Wiley acing the gate electrical engineering part 2

These include instruments for measurement of voltage, current and power; instrument transformers; oscilloscopes and transducers.. The other flux is created by the moving coil, called the

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ELECTRICAL AND ELECTRONIC MEASUREMENTS

Measurement techniques have played a significant role

from the starting from fair exchange of goods in early

civilizations to regulation of trade in industrialised

societ-ies Better measurement and instrumentation techniques

evolved as production of goods became industrialised

and advent of computers saw their enormous

applica-tion to measurement, process control and monitoring In

this chapter, we will discuss the instruments used

com-monly for electrical and electronic measurements and

about their error analysis These include instruments for

measurement of voltage, current and power; instrument

transformers; oscilloscopes and transducers

7.1 CLASSIFICATION OF MEASURING

INSTRUMENTS

Instruments can be classified based on their mode of

operation, manner of energy conversion, measuring

tech-niques and kind of output signal The main instrument

types are discussed as follows

  1.  Primary  (or  absolute)  and  secondary  type: 

Instruments that measure the absolute physical quantity directly in terms of the constants of the instrument and the deflection are called primary or absolute instruments (e.g., tangent galvanometer)

If the actual value of the quantity being measured

is proportional to some other absolute value of the quantity, the instrument is called secondary The instrument is pre-calibrated using the absolute instrument (e.g., voltmeter, ECG recorder, etc.)

  2.  Active and passive type: Instruments that can

be directly used for the quantity being measured are known as the active-type If the quantity being measured simply modulates the magnitude of some external power source the instrument is known as passive type

  3.  Deflection  and  null  type: In a deflection-type instrument, the physical effect generated by the quantity being measured, produces an equivalent opposing effect in some other part of the instru-ment, which in turn causes deflection (or mechanical

displacement) which is a measure of the quantity

In the null-type instrument the physical effect

gen-erated by the physical quantity under

measure-ment is nullified by either a manual or automatic

balancing device The equivalent null causing effect

is the measure of the quantity

  4.  Analog and digital type: In analog instrument,

the physical quantities under measurement show

continuous (step-less) variation with time In

digi-tal instruments, the physical quantities are discrete

and vary in steps with time

Based on the mode of operation, the secondary

instru-ments are further classified into three types:

  1.  Indicating  type: In this category the

measur-ing instrument indicates the quantity bemeasur-ing

mea-sured through a pointer or some type of indicator

Majority of the measuring instruments fall under

this category, for example, voltmeter, ammeter, etc

  2.  Integrating  type: In this category of measuring

instruments, the measurement is done with the

help of integrating device or arrangement over a

period of time For example, in the case of energy

meter the rotation of disc over a period of time

gives the reading of the energy consumed

  3.  Recording  type: In this category, the

measur-ing instrument is used to record certain quantities

to be used for analysis For example, plot chart

recorder, ECG, EEG, etc

7.1.1 Indicating Type Instruments

The different types of torques that function in any

indi-cating measuring instruments are:

  1.  Deflecting torque: This torque, also called

oper-ating torque, is developed by the magnetic,

electro-static, chemical or thermal effects produced by the

quantity to be measured

T

d ∝ Operating quanity

  2.  Controlling  torque: The instruments are so

designed that the controlling torque acts on its

moving part It can (i) control/stop the

move-ment of the pointer beyond the desired reading

and (ii) bring the pointer back to its zero position,

when the operating quantity is removed The

gr is the gravity constant

Note: In instruments with spring control ated scales are used and cramped scales are used for gravity control instruments

gradu-  3.  Damping torque: In an instrument, the combined effect of deflecting and controlling torques on the movement of the pointer on the scale, causes it to oscillate when indicating the final reading These oscillations are prevented by using a damping mech-anism, either by generating air or fluid friction or by action of eddy currents This torque is proportional

to the angular velocity of the moving system and hence operated only when the system is in motion

ddtdamp = damp q

The effect of damping on deflection (q ) is depicted

in Fig (7.1), where graphs I, II and III represent under-damped, critically damped and over-damped instruments, respectively

Figure 7.1 |    Effect of damping on deflection

7.2 TYPES OF INDICATING INSTRUMENTS

The basic components of all indicating instruments include:

  1.  Support for moving system: This can be achieved either by pivoting or suspension

  2.  Permanent magnets: These should have constant strength over a period of time

  3.  Pointers and scales: The pointers should be light

in weight with low constant of inertia A strip of mirror is mounted on the scale beneath the pointer and reading is taken after removing the parallax error between the pointer and its mirror image

  4.  Cases: These are the outer covering of the instrument and should be made-up of non-magnetic material

proportional to the measured quantity, that is, age or current This electromagnetic torque is counter balanced by the mechanical torque of control springs (bronze hair springs) attached to the movable coil The coil is wound on an aluminium former which moves in the magnetic field of the permanent magnet to provide eddy current damping When the torques are balanced, the pointer attached to the moving coil will stop and its angular deflection will represent the amount of electri-cal current to be measured against a fixed reference or scale The light weight pointer is carried by the spin-dle and it moves over this graduated scale The scales

volt-of the PMMC instruments are usually linearly spaced

as the deflecting torque and hence the pointer deflections are directly proportional to the current passing through the coil The scale and pointer on the pivot are depicted

in the top view of PMMC in Fig 7.3

Scale

Pointer

Controlspring

Pivot

Balanceweight

Figure 7.3 |    Top view of PMMC instrument

The electromagnetic torque is equal to the multiplication

of force with distance to the point of suspension The total deflection torque is given by

NBAk

Depending on the mode of operation of the permanent

magnet, the indicating type instruments can be classified

into the following types:

  1.  Moving  coil-type  instruments: This is further

categorised into:

(i) Permanent magnet moving coil: This can

be used for direct current and voltage measurements

(ii) Dynamometer type: This can be used either

directly or through alternating current and voltage measurements

  2.  Moving  iron-type  instruments: This can be

used for AC/DC current and voltage measurement

These instruments are discussed in detail in the

follow-ing sections

7.2.1 Permanent Magnet Moving Coil Instruments

Figure 7.2 shows the construction of a permanent

magnet moving coil instrument The instrument has a

moving coil of fine wire (circular or rectangular), with

N-turns suspended in the uniform, horizontal and radial

magnetic field of a permanent magnet in the shape of a

horse-shoe It is free to turn about its vertical axis The

coil with is placed around an iron core, which is

spheri-cal if the coil is circular, and is cylindrispheri-cal if the coil is

rectangular Since the coil is moving and the magnet is

permanent, the instrument is called permanent magnet

moving coil or a PMMC instrument

ControlspringScale

Pointer

N

S

Permanentmagnet

Rotating coil of N turnsStationary iron core

Figure 7.2 |    Permanent magnet moving coil

instrument

When the current is passed through the coil it

pro-duces another magnetic field and the interaction of this

field with the magnetic field of the permanent magnet

produces an electromagnetic torque The amount of

force experienced by the coil is proportional to the

current passing through the coil which again becomes

and move towards the coil The spindle is rigidly nected to the pointer, controlling weight, moving iron and to the piston The repulsion-type MI instrument consists of two cylindrical soft iron vanes mounted within a fixed current carrying coil One iron vane is kept fixed to the coil frame and other, attached to the pointer shaft, is free to rotate Two irons lie in the mag-netic field produced by the coil and current in the coil makes both vanes to become magnetised with the same polarity The repulsion between the similarly magne-tised vanes produces a proportional deflection of the pointer In MI type instruments, rotation is opposed

con-by a hairspring that produces the restoring torque The damping is achieved by air or fluid friction damping

For an excitation current I carried by the stationary coil, the torque produced that causes the iron disc to move inside the coil is given by

T

I dMd

d =2

The advantages of MI-type of instruments are as follows:

  1.  Suitable for AC and DC circuits

  2.  Simple construction and low cost

  3.  Measures voltage in the range of 0−30 V but a series resistance can be inserted in the circuit to measure higher voltages

  4.  Accuracy is high

  5.  Frictional error is less as torque/weight ratio is high

7.2.3 Electrodynamic Type Meters

Electrodynamic type meters, also known as eter type meters, can measure both DC as well as AC sig-nals up to a frequency of 2 kHz The schematic diagram

dynamom-The advantages of PMMC instruments are listed as follows:

  1.  Uniform scale

  2.  Accurate and reliable

  3.  High sensitivity

  4.  Free from hysteresis error and not affected by

external (stray) magnetic fields

  5.  Simple and effective damping mechanism

  6.  Low power consumption

  7.  Extension into multirange instruments possible

7.2.2 Moving Iron Type Instruments

The moving iron (MI) type instruments can measure

AC signals at frequencies up to 125 Hz, in addition to

DC signals In these instruments, the signal (current)

to be measured is allowed to flow through a

station-ary coil, which produces a magnetic field proportional

to the quantity to be measured The moving iron piece

(made of soft iron) is fixed with the moving system

(a spindle and pointer), gets attracted/repelled

pro-portionately and gives reading on the calibrated scale

These instruments are accordingly classified as

attrac-tion or repulsion type Figure 7.4(a) shows the schematic

of attraction type moving iron type instrument and that

for the repulsion type is shown in Fig 7.4(b)

Fixed coil

Cramped scale

Pointer

Spring

Moving iron disc

(a)

