage signals. Basically, the instrument

consists of a moving-coil meter with a switchable bridge

rectifier (as discussed in moving-coil rectifier

instrument) to allow it to measure a.c. signals, as shown

in Figure 3.11. A set of rotary switches allows the

selection of various multiplier and shunt resistors, which

make the instrument capable of measuring both voltage

and current over a number of ranges. An internal power

source is also provided to allow it to measure

resistances as well. Whilst this instrument is very useful

for giving an indication of voltage levels, the

compromises in its design that enable it to measure so

many different quantities necessarily mean that its

50

Measurement and Instrumentation Analogue Multimeter

accuracy is not as good as instruments that are

purposely designed to measure just one quantity over a

single measuring range.

Figure 3.11: Analogue Multimeter

3.10 ELECTRONIC ANALOGUE VOLTMETER

Electronic voltmeters differ from all other forms of

analogue voltmeters in being active rather than passive

instruments. They have important advantages

compared with other analogue instruments. Firstly, they

have a high input impedance that avoids the circuit

loading

problems associated with many applications of

electromechanical instruments.

Secondly, they have an amplification capability that

enables them to measure small signal levels accurately.

The standard electronic voltmeter for d.c.

measurements consists of a simple direct coupled

amplifier and a moving-coil meter, as shown in Figure

3.14(a). For measurement

51

Measurement and Instrumentation Electronic Analogue Voltmeter

of very low-level voltages of a few microvolts, a more

sophisticated circuit, known as a chopper amplifier, is

used, as shown in Figure 3.14(b). In this, the d.c. input is

chopped at a low frequency of around 250 Hz, passed

through a blocking capacitor, amplified, passed through

another blocking capacitor to remove drift,

demodulated, filtered and applied to a moving-coil

meter.

Three versions of electronic voltmeter exist for

measuring a.c. signals. The average responding type is

essentially a direct-coupled d.c. electronic voltmeter

with an additional

rectifying stage at the input. The output is a measure of

the average value of the measured voltage waveform.

The second form, known as a peak-responding type, has

a half-wave rectifier at the input followed by a capacitor.

The final part of the circuit consists of an amplifier and

moving-coil meter. The capacitor is charged to the peak

value of the input signal, and therefore the amplified

signal applied to the moving-coil meter gives a reading

of the peak voltage in the input waveform.

Finally, a third type is available, known as an r.m.s.-

responding type, which gives an output reading in terms

of the r.m.s. value of the input waveform. This type is

essentially a thermocouple meter in which an

amplification stage has been inserted at the input.

52

Measurement and Instrumentation Electronic Analogue Voltmeter

(a)

(b)

Figure 3.14: D.C Electronic Voltmeter (a) Simple

form; (b) Including chopper amplifier.

3.11 RESISTANCE MEASUREMENT AND

OHMMETER

The standard device and methods available for

measuring change in resitance, which is measured in

units of ohms (), include the d.c bridge circuit, the

voltmeter-ammeter method, the resitance-substitution

method, the digital voltmeter and the ohmmeter. Apart

from the ohmmeter, these instruments are normally

only used to measure medium values of the resistance

in the range of 1 to 1M. Special instruments are

available for obtaining

high-accuracy resistance measurements outside this

range.

3.11.1 Voltmeter-ammeter method

The voltmeter–ammeter method consists of applying a

measured d.c. voltage across the unknown resistance

53

Measurement and Instrumentation Resistance Measurement

and measuring the current flowing. Two alternatives

exist for connecting the two meters, as shown in Figure

3.15. In Figure 3.15(a), the ammeter measures the

current flowing in both the voltmeter and the resistance.

The error due to this is minimized when the measured

resistance is small relative to the voltmeter resistance.

In the alternative form of connection, Figure 3.15(b), the

voltmeter measures the voltage drop across the

unknown resistance and the ammeter. Here, the

measurement error is minimized when the unknown

resistance is large with respect to the ammeter

resistance. Thus, method (a) is best for measurement of

small resistances and method (b) for large ones.

Having thus measured the voltage and current, the

value of the resistance is then calculated very simply by

Ohm’s law. This is a suitable method wherever the

measurement inaccuracy of up to 1% that it gives is

acceptable.

Figure 3.15: Voltmeter-ammeter method for

measuring resistance

3.11.2 Resistance-substitution method

In the voltmeter–ammeter method above, either the

voltmeter is measuring the voltage across the ammeter

as well as across the resistance, or the ammeter is

54


measuring the current flow through the voltmeter as

well as through the resistance. The measurement error

caused by this is avoided in the resistance-substitution

technique. In this method, note the voltmeter and the

ammeter readings with the unknown resistance in the

circuit, then temporarily replaced it by a variable

resistance. Adjust the variable resistance until the

measured circuit voltage and current are the same as

existed with the unknown resistance in place. The

variable resistance at this point is equal in value to the

unknown resistance.

3.11.3 The Ohmmeter

The ohmmeter is a simple instrument in which a battery

applies a known voltage across a combination of the

unknown resistance and a known resistance in series, as

shown in Figure 3.16. Measurement of the voltage, Vm,

across the known resistance, R, allows the unknown

resistance, Ru, to be calculated from:

Where Vb is the battery voltage.

Ohmmeters are used to measure resistances over a

wide range from a few milliohms up to 50M. The

measurement inaccuracy is 2% or greater, and

ohmmeters are therefore more suitable for use as test

equipment rather than in applications where high

accuracy is required. Most of the available versions

55


contain a switchable set of standard resistances, so that

measurements of reasonable accuracy over a number of

ranges can be made.

Most digital and analogue multimeters contain circuitry

of the same form as in an ohmmeter, and hence can be

similarly used to obtain approximate measurements of

resistance.

Figure 3.16: Ohmmeter

3.12 NULL METHODS OF MEASUREMENT

A null method of measurement is a simple, accurate

and widely used method which depends on an

instrument reading being adjusted to read zero current

only. The method assumes:

if there is any deflection at all, then some current is

flowing and if there is no deflection, then no current

flows (i.e null condition).

56

Measurement and Instrumentation Null Methods of Measurement

Examples where the method is used are in the

Wheatstone bridge and in the d.c potentiometer

3.12.1 Wheatstone bridge

Figure 3.17 shows a Wheatstone bridge circuit which

compares an unknown resistance Rx with others of

known values, i.e. R1 and R2, which have fixed values,

Figure 3.17

and R3, which is variable. A d.c voltage Vi is applied

across the points BD and the Resistance R3 is varied

until zero deflection is obtained on the galvanometer G.

No curent then flows through the meter. To analyse the

Wheatstone bridge, define the current flowing in each

arm to be I1...I4 as shown in figure 3.17. Normally, if a

high impedance voltage-measuring instrument is used,

the

57

Im

A

R3

Rx

G

R1

R2

B

I1

I2

I4

I3

C D

Vi


current Im drawn by the measuring instrument will be

very small and can be approximated to zero. If this

assumption is made, then, for Im=0:

I1 = I3 and I2 = I4

Looking at path CAD, we have a voltage Vi applied

across a resistance R1 + R3 and by Ohm’s law:

Similarly for path CBD:

Now we can calculate the voltage drop across CB and

BD:

; .

In the figure 3.17, the potential at point C is Vi and the

potential at point A is Vi-VCA. Likewise the potential at

point B is Vi-VCB.

Thus, the voltage drop across the galvanometer VAB is

given by:

58


Thus, VAB can be calculated as;

At null point VAB = 0, So;

Inverting both sides, we have:

i.e or

3.12.2 D.C potentiometer

The d.c potentiometer is a null-balance instrument

used for determining values of e.m.f’s and p.d’s by

comaprison with a known e.m.f or p.d. In Figure 1.13,

using a standard cell of known e.m.f, E1, the slider S is

moved along the slide wire until balance is obtained (as

explained in the earlier in the wheatstone bridge),

shown as length l1.

The standard cell is now replaced by a cell of unknown

e.m.f. E2 (see figure 2.13b) and again balance is

obtained (shown as l2).

Since E1l1 and E2l2,

59


Then and

(a) (b)

Figure 3.18

Excersice 3

60

S

G

l1

E1

Standard cell

Supply source V

Slide wire of uniform cross-section

l2

S

G

V

E2

Measurement and Instrumentation Chapter Three

1. Define digital and analogue instrument. Hence

explain with an appropriate block diagram, the principle

of operation of a Digital meter.

2. A moving-coil instrument gives a f.s.d when the

current is 40mA and its resistance is 25Ω. Calculate the

value of the shunt to be connected in paralled with the

meter to enable it to be used as an ammeter for

measuring currents up to 50A.

The circuit is shown below:

3. A moving-coil instrument has a coil resistance of

100Ω and gives a full-scale deflection (FSD) for a

current of 500Aμ. Determine the value of shunt

resistance required if the instrument is to be employed

as an ammeter with a FSD of 5A.

4. A moving-coil meter with a coil resistance 100Ω and a

full scale deflection current of 100Aμ is to be used in the

voltmeter circuit as shown in figure below. The

voltmeter ranges are to be 50. Determine the required

value of resistances for each range.

5. With a diagram illustration, describe the principle of

operation of a moving-coil instrument and a Moving coil

61

RS

A

V

IS = 40mA50A

ra

Is

Ra = 100

Rm1

Rm2

Rm3

Measurement and Instrumentation Chapter Three

rectifier instrument. Also explain briefly the advantage

of the latter over the former.

6. With the help of a suitable diagram, differentiate

between the Attraction and the Repulsion type of a

Moving- Iron Instrument.

7. Define the following; i. A voltmeter ii. An ammeter

iii. An Ohmmeter iv. A multirange meter v. A

multimeter.

