Electronic Instrumentation and Measurement Techniques [3 ed.] 0-13-250721-8, 9780132507219

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THIRD EDITION

TECHNIQUES

W

D.

A.D.

COOPER

HELFRICK

5

SUM

ELECTRONIC INSTRUMENTATION AND MEASUREMENT TECHNIQUES

3rd edition

Electronic

Instrumentation

and Measurement Techniques William David Cooper Albert D. Helfrick

Prentice-Hall, Inc. /

Englewood

Cliffs,

New

Jersey

07632

Library of Congress Cataloging

Cooper, William David,

Data

in Publication

(date)

Electronic instrumentation and measurement techniques.

Includes bibliographies and index. 2. Electric meters. Electric measurements. 4. Electronic instruments. Electronic measurements. Helfrick, Albert D. II. Title. 1.

3. I.

TK275.C63

ISBN

1985 0-13-250721-8

621.3815'4

84-18185

Cover design: 20/20 Services, Inc. Manufacturing buyer: Gordon Osbourne

©

1985, 1978, 1970, by Prentice-Hall, Inc.,

Englewood

No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. All rights reserved.

Printed in the United States of America

10

987654321

ISBN

Ul

-13-ESD7r21-fl

Prentice-Hall International, Inc.,

London

Prentice-Hall of Australia Pty. Limited, Sydney Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro Prentice-Hall

Canada

Inc.,

Toronto

Prentice-Hall of India Private Limited, Prentice-Hall of Japan, Inc., Tokyo

New

Delhi

Prentice-Hall of Southeast Asia Pte. Ltd., Singapore

Whitehall Books Limited, Wellington,

New Zealand

Cliffs,

New

Jersey 07632

8 2

CONTENTS

PREFACE Chapter

xi

MEASUREMENT AND ERROR

1

1

1-1

Definitions

1

1-2

Accuracy and Precision

2

1-3

Significant Figures

3

1-4

Types of Error

1-5

Statistical Analysis

1

-6

1-7

Probability of Errors

1

Limiting Errors

16

Questions

1

Problems

18

Chapter 2 2- 1

2-2 2-3 2-4 2-5 2-6

6 10

SYSTEMS OF UNITS OF MEASUREMENT

Fundamental and Derived Units Systems of Units Electric and Magnetic Units International System of Units Other Systems of Units Conversion of Units Problems

20 20 21

23 27 27 30 30 V

0 7

Contents

vi

Chapter 3

STANDARDS OF MEASUREMENT

34

Classification of Standards Standards for Mass, Length, and Volume Time and Frequency Standards Electrical Standards Standards of Temperature and Luminous Intensity IEEE Standards Questions and Problems

3-1

3-2 3-3 3-4

3-5 3- 6

34 36 37 39 46 47 48

DIRECT-CURRENT INDICATING INSTRUMENTS

Chapter 4

Suspension Galvanometer Torque and Deflection of the Galvanometer Permanent-Magnet Moving-Coil Mechanism

4- 1

4-2 4-3

4-5

DC Ammeters DC Voltmeters

4-6

Voltmeter Sensitivity

4-4

4-7

Voltmeter-Ammeter Method of Measuring Resistance

4-8

Series-Type

4-9

Shunt-Type Ohmmeter 1

4-12 4-13 4-14 4-15

50 51

55 61

65 68 72 74 78 80 84 85 94 97 99

Ohmmeter

4-10 Multimeter or 4-1

50

Calibration of

VOM DC Instruments

Alternating-Current Indicating Instruments

Thermoinstruments Electrodynamometers in Power Measurements Watthour Meter 4-1 6 Power-Factor Meter 4- 17 Instrument Transformers Problems

Chapter 5

BRIDGES AND THEIR APPLICATION

101

103 108

1

10

5- 1

Introduction

110

5-2

Wheatstone Bridge

1 1

5-3

Kelvin Bridge

1 1

5-4

5-6

Guarded Wheatstone Bridge AC Bridges and Their Application Comparison Bridges

5- 7

Maxwell Bridge

5-8

Hay Bridge

122 1 25 129 1 32 134 136 138

5-5

5-9

'

Schering Bridge 5-10 Unbalance Conditions

Contents

vii

5-11 5-1 2

Wien Bridge Wagner Ground Connection

5- 13 Potentiometer

Problems

ELECTRONIC INSTRUMENTS FOR MEASURING BASIC PARAMETERS

141

142 144 145

Chapter 6 6- 1

Amplified

6-2

AC

DC

Meter

1

6-3

Voltmeter Using Rectifiers True RMS-Responding Voltmeter

6-4

Electronic Multimeter

Considerations

6-6

Differential Voltmeters

6-7

Digital

Choosing an Analog Voltmeter

Voltmeters

6-8

Component Measuring Instruments

6-9

Q

Meter

6-10 Vector Impedance Meter 6- 1 1 Vector Voltmeter 6- 12 RF Power and Voltage Measurement

Problems

Chapter 7 7-

1

OSCILLOSCOPES

Introduction

7-2

Oscilloscope Block Diagram

7-3

Cathode Ray Tube

7-4

CRT

7-5

Vertical Deflection

7-6

Circuits

System

7-7

Delay Line Multiple Trace

7-6

Horizontal Deflection

7-9

Oscilloscope Probes and Transducers

System

7-10 Oscilloscope Techniques 7- 11

Special Oscilloscopes

Problems

Chapter 8 8- 1

8-2 8-3 8-4

8-5

SIGNAL GENERATION

The Sine-Wave Generator Frequency Synthesized Signal Generator Frequency Divider Generator Signal Generator Modulation Sweep-Frequency Generator

48

151 1 1

6-5

in

147

55 56

161

163 169 1 78 186 195 1 99 203 206

207 207 208 210 223 224 230 233 235 239 242 248 258

259 259 270 274 277 277

Contents

viii

8-6

8-7 8- 8

Pulse and Square-Wave Generators Function Generator Audiofrequency Signal Generation

Problems

Chapter 9

SIGNAL ANALYSIS

9- 1

Wave Analyzers

9-2

Harmonic Distortion Analyzers Spectrum Analysis Problems

9-3

TIME-INTERVAL MEASUREMENTS 10-1

Simple Frequency Counter

10-2

Measurement

10-3

Extending the Frequency Range of the Counter Automatic and Computing Counters Problems

0- 4

291

293 295

296 296 300 306 324

FREQUENCY COUNTERS AND

Chapter 10

1

282

Errors

TRANSDUCERS AS INPUT ELEMENTS 1 1 TO INSTRUMENTATION SYSTEMS

325 325 337 341

345 347

Chapter 11- 1

Classification of Transducers

11-2

Selecting a Transducer

11-3

Strain

11-4

Displacement Transducers Temperature Measurements Photosensitive Devices Problems

11-5 11- 6

Chapter 12 ACQUISITION

Gages

ANALOG AND DIGITAL DATA SYSTEMS

348 348 349 353 359 369 384 384

392

12-4

Digital-to-Analog Conversion

12-5

Analog-to-Digital Conversion

392 394 403 407 409

12-6

Multiplexing

421

12-7

Spatial

12- 1

Instrumentation Systems

12-2

Magnetic Tape Recorders

12-3

Self-Balancing Potentiometer

Encoders

424

Contents

ix

Chapter 13

COMPUTER-CONTROLLED TEST

SYSTEMS

429

13-1

Testing an Audio Amplifier

429

13-2

Testing a Radio Receiver

431

13-3

Instruments

13-4

IEEE 488

13-5

Digital Control Description

13-6

Example of Signal Timing Measurement

Used

in

Computer-Controlled Instrumen-

435 443 445

tation

Electrical Interface

in

a Microprocessor-Based

446 447

Questions

449

APPENDIX Abbreviations, Symbols,

and

450 452

Prefixes

Decibel Conversion Tables

Table

1:

Conversion of Decibels

to

Power and Voltage

Current) Ratios

(or

455

Table 2: Conversion of Voltage (or Current) and Power Ratios to Decibels

457

SELECTED ANSWERS

459

INDEX

463

PREFACE

The

third edition of Electronic Instrumentation

and Measurement Techniques

is

designed to serve as a text for students of electrical and electronic engineering at

both two- and four-year colleges and technical

serve as a refresher or

handbook

institutes.

The book can

also

for the professional engineer. This text provides

good groundwork for the basics of electrical measurement and then presents examples ranging from elementary measurements to the most sophisticated computer-controlled systems.

Several changes have been

made from the previous edition.