PointerSpringMoving iron piece (vane)(b)

Figure 7.4 |    Moving-iron meter: (a) Attraction type

and (b) repulsion type

The attraction-type moving-iron meter, the moving iron

disc (vane) placed near the coil is free to get attracted

for dynamometer type instrument is shown in Fig 7.5

The instrument has a moving circular coil which is placed

in the magnetic field produced by two circular stationary

coils which are wound separately and connected in series

Pointer

Scale

Fixed coilsMoving coil

Figure 7.5 |    Schematic representation of electrodynamic

meter

The deflection torque in this type of wattmeter is

pro-duced by the interaction of two magnetic fluxes One of

the fluxes is produced by a fixed coil, called current coil,

which carries a current proportional to the load current

The other flux is created by the moving coil, called the

voltage or potential coil, which carries a current

pro-portional to the load voltage The deflecting torque is

dependent upon the mutual inductance between the two

coils and can be given by

T I I

dMd

the angular displacement between the coils The torque

is thus proportional to square of the current If the

mea-sured current is alternating, the meter is unable to follow

the alternating torque values and instead displays the

mean value of square of the current The squared or rms

value of the measured current (or any other quantity)

can be obtained by suitable modification of the scale

The advantages of electrodynamic type meters are as follows:

  1.  More accurate than moving-coil and moving-iron

instruments but expensive

  2.  Voltage, current and power can all be measured by

suitable connections of fixed and moving coils

  3.  Used to measure voltages in the range of 0−30 V

but can be modified by placing a series resistance

to measure higher voltages

7.2.4 Measurement of High-Frequency Signals

In the instruments discussed in the sections above, the

maximum frequency limit is of the order of 2 kHz for the

dynamometer type meters and only 100 Hz in the case of

the moving-iron type instrument The limitation of low permissible frequency can be overcome, to an extent, by rectifying the voltage signal and then applying it to a moving-coil meter, as shown in Fig 7.6

Bridge rectifier

Moving-coilmeter

Figure 7.6 |    Measurement of high-frequency

voltage signals

The circuit with bridged rectifier extends the upper limit

of measurable frequency to 20 kHz but makes the surement more sensitive to change in temperature of the environment and resulting non-linear behavioursignifi-cantly impacts measurement accuracy for voltages An alternative method to overcome the low frequency limit

mea-is provided by the thermocouple meter

7.3 BRIDGES AND POTENTIOMETERS

The AC bridge networks are used for the measurement

of inductance and capacitance in the circuits These are modified form of Wheatstone bridge; consisting similarly

of four arms, an excitation source and balance detector

DC bridges along with potentiometers are used for the measurement of resistance This is depicted in the flow chart shown in Fig 7.7

Bridges

AC Bridges

Inductance measurement

Capacitance measurement

DC Bridges

Wheatstone bridge Kelvin double bridge

(Resistance measurement)

De Sauty’s bridge Schering bridge Wein’s bridge

Maxwell bridge Hay’s bridge Owen’s bridge Anderson’s bridge

Figure 7.7 |    Bridges for measurement of inductance,

capacitance and resistance

Figure 7.9 |    Maxwell’s bridge (a) Circuit diagram

(b) Phasor diagram

The construction of Maxwell’s bridge shows:

  1.  One arm consisting of a capacitor C

1 in lel with a resistor R

paral-2 Both these variables have adjustable values

  2.  The opposite arm consisting of an inductor L

1 in series with a resistor R

4 Both these variables are unknown values and need to be measured

  3.  The other two arms consist of resistors R

1 and R

3., for which the values are known

The Maxwell bridge measures inductance after ment of C

adjust-1 and R

2 such that the current through the bridge between points A and B becomes zero, which occurs when the voltages at points A and B are equal

This is known as balancing of circuit

When the Maxwell bridge is balanced, the impedances can be written as

ZRRZ1 1 3 2

where Z

1 is the impedance of resistor R

2 in parallel with capacitor C

2, and Z

2 is the impedance of inductor L

1 in series with resistor R

4 Thus, from Eq (7.3), the relation can be mathematically represented as:

=+

The general form of an AC bridge under balance

condi-tion is shown in Fig 7.8, where all four arms are

consid-ered as impedance (frequency dependent components) If

=+

Figure 7.8 |    AC bridge under balance condition

7.3.1 Measurement of Inductance

Commonly used bridges for measurement of inductance

are Maxwell’s bridge, Maxwell—Wien bridge and Hay’s

bridge; other’s include Owen’s bridge and Anderson bridge

7.3.1.1 Maxwell’s Inductance-Capacitance

Bridge

The Maxwell bridge is used to measure unknown

induc-tance in terms of calibrated resisinduc-tance and capaciinduc-tance

The circuit arrangement for Maxwell’s bridge is shown

in Fig 7.9(a) and the corresponding phasor diagram is

When the Hay’s bridge is balanced, the impedances can

be written as

ZRRZ1 2 3 4

where, Z

4 is the impedance of the arm containing C

4 and R

2 3

1 4

1 4

2 3 1 4

1 4

1 4

1 4

2 3 4

4 4 21

=+ (w )and

R

C R R R

R C1

4 2 3 4

4 4 22

1

=+

w w

2

  2.  Second arm consists of an inductor L

1 in series with

a resistor R

1 These are the values to be determined

  3.  Third arm contains a known capacitor C

1 3 2

From the value of R

4 determined by Eq (7.5), L

1 can be determined using Eq (7.4)

7.3.1.2 Hay’s Bridge

A Hay’s bridge is another AC bridge circuit, which is a

modification of Maxwell’s bridge Figure 7.10 shows the

circuit diagram of the Hay’s Bridge It can be used for

measuring an unknown inductance by balancing its four

arms, one of which contains the unknown inductance

One of the arms of a Hay’s Bridge has a capacitor of

known value, which is the principal component that is

used to determine the unknown inductance value

The construction of Hay’s bridge is as follows:

  1.  One arm of the bridge consists of a capacitor C

4 in series with a resistor R

4 The resistor R

4 and C

4 are both adjustable

  2.  The second arm consists of an inductor L

1 in series with a resistor R

1 These are the unknown values

  3.  The other two arms contain known resistors R

2 and R

3

Equating real and imaginary parts, we have

L R R C

1 = 2 3 4and

R

C RC1

4 3 2

I3

I2D

r

C

I1D

1 and R

1, and Z

4 is the impedance of the arm containing C

4 Then

=

w w

1 = 1 + w 1When the bridge is balanced,

114

3

//

e1 = e2

e3,e4

e(b)

Figure 7.13 |    De Sauty’s bridge (a) Circuit diagram

(b) Phasor diagram

It measures an unknown capacitance by comparing it with a known standard capacitance Two ratio arms of this bridge consist of non-inductive resistors (R

1 and R

2) and two consist of capacitors (C

1 and C

2) where one is of unknown value and another is standard capacitor If C

1

is the capacitor whose capacitance is to be measured and C

2 is the standard (known) capacitance, then the circuit

is balanced is by varying either R

1 or R

2 In the balanced circuit, B and D are at the same potential Then

I R I R

CIjCI

2 2

Dividing Eqs (7.13) and (7.14) we get

RRCC

RR1

2 1 2

1 2

The bridge has maximum sensitivity when C

1 = C

2 The method is simple in construction and use but perfect balance

is difficult to achieve if the capacitors show dielectric loss

7.3.2.2 Schering Bridge

The Schering bridge is used to measure unknown cal capacitance and its dissipation factor The dissipa-tion factor of a capacitor is the ratio of its resistance to its capacitive reactance The circuit for a Schering bridge

I j CR R R j CR R I R

1( w 3 + 3+ w 3 4)= 2 4  (7.12)From Eqs (7.11) and (7.12), we have

I R j L j CR R

I

R RR

j CR R RR

j CR R

1

2 3 4

2 3 4

RR

R R R R R1

2 3 4

1

3 4

7.3.2 Measurement of Capacitance

The AC bridges commonly used for measurement of

capacitance are De Sauty’s bridge and Schering bridge

These are also based on the principle of Wheatstone

bridge and have two arms; one of which has the unknown

capacitance to be determined

7.3.2.1 De Sauty’s Bridge

The De Sauty’s bridge is a modified form of the

Wheatstone bridge with the DC source replaced by an

AC source Figure 7.13 shows the circuit for De Sauty’s

(a)

7.3.2.3 Wien’s Bridge

Wien’s bridge is used for measurement of unknown capacitance and also frequency The circuit for the bridge

is shown in Fig 7.15 The construction is as follows:

  1.  One arm consists of a capacitor C

2 in series with a resistor R

2 These are the quantities to be determined

  2.  The second arm consists of a capacitor C

1 in allel to a resistor R

par-1 Both these quantities are adjustable

  3.  The other two arms consist of one known resistors each R

3 are present on the other two arms

  3.  The fourth arm has the unknown capacitor C

4 with

a resistor (R

4) connected in series (or parallel)