Discribe the principle of resistance measurement using

i. voltmeter-ammeter methods and ii. Ohmmeter.

8. Design d.c voltmeter by using direct method with

d’Arsonval meter of 100Ω and full scale deflection of

100μA to give the following ranges: 10mV, 1V, and

100V.

9. In a wheatstone bridge ABCD, a galvanometer is

connected between A and C, and a battery between B

and D, A resistor of unknown value is connected

between A and B. When the bridge is balanced, the

resistance between B and C is 100Ω, that between C

and D is 10Ω and that between D and A is 400 Ω.

Calculate the value of the unknown resistance.

10. In a d.c potentiometer, balance is obtained at a

length of 400mm when using a standard cell of 1.0186

volts. Determine the e.m.f of a dry cell if balance is

obtained with a length of 650mm

62

4.1 CATHODE RAY OSCILLOSCOPE The cathode ray oscilloscope (CRO) is a device that

allows the amplitude of electrical signals, weather they

are voltage, current; power, etc., to be displayed

primarily as a function of time. The oscilloscope

depends on the movement of an electron beam, which

is then made visible by allowing the beam to impinge on

a phosphor surface, which produces a visible spot.

The cathode ray oscilloscope is probably the most

versatile and useful instrument available for signal

measurement. In its basic form, it is an analogue

instrument and is often called an analogue oscilloscope

to distinguish it from digital storage oscilloscopes which

have emerged more recently.

The analogue oscilloscope is widely used for voltage

measurement, especially as an item of test equipment

for circuit fault-finding, and it is able to measure a very

wide range of both a.c. and d.c. voltage signals. Besides

measuring voltage levels, it can also measure other

quantities such as the frequency and phase of a signal.

It can also indicate the nature and magnitude of noise

that may be corrupting the measurement signal. The

more expensive models can measure signals at

frequencies up to 500MHz and even the cheapest

models can measure signals up to 20 MHz. One

particularly strong merit of the oscilloscope is its high

63

input impedance, typically 1M, which means that the

instrument has a negligible loading effect in most

measurement situations. As a test instrument, it is often

required to measure voltages whose frequency and

magnitude are totally unknown. The set of rotary

switches that alter its timebase so easily, and the

circuitry that protects it from damage when high

voltages are applied to it on the wrong range, make it

ideally suited for such applications. However, it is not a

particularly accurate instrument and is best used where

only an approximate measurement is required. In the

best instruments, inaccuracy can be limited to 1% of

the reading but inaccuracy can approach 10% in the

cheapest instruments. Further disadvantages of

oscilloscopes include their fragility (being built around a

cathode ray tube) and their moderately high cost.

4.2 Oscilloscope Block Diagram:

General oscilloscope consists of the following parts:

1. Cathode ray tube (CRT)

2. Vertical deflection stage

3. Horizontal deflection stage

4. Power supply

64

Measurement and Instrumentation Cathode Ray Oscilloscope

Figure 4.1: General purpose oscilloscope

4.2.1 The Cathode Ray Tube (CRT):

The cathode ray tube, shown in Figure 4.2, is the

fundamental part of an oscilloscope. The cathode

consists of a barium and strontium oxide coated, thin,

heated filament from which a stream of electrons are

emitted. The stream of electrons is focused onto a well

defined spot on a fluorescent screen by an electrostatic

focusing system that consists of a series of metal discs

and cylinders charged at various potentials. Adjustment

of this focusing mechanism is provided by controls on

the front panel of an oscilloscope.

An intensity control varies the cathode heater current

and therefore the rate of emission of electrons, and thus

adjusts the intensity of the display on the screen. These

and other typical controls are shown in the illustration of

the front panel of a simple oscilloscope given in Figure

4.3.

65

Measurement and Instrumentation Cathode Ray Oscilloscope

Figure 4.2: Cathode ray tube

Figure 4.3: Controls of a simple Oscilloscope

Application of potentials to two sets of deflector plates

mounted at right angles to one another within the tube

provide for deflection of the stream of electrons, such

that the spot where the electrons are focused on the

screen is moved. The two sets of deflector plates are

66

Measurement and Instrumentation Cathode Ray Tube

normally known as the horizontal and vertical deflection

plates, according to the respective motion caused to the

spot on the screen. The magnitude of any signal applied

to the deflector plates can be calculated by measuring

the deflection of the spot against a crossed-wire

graticule etched on the screen.

In the oscilloscope’s most common mode of usage

measuring time-varying signals, the unknown signal is

applied, via an amplifier, to the y-axis (vertical)

deflector plates and a timebase to the x-axis

(horizontal) deflector plates. In this mode of operation,

the display on the oscilloscope screen is in the form of a

graph with the magnitude of the unknown signal on the

vertical axis and time on the horizontal axis.

4.2.2 Channel

One channel describes the basic subsystem of an

electron source, focusing system and deflector plates.

This subsystem is often duplicated one or more times

within the cathode ray tube to provide a capability of

displaying two or more signals at the same time on the

screen. The common oscilloscope configuration with two

channels can therefore display two separate signals

simultaneously.

4.2.3 Single-ended input

This type of input only has one input terminal plus a

ground terminal per oscilloscope channel and,

consequently, only allows signal voltages to be

67

Measurement and Instrumentation Oscilloscope Controls

measured relative to ground. It is normally only used in

simple oscilloscopes.

4.2.4 Differential input

This type of input is provided on more expensive

oscilloscopes. Two input terminals plus a ground

terminal are provided for each channel, which allows

the potentials at two non-grounded points in a circuit to

be compared. This type of input can also be used in

single-ended mode to measure a signal relative to

ground by using just one of the input terminals plus

ground.

4.2.5 Time-base circuitThe purpose of a timebase is to apply a voltage to the

horizontal deflector plates such that the horizontal

position of the spot is proportional to time. This voltage,

in the form of a ramp known as a sweep waveform,

must be applied repetitively, such that the motion of the

spot across the screen appears as a straight line when a

d.c. level is applied to the input channel. Furthermore,

this timebase voltage must be synchronized with the

input signal in the general case of a time-varying signal,

such that a steady picture is obtained on the

oscilloscope screen. The length of time taken for the

spot

to traverse the screen is controlled by a time/div switch,

which sets the length of time taken by the spot to travel

between two marked divisions on the screen, thereby

allowing signals at a wide range of frequencies to be

measured.

68

Measurement and Instrumentation Oscilloscope Controls

Each cycle of the sweep waveform is initiated by a pulse

from a pulse generator. The input to the pulse generator

is a sinusoidal signal known as a triggering signal, with

a pulse being generated every time the triggering signal

crosses a preselected slope and voltage level condition.

This condition is defined by the trigger level and trigger

slope switches. The former selects the voltage level on

the trigger signal, commonly zero, at which a pulse is

generated, whilst the latter selects whether pulsing

occurs on a positive- or negative-going part of the

triggering waveform.

Synchronization of the sweep waveform with the

measured signal is most easily achieved by deriving the

trigger signal from the measured signal, a procedure

that is known as internal triggering. Alternatively,

external triggering can be applied if the frequencies of

the triggering signal and measured signals are related

by an integer constant such that the display is

stationary. External triggering is necessary when the

amplitude of the measured signal is too small to drive

the pulse generator, and it is also used in applications

where there is a requirement to measure the phase

difference between two sinusoidal signals of the same

frequency. It is very convenient to use the 50 Hz line

voltage for external triggering when measuring signals

at mains frequency, and this is often given the name

line triggering.

4.2.6 Vertical Sensitivity Control

69

Measurement and Instrumentation Oscillocope Controls

This consists of a series of attenuators and pre-

amplifiers at the input to the oscilloscope.

These condition the measured signal to the optimum

magnitude for input to the mainamplifier and vertical

deflection plates, thus enabling the instrument to

measure a very wide range of different signal

magnitudes. Selection of the appropriate input

amplifier/attenuator is made by setting a volts/div

control associated with each oscilloscope channel. This

defines the magnitude of the input signal that will cause

a deflection of one division on the screen.

4.2.7 Display Position Control

This allows the position at which a signal is displayed on

the screen to be controlled in two ways. The horizontal

position is adjusted by a horizontal position knob on the

oscilloscope front panel and similarly a vertical position

knob controls the vertical position. These controls adjust

the position of the display by biasing the measured

signal with d.c. voltage levels.

4.3 DIGITAL STORAGE OSCILLOSCOPEDigital storage oscilloscopes consist of a conventional

analogue cathode ray oscilloscope with the added

facility that the measured analogue signal can be

converted to digital format and stored in computer

memory within the instrument. This stored data can

then be reconverted to analogue form at the frequency

necessary to refresh the analogue display on the

screen. This produces a non-fading display of the signal

on the screen.

70


The signal displayed by a digital oscilloscope consists of

a sequence of individual dots rather than a continuous

line as displayed by an analogue oscilloscope. However,

as the density of dots increases, the display becomes

closer and closer to a continuous line, and the best

instruments have displays that look very much like

continuous traces.

The density of the dots is entirely dependent upon the

sampling rate at which the analogue signal is digitized

and the rate at which the memory contents are read to

reconstruct the original signal. Inevitably, the speed of

sampling etc. is a function of cost, and the most

expensive instruments give the best performance in

terms of dot density and the accuracy with which the

analogue signal is recorded and represented. Besides

their ability to display the magnitude of voltage signals

and other parameters such as signal phase and

frequency, some digital oscilloscopes can also compute

signal parameters such as peak values, mean values

and r.m.s. values. They are also ideally suited to

capturing transient signals when set to single-sweep

mode. This avoids the problem of the very careful

synchronization that is necessary to capture such

signals on an analogue oscilloscope. In addition, digital

oscilloscopes often have facilities to output analogue

signals to devices like chart recorders and output digital

signals in a form that is compatible with standard

interfaces like IEEE488 and RS232.

