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Solution : As number of digits n = 3

1R = - = 0.001

103

0.5

100 x5

and 1 digit error

Total error

1. Display

2. Unit annunciation

3. Maximum indication

4. Over range

indication

5. Functions

6 Zero adjustment

7. Sampling rate

8. Ranging

9. Polarity

0.5= 100 x 0.1 = 0.00 05 V

0.0105 V

0.0105 x 1000.1

mV, V, mA, n, kD, MD, LOW BAT (Low battery), ac,MANU (manual) and o - - - - - - { > I - -o (diode test)

1999 or - 1999

DC volts, AC volts, DC amps, AC amps, Ohms, Continuity test,

Diode test

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10. Temperature

11. Power

12. Input impedance

13. Accuracy

14. Size

15. Weight

00 to 40'C, < 80% Relative Humidity (RH), storage

-20'C to 60'C, < 70% RH

The digital multimeter is an instrument which is capable of measuring a.c. voltages,

d.c. voltages, a.c. and d.c. currents and resistances over several ranges. The basic circuit of

a digital multimeter is always a d.c. voltmeter as shown in the Fig. 3.15.

Digitaldisplay

d.c.

ohms

Fig. 3.15 Basic scheme of digital multimeter

The current is converted to voltage by passing it through low shunt resistance. The a.c.

quantities are converted to d.c. by employing various rectifier and filtering circuits. While

for the resistance measurements the meter consists of a precision low current source that is

applied across the unknown resistance while gives d.c. voltage. All the quantities are

digitised using analog to digital converter and displayed in the digital form on the display.

The analog multimeters require no power supply and they suffer less from electric noiseand isolation problems but still the digital multimeters have following advantages over

analog multimeters :

i) The accuracy is very high.

ii) The input impedance is very high hence there is no loading effect.

iii) An unambigious reading at greater viewing distances is obtained.

iv) The output available is electrical which can be used for interfacing with

external equipment.

v) Due to improvement in the integrated technology, the prices are going down.

vi) These are available in very small size.

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The requirement of power supply, electric noise and isolation problems are the two

limitations.

The basic building blocks of digital multimeter are s everal AID converters, counting

circuitry and an attenuation circuit. Generally dual slope integration type ADC is prefprredin the multimeters. The single attenuator circuit is used for both a.c. and d.c.

measurements in many commercial multimeters. The block diagram of a digital multimeter

is shown in the Fig. 3.16.

/ . . . ,. . . .

,. . . . ,. . .. . ..

,. . . . ,. . . .

,. . . . . . . ,. . . .

,. . . . ,. . .. . ..

,. . . . ,.

,.,.

,.,.

,.,.,.

,.,.

,.,.

,.,.

,.,.

,.,,,

,

",DCV,

............oACVSIB DCV

ODCMV .... AVCOHMS ....

DCMA

SIC OHMS

AiD

converter

Compensatedattenuator

Decadecounter

Testprobes

SIA DCMA

OHMS

Currentto

voltage

converter

Digitalreadout

Constantcurrentsource

As mentioned above basically it is a d.c. voltmeter. In order to measure unknown

currents, current to voltage converter circuit is implemented. This is shown in the

Fig. 3 .1 7.

10 n

100 n

Unknowncurrent

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The unknown current is applied to the summing junction L:iat the input of op-amp.

As input current of op-amp is almost zero, the current IR is almost same as Ii' This

current lR causes a voltage drop, which is proportional to the current to be measured.

This voltage drop is the analog input to the analog to digital converter, thus providing a

reading that is proportional to the unknown current.

In order to measure the resistances, a constant current source is used. The known

current is passed through the unknown resistance. The voltage drop across the resistance

is applied to analog to digital converter hence providing the display of the value of the

unknown resistance. To measure the a.c. voltages, the rectifiers and filters are used. The

a.c. is converted to d.c and then applied to the analog to digital converter.

In addition to the visual display, the output from the digital multimeters can also be

used to interface with some other equipments.

;

Analog electronic multi meter Digital multi meter

1. No power supply required. 1. Power supply is required.

2. No use of electronic components such 2 It uses electronic components such as

as diodes, transistors etc. diodes, transistors etc.