First, the subject

movements has been reduced and compressed from two chapters to one chapter, and the subject of bridges has been similarly compressed. This was done to make way for the addition of new material on measurement systems using newer technology. Chapter 7, on oscilloscopes, has been completely rewritten and expanded of electromechanical meter

and osciland signal analysis, and the expanded text reflects

to include descriptions of the latest technology in cathode ray tubes

loscope circuits. Chapters 8 and

comprised one chapter

9,

on

signal generation

in the previous edition,

the advances in these instruments. Chapter 13 describes computer-controlled test

equipment for automatic

test systems.

This material, which

is

entirely new,

covers a rapidly growing phase of test and measurement technology.

Those elements essential to a good textbook, such as worked-out examples and chapter-end problems and review questions, have been retained. Included in the new edition to aid the student are answers to selected questions and problems.

w. D. A. D.

COOPER HELFRICK xi

ELECTRONIC INSTRUMENTATION AND MEASUREMENT TECHNIQUES

CHAPTER

1

MEASUREMENT AND ERROR

DEFINITIONS

1-1

Measurement generally involves using an instrument

as a physical

means of

determining a quantity or variable. The instrument serves as an extension of

human

faculties

and

in

many

cases enables a person to determine the value of

an unknown quantity which his unaided

An

instrument, then,

may

human

faculties could not measure.

be defined as a device for determining the value or

magnitude of a quantity or variable. The electronic instrument, as its name is based on electrical or electronic principles for its measurement function. An electronic instrument may be a relatively uncomplicated device of simple construction such as a basic dc current meter (see Chapter 4). As technology expands, however, the demand for more elaborate and more accurate instruments implies,

increases

To

and produces new developments

in

instrument design and application.

use these instruments intelligently, one needs to understand their operating

and to appraise their suitability for the intended application. Measurement work employs a number of terms which should be defined

principles

here.

Instrument: a device for determining the value or magnitude of a quantity or variable.

Accuracy: closeness with which an instrument reading approaches the true value of the variable being measured. Precision: a

measure of the reproducibility of the measurements;

i.e.,

1

Measurement and

2

Error

Chap.

1

is a measure of the degree to from one another.

given a fixed value of a variable, precision

which successive measurements Sensitivity: the ratio of

to a

differ

output signal or response of the instrument

change of input or measured variable. Resolution: the smallest change in measured value to which the

instrument will respond. Error: deviation from the true value of the measured variable.

Several techniques

may

be used to minimize the

example, in making precision measurements,

it is

effects

of errors. For

advisable to record a series of

observations rather than rely on one observation. Alternate methods of mea-

surement, as well as the use of different instruments to perform the same experiment, provide a good technique for increasing accuracy. Although these

techniques tend to increase the precision of measurement by reducing environ-

mental or random error, they cannot account for instrumental error.* This chapter provides an introduction to different types of error in mea-

surement and to the methods generally used to express most reliable value of the measured variable.

1-2

errors, in

terms of the

ACCURACY AND PRECISION

Accuracy

refers to the degree of closeness or

conformity to the true value of the

quantity under measurement. Precision refers to the degree of agreement within

a group of measurements or instruments.

To illustrate the distinction between accuracy and precision, two voltmeters make and model may be compared. Both meters have knife-edged

of the same

and they have carefully same precision. If the value

pointers and mirror-backed scales to avoid parallax, calibrated scales.

They may

therefore be read to the

its readings may be amount. Therefore the accuracy of the two meters may be quite different. (To determine which meter is in error, a comparison measurement with a standard meter should be made.) Precision is composed of two characteristics: conformity and the number of significant figures to which a measurement may be made. Consider, for example, that a resistor, whose true resistance is 1,384,572 ft, is measured by an ohmmeter which consistently and repeatedly indicates 1.4 Mft. But can the observer "read" the true value from the scale? His estimates from the scale

of the series resistance in one meter changes considerably, in error

by a

fairly large

reading consistently yield a value of 1.4 Mft. This

is

as close to the true value

by estimation. Although there are no deviations from the observed value, the error created by the limitation of the scale reading is a as he can read the scale

Melville

B. Stout, Basic Electrical

Hall, Inc., 1960), pp. 21-26.

Measurements, 2nd

ed.

(Englewood

Cliffs, N.J.:

Prentice-

Sec. 1-3

Significant Figures

3

The example illustrates that conformity is a necessary, but not condition for precision because of the lack of significant figures obtained. Similarly, precision is a necessary, but not sufficient, condition for accuracy.

precision error. sufficient,

Too

often the beginning student

at face value.

He

is

is inclined to accept instrument readings not aware that the accuracy of a reading is not necessarily

guaranteed by its precision. In fact, good measurement technique demands continuous skepticism as to the accuracy of the results. In critical work, good practice dictates that the observer make an inde-

pendent

set

of measurements, using different instruments or different measure-

ment techniques, not

subject to the

same systematic

errors.

He must

make known

also

sure that the instruments function properly and are calibrated against a

standard, and that no outside influence affects the accuracy of his measurements.

SIGNIFICANT FIGURES

1-3

An

indication of the precision of the

measurement

of significant figures in which the result

is

actual information regarding the magnitude

a quantity.

The more

For example, resistor

if

a resistor

ft

described as 68.0

is

it is

and the measurement precision of

is

specified as having a resistance of 68

H

The

Cl, it

means

that

its

H,

its

or 69 H. If the value of the

resistance

is

closer to 68.0 fl

ft.

In 68 ft there are two significant figures; in 68.0

latter,

with more significant figures, expresses a mea-

to 67.9 fl or 68.1

there are three.

obtained from the number

significant figures, the greater the precision of measurement.

resistance should be closer to 68 Cl than to 67

than

is

expressed. Significant figures convey

surement of greater precision than the former.

number of digits may not represent measurement numbers with zeros before a decimal point are used approximate populations or amounts of money. For example, the population Often, however, the total

precision. Frequently, large for

of a city

is

reported in six figures as 380,000. This

may imply

that the true value

between 379,999 and 380,001, which is six significant figures. What is meant, however, is that the population is closer to 380,000 than to 370,000 or 390,000. Since in this case the population can be reported only of the population

to

two

significant figures,

A X

10

5 .

figures.

lies

more

how can

large

numbers be expressed?

technically correct notation uses powers of ten, 38

This indicates that the population figure Uncertainty caused by zeros to the

left

is

4

X

10 or 3.8

only accurate to two significant

of the decimal point

is

therefore

usually resolved by scientific notation using powers of ten. Reference to the

would cause no misunderstanding 5 anyone with a technical background. But 1.86 X 10 mi/s leaves no confusion. It is customary to record a measurement with all the digits of which we are sure nearest to the true value. For example, in reading a voltmeter, the voltage may be read as 117.1 V. This simply indicates that the voltage, read by

velocity of light as 186,000 mi/s, for example, to

Measurement and

4

Chap.

Error

1

is closer to 117.1 V than to 117.0 V or 117.2 expressing this result indicates the range of possible error. The voltage may be expressed as 117.1 ± 0.05 V, indicating that the value of the voltage lies between 117.05 V and 117.15 V.

the observer to best estimation,

way of

V. Another

When

a

number of independent measurements

are taken in an effort to

obtain the best possible answer (closest to the true value), the result

expressed as the arithmetic

mean of

all

usually

is

the readings, with the range of possible

error as the largest deviation from that mean. This

illustrated in

is

Exam-

ple 1-1.

Example

A

set

1-1

of independent voltage measurements taken by four observers was recorded as

117.02 V, 117.11 V, 117.08 V, and 117.03 V. Calculate (a) the average voltage, (b) the range of error.

Solution

E + E + E + EA E„ = 2

x

(a)

117.02

=

3

+

+

117.11

117.08

+

117.03

.

=

117.06

=

0.05

V

4

= E max - E =

Range

(b)

av

117.11

-

117.06

V

but also

£ - E mn = av

The average range of

117.06

-

=

117.02

0.04

V

error therefore equals

+

0.05

0.04

=

±0.045

=

±0.05

V

2

When two added, the result that

two

Example

Two

more measurements with dhTerent degrees of accuracy

or is

are

only as accurate as the least accurate measurement. Suppose

resistances are

added

in series as in

Example

1-2.

1-2

R

resistors,

x

and

R

2,

are connected in series. Individual resistance measurements,

using a Wheatstone bridge, give resistance to the appropriate

R =

18.7

l

number of

H

and

R = 2

3.624

ft.

Calculate the total

significant figures.

Solution

R =

18.7 (1 (three significant figures)

R =

3.624

{

2

H

(four significant figures)

R T = R, + R = 2

The doubtful

22.324

fi (five significant figures)

=

22.3

H

R and R 2 no value whatsoever in

figures are written in italics to indicate that in the addition of

the last three digits of the

sum

are doubtful figures. There

is

x

Sec. 1-3

Significant Figures

two

retaining the last

5

digits (the

2 and the 4) because one of the resistances

only to three significant figures or tenths of an ohm.