Under the balanced condition, we have

ZCRZ1 2 3 4

1 11

jRC

R R CC

1 4

4 1

3 2

3 4 4 2

4 3 2

=

C

R CR1 4 3

2

=Note: The balancing of a Schering bridge is independent

of frequency

E

CA

Equating real and imaginary parts, we get

R RR

1 3

2 4

=+

⇒

−and

R RR

1 3

2 4

=+

⇒

−

ZZRR1 2 3 4 =

where Z

1 is the impedance of the arm containing C

1 and R

1 Z

2 is the impedance of the arm containing C

2 and R

2 Then,

RR

R

j C RR

jC

3 4

1

1 1 2

1

=+

2

w w

3 2 1 1 2

Thus, the balanced equation involves a factor of

fre-quency, even though individual bridge elements may be

independent of frequency

7.3.3 Measurement of Mutual Inductance

Mutual inductance can exist only in the presence of

self-inductance An important measure of mutual inductance

(M) is its ratio to the geometric mean of the two self-

L L

=

1 2Different AC bridge circuits are used for measurement of

mutual inductance These include:

7.3.3.1 Heaviside Bridge

In Heaviside bridge, the mutual inductance is measured

in terms of self-inductance The circuit (Fig 7.16)

con-sists of four non-inductive resistors R

1, R

2, R

3 and R

4

connected on the four arms of the bridge The mutual

inductor with unknown inductance is connected in series

of this bridge circuit

7.3.4.1 Kelvin Double Bridge

Kelvin bridge, also known as Kelvin double bridge or Thomson Bridge is widely used to measure an unknown electrical resistance below 1 Ω Its circuit configuration and principle of operation is similar to the Wheatstone bridge except for the presence of additional resistors

The bridge uses a second set of ratio arms and hence the name double bridge The schematic circuit configuration for Kelvin double bridge is shown in Fig 7.18 The first ratio arms is R

1 and R

2 The second set of ratio arms R

1¢ and R

2¢ is used to connect the galvanometer to a point

D at a suitable potential between points M and N such that the effect of connecting lead resistance r between the unknown resistance R

3 and the standard resistance R

4 is eliminated The ratio of resistances in the first arm (R

1/R

2) and second arm (R

1¢/R2¢) are made equal

R2

R′2G

I

Figure 7.18 |    Kelvin double bridge circuit

Under balance conditions there is no current through the galvanometer which means that the voltage drop between

A and B, E

AB is equal to voltage drop E

AMD between A and C Then

The modified Heaviside-Campbell bridge is used to

mea-sure the unknown value of self inductor in terms of mutual

inductance A balancing coil L and resistance r is added to

the arm to which mutual inductor is connected in series

(Fig 7.17) A short circuit switch is connected across R

1

=+

−/

Different methods may be used for measurement of

resis-tance, depending on resistance value:

  1.  Low  resistance: If the resistance is low (of the

order of 1 Ω or low); ammeter-voltmeter method,

Kelvin’s double bridge method and potentiometers

are used

  2.  Medium  resistance: If the resistance is medium

(1 to 10,000); Wheatstone bridge, Carey-Foster

bridge or substitution method are used

  3.  High resistance: If the resistance is high (>10,000 Ω);

Megohm bridge or direct deflection, loss of change

and Megger methods are used

is relatively large The voltage drop in the ammeter may lead to error in the reading.

In the circuit shown in Fig 7.19(b), the measured resistance is given by

RVI

V

I I

RII

+

=+

x

x

x1

If I

x>> IV, the unknown resistance is equal to the sured value of the resistance So this connection of volt-meter-ammeter is used when resistance to be measured

mea-is relatively small The current through voltmeter may lead to error in the reading

The method may be used for low and medium level resistances

An ohmmeter, using only one meter, that is voltmeter

or ammeter, is also used for measurement of resistance

Here, one of the parameters (current or voltage) is kept constant A basic series ohmmeter consists of a perma-nent magnet moving coil instrument connected in series with standard resistance

7.3.4.3 Wheatstone Bridge

Wheatstone bridge is most commonly used for ing medium level resistances Fig 7.20 shows the circuit for Wheatstone bridge It consists of three known resis-tances (R

Figure 7.20 |    Circuit diagram for Wheatstone bridge

Under balanced condition

AD = AB and I R I R

1 1= 2 2Also,

DC = BC and I R I R

3 3 = 4 4

RRRR

R r

RRRR3

1 2 4

2

1 2 1 2

RRRR1 2 1 2

1 2 4

=

There are some commercial devices available with

accu-racies of 2% for resistance ranges between 0.000001 Ω

to 25 Ω

7.3.4.2 Ammeter-Voltmeter Method

This method is mainly used in the laboratories but not in

practical applications It involves use of two meters and

the accuracy is determined by the accuracy of both the

voltmeter and ammeter Their possible arrangements are

as shown in Figs 7.19 (a) and (b)

VA

VIA

IA

V

(b)

Figure 7.19 |    Ammeter-voltmeter method circuits

In the circuit shown in Fig 7.19(a), the measured

resis-tance is given by

RVI

I

RVI

x>> VA, the unknown resistance is equal to the

mea-sured value of the resistance So this connection of

volt-meter-ammeter is used when resistance to be measured

Comparing the two balanced conditions, simplifying and solving, we get

2 are the length of slide rule when slide wire

is calibrated using known resistance R

4 Let l1

′ and l2

′ be the length of slide wires at balance points, when known resistance R

resis-r and the unknown resistance R

x To sure R

mea-x, first switch S

1 is put on point 1, switch S

2 is closed and reading of ammeter is noted Then switch S

1

is moved to point 2 and the known variable resistance R

is adjusted until the ammeter gives the same deflection

as in the first case The value of the unknown resistance

is obtained directly from the known variable resistance, producing the same deflection

Figure 7.22 |    Circuit for substitution method

7.3.4.6 Measurement of High Resistances

The methods that can be adopted for measuring tances of the order of 0.1 MΩ and higher are:

resis-  1.  Direct deflection method

  2.  Loss of charge method

  3.  Megohm bridge

  4.  Megger methodThese are discussed as follows

Direct Deflection MethodFigure 7.23 (a) shows an arrangement for measurement

of high resistance in cables having metallic sheath by

RRRR

R RR1

3 2 4 4

2 3 1

7.3.4.4 Carey-Foster Bridge

The Carey-Foster bridge is a more elaborate

modifica-tion of Wheatstone bridge, particularly useful for

mea-suring or comparing two nearly equal resistances The

circuit for Carey-Foster bridge is shown in Fig 7.21

is added between resistances R

approxi-3/R

4 by sliding contact on slide wire

Let r be the resistance per unit length of the slide wire

Figure 7.21 |    Carey-Foster bridge

When the bridge is balanced, let l

1 be the distance of the sliding contact from the left hand end of the slide-wire

Next the resistances R

3 and R

4 are interchanged and the bridge is balanced by moving the slide rule to distance l

2 Then:

For first balance condition

RR

R l r

R l l r1

RR

R l r

R l l r1

= (−/ ) ⇒ = (−/ ),The insulation resistance is thus,

Figure 7.25 shows the circuit for the Megohm bridge

The circuit is completely self-contained and includes inbuilt power supplies, amplifiers, bridge members, and

an indicating instrument It has range from 0.1 MΩ to

106 MΩ

G

E

SR

RAG

RBGA

V+

−

Figure 7.25 |    Megohm bridge

The accuracy is usually within 3% to possible 10% above

10000 MΩ Sensitivity of balancing at a high resistance

is obtained by usage of adjustable high voltage supplies

of 500 V to 1000 V The use of a sensitive null indicating arrangement such as a high gain amplifier with an elec-tronic voltmeter or a cathode ray oscilloscope can also be used for the purpose

Megger MethodFigure 7.26 shows Megger arrangement for measuring high resistances The current coil is the same as that in

direct deflection method The leakage current I

L is ried by guard wire wound on the insulation and therefore

car-does not flow through the galvanometer as shown

V

Guardwire

IR

IL

Metallicsheath

Conductor Insulating

materialG

(a)

V

−+

IL

IR

wireCable

(b)

Figure 7.23 |    Direct deflection method for measurement

of high resistance

Figure 7.23 (b) shows the arrangement for measurement

of high resistance in cables without metal sheaths The

ends of the cable are immersed in water in a tank The

water and the tank then form the return path of the

cur-rent The insulation resistance of the cable is,

R

VI

=RLoss of Charge Method

Figure 7.24 shows the circuit for loss of charge method of

measuring high resistances In this method, the unknown

resistance is connected in parallel with capacitor and

electrostatic voltmeter The capacitor is charged initially

to a voltage V and then allowed to discharge through the

resistance R The voltmeter reading is v

the use of these meters should not change the quantity to

be measured For this, ideally, the voltmeter should have

an infinite resistance, so that current component is not altered by the inclusion of the voltmeter and an ammeter should have zero resistance so that the load voltage is not altered by the inclusion of the ammeter in the circuit

However, for practical purposes, voltmeters have very high resistance and ammeters have very low resistance

These meters can eb used in both AC and DC circuits

7.4.1 Shunts and Multipliers

Generally moving iron instruments are used as ammeter and voltmeters The use of these meters for operating a moving coil instrument would be impractical due to bulk and weight of the coil required So, to enhance use of these meters and extend their range, shunts (in case of amme-ters) and multipliers (in case of voltmeters) are used