3. Suffer less from electric noise. 3. Suffer more from electric noise.

4. The isolation problems are less. 4. The isolation problems are more.

5. The accuracy is less. 5. The accuracy is high.

6. I The input impedance is less. 6. The input impedance is very high.-;j

Possiblity of ambigious reading which is 7. The realing is unambigious at greater viewing

invisible from distance. distance.

8. The output cannot be interfaced with 8. The output can be easily interfaced withexternal devices. external devices.

9. Size is more and bulky. 9. it is compact in size and light in weight.

10. Simple in construction. 10. Construction is complicated but due to

modern integrated technology, becoming

simple from production point of view.

There are five ranges available from 200 mV to 1000 V.

The resolution is 10 ~V on the lowest range.

The accuracy is 0.03 % of the reading + two digits

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There are five ranges from 200 m V to 750 V

The resolution is 10 J-lV on the lowest range.

The accuracy is frequency dependent but the best accurClcy is 0.5'10 + 10 digits between

45 Hz and 1kHz on all the ranges.

There are five ranges from 200 J-lA to 2000 mA.

The resolution is 0.01 J-lA on the lowest range.

The accuracy is 0.3% of reading + two digits.

iv) A.C. current

There are five ranges from 200 I1A to 2000 mA.

The accuracy is frequency dependent but the best accuracy of 1% + ten digits

between 45 Hz and 2 kHz on all the ranges.

v) Resistance

Six ranges are available from 200 Q to 20 \/112.

The accuracy is 0.1% of reading + two digits + 0.02 Q on the lowest range.

The input impedance is about 10 MQ on all the ranges.

vii) Normal mode noise rejection

It is greater than 60 dB at 50 Hz while the common mode noise rejection is greater

than 90 dB at 50 Hz and greater than 120 dB at d.c.

viii) Overload protection

The overload protection of 1000 V d.c. and 750 Lm.S. a.c. is provided.

The voltage drop across the diode can be measured for which 1 mA 10% of

constant current source is used.

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When 'REL' button is pressed, the displayed reading is stored as a reference and then

subtracted from the subsequent readings to indicate only amount of deviation from the

reference.

xii) Frequency

The frequency range is 200 Hz to 200 kHz autoselection.

The frequenc)' is the measure of repeatation of any signal. The frequency is nothing

but the number of cycles of the signal per unit time. In communication systems it is the

most important physical quantity. Frequency and time are interdependent. The unit o f

frequency is hertz (Hz). The unit hertz is defined as one event per second.

3.14.1 Analog Frequency Meter

The basic principle of analog frequency meter is that first unknown signal frequency is

converted into proportional current. Then the current is converted into the voltage which

is calibrated in terms of the frequency.

The block diagram of analog frequency meter is as s1' lwn in the Fig. 3.18.

Input

signal Precision

charge

dispenser

I toY

converter

and filterMeter

calibrated

interms of

input frequency

Reference

voltage

Advantages :

(i) The design of analog frequency meter is simple.

(ii)The analog frequency meter is suitable for limited frequency range.

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Disadvantages

(i) Due to the aging effect of capacitors, the analog frequency meter has poor

reliability.

(ii)The accuracy and resolution of the analog frequency meter is poor.

(iii) The range of frequency measurement is limited.

(iv) Period, ratio of frequencies can not be measured using the analog filter meter.

The signal waveform whose f requency is to

be measured is converted into tngger pulses

and applied continuously to one terminal of an

AND gate. To the other terminal of the gate, a

pulse of 1 sec is applied as shown in the

Fig. 3.19. The number of pulses counted at the

Fig. 3.19 Principle of digital frequency output terminal during period of 1 sec indicates

measurement the frequency.

The signal whose frequency is to be measured is converted to trigger pulses which is

nothing but train of pulses with one pulse for each cycle of the signal. At the output

terminal of AND gate, the number of pulses in a particular interval of time are counted

using an electronic counter. Since each pulse represents the cycle of the unknown signal,

the number of counts is a direct indication of the frequency of the signal which is

unknown. Since electronic counter has a high speed of operation, high frequency signals

can be measured.