71


4.4 Signal Measurement with C.R.O

For examining periodic waveforms the electron beam is

deflected horizontally (i.e. in the X direction) by a

sawtooth generator acting as a timebase. The signal to

be examined is applied to the vertical deflection system

(Y direction) usually after amplification.

Oscilloscopes normally have a transparent grid of 10mm

by 10mm squares in front of the screen, called a

graticule. Among the timebase controls is a ‘variable’

switch which gives the sweep speed as time per

centimeter, This may be in s/cm ro s/cm, a large

number of switch positions being available. Also on the

front panel of a c.r.o is a amplifier switch marked in

volts per centimeter, with a large number of available

switch positions.

(i) with direct voltage measurement, only the Y

amplifier ‘volts/cm’ switch on the c.r.o is used. With no

voltage applied to the Y plates the position of the spot

trace on the screen is noted. When a direct voltage is

applied to the Y plates the new position of the spot

trace is an indication of the magnitude of the voltage.

For example, in Figure 4.1 with no voltgae applied to

the Y plates, the spot trace is in the centre of the screen

(initial position) and then the spot trace moves 2.5cm to

the final position shown on application of a d.c voltage.

With the ‘volt/cm’ switch on 10 volts/cm the magnitude

of the direct voltage is 2.5 x 10 volts/cm. i.e. 25volts.

72

V/

cm

0.515

10

30

50

0.22

40

20

Initial position

Final position

Measurement and Instrumentation Determining Signal Magnitude with CRO

Figure 4.4

With alternating voltage measurements, let a

sinusoidal waveform be displayed on a c.r.o screen as

shown in figure 4.2. If the time/cm switch is on, say, 5

ms/cm then the periodic time T of the sinewave is

5ms/cm x 4cm (4cm is the width of one complete cycle),

i.e 20ms or 0.03s

Since frequency f = 1/T = 1/0.02 = 50Hz

If the ‘volts/cm’ switch is on, say, 20 volts/cm then the

amplitude or peak value of the sinewave is 20 volts/cm

x 4cm (Peak-to-peak value is 4cm), i.e. 80V.

Since r.m.s Voltage =

r.m.s voltage =

73

V/

cm

0.515

10

30

50

0.22

40

20

Peak-to-peak value

time/cm

100 μs5ms

50ms

2s


Figure 4.5

Worked examples:

Describe how a simpe c.r.o is adjusted to give (a) a spot

trace, (b) a continous horixontal trace on the screen,

explaining the function of the various controls.

(a) To obtain a spot trace on a typical c.r.o screen:

i. Switch on the c.r.o.

ii. Switch the time base control to off. This control is

calibrated in time per centimeters – for example,

6ms/cm or 100s/cm. Turning it to zero ensures no

signal is applied to the X-plates. The Y-plate input is left

open-circuited.

iii. Set the intensity, X-shift and Y-shift controls to

about the mid-range positions.

iv. A spot trace should not be observed on the

screen. If not, adjust either or both of the X and Y-shift

controls. The X-shift control varies the position of the

spot trace in horizontal direction whilst the Y-shift

control varies it vertical position.

74


v. Use the X and Y-shift controls to bring the spot to

the centre of the screen and use the focus control to

focus the electron beam into a small circular spot.

(b) To obtain a continous horizontal trace on the screen

the same procedure as in (a) is initially adopted. Then

the timebase control is switched to a suitalbel position,

initially the millisecond timebase range, to ensure that

the repetition rate of the sawtooth is sufficient for the

persistence of the vision time of the screen phosphor to

hold a given tance.

2. For the c.r.o square voltage waveform shown in the

figure 4.6 below determine (a) the periodic time, (b) the

frequency and (c) the peak-to-peak voltage. The

‘time/cm’ (or timebase control) switch is on 100s/cm

and the ‘volts/cm’ (or amplitude control) switch is on

20V/cm.

(Assume that the squares shown in figure 4.6 are 1cm

by 1cm)

(a) The width of one complet cycle is 5.3cm

75

Hence the period time, T = 5.2cm x 100 x 10-6 s/cm

= 0.52ms

(b) Frequency, f =

(c) The peak-to-peak height of the display is 3.6cm,

hence the peak-to-peak voltage = 3.6cm x 20V/cm =

72V.

3. For the c.r.o display of a pulse waveform shown in

figure 4.4 the ‘time/cm’ switch is on 50ms/cm and the

‘volts/cm’ switch is on 0.2V/cm. Determine (a) the

periodic time, (b) the frequency, (c) the magnitude of

the pulse voltage.

(a) The width of one complete cycle is 4.0cm

Hence the period time, T = 4.0cm x 50ms/cm = 200ms

(b) Frequence, f =

76


(c) The height of a pulse is 3.2cm hence the magnitude

of the pulse voltage = 3.2 x 0.2V/cm = 0.64V.

4.5 Frequency and Phase Measurement with Cathode Ray Osciloscope using Lissajous Pattern.

The cathode ray oscilloscope can be used in two ways to

measure frequency. Firstly, the internal timebase can

be adjusted until the distance between two successive

cycles of the measured signal can be read against the

calibrated graticule on the screen as described in earlier

section.

The alternative way of using an oscilloscopex to

measure frequency is to generate Lisajous patterns.

These are produced by applying a known reference-

frequency sine wave to the y input (vertical deflection

plates) of the oscilloscope and the unknown frequency

sinusoidal signal to the x input (horizontal deflection

plates). A pattern is produced on the screen according

to the frequency ratio between the two signals, and if

the numerator and denominator in the ratio of the two

signals both represent an integral number of cycles, the

pattern is stationary. Examples of these patterns are

shown in Figure 5.3, which also shows that phase

difference between the waveforms has an effect on the

shape. Frequency measurement proceeds by adjusting

the reference frequency until a steady pattern is

obtained on the screen and then calculating the

unknown frequency according to the frequency ratio

that the pattern obtained represents.

77

Measurement and Instrumentation Lisajous patterns

Figure 4.6: Lsajous Patterns.

4.6 SIGNAL GENERATOR

A signal generator is an electronic device that generates

repeating or non-repeating electronic signals (in either

the analog or digital domains). They are generally used

in designing, testing, troubleshooting, and repairing

electronic or electroacoustic devices. There are many

different types of signal generators, with different

purposes and aplications.

4.6.1 Function generators

It is a general purpose generator, a device which

produce simple repetitive waveforms. Such device

contain an electronic oscillator, a circuit that is capable

of creating a repetitive waveform. The most common

waveform is a sine wave, but sawtooth, step (pulse),

square, and triangular waveform oscillators are

commonly available. Function generators are typically

78

Measurement and Instrumentation Signal Generator

used in simple electronics repair and design; where they

are used to stimulate a circuit under test. A device such

as an oscilloscope is then used to measure the circuit’s

output.

4.6.2 Pitch and audio generators

A pitch generator is a type of signal generator optimized

for use in audio and acoustics applications. Pitch

generators typically include sine waves over the audio

frequency range (20Hz-20kHz). Pitch generator are

typically used in conjunction with sound level meters,

when measuring the acoustics of a room or a sound

reproduction system, and/or with oscilloscope or

specialized audio analyzers.

4.6.3 Video signal generators

A video signal generator is a device which outputs

predetermined video and/or television waveforms, and

other signals used to stimulate faults in, or aid in

parametric measurements of, television and video

systems. There are several different types of video

signal generators in widespread use. Regardless of the

specific type, the output of a video generator will

generally contain synchronization signals appropriate

for television, including horizontal and vertical

synchronized pulses (in digital).

79

Measurement and Instrumentation Video Signal Generator

Excersice 4

1. In general electronics use, when measuring AC

voltage signals, what do the two axis (horizontal and

vertical) of the oscilloscope screen represent?

2. The core of an analog oscilloscope is a special type

of vacuum tube known as a Cathode Ray Tube, or CRT.

With a suitable diagram explain how a CRT functions.

What goes on inside the tube to produce waveform

displays on the screen?

3. With the aid of a suitable block diagram, describe an

Oscilloscope.

4. For the square voltage waveform displayed on a

cathode ray oscilloscope shown in the figure bellow, the

volt/cm switch is on 40volt/cm and the time/cm switch

is on 5ms find (a) its frequency, (b) its peak-to-peak

voltage.

5 For the sinusoidal waveform shown in figure (b), the

Volt/cm switch is on 50volts/cm and time/cm switch is

on 5ms determine (a) its frequency, (b) the peak-to-

peak voltage, (c) the r.m.s. (each box rep 1cm x 1cm)

80

Measurement and Instrumentation Chapter Four

7. What is a signal generator as it applies to

electronic design and trouble shooting techniques.

8. Describe the the following types of Signal

generator, stating their properties and uses;

i. Function generator

ii. Audio generator

iii. Vedio generator.

81

Measurement and Instrumentation Chapter Four

The earlier chapters in this book have been essentially

concerned with describing ways of producing high-

quality, error-free data at the output of a measurement

system. Having got the data, the next consideration is

how to present it in a form where it can be readil used

and analysed. This chapter therefore stats by covering

the techniques available to either display measurement

data for current use or record it for future use. Following

this, standards of good prectice for presenting data in

either graphical or tabular form are covered, using

either paper or a computer monitor screen as the

display medium.

5.1 DISPLAY OF MEASURED SIGNALS

Measurement signals in the form of varying electrical

voltage can be displayed either by an oscilloscope or

else by any of the electrical meters described in the

earlier chapters of this book. However, if signals are

converted to digital form, other display options apart

from meters become possible, such as electronic output

displays or using a computer monitor.

5.1.1Electronic output displays

Electronic displays enable a parameter value to be read

immediately, thus allowing for any necessary response

82

to be made immediately. The main requirement for

displays is that they should be clear and unambiguous.