The

reduced to three significant figures or the nearest tenth,

The number of

i.e.,

22.3

significant figures in multiplication

Example

accurate

CI.

may

increase rapidly,

shown

in

recorded in a resistance of 35.68

ft.

but again only the appropriate figures are retained in the answer, as

Example

is

result should therefore also be

1-3.

1-3

In calculating voltage drop, a current of 3.18

A

is

Calculate the voltage drop across the resistor to the appropriate

number of

significant

figures.

Solution

E =

=

IR

(35.68)

X

(3.1(5)

-

M3.4624

=

113

V

Since there are three significant figures involved in the multiplication, the answer can be written only to a

In four;

maximum

Example

and the

1-3,

of three significant figures.

the current,

/,

has three significant figures and

R

has

result of the multiplication has only three significant figures. This

answer cannot be known to an accuracy greater than the if extra digits accumulate in the answer, they should be discarded or rounded off. In the usual practice, if the (least significant) digit in the first place to be discarded is less than five, it and the following digits are dropped from the answer. This was done in Example illustrates that the least

poorly defined of the factors. Note also that

first place to be discarded is five or greater, the previous by one. For three-digit precision, therefore, 113.46 should be rounded off to 113; and 113.74 to 114. Addition of figures with a range of doubt is illustrated in Example 1-4.

1-3. If

the digit in the

digit is increased

Example

Add

1-4

826 ±

5 to

628 ±

3.

Solution

=

826

±

5

(= ±0.605%)

N =

628

±

3

(

N, 2

Sum =

1,454

±

8

=

±0.477%)

(= ±0.55%)

Example 1-4 that the doubtful parts are added, since the ± sign means that one number may be high and the other low. The worst possible combination of range of doubt should be taken in the answer. The percentage doubt in the Note

in

original figure

N

{

and

N

2

does not

differ greatly

from the percentage doubt

in

the final result. If the

interesting

same two numbers are subtracted, as in Example 1-5, there is an comparison between addition and subtraction with respect to the

range of doubt.

Measurement and

6

Example

Error

Chap.

1

1-5

Subtract 628

±

3

from 826 ±

and express the range of doubt

5

in the

answer as a

percentage.

Solution

=

826

±

5

(= ±0.605%)

N =

628

±

3

(= ±0.477%)

=

198

±

8

(= ±4.04%)

N, 2

Difference

Again, in Example

Example numbers

1-5,

same reason as in and subtraction of the same

the doubtful parts are added for the

Comparing the Examples 1-4 and

1-4.

results of addition

when The final result after subtraction shows a large increase in percentage doubt compared to the percentage doubt after addition. The percentage doubt increases even more when the difference between the numbers is relatively small. Consider the case illustrated in Example 1-6. in

1-5,

note that the precision of the results,

expressed in percentages, differs greatly.

Example

1-6

Subtract 437

± 4 from 462 ± 4 and

express the range of doubt in the answer as a

percentage.

Solution AT,

=

N = 2

Difference

Example

=

1-6 illustrates clearly that

462

±

4

(= ±0.87%)

437 ± 4 (= ±0.92%) 25

±

8

(= ±32%)

one should avoid measurement techniques

depending on subtraction of experimental results because the range of doubt the final result

1-4

may

in

be greatly increased.

TYPES OF ERROR

No measurement

can be made with perfect accuracy, but

out what the accuracy actually

is

and how

different errors

it is

important to find

have entered into the

measurement. A study of errors is a first step in finding ways to reduce them. Such a study also allows us to determine the accuracy of the final test result. Errors may come from different sources and are usually classified under three

main headings: Gross errors: largely

human

errors,

among them misreading

of in-

struments, incorrect adjustment and improper application of instruments,

and computational mistakes.

Sec.

1

Types

-4

7

of Error

Systematic errors: shortcomings of the instruments, such as defective

worn

or

parts,

and

effects

of the environment on the equipment or the

user.

Random errors: those due to causes that cannot be directly established because of random variations in the parameter or the system of measurement.

Each of these will

classes of errors will be discussed briefly

and some methods

be suggested for their reduction or elimination.

Gross Errors

1-4.1

This class of errors mainly covers

human

mistakes in reading or using

instruments and in recording and calculating measurement results.

human

beings are involved,

some gross

As long

as

errors will inevitably be committed.

Although complete elimination of gross errors is probably impossible, one should try to anticipate and correct them. Some gross errors are easily detected; others may be very elusive. One common gross error, frequently committed by beginners in measurement work, involves the improper use of an instrument. In general, indicating instruments change conditions to some extent when connected into a complete circuit, so that the measured quantity is altered by the method employed. For example, a well-calibrated voltmeter

may

give a misleading read-

when connected across two points in a high-resistance circuit (Example 1-7). The same voltmeter, when connected in a low-resistance circuit, may give a more dependable reading (Example 1-8). These examples illustrate that the ing

voltmeter has a "loading effect" on the circuit, altering the original situation by the

measurement process.

Example

A

1-7

voltmeter, having a sensitivity of 1,000 fl/V, reads 100

connected across an unknown resistor

When known effect

the milliammeter reads 5

in series

mA,

resistor, (b) actual resistance of the

V

on

its

150-V scale when

with a milliammeter.

calculate (a) apparent resistance of the un-

unknown

resistor, (c) error

due to the loading

of the voltmeter.

Solution (a)

The

total circuit resistance equals

Kr IT

_woy_ Mkn mA 5

Neglecting the resistance of the milliammeter, the value of the

Rx = (b)

20

ka

The voltmeter

resistance equals

Ry

1,000-

X

150

V =

150

kH

unknown

resistor

is

8

Since the voltmeter

in parallel with the

is

R TR V &x = R„ — R = v T M %

(c)

error

=

actual

—

unknown 20

Measurement and

Error

we can

write

resistance,

X ™ —= 150

Example

1

kH

130

apparent

^

X 100% =

actual

=

23.05

Chap.

———- — X 100% 23.05

20

23.05

13.23%

1-8

Repeat Example 1-7 its 150-V scale.

if

the milliammeter reads 800

mA

and the voltmeter reads 40

V

on

Solution

VT

40

V

(b)

R v = 1,000^ X

(c)

%

error

=

150

——50.1

50

V =

150

kH

X 100% - 0.2%

Errors caused by the loading effect of the voltmeter can be avoided by it intelligently. For example, a low-resistance voltmeter should not be used measure voltages in a vacuum tube amplifier. In this particular measurement, a high-input impedance voltmeter (such as a VTVM or TVM) is required. A large number of gross errors can be attributed to carelessness or bad habits, such as improper reading of an instrument, recording the result differently from the actual reading taken, or adjusting the instrument incorrectly. Consider the case in which a multirange voltmeter uses a single set of scale markings

using to

with different number designations for the various voltage ranges.

It is

easy to

use a scale which does not correspond to the setting of the range selector of the voltmeter.

A

gross error

before the measurement

may is

also occur

taken; then

when

all

the instrument

the readings are

is

not set to zero

off.

Errors like these cannot be treated mathematically. They can be avoided only by taking care in reading and recording the measurement data.

Good

making more than one reading of the same quantity, preferably by a different observer. Never place complete dependence on one reading but take at least three separate readings, preferably under conditions in which inpractice requires

struments are switched off-on.

Types

Sec. 1-4

9

of Error

1-4.2 Systematic Errors This type of error

is

usually divided into

two

different categories: (1)

instrumental errors, defined as shortcomings of the instrument; (2) environmental errors, due to external conditions affecting the measurement.

Instrumental errors are errors inherent in measuring instruments because mechanical structure. For example, in the d'Arsonval movement friction

of their

in bearings of various

moving components may cause incorrect

readings. Irreg-

ular spring tension, stretching of the spring, or reduction in tension due to

improper handling or overloading of the instrument

will result in errors.

Other

instrumental errors are calibration errors, causing the instrument to read high or low along a

its

entire scale. (Failure to set the instrument to zero before

measurement has a similar effect.) There are many kinds of instrumental

errors,

making

depending on the type of

instrument used. The experimenter should always take precautions to insure that the instrument he

is

using

is

operating properly and does not contribute

may be detected by checking for erratic behavior, and stability and reproducibility of results. A quick and easy way to check an instrument is to compare it to another with the same characteristics or to one that is known to be more accurate. excessive errors for the purpose at hand. Faults in instruments

may be avoided by (1) selecting a suitable instrument measurement application; (2) applying correction factors after determining the amount of instrumental error; (3) calibrating the instrument Instrumental errors

for the particular

against a standard.