I I

--I 1--, I

Fig. 3.20 Block diagram of digital frequency meter

The signal waveform whose frequency is to be measured is first amplified. Then the

amplified signal is applied to the schmitt trigger which converts input signal into a squarewave with fast rise and fall times. This square wave is then differentiated and clipped. As

a result, the output from the schmitt trigger is the train of pulses for each cycle of the

signal. The output pulses from the schmitt trigger are fed to a START/STOP gate. When

this gate is enabled, the input pulses pass through this gate and are fed directly to the

electronic counter, which counts the number of pulses. When this gate is disabled, the

counter stops counting the incoming pulses. The counter displays the number of pulses

that have passed through it in the time interval between start and stop. If this interval is

known, the unknown frequency can be measured.

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The basic circuit of digital frequency meter used for the measurement of frequency

consists two R-S flip flops. The basic circuit f or measurement of frequency is as shown i nthe Fig. 3.21.

Unknownfrequency

Schmitttrigger

To counter anddisplay unit

Pulse fromtimebase

generator

r----------------- ,

I I

I I

I II

I

I

I

II

I

II

I

I

I

START

gate

I

I

I

I

I

I

I

I

I

: AI

I B

I SffiP II

~ - - - - - - - - - - - - - - - ~ ~ ~ - - - - - - - - - - - - - - - - _ :

Gate control flip-flop

Fig. 3.21 Basic circuit for frequency measurement

The output of unknown f requency is applied to the Schmitt trigger which produces

positive pulse at the output. These are counted pulses present at A of the t11

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With the next pulse from the time base passes through START gate reseting FF - 2 and

it changes state from LOGIC a to LOGIC 1. As Y changes from a to 1, the gating signal isapplied to input B of the main gate which enables the main gate.

Now the pulses from source can pass, through the main gate to the counter. The

counter counts pulses. The state of FF - 1 changes froma

t o 1 by applying same pulsefrom START gate to S input o f F F - 1. Now the START gate gets disabled, while STOP

gate gets enabled. It is important that the pulses of unknown frequency pass through the

maingate to counter till the main gate is enabled.

The next pulse from the time base generator passes through STOP Gate to S input of

F F - 2. This sets output back to 1 and Y = 0 O . Now main gate gets disabled. The sourcesupplying pulses of unknown frequency gets disconnected. In between this pulse and

previous pulse from the time base selector, the number of pulses are counted by the

counter. When the interval of time between two pulses is 1 second, then the count of

pulses indicates the frequency of the unknown frequency source.

For the unknown frequency measurements the digital frequency counter is the most

accurate and reliable instrument available. With the highest accuracy digital frequency

counters, the accuracy of the atomic time standards can be achieved. As most of the events

nowadays can be converted into an electrical signal consisting train of pulses, the digital

frequency counter can be used for counting heart beats, passing of radioactive particles,

revolutions of motor shaft, light flashes etc. The block diagram of digital frequency counteris as shown in the Fig. 3.22

Inputsignal

Schmitttrigger

I circuitI

I

IL _

Input signal conditioningcircuit

Decimalcounter

andDisplay Unit

~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~I I

I I

I Internal time I

: base :I crystal oscillator II I

I Frequency dividers IL I

Fig. 3.22 Block diagram of digital frequency counter

The major components of the digital frequency counter are as given below.

(1) Input signal conditioning circuit

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(2) Time base generator

(3) Gating circuit

(4) Decimal counter and display unit.

Let us study each block of the digital frequency counter one by one.

1. Input signal conditioning circuit :

In this circuit, an amplifier and schmitt trigger are included. The threshold voltage 0 1

the schmitt trigger can be controlled by sensitivity control on the control panel. First ofall

the input signal of unknown frequency is fed into input signal conditioning circuit. There

the signal is amplified and then it is converted into square wave by schmitt trigger circuit.

2. Time base generator:

The crystal oscillator produces a signal of 1 MHz or 100 MHz depending upon therequirement. In general, the accuracy of the digital frequency counter depends on the

accuracy of the time base signals produced, thus the temperature compensated crystal

oscillator is used. rhen output of the oscillator is passed through another schmitt trigger

circuit producing square wave output. Then it is f ed to frequency dividers connected i n

cascade. Thus a train of pulses are obtained after each f requency divider section.

Using time base selector switch 5 the Gate Time can be adjusted.

The gating circuit consists of AND gate. When the enable signal is provided to theA D gate, it allows a train of pulses to pass through the gate for the time period selected

by the time base circuit. The pulses are counted and then the second pulse generated from

the time base generator disables AND gate and thus closes it.