Two common types of character formart used in

displays are, seven-segment and 7 x 5 dot matrix, are

shown in figure 5.1 below. Both types of display have

the advantage of being able to display alphabetic as

well as numeric information, although the seven-

segment format can only display a limited nine-letter

subset of the full 26-letter alphabet. This allows added

meaning to be given to the number displayed by

including a word or letter code. It also allow a single

display unit to send information about several

parameter value, cycling through each in turn and

including alphabetic information to indicate the nature

of the variable currently displayed.

Electronic output units usually consist of a number of

side-by-side cells, where each cell displays one

character. Generally, these accept either serial or

paralled digital input signals, and the input format can

be either binary-coded decimal (BCD) or ASCII.

Technologies used for the individual elements in the

diplay are either light-emitting diodes (LEDs) or liquid-

crystal elements.

83

Measurement and Instrumentation Electronic Display

Figure 5.1: Character formats used in electronic

displays: (a) seven-segment, (b) 7 x 5 dot matrix.

5.1.2 Computer monitor displays

Now that computer are part of the furniture in most

homes, the ability of computer to display information is

widely understood and appreciated. Computers are now

both cheap and highly reliable, and they provide an

excellent mechanism for both displaying and storing

information. As well as alphanumeric displays of

industrial plant variable and status data, for which the

plant operator can vary the size of font used to display

the information at will, it is also relatively easy to

display other information such as plant layout diagrams,

process flow layouts etc. This allows not only the value

of prameters that go outside control limits to be

displayed, but also their location on a schematic map of

the plant. However, this poses a difficulty when there is

a requirement to display the variable’s behaviour over a

long period of time since the length of the time axis is

contrained by the size of the monitor’s screen. To

overcome this, the display resolution has to decrease as

the time period of the display increases.

5.2 Recording of measurement results data

Many techniques now exist for recording measurement

data in a form that permits subsequent analysis,

particularly for looking at the historical behaviour of

measured parameters in fault diagnosis procedures. The

earliest recording instruments used were various forms

84

Measurement and Instrumentation Recorders

of mechanical chart recorder. Whilst many of these

remain in use, most modern form of chart recorder exist

in hybrid forms in which microprocessors are

incorporated to improve performance.

5.3 Mechanical chart recorders

Mechanical chart recorder are a long-established means

of making permanent records of electrical signals in a

simple, cheap and reliable way. Mechanical chart

recorders are either of the galvanometric type or

potentiometric type. Both of these work on the same

principle of driving chart paper at a constant speed past

a pen whose deflection is a function of the magnitude of

the measured signal. This produces a time history of the

measured signal.

5.3.1. Galvanometric recorders

These work on the same principle as a moving-coil

meter except that the pointer draws an ink trace on

paper, as illustrated in Figure 5.2, instead of merely

moving against a scale. The measured signal is applied

to the coil, and the angular deflection of this and its

attached pointer is proportional to the magnitude of the

signal applied.

Inspection of Figure 5.3(a) shows that the displacement

y of the pen across the chart recorder is given by

y = R Sin .

85


Figure 5.2: Simple galvanometric recorder

Figure 5.3: Output of simple chart recorder: (a) y

versus relationship; (b) curvilinear chart paper.

This relationship is non-linear and brings a percentage

of error into the measurement. Also due to pen moving

in an arc it is difficult to relate the magnitude of

deflection with the time axis. One way of overcoming

this is to print a grid on the chart paper in the form of

circular arcs, as illustrated in Figure 5.3(b).

Unfortunately, measurement errors often occur in

reading this type of chart, as interpolation of points

drawn between the curved grid line is difficult. An

alternative solution is to use heat-sensitive chart paper

directed over a knife-edge, and to replace the pen by a

86


heated stylus, as illustrated in Figure 5.4. The input-

output relationship is still non-linear, with the deflection

y being proportional to tan as shown in Figure 5.5(a),

and the reading error for excursion of 100 is still 0.7%.

However, the rectilinearly scaled chart paper now

required, as shown in Figure 5.5(b), allows much easier

interpolation between grid lines.

Figure 5.4: Knife-edge galvanometric recorder.

Figure 5.5: Knife-edge recorder output: (a) y versus

relationship; (b) rectilinear chart paper.

87


5.3.2. Potentiometric recorder

Potentiometric recorders have much better

specifications than galvanometric recorders, with a

typical inaccuracy of š0.1% of full scale and

measurement resolution of 0.2% f.s. being achievable.

Such instruments employ a servo system, as shown in

Figure 5.6, in which the pen is driven by a servomotor,

and a potentiometer on the pen feeds back a signal

proportional to pen position. This position signal is

compared with the measured signal, and the difference

is applied as an error signal that drives the motor.

However, a consequence of this electromechanical

balancing mechanism is to give the instrument a slow

response time in the range 0.2–2.0 seconds. This means

that potentiometric recorders are only suitable for

measuring d.c. and slowly time-varying signals.

Figure 5.6: Servo system of potentiometer chart

recorder

5.3.3Ultra-violet recorders

galvanometric recorders concluded are restricted by its

systems moment of inertia and spring constants

reduces and limit the maximum bandwidth to about 100

Hz. Ultra-violet recorders work on very similar principles

88


to standard galvanometric chart recorders, but achieve

a very significant reduction in system inertia and spring

constants by mounting a narrow mirror rather than a

pen system on the moving coil. This mirror reflects a

beam of ultra-violet light onto ultra-violet sensitive

paper. It is usual to find several of these mirror-

galvanometer systems mounted in parallel within one

instrument to provide a multi-channel recording

capability, as illustrated in Figure 5.7. This arrangement

enables signals at frequencies up to 13 kHz to be

recorded with a typical inaccuracy of 2% f.s. Whilst it

is possible to obtain satisfactory permanent signal

recordings by this method, special precautions are

necessary to protect the ultra-violet-sensitive paper

from light before use and to spray a fixing lacquer on it

after recording. Such instruments must also be handled

with extreme care, because the mirror galvanometers

and their delicate.

89


Figure 5.7 Ultra-violet recorder

5.4 Presentation of data

The two formats available for presenting data on paper

tabular and graphical one and the relative merits of

these are compared below. In some circumstances, it is

clearly best to use only one or other of these two

alternatives alone. However, in many data collection

exercises, part of the measurements and calculations

are expressed in tabular form and part graphically, so

making best use of the merits of each technique.

5.4.1Tabular data presentation

A tabular presentation allows data values to be

recorded in a precise way that exactly maintains the

accuracy to which the data values were measured. In

other words, the data values are written down exactly

as measured. Besides recording the raw data values as

measured, tables often also contain further values

calculated from the raw data. An example of a tabular

data presentation is given in Table 5.1. This records the

results of an experiment to determine the strain

induced in a bar of material that is subjected to a range

90

Measurement and Instrumentation Presentation of Data

of stresses. Data were obtained by applying a sequence

of forces to the end of the bar and using an

extensometer to measure the change in length. Values

of the stress and strain in the bar are calculated from

these measurements and are also included in the table.

The final row, which is of crucial importance in any

tabular presentation, is the estimate of possible error in

each calculated result. A table of measurements and

calculations should conform to several rules as

illustrated in Table 5.1:

(i) The table should have a title that explains what

data are being presented within the table.

Table 5.1: Sample tabular presentation of data

(ii) Each column of figures in the table should refer to

the measurements or calculations associated with one

quantity only.

(iii) Each column of figures should be headed by a title

that identifies the data values contained in the column.

91


(iv) The units in which quantities in each column are

measured should be stated at the top of the column.

(v) All headings and columns should be separated by

bold horizontal (and sometimes vertical) lines.

(vi) The errors associated with each data value quoted

in the table should be given. The form shown in Table

5.1 is a suitable way to do this when the error level is

the same for all data values in a particular column.

However, if error levels vary, then it is preferable to

write the error boundaries alongside each entry in the

table.

5.4.2Graphical presentation of data

Presentation of data in graphical form involves some

compromise in the accuracy to which the data are

recorded, as the exact values of measurements are lost.

However, graphical presentation has important

advantages over tabular presentation.

(i) Graphs provide a pictorial representation of results

that is more readily comprehended than a set of tabular

results.

(ii) Graphs are particularly useful for expressing the

quantitative significance of results and showing whether

a linear relationship exists between two variables.

Figure 5.8 shows a graph drawn from the stress and

strain values given in the Table 5.1. Construction of the

graph involves first of all marking the points

corresponding to the stress and strain values. The next

step is to draw some lines through these data points

92


that best represents the relationship between the two

variables. This line will normally be either a straight one

or a smooth curve. The data points will not usually lie

exactly on this line but instead will lie on either side of

it. The magnitude of the excursions of the data points

from the line drawn will depend on the magnitude of the

random measurement errors associated with the data.

(iii) Graphs can sometimes show up a data point that is

clearly outside the straight line or curve that seems to

fit the rest of the data points. Such a data point is

probably due either to a human mistake in reading an

instrument or else to a momentary malfunction in the

measuring instrument itself. If the graph shows such a

data point where a human mistake or instrument

malfunction is suspected, the proper course of action is

to repeat that particular measurement and then discard

the original data point if the mistake or malfunction is

confirmed.

Like tables, the proper representation of data in

graphical form has to conform to certain rules:

(i) The graph should have a title or caption that explains

what data are being presented in the graph.

(ii) Both axes of the graph should be labelled to express

clearly what variable is associated with each axis and to

define the units in which the variables are expressed.

93


Figure 5.8: Sample graphical representation of data: graph of stress against strain.

(iii) The number of points marked along each axis

should be kept reasonably small – about five divisions is

often a suitable number.