Environmental errors are due to conditions external to the measuring device, including conditions in the area surrounding the instrument, such as the effects of

changes

or electrostatic

instrument

is

in temperature,

fields.

Thus

humidity, barometric pressure, or of magnetic

a change in ambient temperature at which the

used causes a change in the elastic properties of the spring in a

moving-coil mechanism and so affects the reading of the instrument. Corrective

measures to reduce these certain

components

effects include air conditioning, hermetically sealing

in the instrument, use of

magnetic

shields,

and the

like.

Systematic errors can also be subdivided into static or dynamic errors. Static errors are

laws governing

caused by limitations of the measuring device or the physical behavior. A static error is introduced in a micrometer when

its

excessive pressure

is

applied in torquing the shaft.

by the instrument's not responding measured variable.

1-4.3

Random

fast

enough

Dynamic

errors are caused

to follow the changes in a

Errors

These errors are due to unknown causes and occur even when all systematic errors have been accounted for. In well-designed experiments, few random errors

Measurement and

10

usually occur, but they

voltage

is

become important

in high-accuracy work.

being monitored by a voltmeter which

Although the instrument

is

is

Chap.

Error

1

Suppose a

read at half-hour intervals.

operated under ideal environmental conditions and

has been accurately calibrated before the measurement,

it

will

be found that the

readings vary slightly over the period of observation. This variation cannot be corrected by any it

method of

known method

calibration or other

of control and

cannot be explained without minute investigation. The only way to

offset these

by increasing the number of readings and using statistical means to obtain the best approximation of the true value of the quantity under measureerrors

is

ment.

1-5

A

STATISTICAL ANALYSIS

statistical analysis

of measurement data

is

common

an analytical determination of the uncertainty of the of a certain measurement method

may

ments

is

allows

all

the disturbing factors.

To make

methods and interpretations meaningful, a large number of measureusually required. Also, systematic errors should be small compared

with residual or random errors, because

remove a

it

The outcome

be predicted on the basis of sample data

without having detailed information on statistical

practice because

final test result.

fixed bias contained in all the

1-5.1 Arithmetic

statistical

treatment of data cannot

measurements.

Mean

The most probable value of a measured variable is the arithmetic mean of number of readings taken. The best approximation will be made when the number of readings of the same quantity is very large. Theoretically, an infinite number of readings would give the best result, although in practice, only a finite number of measurements can be made. The arithmetic mean is given by the

the

following expression:

_ X

=

x

x

+

x2

+

x3

+

x4

4-

.

.

.

+

xn

n

x=

where

arithmetic

=

1x —

.

(1-1)

n

mean

x v x y x n = readings taken

n= Example

1-1

number of readings

showed how the arithmetic mean

1-5.2 Deviation from the Deviation

is

is

used.

Mean

the departure of a given reading from the arithmetic

of the group of readings. If the deviation of the

first

reading,

x

lt

is

mean d

called

x

,

Sec. 1-5

11

Statistical Analysis

and that of the second reading, x2 from the mean can be expressed as ,

d

=

x

x

l

—

d2

x

is

called

=

x2

d 2i and

—

so on, then the deviations

dn

x

=

—

xn

x

(1-2)

Note that the deviation from the mean may have a positive or a negative value and that the algebraic sum of all the deviations must be zero. Example 1-9 illustrates the computation of deviations. Example

A

set

12.8

of independent current measurements was taken by six observers and recorded as

mA,

mean,

1-9

12.2

mA,

12.5

mA, 13.1mA,

(b) the deviations

12.9

mA, and

12.4

mA.

Calculate (a) the arithmetic

from the mean.

Solution (a)

Using Eq.

x

we

(1-1),

=

12.8

+

mean

see that the arithmetic

12.2

+

+

12.5

13.1

+

equals

+

12.9

12.4

=

12.65

mA

6 (b)

Using Eq.

(1-2),

we

see that the deviations are

=

12.8

-

12.65

=

d2

=

12.2

-

12.65

=

d3

=

12.5

-

12.65

=

dA

=

13.1

-

12.65

=

d

5

=

12.9

-

12.65

=

d6

=

12.4

-

12.65

=

d

x

Note that the algebraic sum of 1-5.3

all

mA -0.45 mA -0.15 mA 0.45 mA 0.25 mA -0.25 mA

0.15

the deviations equals zero.

Average Deviation

The average

deviation

an indication of the precision of the instruments

is

used in making the measurements. Highly precise instruments will yield a low

By

average deviation between readings.

definition, average deviation

of the absolute values of the deviations divided by the absolute value of the deviation deviation

may

number of

is

the

readings.

sum The

the value without respect to sign. Average

is

be expressed as

D=

\d,\+\d 1

\

+ \d

i

\+

...

+K| m

i\d\ _

n

n

Example 1-10 shows how average deviation

is

calculated.

Example 1-10 Calculate the average deviation for the data given in

Example

1-9.

Measurement and

12

Error

Chap.

1

Solution

+

0.15

D =

0.45

+

0.15

+

+

0.45

+

0.25

0.25

=

mA

0.283

1-5.4 Standard Deviation In statistical analysis of

standard deviation cr

of an infinite

is

random

errors, the

a very valuable aid.

number of data

is

By

root-mean-square deviation or

definition, the standard deviation

the square root of the

deviations squared, divided by the

number of

sum

of all the individual

readings. Expressed mathemati-

cally:

In practice, of course, the possible

number of observations

standard deviation of a finite number of data

Equation (1-5)

will

is

is

4-

.

.

.

+

(1 " 5)

essentially the is

the

same

same quantity

is

the variance or

as the standard deviation except that

not extracted. Therefore (

V)

= mean

square deviation

a convenient quantity to use in

The standard

scientific results are

now

=

cr

1

many computations because

deviation, however, has the advantage of

being of the same units as the variable, making

1-6

\^d]

d\

be used in Example 1-11.

variances are additive.

Most

The

I

variance

The variance

d\

is finite.

given by

V

Another expression for mean square deviation, which the square root

+

f d\

Id]

-

is

it

easy to compare magnitudes.

stated in terms of standard deviation.

PROBABILITY OF ERRORS 1-6.1

Normal Distribution of Errors

Table

l-l

shows a tabulation of 50 voltage readings

small time intervals and recorded to the nearest 0.1 V. the measured voltage

that

were taken

at

The nominal value of

was 100.0 V. The result of this series of measurements in the form of a block diagram or histogram in

can be presented graphically

which the number of observations reading.

The histogram of

is

plotted against each observed voltage

Fig. 1-1 represents the data of

Table

1-1.

Sec. 1-6

13

Probability of Errors

TABLE

1-1

Tabulation of Voltage Readings

Voltage reading

Number

(volts)

of readings

99.7

1

99.8

4

99.9

12

100.0

19

100.1

10

100.2

3

100.3

1

50

Figure

1-1

shows that the

largest

number of readings

(19) occurs at the

central value of 100.0 V, while the other readings are placed

more or

less

symmetrically on either side of the central value. If more readings were taken at smaller increments, say

200 readings

at

0.05-V intervals, the distribution of

observations would remain approximately symmetrical about the central value

and the shape of the histogram would be about the same as before. With more and more data, taken at smaller and smaller increments, the contour of the histogram would finally become a smooth curve, as indicated by the broken line in Fig. 1-1. This bell-shaped curve is known as a Gaussian curve. The sharper and narrower the curve, the more definitely an observer may state that the most is the central value or mean reading. Normal law of error forms the basis of the analytical The Gaussian or mathematical treatment of this subject effects. Although the study of random

probable value of the true reading

Number

19

of

Observed Readings

12 io

i—1\

x oo

a>

a>

&>&>&>

Figure 1-1

o o

1-1.

o o

o o

•Volts

Histogram showing the frequency of occurrence of the 50 voltage readings

The broken curve represents the number of readings at small increments

of Table large

q d o

1

limiting case of the histogram

are taken.

when

a

Measurement and

14

is beyond the scope of on the Normal law:

(a) All

We

this text, the following qualitative statements are

Random

(c)

There

is

1

based

random

errors.

an equal probability of positive and negative random

errors.

observations include small disturbing

(b)

Chap.

Error

effects, called

errors can be positive or negative.

can therefore expect that measurement observations include plus and minus more or less equal amounts, so that the total error will be small and

errors in

the

mean The

value will be the true value of the measured variable. possibilities as to the

form of the error distribution curve can be stated

as follows:

(a)

Small errors are more probable than large errors.

(b)

Large errors are very improbable.