Tn this unit, decade counters are connected in the cascade. The output of the A T D gate

is connected to the clock input of the f irst decade counter. Then the output of this counter

to the clock inpllt of next and so on. Using these counters the number of pulses are

counted and are displayed by the display unit. As the number of pulses counted are

proportional to the input signal frequency, the final display is proportional to the

unknown frequency of the input signal.

Using the frequency counter, the period measurement is possible. As we know, time

period T = = 1/ f. 50 if the frequency to be measured is low, then the accuracy of the

frequency counter decreases as less number of pulses are connected to the gating circuit.

Thus in low frequency region it is better to measure period rather than frequency. The

block diagram of the period mode of the digital frequency counter is as shown in theFig 3.23.

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Internal Time

Base

(crystal oscillator)

Input

signal

Decimal

counter

and

Display Unit

Fig. 3.23

The main difference in the frequency mode and period mode of the digital frequencycounter is that the unknown input signal controls the gate time of the gating circuit while

the time base frequency is counted in the decade counter assembly.

Note that in the period mode, the input signal conditioning circuit produces a train of

pulses. So the positive going zero crossing pulses are used as trigger pulses for opening

and closing of AND gate in the gating circuit.

The main advantage of the period mode is that the accuracy is grealer for the low

frequency input signals.

3.18.1 Multiple Period AveragingIn simple period mode, the pulses obtained .from time base circuit are counted in one

cycle tim e o f an unknown input signal. It leads to getting error. To overcome this, the

pulses are measured for more than one cycle of the input signal. Here the mput signal

frequency is first divided by the decade counters and then it is applied to the gating

circuit as shown in the Fig. 3.24.Amplifier

Input

signal

Decimal

Counter

and

Display Unit

Internal Time

Base

Local Oscillator

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The time interval measurement is basically similar to the period measurement. In the

time interval measurement mode, gate control flip flop is used as shown in the Fig.3.25.

Decimal

Counter

and

Display Unit

Internal Time

Base

Crystal Oscillator

Fig. 3.25 Time interval measurement

In this measurement mode, two inputs are used to start and stop the counting. Here

similar to the period measurement, the internal frequency pulses generated by time base

generator circuit are counted. The start and stop signals are derived from two inputs. The

AND gate is enabled with the external input 1 applied. The counting of the pulses starts at

this instant. The AND gate is disabled with the input 2 applied. Thus pulses are counted

in the time interval which is proportional to the time interval between application o f

inputs 1 and 2.

By using the frequency counter, the ratio of two frequencies can be measured. It is

again similar to period measurement. The block diagram is as shown in the Fig. 3.26.

High

Frequency

Input

(f2)

Decimal

Counter

and

Display Unit

Low

Frequency

Input

(f1)

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In this mode, the low frequency signal is used as gating signal, while the pulses are

counted for the high frequency signal. Hence it is clear that the low frequency represents

the time base.

The number of pulses corresponding to the high frequency signal f2 are counted

during the period of the low frequency signal f1 , by the decade counters and displayed by

thedispl

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Thus the crossover frequency fo at which Np = Nt is given by

fc f~ 0

Thus from equation (3) we can conclude that, to mlmmize the 1 count gating error

effect, frequencies lower than the cross over frequency fo are measured in "period" mode 0 1

measurement; while the frequencies greater than the crossover frequency fo are measured

in "frequency" mode of measurement.

In frequency measurement, due to inaccuracies in the time base, errors occur in the

measurement. The common time base errors are oscillator calibration errors, short term

crystal stability errors and long term crystal stability errors.

The oscillator calibration errors can be overcome by using different simple calibration

techniques. In one of the techniques, we get accuracy of order of 1 part in 106 with

standard frequency. If zero beating is done by using visual means such as oscilloscope, the

calibration accuracy increases to 1 part in 107.

The main cause of short term crystal stability errors is the variation in freguency of the

oscillator momentarily. It may takes place due to the voltage transients, electrical

interference, cycling of crystal oven, shocks and vibrations etc. These errors can be reduced

by llsing long gate times such as 10s and 100s during frequency measurements. A typical

value for short term stability for standard crystal is of the order of 1 or 2 parts in 1Q7.