7.4.1.1 Extension of Range of Ammeters

The circuit for extension of an ammeter is shown in Fig 7.27

I RIsh

m m sh

=

sh = − mThus

R

I R

I Ish

m m m

=

−

II

RRm

m sh

G

Figure 7.26 |    Megger method for measuring high

resistance

The voltage coil V

1 is in weak magnetic field when the pointer is at infinity and so this coil exerts lesser torque

The torque exerted by V

1 increases as it moves into a stronger field This torque becomes maximum when it is

under the pole face of the magnet and under this

condi-tion the pointer will be at zero of the resistance scale

In order to modify the torque in the voltage circuit,

2 combined function like a spring

of variable stiffness, such that It is very stiff near zero

when the current in the current coil is very small due

to the presence of unknown resistance R

x which is very large As a consequence, the low resistance portion of the

scale is compressed and high resistance part of the scale

opens up

The voltage range for measurement using a Megger

circuit can be controlled by varying the series resistance

R (to R′or R′′) connected with the current coil The test

voltages can be varied as 500, 1000 or 2500 V and can be

supplied using generator G

7.4 MEASUREMENT OF CURRENT

AND VOLTAGE

An ammeter is used to measure the current in a circuit

which is connected in series with the components

carry-ing the current A voltmeter is required to measure the

voltage across a particular element in the circuit and is

connected in parallel with the component across which

the voltage is to be measured For accurate measurement,

The sensitivity of a voltmeter is determined in ohms per volt It is found by the division of the sum of the resistance of the meter (R

m), plus the series resistance (R

s), by the full-scale reading in volts Mathematically sensitivity is expressed as:

Power consumed in DC circuits is measured as a product

of reading of ammeter and voltmeter, that is,

P =VIHowever, in order to obtain correct power consumed by

a load, corrections must be applied for the power loss in the instrumentthat is it should include the power con-sumed by the instrument closer to the load terminal

Therefore, considering power loss in ammeter, power consumed by a load is

V VI I R

L = − 2 aAnd considering power loss in voltmeter, power con-sumed is

V VI

VRL

where cosf is the power factor of the load.

7.5.1 Measurement of Power in AC Circuits

For measurement of AC power wattmeter is used instead

of voltmeter and ammeter The most commonly used

is electrodynamic- or dynamomter-type wattmeter

Induction-type wattmeter gives the integrated measure

of power with respect with time, which is the measure of energy It is hence called induction type energy meter

7.5.1.1 Dynamometer-Type Wattmeter

Figure 7.29 shows the circuit for type wattmeter In this instrument, there are two low-resistance current coils (CC), which are fixed at their positions A high-resistance moving coil called the poten-tial or pressure coil (PC) is placed between the two fixed coils, such that it may cut the magnetic field created by the two coils The spindle, carrying spring S and pointer

electrodynamometer-II

RRm

m sh

= +1

IImm

=

The ratio of current to be measured and the full scale

deflection current is known as the instrument constant or

the multiplying factor For the same instrument with

dif-ferent shunts, the instrument constant will be difdif-ferent

resistance of the shunt is

R

Rm

RIIsh

7.4.1.2 Extension of Range Voltmeters

For extension of range of voltmeters, a series resistor or a

multiplier is required as shown in the circuit in Fig 7.28

s is multiplier tance and V is full range voltage of instrument

resis-Then

V =I R +R

m( s m)R

V I RI

VIRs

m m

s m

= + 1The circuit for multiple range of extension of voltmeter

can be achieved using more number of multiplier

resis-tances in series

7.4.2 Sensitivity of Ammeter and Voltmeter

The amount of current required by the meter coil to

produce full-scale deflection of the pointer is known as

ammeter sensitivity If the amount of current required

to produce the full-scale deflection is low, the sensitivity

of the meter is high

Since the deflection of such instruments is proportional

to the average power they almost have uniform scales

So, this type of instruments can be used in both ac and

it Hence the angle between the current in the rent coil and current in the potential coil is less than f If the angle is f′ = −f b, then the watt-meter reading is proportional to VIcos(f - b)′cos f

cur-whereas the true power should be VIcosf So the

correction factor is

coscos( ) cos

  3.  Due  to  mutual  inductance  of  coils: These errors resulting from mutual inductance between current and potential coils are more operative at higher frequencies As a consequence of this error, the phase angle for connection of voltage coil on the load side is increased and phase angle when current coil is connected to load is decreased

  4.  Due  to  Eddy  current: Alternating magnetic field of the current coil, leads to the generation of Eddy currents The magnetic field generated by the Eddy currents modifies the phase and magni-tude of current in the current coil, thus introduc-ing errors

  5.  Due to connections: The diagram for connection

of a wattmeter in a circuit with small load current

is shown in Fig 7.30 Error is introduced in power measurement due to loss of power in current or voltage coils

P on it, is rigidly connected with the fixed coil The two

current coils are connected in series with each other

The sense of winding in them is such that they produce

magnetic field in the same direction (Fleming’s

right-hand rule)

Fixed coil(CC)

Moving coil(MC)

Load High

resistance (R)Supply

Figure 7.29 |    Dynamometer type wattmeter

One of the fluxes is produced by a fixed coil which carries

a current proportional to the load current and, therefore,

is called the current coil The other flux is created by

a coil which carries a current proportional to the load

voltage and thus called the voltage or potential coil A

high non-inductive resistance is connected to the

poten-tial coil so that its current is almost in phase with the

load voltage The deflecting torque is produced by the

magnetic effect of electric current The control torque

is provided by control springs The damping torque is

provided by air friction damping

T

=

m m1

0sinw sin(w ±f)

P =V Irms rmscosf Watt

There are two electromagnets in this instrument which comprise the driving system The series magnet is con-nected in series with the load and is energised by the

CC The shunt magnet takes the pressure coil which carries the current proportional to the supply voltage

The magnetic fields produced by the two magnets act upon an aluminium disc, which is free to rotate around a spindle It cuts the fluxes of both the magnets A deflect-ing torque is produced by the flux of each magnet, which tries to rotate the disc This is known as the moving system of the energy meter The magnetic effects of cur-rents through CC and PC will keep acting on a rotating disc to give a cumulative value of power consumed with respect to time (i.e energy)

A permanent magnet known as the brake (or drag) magnet is used to control the movement of the disc

It forms the braking system of the energy system It placed near the edge of aluminium disc Eddy currents are induced due to the rotation of the disc in the field

of braking magnet and the flux produced by the eddy current opposes the main flux This produces a torque proportional to the speed of disc

The spindle of the disc is connected to a counting mechanism, which records the number of revolutions of disc and indicates the energy consumed directly in kWh

The number of revolutions made by the disc for sumption of one kilowatt hour of energy is known as meter constant (K) Therefore,

con-Number of revolutions Energy in kWh,Number of revolut

=

=

KK

×iionskWh

7.5.2 Measurement of Power in a Three-Phase Circuit

Consider the star connected three-phase circuit shown

Figure 7.30 |    Connections of wattmeter in a circuit

The voltage across the potential coil is equal to the sum of

voltages across the current coil and load The wattmeter

measures the power consumed by the load and power loss

in the current coil This error can be removed by use of a

compensating coil connected in series with the potential

coil and identical and coincident with the current coil

7.5.1.2 Induction Type Energy Meter

Measurement of energy means integrated measurement

of power with respect to time

E=∫ P dtHence, an energy meter would work to continuously

measure the cumulative effects of currents and

volt-ages in the circuit The energy meter is an instrument

that measures the electrical energy consumed It is also

known as watt-hour or kilowatt-hour meter

In an energy meter, a single pointer is not sufficient to

measure the total energy consumed The time dependent

measurement can be achieved by having a continuous

rotation of a disc rather than a deflection If the number of

revolution at a constant speed are proportional to the time

and the speed is proportional to the power; the energy

consumed can be obtained easily Figure 7.31 shows the

schematic diagram for induction type energy meter

Shuntmagnet

Movingaluminimdisc

Seriesmagnet

Currentcoil(CC)

Load

Figure 7.31 |    Schematic of induction type energy meter

Various methods of measurement of three phase power use different number of wattmeters:

  1.  One-wattmeter  method: In this method, the voltage coil of the wattmeter is connected across the phase and the current coil is connected in series with the phase Thus, at a time, the wattmeter gives power in one phase only So after the measure-ment in one phase, the wattmeter is disconnected and then reconnected in each of the two remaining phases The three reading are finally added to get total power The method is thus time consuming

  2.  Two-wattmeter  method: In this method two wattmeters are connected in an appropriate manner, such that the sum of the two wattmeter readings gives the total three-phase real power

This is discussed in detail in the next section

  3.  Three-wattmeter method: In this method, three wattmeters are used; one connected across each phase This gives the total three-phase power by summing up the readings of the three wattmeters

The method is faster but expensive as it requires use of three wattmeters simultaneously

7.5.2.1 Two Wattmeter Method of Power Measurement

Figure 7.34 shows the schematic circuit diagram for wattmeter method of power measurement in a three-phase star-connected system

Figure 7.34 |    Schematic circuit diagram for two-wattmeter

method of power measurement in a phase star-connected system

three-The current coils of the wattmeters 1 and 2, are in series with the two phases, R and B The pressure or volt-age coils are connected between RY and BY phases for the two wattmeters The total instantaneous power con-sumed in the load circuit is given by,