(c)

There

is

an equal probability of plus and minus errors so that the

probability of a given error will be symmetrical about the zero value.

The

error distribution curve of Fig. 1-2

is

based on the Normal law and shows

may

a symmetrical distribution of errors. This normal curve limiting

form of the histogram of

the true voltage

is

the

mean

Fig. 1-1 in

be regarded as the

which the most probable value of

value of 100.0 V.

1-6.2 Probable Error

The area under limits

+

oo

and

Figure 1-2

—

oo

Curve

the Gaussian probability curve of Fig. 1-2, between the ,

represents the entire

for the

probable error, where r

=

Normal

law.

±0.6745o-.

number of

The shaded portion

observations.

The area

indicates the region of

Sec. 1-6

15

Probability of Errors

under the curve between the + cr and — cr limits represents the cases that differ from the mean by no more than the standard deviation. Integration of the area under the curve within the ± or limits gives the total number of cases within these limits. For normally dispersed data, following the Gaussian distribution, approximately 68 per cent of all the cases lie between the limits of +

WW-:

R2 V 2 ¥rZero Adjust

1.5V

^22,988

^

ft'

Negative

Positive

(a)

Ohmmeter

Rx1 Range

Circuit

M

—wa

l.5ft

M38ft 21,850ft ^AAAr^^^v^AA

lOkft

Zero Adjust

~M49.5ft

I.5V

Negative,,

Positive (b)

Ohmmeter

Circuit

Rx 100 Range

--w-

11.5ft

"w—J\AAA/

21,850ft

1138ft

WA

lOkft^

WvV^r^VVvV-

22,999.5

ft'

Negative (c)

Figure 4-27

Ohmmeter

Ohmmeter

section of the

Circuit

R

x

10,000 Range

ft**

Simpson Model 260 multimeter (courtesy

Simpson Electric Company).

4-11 CALIBRATION

OF DC INSTRUMENTS

Although detailed calibration techniques are beyond the scope of this chapter, some general procedures for the calibration of basic dc instruments are given. Calibration of a dc ammeter can most easily be carried out by the arrangement of Fig. 4-28. The value of the current through the ammeter to be calibrated is determined by measuring the potential difference across a standard resistor by the potentiometer method and then calculating the current by Ohm's

Sec. 4-12

Alternating-Current Indicating Instruments

85

Rheostat

dc

Ammeter

Constant Source

Under Test

R -AAA/V

Standard Resistor

Figure 4-28

Potentiometer method of cal-

ibrating a dc

ammeter.

Potentiometer

The result of this calculation is compared to the actual reading of the ammeter under calibration and inserted in the circuit. (Voltage measurements by the potentiometer method are discussed in Sec. 5-13.) A good source of constant current is required and is usually provided by storage cells or a precision power supply. A rheostat is placed in the circuit to control the current to any desired value, so that different points on the meter scale can be calibrated. A simple method of calibrating a dc voltmeter is shown in Fig. 4-29, where the voltage across dropping resistor R is accurately measured with a potentiometer. The meter to be calibrated is connected across the same two points as the potentiometer and should therefore indicate the same voltage. A rheostat is placed in the circuit to control the amount of current and therefore the drop across the resistor, R, so that several points on the voltmeter scale can be calibrated. Voltmeters tested with the method of Fig. 4-29 can be calibrated with an accuracy of ±0.01 per cent, which is well beyond the usual accuracy of a d'Arsonval movement. The ohm meter is generally considered to be an instrument of moderate law.

accuracy and low precision.

A

rough calibration may be done by measuring a

standard resistance and noting the reading of the ohmmeter. Doing this for several points

on the ohmmeter

scale

and on several ranges allows one

to obtain

an indication of the correct operation of the instrument.

-^rtZ— Rheostat

Regulated dc Source

Figure 4-29

©Voltmeter Under

Potentiometer

Test

Potentiometer method of calibrating a dc voltmeter.

4-12 ALTERNATING-CURRENT INDICATING INSTRUMENTS The d'Arsonval movement responds to the average or dc value of the current through the moving coil. If the movement carries an alternating current with

Electromechanical Indicating Instruments

86

positive

and negative

half-cycles, the driving torque

for the positive alternation

and

If the frequency of the ac

is

is

in

one direction

in the other direction for the negative alternation.

very low, the pointer would swing back and forth

around the zero point on the meter the coil

would be

Chap. 4

scale.

At higher

frequencies, the inertia of

so great that the pointer cannot follow the rapid reversals of the

driving torque and hovers around the zero mark, vibrating slightly.

To measure

ac on a d'Arsonval movement,

some means must be devised

to obtain a unidirectional torque that does not reverse each half-cycle.

One

method involves rectification of the ac, so that the rectified current deflects the coil. Other methods use the heating effect of the alternating current to produce an indication of its magnitude. Some of these methods are discussed in this chapter.

4-12.1 Electrodynamometer

One

of the most important ac movements

is

the electrodynamometer.

It is

and ammeters, not only at the powerline frequency but also in the lower audiofrequency range. With some slight modifications, the electrodynamometer can be used as a wattmeter, a VARmeter, a power-factor meter, or a frequency meter.' The electrodynamometer movement may also serve as a transfer instrument, because it can be calibrated on dc and then used directly on ac, establishing a direct means of equating ac and dc measurements of voltage and current. Where the d'Arsonval movement uses a permanent magnet to provide the magnetic field in which the movable coil rotates, the electrodynamometer uses the current under measurement to produce the necessary field flux. Figure 4-30 shows a schematic arrangement of the parts of this movement. A fixed coil, split into two equal halves, provides the magnetic field in which the movable coil rotates. The two coil halves are connected in series with the moving coil

often used in accurate ac voltmeters

Scale

Fixed Coils Figure 4-30

Schematic diagram of an electrodynamometer movement.

Sec. 4-12

Alternating-Current Indicating Instruments

87

and are fed by current under measurement. The fixed coils are spaced far enough apart to allow passage of the shaft of the movable coil. The movable coil carries a pointer, which is balanced by counterweights. Its rotation is controlled by springs, similar to the d'Arsonval movement construction. The complete assembly is surrounded by a laminated shield to protect the instrument from stray magnetic fields which may affect its operation. Damping is provided by aluminum air vanes, moving in sector-shaped chambers. The entire movement is very solid and rigidly constructed in order to keep its mechanical dimensions stable and its calibration intact. A cutaway view of the electrodynamometer is shown in Fig. 4-31.

The operation of the instrument may be understood by returning expression for the torque developed by a coil suspended in a magnetic

to the

field.

We

previously stated, Eq. (4-1), that

T=BXA XlXN which deflects the movable coil, is directly propor(A and N), the strength of the magnetic field in moves (B), and the current through the coil (/). In the electrowhich the coil (B) depends on the current through the fixed coil dynamometer the flux density indicating that the torque,

tional to the coil constants

and

is

coil

dimensions and the number of turns on the

therefore directly proportional to the deflection current (/). Since the

Figure 4-31

ment of

fixed

coil

frame are fixed quantities

Phantom photograph of an electrodynamometer, showing the arrangeand movable coils. The rigidly constructed mechanism is surrounded

by a laminated shield to minimize the indication (courtesy

effect

Weston Instruments,

of external magnetic fields on the meter

Inc.).

88

Electromechanical Indicating Instruments

Chap. 4

any given meter, the developed torque becomes a function of the current

for

squared (I

2 ).

If the

law scale

is

electrodynamometer easily noticed, with

exclusively designed for dc use,

is

crowded

values, progressively spreading out at

developed torque squared

at

any instant

is

markings

its

square-

low current the higher current values. For ac use, the scale

at the very

proportional to the instantaneous current

2

The instantaneous value of i 2 is always positive and torque pultherefore produced. The movement, however, cannot follow the rapid

(i ).

sations are

variations of the torque

and takes up a position

in

which the average torque

balanced by the torque of the control springs. The meter deflection a function of the

mometer

is

mean

of the squared current.

The

is

is

therefore

scale of the electrodyna-

usually calibrated in terms of the square root of the average current

squared, and the meter therefore reads the rms or effective value of the ac.

The transfer properties of the electrodynamometer become apparent when we compare the effective value of alternating current and direct current in terms of their heating effect or transfer of power.

An

alternating current that produces

heat in a given resistance at the same average rate as a direct current (7) has,

by

definition, a value of

/ amperes. The average rate of producing heat by a dc R is PR watts. The average rate of producing heat

of / amperes in a resistance

by an ac of

By 1

amperes during one cycle

i

in

the

same

R

resistance

is

definition, therefore,

Jo

and

2 i

This current,

/, is

a

mark

is

=

^average

is

often referred to as the equivalent dc value.

electrodynamometer

is

calibrated with a direct current of

have an rms value of its

1

A

and

placed on the scale to indicate this 1-A dc value, then that alternating

current which causes the pointer to deflect to the same

to

2

i

then called the root-mean-square (rms) or effective value of

the alternating current and If the

dt

1

A.

