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2.1V Disadvantages

i) The harmonic distortion in the input, causes the errors.

y) The instrument has limited sensitivity due to imperfect and nonlinear diodecharacteristics.

iiJ)A'he error is introduced if input waveform is not symmetrical.

The r.m.s. value means root-mean-square value. As mentioned earlier it is obtained by

squaring the input signal and then calculating square root of its average value. The r.m.s.

value is also called effective value. It compares the heating effect produced by a.c. and

d.c.

The true r.m.s. responding voltmeter produces a meter deflection by sensing the

heating power of the waveform. This heating power is proportional to the square of the

input r.m.s. value. The measurement of heating power is achieved by the use of

thermocouple. The input voltage to be measured is applied to the heater. The heating

effect of the heater is sensed by a thermocouple attached to the heater. The thermocouple

generates the corresI:0nding voltage. The a.c. input is amplified and then given to the

heater element to achieve enough heating so that thermocouple can generate enough level

of voltage to cause meter deflection.

Key Point: The output voltnge is proportion nl to the r .m.s . Vnllll! of the n.c. input.

Power

E2rms

= R heater

Eo x heat ex power

Eo =KE2rms

Rheater

Eo Output voltage of thermocouple

K Constant of proportionality

The value of K depends on the distance between the heater and the thermocouple and

also on the materials used in the heater and the thermocouple.

The main diff iculty in such a meter is the nonlinear characteristics of a thermocouple.

In some instruments this difficulty is ovecome by placing two thermocouples in the same

thermal environment. The effect of the nonlinear behaviour of t he input thermocouple is

cancelled by similar nonlinear effect caused by thermocouple in the feedback path. The

input thermocouple is called measuring thermocouple while the thermocouple in the

feedback path is called balancing thermocouple. The true r.m.s responding voltmeterusing two thermocouples is shown in the Fig. 2.15.

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d.c.

amplifier

Heating elements :

Same thermal ~environment 1 _

I Feedbackt current

The two thermocouples balancing and measuring, forms a balanced bridge in the input

circuit of the d.c amplifier.

When the a.c. input is applied, the measuring thermocouple produces the voltagt' VI

which upsets the balance of the bridge. The d.c. amplifier amplifies the unbalanced

voltage. This amplified voltage is feedback to the balancing thermocouple, which heats the

heater element to produce V2 such that the balance of the bridge is re-e5tablished.

Thus the d.c. feedback current is the curnint which is producing same heating effect as

that of il.C input current i.e. the d.c. current is nothing but the r.m.5. value of tht' input

current. The meter deflection is thus proportional to r.m.s or eff ective value of the a.c

input.

Mathematically we can write,

I Vo A (VI -V2)

high gain of d.c amplifier

Vo

"" aA

In balanced condition of bridge and as A is very high,

I VI = V2 I

VI = output of measuring thermocouple

V2 = output of balancing thermocouple

VI = KE?ms I

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I V2 = KVJ

VO = output d.c. voltage

I Vo = Erms I

2.11.1 Advantages

~ nonlinear behaviour is avoided by using two thermocouples placed in same

. thermal environment.

2) The true r.m.s. value measured is independent of the waveform of the a.c. input, i f

the peak amplitude of a.c. input is within the dynamic range of the a.c. amplifier.

,.3 -) S_ensitivities in the millivolt region are possible. The voltages throughout a range of

.\00 p V to 300 V within a frequency range of 10 Hz to 10 MHz can be measured,

with good instruments.

Ilowver the response of t hermocouples is slow hence the overall response of the

meter is ~llIggish. Similarly the crest factor puts the limitation on the meter reading in case

of highly nonlinear waveforms. The meter cost is high compared to average and peak

responding meters.

A typical laboratory type r.m.s. responding voltmeter provides the accurate r.m.s.

rCdding of complex waveforms having a crest factor (ratio of maximum to r.m.s. value) of

10/1.

The response of thermocouples is slow and hence overall meter response is sluggish.

To Zl\'oid this, trZlnsistorised non-thermocouple type true RMS voltmeter is used.

Principle of operation : Consider

two transistors connected in parallel. A

small a.c. voltage is applied between the

bases of the transistors. Then the a.c

component of the voltage developed

across the common collector resistors of

the two transistors is proportional to the

square of the applied input voltage.

The Fig. 2.16 shows such a squaringdevice which uses transistors in parallel

alongwith the bridge arrangement. In the

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bridge arrangement d.c. component is cancelled out. Such a bridge is used in

non-thermocouple type true RMS voltmeter.

The Fig. 2.17 shows the non-thermocouple type transistorised true RMS vol tmeter. It

uses a squaring device and other components.

Sensitivityadjustment

P2

Zero

adjustment

The transistors Q2 and Q 3 form a squaring device. The resistance R6 is common

collector resistance. The potentiometer Pj is used for bias setting. The other side of the

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bridge consists of the transistor Q4 The potentiometer P2 is used for bias setting which is

nothing but zero adjustment. It adjusts output zero for zero a.c. input i.e. shorting the

terminals A and B. Under this condition the bridge is balanced and drops across R6 and

RI.) are equal.

The transistor Ql is used to i mprove temperature stability, through emitter resistance

R 3 The biasing to Ql is adjusted using R1 and R2 such that drop across R 3 is 0.7 V f or

silicon transistors.