W =i v +i v +i v

RN⋅ RN YN⋅ YN BN⋅ BN

Real power= L cos Watts

phVI3

Reactive power= L sin VAR

phVI3

33

×V ×I

Figure 7.33 |    Three-phase delta circuit

If the per phase voltage is V

L and magnitude of per phase current is I

L/ 3 then per phase

Apparent power= VA

L LVI3

Real power= Watts

L LVI3cosf

Reactive power= VAR

L LVI3sinf

The real power in an three-phase electrical circuit is

measured using the wattmeter It consists of two coils,

namely the voltage coil (also called the potential coil or

the pressure coil) carrying large number of thin turns

and the current coil carrying less number of thick turns

The voltage coil is connected in parallel and the current

coil is connected in series to the load in which the power

is to be measured The reading given by the wattmeter

is the product of the rms values of the voltage (across

the voltage coil), rms value of the current (in the current

coil) and the cosine of the angle between them

P =VIcosf

The reading of the first wattmeter W

The line voltage, V

RY leads the respective phase voltage, V

RN by 30o, and the phase voltage, leads the phase rent, I

cur-RN by f Therefore, the phase difference between

V

RY and I

RN is 30o+ f which can also be seen from the

phasor diagram From Eqs (7.21 and 7.22), the sum of the two wattmeter readings is given by,

on the power factor of the load is given in Table 7.1

From Fig 7.34, the voltage across the pressure coil in

the wattmeterW

1 is

RY = RN− YNand the current through the current coil is i

RN Then the instantaneous power measured by this wattmeter W

1 is given by,

RN⋅ RY RN( RN− YN)Similarly, the instantaneous power measured by the W

Substituting the value of i

YN from Eq (7.20) in Eq (7.19),

we get

RN⋅ RN BN⋅ BN YN⋅ YN

So, it can be concluded that the sum of the two

watt-meter readings is the total power consumed in the

three-phase circuit

The phasor diagram for a three-phase balanced

star-connected circuit is shown in Fig 7.35 Here V

BY and V

RY are line voltages and V

RN is the phase voltage

Figure 7.35 |    Phasor diagram for two-wattmeter

method of power measurement

Table 7.1 | Variation of two-wattmeter readings with change in power factor of the load current

Power Factor of Load

Wattmeter Readings (W)

InferenceW

Instrument transformers are used for metering and

pro-tection in a power system Electrical measurements and

relaying decisions in a power system are made based

on the current and voltage obtained from the system

Relays work with smaller magnitudes of these signals

Real life currents and voltages thus have to be scaled

to lower levels This job is done by current and

volt-age transformers also known as instrument transformers

They also electrically isolate the relaying system from

the power equipment and working personnel

7.6.1 Current Transformer

Current transformers (CTs) are extensively used in

power system for power measuring circuits CTs are

gen-erally used in panel boards in substations or grid station

to measure the high valued bus bar currents These are

also used in combination with the relays for protection

purposes Current transformer can measure high

rents in a conductor The conductor carrying high

cur-rent passes through circular and laminated iron core of

the transformer The conductor is the single turn

pri-mary winding The secondary winding will constitute of

large number of turns of wire wound around this circular

core The secondary current (I

S) in turn is reduced to a lower value than the higher valued primary current (I

P)

as the secondary voltage is stepped up The secondary

is connected to an ammeter for current measurement A

typical current transformer is shown in Fig 7.36

Laminatediron coreConductor

carrying

IP

Secondarywindingaround core

A

Figure 7.36 |    Current transformer

There may be different kinds of current transformers based on their use in metering and protection circuits

When a current transformer is used for both metering and protection purposes, it has to be of required accu-racy class to suit both accuracy of measurement and protection It has to be precise and sensitive for both small and large values of current

Circuit for measurement of current using a CT is given

in Fig 7.37

g

a g d

Figure 7.38 |    Phasor diagram for CT

7.6.2 Voltage Transformer

Voltage or Potential transformer (PT) is a type of former used to measure high voltages; they basically function as step down transformers They have smaller number of secondary turns than turns in the primary

trans-Figure 7.39 shows a voltage transformer circuit

VVoltage to be

measured

Voltmeter

Figure 7.39 |    Voltage transformer

The voltage to be measured is connected across the mary circuit The low voltage secondary circuit is con-nected to a voltmeter The power rating of this type of transformer is usually lower The circuit for measure-ment of voltage using a PT is given in Fig 7.40

pri-LoadV

Primarywinding

Secondarywinding

ACSupply

Figure 7.40 |    Circuit for measurement of voltage

using a PT

Load

Primarywinding

ACSupply

Secondarywinding

Three types of core construction can be employed for

CTs namely, core type, shell type and ring type The

core type construction has an advantage that sufficient

space is available for insulation purposes which makes

it more suitable for high voltage work Shell type gives

better protection for the windings Ring type is the most

common of the core constructions for CT It has very

small leakage reactance as it has no joints in the core

7.6.1.1 Transformer Burden

In CTs, the secondary has very small impedance referred

to as burden, so the CT practically operates on short

circuit conditions The burden for CT is the volt-ampere

(VA) loading which is imposed on the secondary at rated

current The burden can also be expressed as the ratio

between secondary voltage and secondary current

A metering CT has lower VA capacity than a

pro-tection CT A metering CT has to be accurate over its

complete measuring range Such a CT’s magnetising

impedance at low current and hence low flux should be

very high The magnetising impedance is not constant

for a CT’s operating range due to the non-linear

charac-teristics of the B-H curve It cannot give linear response

during large fault currents For protection CT, linear

response is expected for up to 20 times the rated current

It is also expected to give precise performance in the

normal operating currents up to high fault level currents

7.6.1.2 CT Phasor Diagram

Figure 7.38 shows the phasor diagram for the current

transformer Here, flux fm is taken as the reference The

are respectively the induced emf for the primary and

secondary windings lagging behind the flux by 90° The

magnitudes of the emf are proportional to their number

of turns in windings

7.6.3 Linear Variable Differential Transformer (LVDT)

The linear variable differential transformer (LVDT) is a passive inductive transformer which requires an external source of power It is used to measure linear displace-ment It consists of a primary winding and two second-ary windings These windings are wound over a hollow tube and the primary winding is kept between the two secondaries Figure 7.42 shows the schematic and work-ing of LVDT

Vin

Primarycoil

Primarycoil

Iron core

Secondarycoil

Secondarycoil

Advantages of LVDT: It can produce high output voltage with relatively low change in core position It is also less costly, solid and robust in construction

7.6.4 Errors in Instrument Transformers

There can be two types of errors in instrument formers These are listed as follows:

trans-  1.  Ratio error: For CTs, the current transformation ratio should be constant It should also be within the given limits Practically, it can be seen some-times this ratio may vary with power factor This gives an error known as the ratio error

The ratio between actual current transformation and the normal ratio is known as ratio correction factor (RCF) Mathematically,

n

=kk

7.6.2.1 PT Phasor Diagram

Figure 7.41 shows the phasor diagram for a voltage

transformer Starting with the flux reference, E

2 is the induced emf in the secondary winding and V

2 is the minal voltage across the secondary Then

2 = 2− 2 2cosf2− 2 2sinf2The primary induced emf E

q q

q

f f

f

f0

f2

fin

Figure 7.41 |    Phasor diagram for PT

7.6.2.2 Differences between a PT and a CT

The main points of difference are listed as follows:

  1.  The secondary of the CT is under short circuit as the

primary circuit is energised, a PT can operate with

its secondary under open circuit conditions without

any damage to the transformer or to the operator

  2.  Under normal operating conditions, the line

volt-age of the PT is nearly steady The flux density

and the exciting current of a PT vary between

small ranges On the other hand, the primary

cur-rent of a CT varies over wide ranges under normal

operating conditions

  3.  The primary current of CT is independent of

sec-ondary winding conditions, while primary current

in a PT depends on the secondary burden

  4.  For a PT, the primary is connected across full

volt-age In case of CT, the primary is in series with a

line and therefore a very small voltage exists across

the terminals The CT primary on the other hand

carries full line current

  5.  Potentiometric  type: It is based on used of a calibrated potentiometer The unknown voltage

is measured by comparison with reference voltage whose value is fixed using the potentiometer

The advantages of DVM over conventional voltmeters are:

  1.  Higher accuracy (+0.5% or better in some cases)

  2.  Less human error as reading is displayed not read

  3.  Voltage input range from +1.000 V to +1000 V with the automatic range selection and indication for overload condition

  4.  Higher resolution as 1 µV reading can be measured

on 1 V range

  5.  Input impedance is as high as 10 MΩ

  6.  Small in size and hence portable

A digital multimeter on the other hand is an electronic volt ohm meter with a digital display It is capable of measuring AC and DC voltages and circuits and resis-tances over several ranges The basic circuit of a digital multimeter is generally a DC voltmeter, so any param-eter that is to be measured is first converted into voltage form The analog voltage form is then converted into digital form using analog digital converter and the digi-tal data displayed in decimal or BCD form It has supe-rior accuracy than analog instruments