We

mark on

the scale

must

can therefore "transfer" a reading made with dc

corresponding ac value and have thereby established a direct connection

between ac and

dc.

The electrodynamometer then becomes very

calibration instrument

and

is

often used for this purpose because of

useful as a its

inherent

accuracy.

is its

The electrodynamometer, however, has certain disadvantages. One of these high power consumption, a direct result of its construction. The current

under measurement must not only pass through the movable coil, but it must To get a sufficiently strong magnetic field, a high

also provide the field flux.

Sec. 4-12

mmf is

Alternating-Current Indicating Instruments

89

required and the source must supply a high current and power. In spite

of this high power consumption, the magnetic

field is

very

much weaker

than

movement because there is no iron in the path consists of air. Some instruments have been

that of a comparable d'Arsonval circuit,

i.e.,

the entire flux

designed using special laminated steel for part of the flux path, but the presence of metal introduces calibration problems caused by frequency and waveform

Typical values of electrodynamometer flux density are in the range of approximately 60 gauss. This compares very unfavorably with the high flux densities (1,000-4,000 gauss) of a good d'Arsonval movement. The low flux effects.

density of the electrodynamometer immediately affects the developed torque and therefore the sensitivity of the instrument

The addition of a

is

typically very low.

series resistor converts the

electrodynamometer into a

voltmeter, which again can be used to measure dc and ac voltages. For reasons

previously mentioned, the sensitivity of the electrodynamometer voltmeter

meter).

The reactance and

is

H/V (compare this to the 20 kfl/V of a d'Arsonval

low, approximately 10 to 30

resistance of the coils also increase with increasing

frequency, limiting the application of the electrodynamometer voltmeter to the

lower frequency ranges.

and

It is,

however, very accurate at the powerline frequencies

therefore often used as a secondary standard.

is

The electrodynamometer movement (even unshunted) may be regarded as it becomes rather difficult to design a moving coil which can carry more than approximately 100 mA. Larger current would have to be carried to the moving coil through heavy lead-in wires, which would lose their flexibility. A shunt, when used, is usually placed across the movable coil only. The fixed coils are then made of heavy wire which can carry the large total current and it is feasible to build ammeters for currents up to 20 A. Larger values of ac an ammeter, but

currents are usually measured by using a current transformer and a standard

5-A ac ammeter -

(Sec. 4-17).

4-12.2 Rectifier-type Instruments

One obvious answer

to the question of ac

measurement

is

found by using

a rectifier to convert ac into a unidirectional dc and then to use a dc

method

movement

is

very attractive, because

a dc movement generally has a higher sensitivity than mometer or the moving-iron instrument.

either the electrodyna-

to indicate the value of the rectified ac. This

PMMC movement in combisome rectifier arrangement. The rectifier element usually consists of a germanium or a silicon diode. Copper oxide and selenium rectifiers have become obsolete, because they have small inverse voltage ratings and can handle only limited amounts of current. Germanium diodes have a peak inverse voltage Rectifier-type instruments generally use a

nation with

(PIV) on the order of 300

Low-current rating

V

and a current rating of approximately 100 mA. have a PIV of up to 1,000 V and a current

silicon diode rectifiers

on the order of 500 mA.

90

Electromechanical Indicating Instruments

Rectifiers for instrument

work sometimes

Chap. 4

consist of four diodes in a bridge

shows an ac voltand a PMMC move-

configuration, providing full-wave rectification. Figure 4-32

meter circuit consisting of a multiplier, a bridge

rectifier,

ment.

The bridge rectifier produces a pulsating unidirectional current through movement over the complete cycle of the input voltage. Because of inertia of the moving coil, the meter will indicate a steady deflection pro-

the meter the

portional to the average value of the current. Since alternating currents and voltages are usually expressed in

rms

values, the

meter scale

is

calibrated in

terms of the rms value of a sinusoidal waveform.

Example 4-9 4-32(a), where the PMMC movement and requires a dc current of 1 mA for full-scale deflection. Assuming ideal diodes (zero forward resistance and infinite reverse resistance), calculate the value of the multiplier R s to obtain full-scale meter deflection with 10 V ac

An experimental ac voltmeter uses the circuit of Fig. has an internal resistance of 50

H

(rms) applied to the input terminals. Solution

For full-wave

rectification,

(b) Rectified Current

Figure 4-32

Through Meter Movement Full-wave

rectifier

ac voltmeter.

Sec. 4-12

Alternating-Current Indicating Instruments

91

and

E = dc

The

X

0.9

10

total circuit resistance, neglecting the

R,

V =

9 1

A

n -

V

mA

s

9,000

V

forward diode resistance,

= R + R

r=

9

50

n =

=

kn

9

n

8,950

nonsinusoidal waveform has an average value that

erably from the average value of a pure sine

is

wave

may

differ consid-

which the meter is calibrated) and the indicated reading may be very erroneous. The form factor relates the average value and the rms value of time- varying voltages and currents: (for

effective value of the ac

form factor

wave

average value of the ac wave

For a sinusoidal waveform: form factor

(y/2/2)E,

=

=

1.11

(4-27)

(2/ir)E n

Note that the voltmeter of Example 4-9 has a scale suitable only for sinusoidal The form factor of Eq. (4-27) is therefore also the factor by which the actual (average) dc current is multiplied to obtain the equivalent rms ac measurements. scale markings.

The

ideal rectifier element should

resistance. In practice,

however, the

the characteristic curves of Fig. 4-33. rectifier

have zero forward and

rectifier is

At low values of forward

operates in an extremely nonlinear part of

the resistance

is

large as

The lower part of the

compared

is

therefore often crowded, scale, calibrated espe-

resistance in the early part of the rectifier

Current

1

-e Keverse Current

'

f /

J.

Figure 4-33

and

to the resistance at higher current values.

ac scale of a low-range voltmeter

The high

current, the

characteristic curve,

its

and most manufacturers provide a separate low-voltage cially for this purpose.

infinite reverse

a nonlinear device, indicated by

Forward

Reverse

Forward

Voltage

Current

Current

Characteristic curves of a solid-state rectifier.

Electromechanical Indicating Instruments

92

on the

characteristics also sets a limit

sensitivity

Chap. 4

which can be obtained

in

microammeters and voltmeters.

The

resistance of the rectifying element changes with varying temperature,

one of the major drawbacks of rectifier-type ac instruments. The meter accuracy is usually satisfactory under normal operating conditions at room temperature

and is generally on the order of ± 5 per cent of full-scale reading for sinusoidal waveforms. At very much higher or lower temperatures, the resistance of the rectifier

changes the total resistance of the measuring circuit

sufficiently to cause

the meter to be gravely in error. If large temperature variations are expected, the meter should be enclosed in a temperature-controlled box.

Frequency also

affects the operation

exhibits capacitive properties

readings

may

and tends

be in error by as

much

of the rectifier elements.

The

rectifier

to bypass the higher frequencies.

as 0.5 per cent decrease for every

Meter 1-kHz

rise in frequency.

4-12.3 Typical Multimeter Circuits General rectifier-type ac voltmeters often use the arrangement shown in Fig. 4-34.

the

Two

movement

Diode

D

x

diodes are used in this circuit, forming a full-wave rectifier with so connected that

it

receives only half of the rectified current.

conducts during the positive half-cycle of the input waveform and

The draw more current

causes the meter to deflect according to the average value of this half-cycle.

meter movement

shunted by a resistance

is

through the diode

D

x

and move

its

R

in order to

sh ,

operating point into the linear portion of

the characteristic curve. In the absence of diode Z> 2 the negative half-cycle of ,

the input voltage

would apply a reverse voltage across diode

leakage current in the reverse direction.

would therefore be lower than deals with this problem.

On

it

D

x ,

causing a small

The average value of the complete

cycle

should be for half-wave rectification. Diode

the negative half-cycle,

the current through the measuring circuit, which

is

D

now

2

D

2

conducts heavily, and

in the opposite direction,

bypasses the meter movement.

The commercial multimeter its

often uses the

same

scale

markings for both

dc and ac voltage ranges. Since the dc component of a sine wave for

wave

rectification equals 0.45 times the

rms

value, a

problem

Selector

Figure 4-34

half-

arises immediately.

Typical ac voltmeter section of a commercial multimeter.