The input is applied through an attenuator consisting of resistances Rs1 to Rs7' The

switch S is a range selector switch and used to select the proper range. When input is

applied, the bridge is unbalanced and drop between R6 and R9 is proportional to RMS

value of input. This is given to the meter. The sensitivity of meter can be adjusted using

P3

III. Example 2.11 : A 25 mA ful l scale current meter with a n interna l resistance of 100 n isavailable for con structin g an a.c . vo ltm eter with a volta ge ra nge of 200 V r.l11.s. Tile meter

IIses the bridge configu ra tio n fo r the rectifier of the instrul11ent. If each diode ha s a forward

res istance of 500 0. and infinite reverse resistance, calculate the value of the' series res is ta 1 1 C I',

to / iI I/it the cur ren t to th e ra te d v alu e a t t he ra t ed voltage.

Solution : Tn case of a.c. voltmeters using bridge type f ull wave rectifier

Ede 0.9 Erms

Now RsEde _ R 0.9 Erms

- RmIde m Ide

Now Ide ::= full scale current ::= 25 mA

But in this case, diode forward resistance is given as 500 D.. Due to the bridge

configuration, two diodes will be in series at a time.

0.9 Erms

Ide

0.9x 200 _ 1100 ::= 6100 0.2.5xlO-3

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The principle of this type of detection is based on the factor thelt for any given

waveform, the Lm.S. value of the waveform can be expressed in terms of maximum and

average val ue as,

The K1 and K2 are the proportionality constants for peak and the average value

respectively.

Di"iding both sides of the above equation by ViI\ we get,

The r'ltio Yrms/Y ;1 \ is nothing but the form f actor of the waveform. Thus if the torm

factor clnd the ratio of peak to average value is known, the constants K] and K2 can be

obtained and hence r.m.s. value can be measured.

This requires the peak detector and the average detector in the circuit. This technique

used to measure r.m.s. value of the voltage using peak and the average detector is called

quasi-rms detection.The block diagram of such quasi-rms detector is shown in the

Fig 2 18

VpR/K1 R

Peakdetector

Peak

r.m.s.

a.c.I " ' P O \input V

av

R/K2

AmplifierAveragedetector

Average

Fig. 2.18 Quasi-rms detector

The form factor and the ratio of peak to average is used in the design of this detector.

The combination of peak and average detector is shown in the Fig. 2.19.

The ratio of the two resistances R] and R2 can be adjusted empirically to obtain the

r.m.s. value at the output over a wide frequency range.

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a.c.

input

Fig. 2.19 Combination of peak and average detector

2.12 Electronic Multimeter

For the measurement of d.c. as well as a.c. voltage and current, resistance, an

electronic multimeter is commonly used. It is also known as Voltage-Ohm Meter (VOM) or

multimeter The important salient features of YOM are as listed below.

1) The basic circuit of YOM includes balanced bridge d.c. amplifier.

2) To limit the magnitude of the input signal, RANGE switch is provided. By

properly adjusting input attenuator input signal can be limited.

3) It also includes rectifier section which converts a.c. input signal to the d.c. voltage.

4) It facilitates resistance measurement with the help of internal battery and

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R1 R2 R3 R4 RS+

250 V 10 V

1000 V 2.5 V0 S

R6Range

selector switch

5000 V d.G. +D.C. Voltage

Fig. 2.21

For getting different ranges of voltages, different series resistances are connected in

series which can be put in the circuit with the range selector switch. We can get different

ranges to measure the d.c. voltages by selecting the proper resistance in series with the

basic meter.

To get different current ranges, different shunts are c onnected across the meter with

the help of range selector switch. The working is same as that of PMMC ammeter

The Fig. 2.22 shows the arrangement used in the multimeter to use is as an ammeter.

+ ;I

M

Range

selectorswitch

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2.12.3 Use of Multimeter for Measurement of A.C. Voltage

The Fig. 2.23 shows voltmeter section of a multimeter.

10 V

2.5 V

--------1

I

I

I

I

I----J

1

1

I

I

I

I

: R6

1____ 1Switch

S

A.C. voltage

input

The rectifier used in the circuit rectifies a.c. voltage into d.c. voltage for measurement

of a.c. voltage before current passes through the meter. The other diode is used for the

protection purpose.

The Fig. 2.24 shows ohmmeter section of multimeter for a scale multiplication of 1.

Before any measurement is made, the instrument is short circuited and "zem adjust"

control is varied until the meter reads zero resistance i.e. it shows full scale current. ow

the circuit takes the form of a variation of the shunt type ohmmeter. Scale multiplications

of 100 and 10,000 can also be used for measuring high resistances. Voltages are

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The advantages of an electronic multimeter are,

1. The input impedance is high.

~ The frequency range is high .

. . < r . ' The circuit is simple.

~ The cost is less.

K The construction is rugged.

It is less suffered from electric noise.

2.12.6 Disadvantages

The disadvantages of an electronic multimeter are,

;r The accuracy is less.

/2. The resolution is poor.

3. It is difficult to interface the output with the external devices.

yNot compact in size.

5. The reliability and repeatability are poor.

"1. What i~ sen siti l'ity of uoltmcters 7 Explain.

2. Wha t i~ a loa din g e ffect 7 Explain with the suitable example.

3. Explain the operation of basic d.c. voltm eter.

4. Explain the

i) full wavl' rectifier

ii) 110Ifwavl' rl'ctifier.

9. What is qua si-ull.s. detector 7 Explain with the suitable c irwit diagram.

10. Dra w and l'Xplain trlle RM S voltml'ter with ou t thermocouples.

11. What does an electronic ana log voltmeter measu1'1'? Sh ow typical cirw it to lIll'asurc.

(Ans. : An electronic analog voltmeter always measures average value.

It is calibrated to read rms or peak values.)

12. Explain the working of an electronic analog l11ultimcter.