7.8 CATHODE RAY OSCILLOSCOPE

The cathode-ray oscilloscope (CRO) is a common ratory instrument which can provide accurate time and amplitude measurements of voltage signals over a wide range of frequencies Its reliability, stability and ease of operation make it suitable for usage as a general purpose laboratory instrument for various signal measurements

labo-The block diagram for a CRO is shown in Fig 7.43

Horizontalinput

Horizontalamplifier

Vetricalinput

Vetricalamplifier

CRT

Sweepgenerator

Sweeptrigger

AC linesignal

Externaltrigger

Figure 7.43 |    Block diagram for cathode ray

oscilloscope

The most important component of CRO is the cathode ray tube (CRT) (Fig 7.44)

  2.  Phase  angle  error:  This is the angle by which

the secondary current differs in phase from the

pri-mary current when reversed This error is due to

no-load or exciting current in the transformer

7.6.4.1 Error Minimisation Methods

The magnetising and core loss component of currents

have to be kept at low values The core material should

have high value of permeability, large cross-section and

shorter magnetic path in order to minimise these

cur-rents The materials from which the core can be

con-structed for this purpose are hot rolled silicon, cold

rolled grain oriented silicon steel and nickel iron alloys

Suitable turns ratio can be provided and number of

secondary turns can be minimised by one or two turns

Large current on the secondary should be reduced by

put-ting a suitable valued shunt on either side This process also

reduces phase angle error in the instrument transformers

7.7 DIGITAL VOLTMETERS AND

MULTIMETERS

Digital voltmeters or DVM are analog to digital

convert-ers with a digital display unit These measure voltage

across two points in a circuit and display the voltage in

the form of discrete numerical instead of pointer

deflec-tion They can be used to measure both AC and DC

voltages The most important component of DVM is

analog to digital converter (ADC), which converts any

analog signal into digital For any input analog voltage,

the output is in the form of binary digital values

Digital meters achieve the required measurements

by converting the analog input into digital signal by a

sequence of digital samples spaced uniformly in time The

input signals are processed in discrete time domain with

the measured signal displayed in digital structure Thus

unlike analog instruments whose signals are processed in

continuous time domain, digital instruments have the

sig-nals processed in discrete time domain hence the name

Different types of digital voltmeters are:

  1.  Ramp  type: It uses ramp signals as reference to

convert analog input into digital form

  2.  Continuous  balance  type: It uses a number of

test voltages in succession to calibrate the voltmeter

  3.  Successive approximation type: It uses a sequence

of test voltages to calibrate the voltmeter It is more

rapid in operation that continuous balance type but

more complex in construction and expensive

  4.  Integrating  type: It is based on voltage to

fre-quency conversion and measures the actual average

of the input voltage over a fixed measuring time

same time a voltage that increases linearly with time is applied to the horizontal deflection plates This causes the beam to be deflected horizontally at a uniform or constant rate The signal applied to the vertical plates can be thus displayed on the screen as a function of time

The horizontal axis thus serves as a uniform time scale

The linear deflection or sweep of the beam horizontally

is actually accomplished by the use of a sweep generator which is part of oscilloscope control circuitry The volt-age output of such a generator is a saw tooth wave as shown in Fig 7.45

a0

V

t

Figure 7.45 |    Voltage difference V between horizontal

plates as a function of time t

Application of one cycle of this voltage to the tal plates causes the beam to deflect across the tube face also linearly with time When the voltage suddenly falls to zero at the end of each sweep (points a, b, c, d

horizon-in Fig 7.45), each of the beam flies back to its horizon-initial position The horizontal deflection of the beam is thus repeated periodically and the frequency of this periodic-ity is adjustable by external controls

The working of CRO involves the following steps:

  1.  The signal to be displayed is first amplified by the vertical amplifier and then applied to the vertical deflection plates of the CRT

  2.  A portion of the signal in the vertical amplifier is also applied to the sweep trigger as a triggering signal

Electron gun

+

−

FocusinganodeAcceleratinganode

Electron beam Vacuum

DeflectingsystemHigh

voltagesupply

6V

Figure 7.44 |    Schematic of cathode-ray tube

The important components of cathode ray tube their

and functions are listed as follows:

  1.  Electron gun: It is the total assembly of the

fila-ment, cathode, control (intensity) grid, focus grid

and accelerating anode It generates the electron

beam and control its intensity and focus

(i) Filament gets heated up when current is passed through it and then heats up the cathode

(ii) Cathode (a negative electrode)emits electrons

when heated

(iii) Control (intensity) grid controls the number

of electrons reaching the fluorescent screen

(iv) Accelerating anode accelerates the electrons

towards the fluorescent screen

(v) Focusing gird (anode focuses the beam of

elec-trons on the screen

  2.  Deflecting plates: These are pair of metal plates

that are oriented in a manner that one set provided

horizontal deflection (Y-plates) and the other set

vertical deflection (X-plates) The combined effect

of these plates help control the deflection of

elec-tron beam to reach any desired point on the

fluo-rescent screen

  3.  Fluorescent  screen: It is a glass screen coated

with fluorescent material, which converts the kinetic

energy of the electrons colliding with the screen into

heat and light So wherever the electron beam hits

the screen, the fluorescent material (phosphor) is

excited and light is emitted from that point

7.8.1 Working of CRO

To study a signal in oscilloscope, it is first amplified and

then applied to the vertical deflection plates and at the

(ii) Sweep time/cm variable: Provides ously variable sweep rates The calibrated position is fully clockwise.

continu-(iii) Position: Controls horizontal position of trace

on screen

(iv) Horizontal variable: Controls the attenuation

or reduction of the signal applied to horizontal amplifier through external horizontal connector

  4.  Trigger: This section selects the timing of the beginning of the horizontal sweep and has the fol-lowing related controls

(i) Slope: Selects whether the triggering occurs

on an increasing (+) or decreasing (−) tion of trigger signal

por-(ii) Coupling: Selects whether triggering occurs at

a specific DC or AC level

(iii) Source: Selects the source of the triggering signal

(iv) Level: Selects the voltage point on the ing signal at which sweep is triggered It also allows automatic (auto) triggering

trigger-7.8.3 Measurements of Voltage

Consider the circuit shown in Fig 7.46(a) that can be used for the measurement of voltage The signal genera-tor is used to produce a 1000 Hz sine wave The AC voltmeter and the leads to the vertical input of the oscil-loscope are connected across the generator’s output By adjusting the horizontal sweep time/cm and trigger, a steady trace of the sine wave may be displayed on the screen as shown in Fig 7.46(b) The trace represents a plot of voltage vs time The vertical deflection of the trace about the line of symmetry (DC) is proportional

to the magnitude of the voltage at any instant of time

Signalgenerator

Voltmeter

VerticalinputAC

(a)

Vm

Vp-pDC

(b)

Figure 7.46 |    Measurement of voltage

  3.  The sweep trigger then generates a pulse which is

coincident with a selected point in the cycle of the

triggering signal This pulse turns on the sweep

generator and thereby initiating the saw-tooth

wave form

  4.  The saw-tooth wave is then amplified by the

hori-zontal amplifier and applied to the horihori-zontal

deflection plates

  5.  Some additional provisions for external signals are

usually made for applying an external triggering

signal or utilising the 60 Hz line for triggering

Also, in some cases, the sweep generator may not

be used and an external signal applied directly to

the horizontal amplifier

7.8.2 CRO Controls

The controls present in most oscilloscopes provide a wide

range of operating conditions and thus make the

instru-ment suitable for measuring a wide variety of signals A

brief description of controls that are common to most

oscilloscopes (as depicted in Fig 7.44) are as follows:

  1.  Cathode-ray  tube  (CRT): This section

per-forms the following control functions:

  (i) Power and scale illumination: Turns the

instrument on and controls illumination of the screen

  (ii) Focus: Adjusts the focus the spot or trace on

the screen

  (iii) Intensity: Regulates the brightness of the spot

or trace

  2.  Vertical  amplifier  section: This section

com-prises of the following control functions:

  (i) Position: Controls vertical positioning of

oscil-loscope display

  (ii) Sensitivity: Selects the sensitivity of the

verti-cal amplifier in verti-calibrated steps

  (iii) Variable sensitivity: Provides a continuous

range of sensitivities between the calibrated steps

  (iv) AC-DC-GND: Selects the desired coupling

( AC or DC) for incoming signal applied to the vertical amplifier or grounds (GND)the amplifier input If DC coupling is selected, the input is directly connected to the amplifier

When AC coupling is selected, the signal is first passed through a capacitor to block out any constant or DC component, before enter-ing the amplifier

  3.  Horizontal  sweep  section: This section

com-prises of the following control functions:

  (i) Sweep time/cm: Selects the desired sweep

rate from calibrated steps or admits external signal to horizontal amplifier

7.8.4.1 Lissajous Figures

When the inputs to the horizontal and vertical ers are sine-wave signals of different frequencies, a sta-tionary pattern is formed on the CRT When the ratio

amplifi-of the two input frequencies is an integral fraction such

as 12234315, , , , etc., these stationary patterns are known

as Lissajous figures and can be used for comparison and measurement of frequencies (Fig 7.47) Using two oscil-lators of different frequencies, some simple Lissajous figures can be generated, like those shown in Fig 7.48