(iv) No attempt should be made to draw the graph

outside the boundaries corresponding to the maximum

and minimum data values measured, i.e. in Figure 5.8,

the graph stops at a point corresponding to the highest

measured stress value of 108.5.

Fitting curves to data points on a graph

The procedure of drawing a straight line or smooth

curve as appropriate that passes close to all data points

on a graph, rather than joining the data points by a

jagged line that passes through each data point, is

justified on account of the random errors that are known

to affect measurements. Any line between the data

points is mathematically acceptable as a graphical

representation of the data if the maximum deviation of

any data point from the line is within the boundaries of

the identified level of possible measurement errors.

94


However, within the range of possible lines that could

be drawn, only one will be the optimum one. This

optimum line is where the sum of negative errors in

data points on one side of the line is balanced by the

sum of positive errors in data points on the other side of

the line. The nature of the data points is often such that

a perfectly acceptable approximation to the optimum

can be obtained by drawing a line through the data

points by eye.

Excersice 5

1. Explain the advantage(s) of electronic digital

display over analogue one.

2. Compare the principle of a Moving-coil recorder

with that of an Ultra-violet recorder, dicussing

the advantages of the latter over the former.

3. Differentiate between a tabular and graphical

representation of data. Enumerating the merits

and demerit of each one.

95

Measurement and Instrumentation Chapter Five

6.1 Principles of Temperature Measurement

Temperature measurement is very important in all

spheres of life and especially so in the process

industries. However, it poses particular problems, since

temperature measurement cannot be related to a

fundamental standard of temperature in the same way

that the measurement of other quantities can be related

to the primary standards of mass, length and time. If

two bodies of lengths l1 and l2 are connected together

end to end, the result is a body of length l1 + l2. A similar

relationship exists between separate masses and

separate times. However, if two bodies at the same

96

temperature are connected together, the joined body

has the same temperature as each of the original

bodies.

This is a root cause of the fundamental difficulties that

exist in establishing an absolute standard for

temperature in the form of a relationship between it and

other measurable quantities for which a primary

standard unit exists. In the absence of such a

relationship, it is necessary to establish fixed,

reproducible reference points for temperature in the

form of freezing and boiling points of substances where

the transition between solid, liquid and gaseous states

is sharply defined. The International Practical

Temperature Scale (IPTS) uses this philosophy and

defines six primary fixed points for reference

temperatures in terms of:

the triple point of equilibrium hydrogen -

259.34°C

the boiling point of oxygen -182.962°C

the boiling point of water 100.0°C

the freezing point of zinc 419.58°C

the freezing point of silver 961.93°C

the freezing point of gold 1064.43°C

(all at standard atmospheric pressure)

Instruments to measure temperature can be divided

into seperate classes according to the physical principle

on which they operate. The main principles discussed in

this book are:

1. Thermoelectric effect

97

Measurement and Instrumentation Thermoelectric effect

2. Resistance Thermometer

3. Sensitivity of semiconductor device (Thermistor).

4. Thermal Expansion method.

5. Acoustic Thermometer.

6.2 Thermoelectric effect (thermocouples)

Thermoelectric effect sensors rely on the physical

principle that, when any two different metals are

connected together, an e.m.f, which is a function of the

temperature, is generated at the junctoin between the

metals.

A thermocouple is a device based upon these principle,

which was discorvered by SEEBECK (1821). He showed

that a small electric will flow in a circuit composed of

two dissimilar conductors when their junctions are kept

at different temperatures. The electromotive force (emf)

produced under these conditions is known as the

“Seebeck emf”. The pair of conductors that constitute

the thermoelectric circuit is called thermocouple. The

output of a thermocouple circuit is a voltage, and there

is a definite relationship between this voltage, and

temperatures of the junctions that make up the

thermocouple circuit.

The reading V0 of the voltmeter in figure 6.1 below is

given by:

................. equation 6.1

98

Measurement and Instrumentation Thermocouple

C is the sensitivity of the thermocouple circuit.

Figure 6.1: Seebeck effect (Thermocouple principle)

6.2.1Fundamental Thermocouple Laws

1. Law of Homogeneous Materials: A

thermoelectric current cannot be sustained in a circuit

of a single homogeneous material by the application of

heat alone, regardless of how it might vary in cross

section.

2. Law of Intermediate Materials: The algebraic

sum of the thermoelectric forces in a circuit composed

of any number of dissimilar materials is zero if all of the

circuit is at a uniform temperature.

3. Law of Successive or Intermediate

Temperatures:

If two dissimilar homogeneous materials produce

thermal emf1 when the junctions are at T1 and T2 and

produce thermal emf2 when the junctions are at T2 and

T3 , the emf generated when the junctions are at T1 and

T3 will be emf1 +emf2.

99


It is important to note that thermocouple measure the

temperature difference between two points, not

absolute temperature.

Worked Example 6.1

A thermocouple was found to have linear calibration

between 00C and 4000C with emf at maximum

temperature (reference junction temperature 00C) equal

to 20.68 mV.

a) Determine the correction which must be made to the

indicated emf if the cold junction temperature is 250C.

b) If the indicated emf is 8.82 mV in the thermocouple

circuit, determine the temperature of the hot junction.

Solution:

(a) Sensitivity of the thermocouple C is given by

C = 20.68/(400-0) = 0.0517 mV/0C

Since the thermocouple is calibrated at the reference junction of 00C and is being used at 250C, then the correction which must be made, Ecorr between 00C and 250C

Ecorr = 0.0517 x 25Ecorrr = 1.293 mV

(b) Indicated emf V0 between the hot junction T2 and reference junction T1 at 250C = 8.92 mV

V0 = C(T2 – T1)

100


Since the reference junction temperature T1 is 250C, hot junction temperature T2 is given by;

T2 = 172.53 + 25 = 197.530C.

6.3 Resistance thermometer or Resistance

temperature detector (RTDs).

Resistance thermometer, also called resistance

temperature detector (RTDs), are temperature sensors

that exploit the predictable change in electrical

resistance of some metals with changing temperature.

The resistance ideally varies linearly with temperature

according to the relationship:

This equation is non-linear and so is inconvenient for

measurement purpose. The equation becomes linear if

all the terms in 2T2 and higher powers of T are

negligible such that the resistance and temperature are

related according to:

T1<T<T2

R(T) = approximation of resistance at temperature T.

R(T0) = resistance at temperature T0

0 = fractional change in resistance per degree of

the temperature at T0.

ΔT = T – T0

This equation is approximately true over a limited

temperature range for some metals, notably platinum,

copper and nickel.

Resistance vs Temperature Linear

Approximations

101

Measurement and Instrumentation Resistant Thermometter

Straight line equation

.............. equation 6.2

R2 = resistance at T2

R1 = resistance at T1

Worked example 6.2

A sample of metal resistance versus temperature has

the following measured values:

T(0F) R()

60 106.0

65 107.6

70 109.1

75 110.2

80 111.1

85 111.7

90 112.2

Find the linear approximation of resistance versus

temperature between 600 and 900F.

Solution:

Since 750F is the midpoint, this will be used for T0 so the

R0 = 110.2, Then the slope can be found from

equation 5.2:

Thus, the linear approximation for resistance is

R(T)= 110.2[1+0.001875(T-75)]

102

Measurement and Instrumentation Resistant Thermometer

Construction of a Platinum resistance

Thermometer

Figure 6.2

6.4 Thermistor

These are semiconductor resitance sensors, unlike

metals, thermistors respond negatively to temperature.

That is, as the temperature of the semiconductor

material is increased their resistance decreases. The

symbol of thermistor is shown in figure 6.3 below

Figure 6.3: Symbol of Thermistor

6.5 Thermal Expansion Method

Thermal expansion methods of temperature

measurement make use of the fact that the dimensions

of all substances whether solids, liquids or gases,

change with temperature. Instruments operating on this

physical principle include the liquid-in-glass

thermometer, the bimetallic thermometer and the

pressure thermometer.

6.5.1Liquid-in-glass thermometers

103

Measurement and Instrumentation Thermal Expansion method

The liquid-in-glass thermometer is a well-known

temperature-measuring instrument that is used in a

wide range of applications. The fluid used is usually

either mercury or coloured alcohol, and this is contained

within a bulb and capillary tube, as shown in Figure 6.4.

As the temperature rises, the fluid expands along the

capillary tube and the meniscus level is read against a

calibrated scale etched on the tube.

Figure 6.4a: Mercury-glass-thermometer

6.5.2Bimetallic thermometer

The bimetallic principle is probably more commonly

known in connection with its use in thermostats. It is

based on the fact that if two strips of different metals

are bonded together, any temperature change will

cause the strip to bend, as this is the only way in which

the differing rates of change of length of each metal in

the bonded strip can be accommodated. In the

bimetallic thermostat, this is used as a switch in the

contol applications. If the magnitude of bending is

measured, the bimetallic device becomes a

thermometer. For such purposes, the strip is often

104

arranged in a spiral or helical configuration, as shown in

Figure 5.4b.

Figure 6.4b: Bimetallic strip

6.6 Acoustic Thermometer

The principle of acoustic thermometry was dicovered as

long ago as 1873 and uses the fact that the velocity of

sound through a gas varies with temperature according

to the equation:

................. equation 6.3

Where v is the sound velocity, T is the gas temperature,

M is the molecular weight of the gas and both R and

are constants. Until very recently, it had only been used

for measuring cryogenic (very low) temperatures, but it

is now also used for measuring higher temperature and

can potentially measure right up to 20, 0000C.

105

Measurement and Instrumentation Thermal Expansion method

Measurement and Instrumentation Acoustic Thermometer

Exercise 6

1. The table below shows the hot junction temperatures

T2 of a thermocouple when the reference junction

temperature T1 is maintained at 00C with the

corresponding outputs e.m.f E0 in mV. Plot the graph of

T2-T1 against E0. Hence find the sensitivity of the

thermocouple.