Due to the aging and deterioration of the crystal, long term crystal stability errors

occur. When temperature cycled crystal is kept in continuos oscillation, internal stresses are

relived. Because of this, the minute particles at the surface of the crystal get shed causing

reduction in the thickness. This increases the frequency of the oscillator.

3.21.3 Trigger Level Error

In period and frequency measurement the trigger level error is decided by the

accuracy with which the gate is opened or closed. In general, in the frequency

measurement set up, the schmitt trigger provides gate control pulses. But it is commonly

observed that input signal consists noise i.e. unwanted quantity. These unwanted

components also get amplified along with the actual input signal. The triggering of the

schmitt trigger occurs due to input signal amplification and its signal to noise ratio. So to

limit the trigger level error, large signal amplitudes and fast rise times in the signal are

best suited.

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The obtain maximum accuracy following precautions must be taken.

1. The crossover frequency must be selected as J[; where fe clock frequency of thecounter.

2. The frequency measurement must be carried out above J[; while the periodmeasurement must be carried out below J[;.

3. The accuracy of the measurement is a function of time since the last calibration

against the standard.

4. The large amplitude signals and fast rise times minimize trigger level errors.

The digital frequency meter can count frequency from a Hz to few lO a MHz. The

counters used in the digital frequency meter limit the frequency range. These counters

cannot count the high frequency at high speed. The frequency upto 100 MHz covers only a

small portion of the frequency spectrum. So some other techniques are necessary to extend

the range of digital frequency meter above 40 MHz. The input frequency is reduced or

minimised and then it is applied to the digital counter. Following are some techniques

used for high frequency measurements.

By using high seed counters the high frequency is divided by integers such as 2, 4, 6

etc. So that the frequency lies within the frequency range that can be counted by digital

frequency meter.

By using heterodyne techniques, the high frequency signals are converted into low

frequency signal which can lie within frequency range of the digital frequency meter.

The harmonic of L.F. oscillator is mixed to produce zero frequency with high

fre'ldLI.-:\ s!gnal. The frequency of L.F. oscillator is measured and mlllt~p[jed by an integerIIhlch i~ qual to the ratio of two frequencies.

Tlk high frequency is reduced by some factor such as 100 : 1 lI-"l11g automatically

tuned cIrcuits. These circuits generate output frequency equal to 1/ 1000lh of the input

frequency.

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1. State th e a du nllta ge s o f digital voltmeters Ol 'er oth er v oltm eters .

2. Explai ll w ith nm t circ llit diagrams th e w or king of the follow ing digital vo ltlnetcr~.

I) Successive approxlll1ation type DVM

Ii) Lllh'ar ralllp t ype DVM

iii) Staicase ralllp t ype DVM

ivY Voltage to freqll('/ Icy converter type illtegrating DVM

z:) Dllal slope integrat ing type DVM

3. Co mpare the linear and staircase ramp tec hniques .

4. W hy reversible coullter is used in V I f converter type DVM ?

5. Explain the follow ing terllls a s ap plied to digi tal displays:

i) Resoilltion ii) Difference in 3~ alld -t~ digit d isplf/Y

iii) Sensitil'ity IV) ACCllmcy specification s

6. Co mpare analog lI1ul tillleter with digi tal mlll timeter (DMlvV.

7. D r(/({' and e xplain the basic block d iagra m o f D MM .

8. State the unrio lls sp ccifications of DMM.

9. A 3~ digi t I'o ltmcler is used for measuring vo ltage

i) Find it s resoilltion

Ii) Hal l' wO lild the I'olta ge o f 14.53 V be disp layed on 10 V scale?ii,) How w Ollld the reading of 14.53 V be displayed on 100 V scale?

10. Th e lowest rt1llge all a 4~ digit DVM is 10 In V ful l scale. What is its sen sitivity? [A . 1 Vjns .. p

11. Ex plain analog freqllency meter with t he help of bloc k diag ram .

12. Write a d vantages alld disad vantages o f the analog frequenc y m ele r.

13. Expla in t he principle of digital fre qu ency meter.

14. Explaill digital freq llency counter with neat diagram. Explain each Nock of digi tal frc quency

cOlmter in detail.

15. Ex plain how frequency is measured using the digital frequency counter.

16. Ex plain how digital freq uency counter is used to measure,

(i) frequ ency, (ii) period, (iii) time interval, (iv) ra t io of fr equencies.