Figure 7.47 |    Lissajous figures for horizontal-to-vertical

frequency ratios of (a) 1:1, (b) 2:1, (c) 1:2 and (d) 3:1

Phase difference x-y

Frequency ratio y/x

180°

Figure 7.48 |    Lisajous patterns

To determine the size of the voltage signal appearing at

the output of terminals of the signal generator, an AC

voltmeter is connected in parallel across these terminals

The AC voltmeter is designed to read the effective DC

value of the voltage This effective value is also known as

the rms value of the voltage The peak or maximum

volt-age is V

m volts and is represented by the distance from the symmetry line CD to the maximum deflection The

magnitude of the peak voltage displayed on the

oscil-loscope is related to the effective or rms voltage (V

rms) displayed on AC voltmeter as

V

rms = 0.707 V

m (for a sine or cosine wave)

VV

m = rms

0 707.For a symmetric sinusoidal wave, the value of peak volt-

age V

m can be taken as 1/2 the peak to peak of the

volt-age signal (V

p-p)

Note: The mathematical realtion for rms signals is valid

only for sinusoidal signals

7.8.4 Measurement of Frequency

With the application of horizontal sweep voltage, the

voltage measurements can be obtained from the

ver-tical deflection and the signal can be displayed as a

function of time If the time base (or the, sweep) is

calibrated, such that measurements of pulse duration

or signal period can be made, then frequency of the

signals can then be determined as reciprocal of the

time period

To measure the frequency of a signal, the following

steps are required:

  1.  Set the oscillator to 1000 Hz and display the signal

on the CRO

  2.  Then set the horizontal gain so that only one

com-plete wave form is displayed

  3.  Measure the period of the oscillations using the

horizontal distance between two points such as C

to D as shown in Fig 7.46(b)

  4.  Then reset the horizontal gain until five waves are

seen on the screen Keep the time base control in a

calibrated position

  5.  Measure the distance (and hence time scale) for

five complete cycles and calculate the frequency

from this measurement

f

T(Hz)= seconds

1

  6.  Repeat the measurements for other frequencies

(e.g 150 Hz, 5 kHz and 50 kHz) as set on the

signal generator

The quality factor (Q) of a coil is the ratio of reactance

to resistance in a frequency dependent circuit tion The Q factor or quality factor of an inductance is commonly expressed as the ratio of its series reactance to its series resistance For inductor in series or parallel, the ratio of reactance to resistance in a frequency dependent circuit configuration is given by

configura-QXRLR

= s =s s s

w

QRXRL

p p p p

w

The value of Q varies from 5 to 1000

The Q factor of a capacitance is the ratio of its series reactance to its series resistance, although for capaci-tors, generally dissipation factor (D) is used which is the reciprocal of Q For capacitor in parallel or series, the ratio of reactance to resistance in a frequency dependent circuit configuration is given by

DX

C R

= s =s

A signal generator can be used to measure the frequency

of an unknown sinusoidal signal It is connected to the

vertical amplifier (or horizontal) and the calibrated

signal source of frequency is fed to the horizontal

ampli-fier (or vertical) The frequency of the signal generator is

adjusted so that a steady Lissajous pattern is obtained

If f

v and f

h are the frequencies of the signals applied

to vertical and horizontal amplifiers, respectively, then

these are related to the number of tangencies (points

at the edge of arcs) along the vertical and horizontal

iizontaltangencies crossings( )

If f

h is known, the unknown frequency f

v can be lated using the above relation

calcu-Note: It is difficult to maintain the Lissajous figures in a

fixed configuration because the two oscillators are not in

phase and frequency locked Their frequencies and phase

drift slowly causes the two different signals to change

slightly with respect to each other

7.8.5 Measurement of Phase Difference

When both applied waveforms are sinusoidal, the

result-ing Lissajous pattern may take many forms dependresult-ing

upon the frequency ratio and phase difference between

the waveforms If straight line is obtained, the phase

angle difference will either be zero or 180° However if an

ellipse is obtained, the phase difference between the two

signals can be determined from the Lissajous figure The

formation of ellipse is illustrated in Fig 7.49

Let the two sinusoidal voltage signals be given by

x y

=

1 2sinsin

Since deflection is directly proportional to the

ampli-tude of voltage, we have from the figure

sinf = =

YYXX1 2 1 2Note: The ellipse forms can be used to determine only

the phase angle between two sinusoidal voltages It

does not indicate which one is leading and which one is

lagging

An active transducer is one which does not require any power source for operation The input of physical quantity generates a proportional electric signal A pas-sive transducer requires external power source for opera-tion The output signal represents variation of electrical parameters (R, C, etc.) and needs to be converted into equivalent current or voltage signal.

7.10.1 Strain Gauge

A strain gauge is an instrument used to measure strain produced on a wire by a force generated by varying the electrical resistance of the wire It is an example of a passive transducer It can effectively measure strain, displacement, weight, pressure or mechanical force A bonded strain gauge is made of fine wire looped from side to side on a mounting plate which is attached to the element which is experiencing the stress Consider the equation of resistance,

RLA

= r

where r is the specific resistance of conductor wire L is

the length of the conductor (in m) while A is the cross sectional area (in m2) When under strain, the length will increase and the area will decrease As a result, the value

of resistance will increase The gauge factor is given as

kRRLL

Vxtxf

=∆ n =∆where, n is the number of detection elements which passes the detector in t seconds f is the frequency of output signal

A Q-meter is used to measure the Q-factor of a coil and

related electrical properties It is based on the principle that

Q-factor of a resonant circuit is equal to its voltage

magni-fication factor and can be expressed as the ratio of voltage

developed across its reactive elements to the voltage injected

in series with the circuit to produce the developed voltage

The basic circuit for a Q-meter is shown in Fig 7.50

The circuit contains terminals for connecting the

induc-tance (L

x) to be measured and this is brought in resonance

by a variable tuning capacitor (C) There are terminals

available for adding capacitance (C

x), if required

When an unknown coil is connected to the test

termi-nals, the circuit is excited by a tunable signal source

This is achieved by setting the oscillator to a given

fre-quency and varying the internal capacitor (C) or adding

a capacitor C

x of the desired value and adjusting the frequency of the oscillator This leads to development of

voltage across a resistor in series with the tuned circuit

The resistance of the resistor should be very small

(frac-tional in ohms) so that it can be neglected in comparison

to the loss resistance of the components to be measured

The AC injection voltage (V

in) across the series resistor and the AC output voltage (V

out) across the terminals of the tuning capacitor are measured using voltmeters The

circuit for output measurement must be a high input

impedance circuit so that loading of the tuned circuit by

the metering circuit is prevented

The Q-factor is measured by adjusting the source

fre-quency and/or the tuning capacitor for a peak output

voltage corresponding to resonance Q-factor is

deter-mined as the ratio of output voltage measured across the

tuned circuit to voltage injected into it When L

x and C

x

are at resonance:

QVV

= outinThe voltage across the variable capacitor is measured

with electronic voltmeter V

2, in which the scale is brated to read Q directly

cali-7.10 TRANSDUCERS

An electrical transducer is a device which can convert a

non-electrical physical quantity into an electrical quantity,

like current or voltage and generates an electrical signal

Unknown coil

Lowresistance

Tunablesignalsource

Highimpedanceinterface(R)

Figure 7.51 shows a typical configuration of thermocouple.

Wire A

Wire B

ColdHot

Figure 7.51 |    A typical thermocouple

The temperature ranges of thermocouple vary with the metals used for making them Temperature ranges of some common thermocouples are listed below:

Chromel-Alumel −270 to 1370o

CChromel-Constantan −270 to 790o

CIron-Constantan −210 to 1050o

CCopper-Constantan −270 to 400o

CNicros-Nisil −260 to 1300o

Pitot tube is extensively used for velocity measurement

in aircraft It works on the principle that if a blunt object

is placed in the flow channel, the velocity of fluid before

it will be zero; considering the fluid to be incompressible

Thus from Bernoulli’s equation,

p vg

p vg

A typical Pitot tube is shown in Fig 7.52

This is usually performed optically, mechanically,

inductively or capacitively

7.10.2.1 Tachometer

Tachometers are used to measure speeds or rotational

movements, revolutions per minute, or sometimes they

can be used to measure rate of flow A scale factor can be

applied to produce readings of the desired type They may

be the analog or digital types with contact or non-contact

types Tachometers can be energised by either AC or DC

7.10.3 Temperature Sensing Devices

7.10.3.1 Resistance Temperature Detector

(RTD)

RTDs are temperature detectors that are based on the

change in electrical resistance of some materials with

change in temperature The resistance changes linearly

with temperature, within a limited temperature range

The relation is given as,

made of platinum as it has high chemical stability and

highly reproducible electrical properties Although they

are accurate and stable, they have higher initial cost

They are known to be less rugged in vibration locations

7.10.3.2 Thermistors

Thermistors are also temperature sensing devices They

can be negative temperature coefficient type used for

tem-perature sensing or positive temtem-perature coefficient type

used for temperature control They have a typical

tem-perature range of −70 to 300°C (~ −100°F to 600°F)