E0 (mV) T2-T1(0C)

106

Measurement and Instrumentation Chapter Six

10 15620 31230 46840 62350 780

2. If the output of the thermocouple in 1 above it

6.41mV, when the reference junction temperature

is maintained at 00C and the hot junction is

immersed in a fluid. Determine the temperature

of the fluid.

3. Define thermocouple and explain the Laws that

governs its principle of operation.

Pressure measurement is a very common requirement

for most industrial process control systems and many

different types of pressure-sensing and pressure-

measurement systems are available. However, before

considering these in detail, it is important to explain

some terms used in pressure measurement and to

107

define the difference between absolute pressure, guage

pressure and differential pressure.

Absolute pressure: This is the difference between the

pressure of a fluid and the absolute zero of pressure.

Guage pressure: This describes the difference

between the pressure of a fluid and atmospheric

pressure. Absolute and guage pressure are therefore

related by the expression:

Absoulte pressure = Gauge pressure + Atmospheric pressure

Thus, guage pressure varies as the atmospheric

pressure changes and is therefore not a fixed quantity.

Differential pressure: This term is used to describe

the difference between two absolute pressure values,

such as the pressures at two different points within the

same fluid.

In most applications, the typical values of pressure

measured range from 1.013 bar (the mean atmospheric

pressure) up to 7000bar. This is considered to be the

normal pressure range, and a large number of pressure

sensors are available that can measure pressures in this

range. Measurement requirements outside this range

are much less common. Whilst some of the pressure

sensors developed for the ‘normal’ range can also

measure pressures that are either lower or higher that

this, it is preferable to use special instruments that have

been specially designed to satisfy such low-and high-

pressure measurement requirements.

The discussion below summarize the main types of

pressure sensor that are in use. This discussion is

108

Measurement and Instrumentation Diaphragms

primarily concerned only with the measurement of

static pressure, because the measurement of dynamic

pressure is a very specialized area that is not of general

interest.

7.1 DIAPHRAGMS

The diaphragm, shown schematically in figure 7.1, is

one of three types of elesatic element pressure

transducer. Applied pressure causes displacement of

the diaphragm and this movement is measured by a

displacement transducer. Different versions of

diaphragm sensors can measure both absolute pressure

(up to 50bar) and guage pressure (up to 2000bar)

according to whether the space on one side of the

diaphragm is respectively evacuated or is open to the

atmosphere. A diaphragm can also be used to measure

differential pressure (up to 2.5 bar) by applying the two

pressures to the two sides of the diaphragm. The

diaphragm can be either plastic, metal alloy, stainless

steel or ceramic. Plastic diaphragms are cheapest, but

metal diaphragms give better accuracy. Stainless steel

is normally used in high temperature or corrosive

environments. Ceramic diaphragms are resistant even

to strong acids and alkalis, and are used when the

operating environment is particularl harsh.

109

Measurement and Instrumentation Bellow

Figure 7.1: Diaphragm

7.2 BELLOW

The bellows, schematically inllustrated in figurre 7.2, is

another elastic-element type of pressure sensor that

operates on very similar principles to the diaphragm

pressure sensor. Pressure changes within the bellows,

which is typically fabricated as a seamless tube of either

metal or metal alloy, produce traslational motion of the

end of the bellows that can be measured by capacitive,

inductive or potentiometric transducers. Different

versions can messure either absolute pressure up to

(2.5 bar) or guage pressure (up to 150 bar).

Figure 7.2: Bellows

110

Measurement and Instrumentation Bourdon Tube

7.3 BOURDON TUBE

The Bourdon tube is also an elastic element type of

pressure transducer. It is relatively cheap and is

commonly used for measuring the guage pressure of

both gaseous and liquid fluids. It consists of a specially

shaped piece of ova-section, flexible, metal tube that is

fixed at one end and free to move at the other end.

When pressure is applied at the open, fixed end of the

tube, the oval cross-section becomes more circular. In

consequence, there is a displacement of the free end of

the tube. This displacement is measured by some form

of displacement transducer, which is commonly a

potentiometer.

The three common shapes of Bourdon tube are shown

in figure 7.3. The maximum possible deflection of the

free end of the tube is propostional to the angle

subtended by the arec through which the tube is bent.

For a C-type tube, the maximum value for this arc is

somewhat less that 3600. Where greater measurement

sensitivity and resolution are required, spiral and helical

tubes are used. These both give a much greater

deflection at the free end for a given applied pressure.

However, this increased measurement performance is

only gained at the expense of a sustantial increase in

manufacturing difficult and cost compared with C-type

tubes, and is also associated with a large decrease in

the maximum pressure that can be measured. Spiral

and hlical types are sometimes provided with a rotating

111

pointer that moves against a scale to give visual

indication of the measured pressure.

Figure 7.3: Bourdon Tube

7.4 MANOMETER

Manometers are passive instruments that give a visual

indication of pressure values. Various types exist.

The U-tube manometer, shown in Figure 7.4a, is the

most common form of manometer. Applied pressure

causes a displacement of liquid inside the U-shaped

glass tube, and the output pressure reading P is made

by observing the difference h between the level of liquid

in the two halves of the tube A and B, according to the

equation P=hg. Where is the specific gravity of the

fluid. If an unknown presure is applied to side A, and

side B is open to the atmosphere, the output reading is

guage pressure. Alternativel, if the side B of the tube is

sealed and evacuated, the output reading is absolute

112

Measurement and Instrumentation Bourdon Tube

pressure. The U-tube manometer also measures the

differential pressure (p1-p2), according to the expression

(p1-p2)=hg, if two unknown pressures p1 and p2, are

applied respectively to sides A and B of the tube.

Output readings from U-tube manometers are subject to

error, principally because it is very difficult to judge

exactly where the meniscus levels of the liquid are in

the two halves of the tube. In absolute pressure

measurement, an addition error occurs because it is

impossible to totall evacuate the closed end of the tube.

U-tube manometers are typically used to measure

gauge and differential pressures up to about 2 bar. The

type of liquid used in the instrument depends on the

pressure and characteristics of the fluid being

measured. Water is a cheap and convenient choice, but

it evaporates easil and is difficult to see. Nevertheless, it

is used extensively, with the major obstacles to its use

being overcome by useing coloured water and by

regularl topping up the tube to counteract eveporation.

However, water is

definitely not used when measureing the pressure of

fluids that react with or dissolve in water. Water is also

unsuitable when high-pressure measurements are

required. In such circumstances liquids such as aniline,

carbon tetrachloride, bromoform, mercur or transformer

oil are used instead.

113

Measurement and Instrumentation Manometer

Figure 7.4: Manometers: (a) U-tube; (b) Well type; (c) inclined

type.

The well-type or critern manometer, shown in figure

7.4(b), is similar to a U-tube manometer but one halt of

the tube is made very large so that it forms a well. The

change in the level of the well as the measured

pressure varies is negligible. Therefore, the liquid level

in only one tube has to be measured, which makes the

instrument much easier to use than the U-tube

manometer. If an unknown pressure P1 is applied to

port A, and port B is open to the atmosphere, the guage

pressure is given by P1=h. It might appear that the

instrument would give a better measurement accurac

than the U-tube manometer because the need to

subtract two liquid level measurements in order to

assive at the pressure value is avoided. However, this

benefit is swamped by errors that arise due to the

typical cross-sectional area variations in the glass used

to make the tube. Such variations do not affect the

accuracy of the U-tube manometer to the same extent.

114

The inclined manometer or draft guage, shown in figure

7.4(c), is a variation on the well-type manometer in

which one leg of the tube in inclined to increase

measurement sensitivity. However, similar comments to

those above apply about accuracy.

Excersice 7

115

Measurement and Instrumentation Manometer

Measurement and Instrumentation Chapter Seven

1. Define the following; i. Absolute pressure, ii.

Guage pressure and iii. Differential pressure,

as they apply to pressure measurement.

2. Relating their principle of operation,

differentiate between the a diaphragm and a

manometer in pressure measurement.

3. Describe how a diaphragm can be employed

to measure Absolute, guage and differential

pressure.

116

Measurement and Instrumentation pH Measurement

A very important measurement in many liquid chemical

processes (industrial, pharmaceutical, manufacturing,

food production, etc.) is that of pH.

pH is a parameter that quantifies the level of acidity or

akalinity in a chemical solution. It defines the

concentration of hydrogen atoms in the solution in

grams/litre and is expressed as:

pH = log10[1/H+]

where H+ is the hydrogen ion concentration in the

solution.

The value of pH can range from 0, which describes

extreme acidity, to 14, which describes extreme

akalinity. Pure water has a pH of 7.

The common pH scale extends from 0 (strong acid) to

14 (strong caustic), with 7 in the middle representing

pure water (neutral) (figure 5.1):

Figure 8.1

8.1 Definition of pH

In its most common interpretation, pH is used to specify

the degree of acidity or basicity of an aqueous solution.

pH is defined as follows: the lower-case letter "p" in pH

117

stands for the negative common (base ten) logarithm,

while the upper-case letter "H" stands for the element

hydrogen. Thus, pH is a logarithmic measurement of the

number of moles of hydrogen ions (H+) per liter of

solution. Incidentally, the "p" prefix is also used with

other types of chemical measurements where a

logarithmic scale is desired, pCO2 (Carbon Dioxide) and

pO2 (Oxygen) being two such examples.

8.1.1 Logarithmic scale

The logarithmic pH scale works like this: a solution with

10-12 moles of H+ ions per liter has a pH of 12; a solution

with 10-3 moles of H+ ions per liter has a pH of 3. While

very uncommon, there is such a thing as an acid with a

pH measurement below 0 and a caustic with a pH above

14. Such solutions, understandably, are quite

concentrated and extremely reactive.