1

Sec. 4-12

Alternating-Current Indicating Instruments

93

In order to obtain the same deflection on corresponding dc and ac voltage ranges, the multiplier for the ac range must be lowered proportionately. Fig. 4-35 illustrates a solution to the

Example

in

problem and

is

The circuit of some detail

discussed in

4-10.

AAAAr

1D2 A

ac Input

Computation of the multi-

Figure 4-35

and the ac voltmeter

plier resistor

sensitiv-

ity.

Example 4-10

A

meter movement has an internal resistance of 100

R

scale deflection. Shunting resistor

H. Diodes to

have

D

x

and

D

Cl

and requires

1

mA

dc for

full-

placed across the movement, has a value of 100

sh ,

have an average forward resistance of 400

2

CL each and are assumed For a 10-V ac range, calculate (a) the the voltmeter sensitivity on the ac range.

infinite resistance in the reverse direction.

value of multiplier

R

(b)

s ,

Solution (a)

Since

Rm

and

scale deflection

R

are both 100 H, the total current the source

ih

is I,

=

2

rectified ac voltage will

mA. For

total resistance of the

is

0.45

X

instrument circuit then

R=E f This total resistance

made up

4.5

2

10

V =

V

V

a

2,250

mA

4.5

is

we are interested only in the movement receives current, we can

of several parts. Since

resistance of the circuit during the half-cycle that the

eliminate the infinite resistance of reverse-biased diode

R,

D

2

from the

R„R

= R + R D] + s

R„ + R

and

R = R + s

The value of

100

400

the multiplier therefore s

The

4-

X

100

= R + s

200

R = (b)

for full-

be

= The

must supply

half-wave rectification the equivalent dc value of the

-

2,250

sensitivity of the voltmeter

_

is

on

this

n V

450

=

10-V ac range

2,250 10

1,800 Cl

225

n/v

is

450

ft

circuit.

Therefore

94

Electromechanical Indicating Instruments

The same movement, used 1,000

in a

Chap. 4

dc voltmeter, would have given a sensitivity figure of

n/v. Section 4-10 dealt with the dc circuitry of a typical multimeter, using the

diagram of Fig. 4-24. The circuit for measuring ac volts (subfrom Fig. 4-24) is reproduced in Fig. 4-36. Resistances R 9 R n R 7 and R 6 form a chain of multipliers for the voltage ranges of 1,000 V, 250 V, 50 V, and 10 V, respectively, and their values are indicated in the diagram of Fig. 4-36. On the 2.5-V ac range, resistor R 23 acts as the multiplier and corresponds simplified circuit

tracted

to the multiplier

,

R

s

of

Example 4-10 shown

in Fig. 4-35. Resistor

,

,

R 24

is

the

meter shunt and again acts to improve the rectifier operation. Both values are unspecified in the diagram and are factory selected. A little thought, however, will

convince us that the shunt resistance could be 2,000

resistance. If the average

forward resistance of the

(a reasonable assumption), then resistance

R 2i

ft,

rectifier

equal to the meter

elements

is

500

must have a value of 1,000

This follows because the meter sensitivity on the ac ranges

is

ft ft.

given as 1,000 ft/

V; on the 2.5-V ac range, the circuit must therefore have a total resistance of ft. This value is made up of the sum of R 23 the diode forward resistance, and the combination of movement and shunt resistance, as shown in Example

2,500

,

4-10. Three-terminal Rectifier

Figure 4-36

Multirange ac voltmeter circuit of the Simpson Model 260 multimeter

(courtesy of the Simpson Electric

Company).

4-13 THERMOINSTRUMENTS 4-13.1 Thermocouple Instrument Figure 4-37 shows a combination of a thermocouple and a

ment

that can be used to

measure both ac and

a thermocouple instrument, since

thermocouple element.

When two

its

operation

dc. This is

PMMC move-

combination

is

called

based on the action of the

dissimilar metals are mutually in contact, a

Sec. 4-13

Thermoinstruments

95

PMMC

Movement

Figure 4-37

Schematic representation of a basic thermocouple instrument using

thermocouple

CDE

and a

PMMC

movement.

generated at the junction of the two dissimilar metals. This voltage

voltage

is

rises in

proportion to the temperature of the junction. In Fig. 4-37,

represent the two dissimilar metals, joined at point E, and are

CE and DE

drawn

as a light

and a heavy line, to indicate dissimilarity. The potential difference between C and D depends on the temperature of the so-called cold junction, E. A rise in temperature causes an increase in the voltage and this is used to advantage in the thermocouple. Heating element AB, which is in mechanical contact with the junction of the two metals at point E, forms part of the circuit in which the current is to be measured. AEB is called the hot junction. Heat energy generated by the current in the heating element raises the temperature of the cold junction and causes an increase in the voltage generated across terminals C and D. This potential difference causes a dc current through the PMMC-indicating instrument. The heat generated by the current is directly proportional to the current 2 squared (I R), and the temperature rise (and hence the generated dc voltage) is proportional to the square of the rms current. The deflection of the indicating instrument will therefore follow a square-law relationship, causing crowding at the lower end of the scale and spreading at the high end. The arrangement of Fig. 4-37 does not provide compensation for ambient temperature changes. The compensated thermoelement, shown schematically in Fig. 4-38, produces a thermoelectric voltage in thermocouple CED, which is directly proportional to the current through circuit AB. Since the developed couple voltage is a function of the temperature difference between its hot and cold ends, this temperature difference must be caused only by the current being measured. Therefore, for accurate measurements, points C and D must be at the mean temperature of points A and B. This is accomplished by attaching couple ends

Figure 4-38

Compensated thermocouple

measure the thermo voltage produced by current i alone. Couple terminals C and D to

are in thermal contact with heater terminals

A and

from them.

B, but are electrically insulated

PMMC

96

C

Electromechanical Indicating Instruments

D

Chap. 4

whose ends are in thermal from them. Self-contained thermoelectric instruments of the compensated type are available in the 0.5-20- A range. Higher current ranges are available, but in this case the heating element is external to the indicator. Thermoelements used for current ranges over 60 A are generally provided with air cooling fins. Current measurements in the lower ranges, from approximately 0.1-0.75 A, use a bridge-type thermoelement, shown schematically in Fig. 4-39. This arrangement does not use a separate heater: the current to be measured passes directly through the thermoelements and raises their temperature in proportion to PR. The cold junctions (marked c) are at the pins which are embedded in the insulating frame, and the hot junctions (marked h) are at splices midway between the pins. The couples are arranged as shown in Fig. 4-39, and the resultant thermal voltage generates a dc potential difference across the indicating instrument. Since the bridge arms have equal resistances, the ac voltage across the meter is 0 V, and no ac passes through the meter. The use of several thermocouples in series provides a greater output voltage and deflection than is possible with a single element, resulting in an instrument with increased and

to the center of separate

contact with

A and

copper

strips,

B, but electrically insulated

sensitivity.

c

Figure 4-39

Bridge-type thermocouple instrument.

Thermoinstruments may be converted into voltmeters using low-current series resistors. Thermocouple voltmeters are available in ranges of up to 500 V and sensitivities of approximately 100 to 500 ft/V. A major advantage of a thermocouple instrument is that its accuracy can be as high as 1 per cent, up to frequencies of approximately 50 MHz. For this thermocouples and suitable

reason,

it is

classified as

an

RF instrument.

Above 50 MHz,

the skin effect tends

to force the current to the outer surface of the conductor, increasing the effective

and reducing instrument accuracy. For small is solid and very thin. Above 3 A the made from tubing to reduce the errors due to skin effect.

resistance of the heating wire

currents (up to 3 A), the heating wire

heating element

is

Sec. 4-14

Electrodynamometers

in

Power Measurements

97

ELECTRODYNAMOMETERS IN POWER MEASUREMENTS

4-14

4-14.1 Single-phase Wattmeter

The electrodynamometer movement power.

It

may

used extensively in measuring

is

be used to indicate both dc and ac power for any waveform of

voltage and current and

it is

not restricted to sinusoidal waveforms.

As

described

electrodynamometer used as a voltmeter or an ammeter has and the movable coil connected in series, thereby reacting to the

in Sec. 4-12.1, the

the fixed coils effect

of the current squared.

When

used as a single-phase power meter, the

coils

are connected in a different arrangement (see Fig. 4-40).

Current Coil

-\JJUUUU

1

Potentiol Coil

Diagram of an electrodynamometer wattmeter connected power of a single-phase load.