Thermistors are widely accepted as the most

advanta-geous and less costly sensors for a number of applications

for temperature measurement and control

7.10.3.3 Thermocouples

Thermocouple is a temperature sensing device which

works on the principle of Seebeck effect This effect

causes a voltage generation in a circuit containing two

different metals with their junctions kept at different

temperatures These devices are rugged but sensitive

and widely as they are inexpensive and can be used over

a wide temperature range

7.10.4.3 Rotameter

Rotameter works as a constant pressure drop and able area meter for measuring fluid flow It is easy to install and simple in construction but has lower accuracy and can only be installed in vertical pipelines

vari-7.10.4.4 Venturimeter

Venturimeter can measure horizontal flow rate and has two pressure taps It has high mechanical strength but has higher cost Figure 7.54 shows a venturimeter

on the diaphragm will cause a change in distance between the diaphragm and the static plate causing a change in capacitance This change in capacitance is measured using a bridge circuit or tank circuit

Dielectric

Static plateDiaphragm

Pressure

Insulatingmaterial

Figure 7.55 |    Capacitive transducer

7.10.6 Piezo-Electric Transducer

Piezo-electric transducer is used to measure pressure as

a function of voltage generated Force and acceleration can also be measured using this transducer As the name suggests, it contains a piezo-electric crystal in which an

Figure 7.52 |    Pitot tube

7.10.4.2 Orifice Meter

Orifice meter is the most common type of instruments

used to measure the fluid flow Here an orifice plate is

used in a pipeline Figures 7.53(a) and (b) show an

ori-fice meter and the structure of oriori-fice plate respectively

The volumetric flow rate Q in an orifice meter can be

obtained at different diameters d

1 and d

2 of the orifice plate as,

1, A is cross-sectional area g and g are

acceleration due to gravity and specific weight of fluid

7.10.8 Bellows

Bellows are made of soft material and are pressed to form convolutions One end is fixed where air can go inside using a port while the other end is free to move (Fig 7.58)

A spring is used often to counter the bellow movement

The pressure to be measured can be obtained as,

pkxA

Figure 7.58 |    Bellows

7.11 ERROR ANALYSIS

Error analysis is an essential part of measurement Error

in measurement can be defined in as,Error = Instrument reading — true reading

Percentage error

=Instrument reading true reading

True readi

−nng

×100

7.11.1 Types of Errors

There can be three types of errors, namely gross error, systematic error and random error and these are explained as follows

  1.  Gross error: It arises due to human mistakes ing to wrong reading of values, mistake in record-ing measured data, parallax error, etc

lead-  2.  Systematic error: Zero error and instrument bias are source of systematic error There may be con-structional error in instruments They may be due

to error in construction of the instrument scale, pointer, etc This error can lead to error in every reading taken while measuring

  3.  Random  error: It occurs when the exact cause

of error cannot be determined These can never be corrected but can be reduced to a certain extent by averaging or finding the error limits The random errors have a deviation of the readings and it

electric charge is produced on the surface on application

of force Voltage produced will be proportional to the

applied force Usually a quartz crystal is a piezoelectric

crystal An instrument amplifier is used on its output for

measurement purpose Figure 7.56 shows a piezoelectric

transducer

Outputvoltage

Pressure port

Quartzcrystal

Forcesummingmember

Base

Figure 7.56 |    Piezo-electric transducer

7.10.7 Bourdon Tube

Bourdon tube is used for pressure measurement It

con-sists of a C-shaped hollow tube whose one end is fixed

and connected to a pressure tapping while the other end

is kept free (Fig 7.57) When a pressure is applied, the

circular tube tries to straighten, which makes the free

end to move A deflecting mechanism attached to an

indicating instrument is attached to the free end that

moves a pointer The materials commonly used for this

tube are brass, phosphor bronze, and beryllium-copper

They can measure very high differential pressures of

700 MPa

p

Free end ofthe tubeDeflecting

mechanism

Pointer

Figure 7.57 |    Bourdon tube

follows a particular distribution which is generally

normal distribution

7.11.2 Mean Value and Deviation

Mean value is the most probable value for a set of

read-ings, which can be given as,

xnxi

n

=

i11

=

∑

where, n is the total number of readings and x

i is the individual readings value The deviation d of readings

from this value can be derived as,

i =

i−

7.11.3 Precision and Calibration

The precision of measurement is sometimes defined as

this deviation from the mean value The mean square

deviation or variance can now be used to measure the deviation from a set of readings as,

Vn

x xn

i1

1

2 1

2

− i=∑( − ) s

where, s is the standard deviation.

Calibration is the process of comparing the measured value obtained from a particular instru-ment to that of a standard instrument Comparison of actual input values with the output indication of the system will result determination of systematic errors

Errors at these calibrating points are then reduced

by adjusting the components or by using calibration charts

The true values can also be obtained from standard look up tables prepared for this purpose Calibration can

be re-performed from time to time to reduce the effects

of instrument wear over time

IMPORTANT FORMULAS

  1 Types of torque in indicating instruments

  (a) Deflecting torque

T

d ∝ Operating quanity  (b) Controlling torque

  2 Permanent magnet moving coil (PMMC) instrument:

Deflecting torque T = NbAI

  3 Moving iron type instrument:

Deflecting torque, T

I dMd

=2

2 q

Deflecting angle, q

q

=IkdMd22

  4 Electrodynamic instrument:

Deflecting torque, T I I

dMd

4 are the impedance

of AC bridge arms, then at balance point:

I Z I ZI

=+

1 3 2

  (b) Heaviside-Campbell bridge

L

R R2

1

=+

−/

  9 Measurement of resistance  (a) Kelvin double bridge

RRRR3

1 2 4

=  (b) Ammeter-voltmeter method

RVI

I

RVI

RVI

V

I I

RII

+

=+

x V x1

  (c) Wheatstone bridge

R

R RR4

2 3 1

=R  (f) Loss of charge method

V ve

Vve

=ln

  10 Measurement of current and voltage  (a) Extension of ammeter range

II

RRmm

m sh

1

4 2 3 4

4 4

121

=+

=+

and

w w w

=

w w

1= 1+ w 1

C RC

4 3 2

  (d) Anderson bridge

R

R RR

RR

R R R R R1

2 3 4

1

3 4

1 2

4

4 41

=+ w

j C

R1

1 11

w

C

R CR1 4 3

2

=  (c) Wein’s bridge

RRRRCC4

3 2 1 1 2

f

R R C C

=12

1

1 2 1 2

  8 Measurement of mutual inductance

  (a) Heaviside bridge

Rm

RIIsh

  (b) Extension of voltmeter range

V

I R

RR

m m

s m

  11 Measurement of power and energy in AC circuits

  (a) Dynamometer type wattmeter

P =V Irms rmscosf

  (b) Induction type energy meter

Number of revolutions = K×Energy in kWhwhere K is meter constant

  (c) In three-phase (star) circuits total power

consumed by the balanced load is equal to (W

1+W

2)

  12 Power factor angle f =

+tan− 

  13 Cathode ray oscilloscope (CRO)

  (a) Voltage measurement

VV

m = rms

0 707.  (b) Frequency measurement

ffh v

=Number of vertical tangencies crossingsNumber of hor

iizontaltangencies(crossings)  (c) Measurement of phase difference

sinf = =

YYXX1 2 1 2

  14 Q-Meter

QVV

= outin

  15 Transducers  (a) Strain gauge

Vxtxf

=∆ =

∆n

  (c) Resistance temperature detector

=Instrument reading true reading

True readi

−nng

×100

  (a) Mean x

nxn

=

i

i =11

∑

  (b) Deviation d x x

i = i−  (c) Variance (mean square deviation)

Vn

x xi

n

i1

1

2 1

2

− ∑= ( − ) s

SOLVED EXAMPLES

Types of Indicating Instruments

1 The coil of a PMMC instrument has dimensions

15 mm × 12 mm The flux density is given as

4 A 10 A electrodynamic ammeter is controlled by

a spring having a constant of 0.1 × 10−6 Nm/

degree The full scale deflection is 110° Determine

the inductance of the instrument when measuring

a current of 10 A Given that the mutual tance at 0° deflection is 2 µH and the change in the mutual inductance is linear with deflection

induc-(a) 4.42 µH (b) 7.2 µH(c) 2.21 mH (d) 2.21 µHSolution:  We have

110 0 1 10100

m

Thus total inductance = 2 + 0.21 µH = 2.21 µH

Ans (d)

Bridges and Potentiometers

5 A Maxwell’s capacitance bridge is used to sure an unknown inductance in comparison with a known capacitance as shown in the figure below

(a) 240 Ω (b) 24 Ω(c) 2.4 kΩ (d) 240 kΩ

V

Thus, R

1 =10kΩ20kΩ=6 67 kΩ

R

2 =10kΩ20kΩ=7 14 kΩThus,

100 48 3 51 7100

9 For the given circuit, if the voltmeter reads 60 V, the value of the unknown resistance R will be

100 VDC+

−

R

100kΩ V

(a) 2.2 kΩ (b) 50 kΩ(c) 32.2 Ω (d) 100 ΩSolution:  Voltmeter reading = 60 VThus,

100

50 100150

10

403

+

=RR

Solving we get R = 2.2 kΩ

Ans (a)

10 A moving coil instrument of resistance 5 Ω requires

a potential difference of 75 mV to give a full scale deflection The value of shunt resistance needed to give a full scale deflection at 30 A is

2 3 4

600 4001000

240

WAns (a)

7 An Owen’s bridge is used to measure the impedance

of a steel specimen at 2 kHz Given that

R

2 = 834 Ω, C2 = 0.124 µF,R