8.2 Electrochemical Methods of pH Measurement

Electrochemical measurement of pH utilizes devices

that transduce the chemical activity of the hydrogen ion

into an electronic signal, such as an electrical potential

difference or a change in electrical conductance. This

section review electrochemical pH measurement, with

emphasis on the glass membrane electrode.

8.2.1 The Glass Membrane Indicator Electrode

118



The most widely used method for measuring pH is the

glass membrane electrode. As illustrated schematically

in Figure 8.2, a pH meter measures the electrical

potential difference (voltage) that develops between a

glass membrane pH indicator electrode and a reference

electrode immersed in the sample to be tested. The

indicator and reference electrode are commonly

combined into a single, functionally equivalent, probe,

referred to as a combination electrode. The glass

membrane of the indicator electrode develops a pH-

dependent potential, as as a result of ion-exchange

between hydrogen ion in solution and univalent cations

in the glass membrane. The sensitivity of the glass

electrode membrane potential to changes in pH is small,

so a suitably designed reference electrode and a high

input impedance meter are required in order for the

potential to be precisely measured.

119

Figure 8.2: pH measurement using a glass membrane electrode: (a) measurement system comprising a pH meter, indicator, and reference electrodes; (b) indicator electrode construction; (c) reference electrode construction; and (d) amplifier circuit.

Great care is necessary in the use of the glass electrode

type of pH probe. Firstly, the measuring probe has a

very high resistance (typically 108) and a very low

output. Hence, the output signal from the probes must

be electrically screened to prevent any stray pick-up

and electrical insulation of the assemble must be very

high. The assembly must also be very efficiently sealed

to prevent the ingress of moisture.

A second problem with the glass electrode is the

deterioration in accuracy that occurs as the glass

membrane becomes coated with various substances it

is exposed to in the measured solution. Cleaning at

prescribed intervals is therefore necessary and this

must be carried out carefully, using the correct

procedures, to avoid damaging the delicate galss

membrane at the end of the probe. The best cleaning

procedure varies according to the nature of the

contamination. In some cases, careful brushing or

wiping is adequate, whereas in other cases spraying

with chemical solvents is neccessary. Ultrasonic cleaing

is often a useful technique, though it tends to be

expensive. Steam cleaning should not be attempted, as

this damages the pH-sensitive membrane. Mention

must also be made about storage. The glass electrode

must not be allowed to dry out during storage, as this

would cause serious damage to the pH-sensitive layer.

Finally, caution must be taken about the response time

of the instrument. The glass electrode has a relatively

large time constant of one to two minutes, and so it

120


must be left to settle for a long time before the reading

is taken. If this causes serious difficulties, special forms

of low-resistivity glass electrode are now available that

have smaller time constants.

8.3 Instrumentaion of pH meter

The pH meter pictured in Figure 8.2 measured the

potential developed between the pH indicator and

reference electrodes, from which the pH of the sample

is determined using a previously established calibration

and possibly the sample temperature. The

measurement of the potential, which may range in

magnitude up to a few hundred milivots, is complicated

by the large electrical resistance presented by the glass

memebrane. This may range from 100M to greater

than 1000M, and necessitates the use of high input

impedance amplifiers with FET input stages if the glass

membrane potential is to be accurately measured.

While the relatively low cost and high performance of

commerciall available meters obviates the need for

amplifier construction, Figure 8.2(d) presents a simple

amplifier suitable for use with a glass electrode. The

amplifier circuitr of commercial pH meters incorporates

additional functions to improve the accuracy and stabilit

of the measurement, such as a driven shield to reduce

noise pickup and chopper stabilization to reduce drift.

8.4 Calibration of pH meter

121


Calibration of pH meter is usually reffered to as pH

electrode calibration. To calibrate the electrode you

need at least two solutions of knonw pH. Most

commonly used commercially available calibration

buffers (A buffer solution is an aqueous solution

consisting of a mixture of a weak acid and its conjugate

base or a weak base and its conjugate acid. It has the

property that the pH of the solution changes very little

when a small amount of strong acid or base is added to

it. Buffer solution are used as a means of keeping pH at

a nearly constant value in a wide variety of chemical

applications.) have pH of 4.01, 7.00 and 10.00.

1. The first step to take is usually related to

temperature correction. The pH meter must be able to

measure temperature or use external temperature

probe because the butter pH changes with temperature.

2. The next step is to put the electrode into pH 7.00

buffer. Take care not to hit the bottom of the beaker

with the electrode. Wait for the reading to stabilize.

Rinse the electrode with distilled water from a wash

bottle into an empty beaker before immersing it into

new solution.

3. The next step will depend on the solution you want

your pH meter to measure. If you plan to measure pH in

acidic solutions, use pH=4.01 buffer. If you plan to

measure high pH use pH=10.00 buffer.

4. After you are ready, then you can take your

measurement.

122


Excersice 8

1. Define pH and with a simple sketch, describe a pH

scale.

2. Determine the number of moles of H+ ions per liter

of a solution with pH of 8.6.

3. What is pH meter; With a suitable diagram briefly

describe the function of pH electrode in pH meter.

4. Explain the basic steps involved in calibration of a pH

meter.

123

Measurement and Instrumentation Chapter Eight

9.1 Power supply unit (PSU)

A device that transfer electric energy from a source to

a load using electronic circuit is called power supply unit

(PSU). A typical application of power supplies is to

convert a utility AC input voltage into regulated DC

voltage(s) required for electronic equipment. A power

supply could be something as simple as a 9V battery or

it could be as complex as a precission laboratory power

supply.

Most electronic circuits need a DC supply such as a

battery to power them. Since the main supply is AC it

has to be converted to DC to be useful in electronics.

This is what a power supply does.

Figure 9.1: Block diagram of a power supply unit.

First the AC mains supply passes through an isolating

switch and safety fuse before it enters the power supply

unit.

124

In most cases the high voltage mains supply is too high

for the electronic circuitry. It is therefore stepped down

to a lower value by means of a Transformer. The main

voltage can be stepped up where high DC voltages are

required.

From the transformer the AC voltage is fed to a rectifier

circuit consisting of one or more diodes. The rectifier

converts AC voltage to DC voltate.

This DC is not steady as from a battery. It is pulsating.

The pulsations are smoothed out by passing them

through a smoothing circuit called a filter. In its spmples

form the filter is a capacitor and resistor. Any remaining

small variations can, if necessary, be removed by a

regulator circuit which gives out a very steady voltage.

This regulator also removes an variations in the DC

voltage output caused by the AC mains voltage

changing in value. Regulators are available in the form

of integrated circuits with only three connections.

9.3 RECTIFICATION

Rectification is an electronic circuit process of

converting an AC signal into a DC signal, this is done by

a rectifier. A rectifier (or simply called a diode) is a

semiconductor that conducts electricity in just one

direction. Rectifier circuits generally take the form of

either half-wave rectification or full-wave rectification.

The half-wave rectifier circuit is the simplest circuit,

consisting of a single diode connected in series with the

source. This type of circuit converts wave or cycle of the

AC source into a DC supply.

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Measurement and Instrumentation Power Supply Unit

(a) (b) (c)

Figure 9.2: (a) AC input waveform. (b) Schematic

diagram of an Half-wave rectifier. (c) DC output

waveform of an Half-wave rectifier.

The voltage at point A does the opposite of that at point

B. When A is increasing in a positive direction, B is

increasing in a negative direction. It is rather like the

two ends of a see-saw.

During the firs half cycle of the waveform shown in

figure 9.1a, A is positive and B is negative. The diode is

forward biased and current flows around the circuit

formed by the diode, the transform winding and the

load.

Since the current through the load, and the voltage

across the load are in the same proportions, then the

voltage across the load is as shown in the figure 9.2(b),

during the first half cycle. During the second half cycle,

A and the anode are negative, B and the cathode are

positive. The diode is reverse biased and no current

flows This is idicated by the horixontal in figure 9.2(b).

The diode only conducts on every other half cycle. The

126

Measurement and Instrumentation Rectification

diode only conducts during half the cycle, Hence, half-

wave rectification.

The full-wave rectifier circuit is the most efficient

method of producing a DC supply from an AC source as

it converts both half cycles of the AC into a DC supply.

Although there are several methods available, the most

common circuit is that of the bridge rectifier which uses

four individual rectifying diodes connected in a

“bridged” configuration to produce the DC output.

(a)

(b) (c)

(d) (e)

Figure 9.3: (a) Schematic circuit diagram of a full-wave

rectifier. (b) Shows diodes in operation during the first

half cycle. (c) Shows diode in operation during the

127


second half cycle. (d) Input voltage waveform. (e) Ouput

voltage waveform.

Figure 9.3(d) is the waveform of the input voltage. The

voltages at points A and B on the transformer are

changing in opposite directions. When A is increasing in

a positive direction, B is increasing negatively. During

the first half ccle, A is positive and B is negative, D1 has

positive on its anode, D2 has negative on its cathode.

Both are forward biased.

Current flows around the circuit formed by these diodes,

the load and the transformer winding, as shown in

figure 9.3 (b). During the next half cycle, A is negative

and B is positive D4 has positive on its anode, D3 has

negative on its cathode. Both are forward biased

Current flows around the circuit as shown in figure

9.3(c). Since the full cycle is used this circuit is called a

full-wave rectifier and the ouput waveform of the

current that flows in the circuit is as shown in figure

9.3(e).

9.4 Troubleshooting technique

This is the process of locating and repairing

malfunctions in equipment by means of systematic

analysis and testing. For you to become a good

electronics technician or troubleshooter you will need to

have a thorough understanding of electronics, test

equipment, troubleshooting techniques, and system

repair. All scientist does not need to be an electronic

technician, but if you make use of electronic equipment

in the laboratory it is require of you to have the basic

128


knowledge of what goes wrong when you equipment

malfunction so that you can inform the electronic

technician appropriately in a technical term what goes

wrong with your equipment or instrument.

9.5 Basics of Troubleshooting

Use the following as a guide to help you find and repair

basic electronic/electrical circuits.

Step 1: Recognize the symptom

Before you attempt to repair a piece of equipment be

sure you understand how the equipment operates.

Refer to operator’s manuals, technical manuals, and any

other documentation that applies to the equipment that

seems to be faulty in some way. A lot of technicians

bypass this step and go directly to in-depth

troubleshooting just to find out that the real problem

was user error.

Familiarize yourself with the circuit or system operation;

this will help you determine what functions work and

what functions seem to be “not working properly”. Make

sure you obtain as much information as you can from

the person reporting the fault so as to understand if

there is;

1. Circuit failure – A malfunction or failure in a

component or circuit or

2. User Error – Incorrect use of controls, system or

circuit.

Step 2: Create a list of faulty circuit blocks

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Measurement and Instrumentation Troubleshooting

Refer to the equipment system diagram and list all the

likely circuit blocks that you feel may be the cause of

the malfunction that you have isolated during step 1.

Step 3: Locate the faulty circuit block

A “Half-Split Method” (A trouble shooting technique

used to isolate a faulty circuit block in a system. Testing

midway in a system to determine the location of a

fault.) can be used here to isolate the faulty circuit

block. As an example a system may have a good input

signal and a bad output signal. Instead of checking

every circuit block a test point is chosen midway in the

system between input and output. If the signal is bad

that means the problem will likely be in the first half of

the system.

Note: Always look for the obvious, for example; power

not connected, input disconnected (i.e. cable from an

antenna).

Use your senses; sight, sound and smell. Check for

burnt components, crackling connections etc.

If it looks like the whole system is dead and you have

checked for the obvious (fuses, power source – 220

VAC) then you probably have a power supply problem.

Use a voltmeter to measure the ac input and the dc

outputs of the power supply.

Step 4: Locate the faulty component(s)

Having found the faulty circuit block the next step will

be to find the faulty component(s). Most equipment

manufactures will include a troubleshooting guide as a

part of their operating/service manual. These guides will

130


often point directly at circuits in the circuit block that

may be the cause of the problem. Manufacturers

troubleshooting guides may also include voltage,

current and waveform information to assist you in

troubleshooting.

Step 5: Replace the faulty component

Troubleshooting and repair of a system in most cases

must be completed quickly as equipment failure (down

time) can cost considerable loss of money due to lost

productivity. There are two techniques often used to

expedite repair.

Board level substitution is a method of

troubleshooting often used in the industry to expedite

repair. This rapire technique requires that the service

technician be totally familiar with the system operation.

The technician would quite simply power down the

system, pull out the faulty component and replace it

with an equal known good component.

Component Level substitution is a method of

troubleshooting that may lessen the repair time. In this

method the service technologist/technician would have

located the faulty circuit (general area of the fault). The

technician would replace components in the circuit, one

at a time with known good comonents (having the same

electrical ratings) until the problem is resolved. This

method may seem to take time, but it can save time for

hard to find problems.

131


Step 6: Repair, Testing the system and

completing the “Service Report”

Completing the repair might be easy – changing a fuse.

Replacing a power cord. Usually repair will require the

removal and replacement of a component. Your

knowledge of desoldering and soldering techniques will

make the repair process much easier.

It is very important to make a sketch of the circuit you

are working on, to record the placement and orientation

of the component and any wiring prior to removing it.

This sketch will assist you when you go to replace the

component to make sure you position it properly. Also

be sure to handle static sensitive components carefully.

If you believe you have completed the repair to the

system you will need to test it to be sure it performs

properly according to specification given by the

manufacturer. Following the testing and verification of

the system you will need to complete a “service report”.

These are some reasons to fill out a service report:

1. To create a historical record for a piece of

equipment

2. To record the repair to assist with any future

repairs.

3. To show reliability of the equipment over time.

4. To maintain a record of repair time and cost.

5. To record contacts with off site service

personel.

6. To identify a manufacturers design flaw.

7. To supply a service report to the owner.

132


EXCERSICE 9

1. What is a power supply unit? Explain its important

in electronic instruments and equipments.

2. Describe with the block diagram the components

of a simple power supply units, explain the

importance of each component to the operation

of the PSU.

3. What is Rectification? Discuss with a suitable

diagram, the difference between an half-wave

rectifier and a full-wave rectifier.

4. Define trouble shooting, as it applies to electronic

instruments.

5. Discuss in detail, the basic steps involve in

troubleshooting an electronic device.

6. As an electronic techicia, design a service report

for a device you just repaired.

133

Measurement and Instrumentation Chapter Nine

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John Bird; Electrical Circuit Theory and Technology;

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Rd, Bulington, MA 01803.

R S Khandpur; Troubleshooting Electronic Equipment;

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134

Measurement and Instrumentation References

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York: American National Standards Institute.

ASTM; Manual on the Use of Thermocouples in

Temperature Measurements; Philadelphia: ASTM, 1981.

Beckwith, T. G.; Mechanical Measurements; Reading,

Mass: Addison-Wesley, 1993.

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Pressure and Flow Measurements 3rd ed; New York:

Wiley, 1984.

Berkeley Physics; Electricity and Magnetism, vol. II; New

York: McGraw-Hill, 1985.

Doeblin, Ernest O.; Measurement Systems and Design;

New York: McGraw-Hill, 1994.

Fowler, Richard J.; Electricity Principles and Applications;


Harris, Forest K.; Electrical Measurements; New York:

Wiley, 1952.

IEEE Transactions; Instrumentation and Measurement

(periodical); New York: IEEE, 2005.

Keast, D. H.; Measurements in Mechanical Dynamics;


Keithley, Joseph, F.; The Story of Electrical and Magnetic

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IEEE Press, 1998.

Mangum, B. W., and Furukawa, G. T.; Guidelines for

Realizing the International Temperature Scale of 1990;

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NIST Technical Note 1265. Bethesda, Md.: NIST, 1990.

Thompson, Lawrence M.; Electrical Measurements and

Calibration: Fundamentals and Applications; Research

Triangle Park, N.C.: Instrument Society of America,

1994.

Tunbridge, Paul; Lord Kelvin, His Influence on Electrical

Measurements and Units; London: P. Peregrinus, on

behalf of the Institution of Electrical Engineers, 1992.

Webster, John G., ed.; Electrical Measurement, Signal

Processing, and Displays; Boco Raton: CRC Press, 2003.

Hickman, I. (1997); Digital Storage Oscilloscopes;

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Johnson, J.S. (1994); Optical sensors: the OCSA

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Benson, I.B. (1989); Industrial applications of near

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137

INDEX

AAbsoulute pressure, 104Acoustic thermometer, 101Acuracy, 14 Audio generator, 76Analogue; Multimeter -, 48BBellows, 106Bimetallic thermometer,Bourdon tube, 107 CCathode Ray, - Oscilloscope , 60 Digital storage -, 67 Signal measurement with -, 68 - Tube, 62DD.C potentiometer ,57DiaphragmsDifferential pressure, 104

EElectronic display, 79Error, 16 Caliberation -, 18 Environmental -, 18 Gross (Human) -, 17 Instrumentation -, 17 Percentage - , 14, 15 Range -, 18 Random -, 20 Systematic -, 17 Zero -, 18 Non-linear -, 19GGalvanometric recorder, 82Guage pressure, 104FFunction generator, 75HHysteresis -, 19 IInstruments, 1 Absolute -, 27 Analogue-, 26

138

Measurement and Instrumentation Index

Classification of -, 26 Digital -, 26 Electronic - , 26 measuring -, 10 Moving-coil -, 30 Moving-iron -, 30, 31 Moving-coil rectifier, 36 performance characteristics of -, 13 Secondary -, 26LLED display, 80Liquid-in-glass thermometer, 100Lissajous Pattern, 73, 74Loading effect 15,Logarithmic scale, 114MManometer, 108Measurement, 1, Application of -, 10 -Data, 79 Display of -, 79 Representation of - , 79 Recording of -, 79 Temperatrue -, 93 Error, 16 Null method of -, 54 Resistance -, 51 Standards of -, 7 Units, 2Mechanical chart recorder, 82Meters, Analogue -, 29 Digital -, 27 Electrodynamic - , 35, 36Multiplier, 38Multirange, DC meter, 43 Ammeter, 43, Direct method, 43 Indirect method, 44 Voltmeter, 47, Direct method, 47

Indirect method, 48OOhmeter, 51, 53PpH measurement, 113 Electrochemical methods, 115pH meter, Caliberation of -, 118 Instrumentation of -, 117 Potentiometric recorder, 84Power supply unit, 121Presentation of data, 87 Tabular -, 87 Graphical - ,89Pressure measurement, 104UUltra-violet recorder, 85, 86Units Imperial system of - , 2 Metric system of -, 3 S.I - , 3 Fundamental and derived - , 4 - symbol, 5 Multiples and Submultiples of -, 7VVideo generator, 76RRectifier, Half wave -, 122 Full wave -, 123Rectification, 122Resistance thermometer, 97Resolution, 16SScale, 9 Linear -, 9 Non-linear -, 9Sensitivity, 15Shunt, 39Signal generator, 75T

139

Thermistor, 99Thermoelectric effect, 94Thermocouple, 94, 95, 96 Fundamental laws of - ,95Troubleshooting techniques, WWheatstone bridge , 55

140

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