Figure 4-40 the

The

fixed coils, or field coils,

shown here

connected in series and carry the total

as

to

measure

two separate elements, are The movable coil,

line current (i c ).

located in the magnetic field of the fixed coils,

is

connected in

with a

series

and carries a small current (ip ). The instantaneous value of the current in the movable coil is i p = e/R p where e is the instantaneous voltage across the power line, and R p is the total resistance of the movable coil and its series resistor. The deflection of the movable coil is proportional to the product of these two currents, ic and ip and we can write current-limiting resistor across the

power

line

,

,

for the average deflection over

one period:

0„

=k\\

T ic i

p

dt

(4-28)

Electromechanical Indicating Instruments

98

where

=

0 av

K=

average angular deflection of the coil

instrument constant

ic

=

instantaneous current in the

i

=

instantaneous current in the potential coil

p

Chap. 4

field coils

Assuming for the moment that ic is equal to the load current, i (actually, ic = + /'), and using the value for ip = e/R p we see that Eq. (4-28) reduces to i p ,

(4-29)

By

definition, the average

power

in a circuit is

P„

= if

eidt

(4-30)

which indicates that the electrodynamometer movement, connected

in the con-

figuration of Fig. 4-40, has a deflection proportional to the average power. If e

and

i

are sinusoidally varying quantities of the form e

sin (cot

±

0),

0 av

where

E

= Em

sin

at and

i

=

Im

Eq. (4-29) reduces to

= K,EI cos

0

(4-31)

and / represent the rms values of the voltage and the current, and 6

represents the phase angle between voltage and current. Equations (4-29) and (4-30)

show

that the electrodynamometer indicates the average

power delivered

to the load.

Wattmeters have one voltage terminal and one current terminal marked the marked current terminal is connected to the incoming line, and the marked voltage terminal is connected to the line side in which the current coil is connected, the meter will always read up-scale when power is connected to the load. If for any reason (as in the two- wattmeter method of measuring "

± ." When

three-phase power), the meter should read backward, the current connections (not the voltage connections) should be reversed.

of

The electrodynamometer wattmeter consumes some power for maintenance magnetic field, but this is usually so small, compared to the load power, it may be neglected. If a correct reading of the load power is required, the

its

that

current coil should carry exactly the load current, and the potential coil should

be connected across the load terminals. With the potential coil connected to point A, as in Fig. 4-40, the load voltage

through the

field coils is

high by the amount of additional the potential coil

is

is

properly metered, but the current

amount ip The wattmeter therefore reads power loss in the potential circuit. If, however,

greater by the

connected to point

.

B

in Fig. 4-40, the field coils

correct load current, but the voltage across the potential coil

amount of but

the drop across the field coils.

now by

the

amount of the

PR

The wattmeter

is

meter the

higher by the

will again read high,

losses in the field windings.

Choice of the

Sec. 4-15

Watthour Meter

99

correct connection depends tential coil at point at

B

A

on the

situation. Generally, connection of the po-

preferred for high-current, low-voltage loads; connection

is

preferred for low-current, high-voltage loads.

is

The

difficulty in placing the connection of the potential coil is overcome compensated wattmeter, shown schematically in Fig. 4-41. The current coil consists of two windings, each winding having the same number of turns. One winding uses heavy wire that carries the load current plus the current for

in the

the potential

coil.

The other winding

uses thin wire and carries only the current

to the voltage coil. This current, however,

is

in a direction opposite to the current

heavy winding, causing a flux that opposes the main flux. The effect of therefore canceled out, and the wattmeter indicates the correct power.

in the i

p

is

Current Coil

*

oFigure 4-41

Diagram of

a compensated wattmeter in which the effect of the current

canceled by the current in the compensating winding.

in the potential coil is

4-15

o

WATTHOUR METER

The watthour meter

is

not often found in a laboratory situation but

used for the commercial measurement of electrical energy. In

fact,

it is it is

widely evident

wherever a power company supplies the industrial or domestic consumer with electrical energy. Figure 4-42 shows the elements of a single-phase watthour meter

in

schematic form.

The current is

coil is

connected across the

connected in

line.

Both

series

coils are

with the

wound on

line,

and the voltage

coil

a metal frame of special

A light aluminum disk is suspended in which causes eddy currents to flow in the disk. The reaction of the eddy currents and the field of the voltage coil creates a torque (motor action) on the disk, causing it to rotate. The developed torque is proportional to the fieldstrength of the voltage coil and the eddy currents in

design, providing

two magnetic

the air gap of the current-coil

circuits.

field,

Electromechanical Indicating Instruments

100

?

Figure 4-42

Chap. 4

Line

9

Elements of a single-phase watthour meter.

the disk which are in turn a function of the fieldstrength of the current

coil.

The number of rotations of the disk is therefore proportional to the energy consumed by the load in a certain time interval, and is measured in terms of kilowatthours (kWh). The shaft that supports the aluminum disk is connected by a gear arrangement to the clock mechanism on the front of the meter, providing a decimally calibrated readout of the number of kWh. Damping of the disk is provided by two small permanent magnets located opposite each other at the rim of the disk. Whenever the disk rotates, the permanent magnets induce eddy currents in it. These eddy currents react with the magnetic fields of the small permanent magnets, damping the motion of the disk. A typical single-phase watthour meter is shown in Fig. 4-43. Calibration of the watthour meter is performed under conditions of full rated load and 10 per cent of rated load. At full load, the calibration consists of adjustment of the position of the small permanent magnets until the meter reads correctly. At very light loads, the voltage component of the field produces a torque that is not directly proportional to the load. Compensation for the error is provided by inserting a shading coil or plate over a portion of the voltage coil, with the meter operating at 10 per cent of rated load. Calibration of the meter at these two positions usually provides satisfactory readings at all other loads.

disk.

The The

the shaft

floating-shaft watthour meter uses a unique design to suspend the

magnet at each end. The upper magnet of magnet in the upper bearing, and the lower magnet attracted to a magnet in the lower bearing. The movement thus

rotating shaft has a small is

of the shaft

attracted to a is

Sec. 4-16

Power-Factor Meters

Figure 4-43

Watthour meter

101

for industrial or

domestic application (courtesy West-

inghouse Electric Corporation).

floats

without touching either bearing surface, and the only contact with the

movement

is

that of the gear connecting the shaft with the gear train.

Measurements of energy in three-phase systems are performed with polyphase watthour meters. Each phase of the watthour meter has its own magnetic circuit and its own disk, but all the disks are mounted on a common shaft. The developed torque on each disk is mechanically summed and the total number of revolutions per minute of the shaft is proportional to the total three-phase energy consumed.

4-16 POWER-FACTOR METERS The power

factor, by definition, is the cosine of the phase angle between voltage and current, and power-factor measurements usually involve the determination of this phase angle. This is demonstrated in the operation of the crossed-coil power-factor meter. The instrument is basically an electrodynamometer movement, where the moving element consists of two coils, mounted on the same

102

Electromechanical Indicating Instruments

shaft but at right angles to each other. field

provided by the

The moving

field coil that carries

coils rotate in the

Chap. 4

magnetic

the line current.

The connections

for this meter in a single-phase circuit are shown in the diagram of Fig. 4-44. The field coil is connected as usual in series with the line and carries the line current. One coil of the movable element is connected in series with a resistor across the lines and receives its current from the applied potential difference. The second coil of the movable element is connected in series with an inductor across the lines. Since no control springs are used, the circuit

balance position of the movable element depends on the resulting torque de-

veloped by the two crossed

coils.

When

the movable element

is

in a balanced

by each element must be equal but each coil is a function of the current

position, the contribution to the total torque

of opposite sign.

The developed torque

in

and therefore depends on the impedance of that coil circuit. The torque is also proportional to the mutual inductance between each part of the crossed coil and the stationary field coil. This mutual inductance depends on the angular position of the crossed-coil elements with respect to the position of the stationary field coil. When the movable element is at balance, it can be shown that its angular displacement is a function of the phase angle between through the

coil

line current (field coil)

pointer,

which

is

and

The

line voltage (crossed coils).

connected to the movable element,

indication of the

calibrated directly in

is

terms of the phase angle or power factor.

Figure 4-44

Connections for a single-phase crossed-coil power-factor meter.

The polarized-vane power-factor meter of Fig. 4-45. This instrument

because

The

its

is

shown

in the construction sketch

used primarily in three-phase power systems,

operating principle depends on the application of three-phase voltage.

outside coil

of the system. it

is

is

The

the potential coil, which

is

connected to the three phase

to act like the stator of a three-phase induction

magnetic flux. The central of the phase

lines,

lines

application of three-phase voltage to the potential coil causes

and

coil,

or current

motor

coil, is

in setting

connected

this polarizes the iron vanes.

The

up a

in series

rotating

with one

polarized vanes

move

Sec. 4-17

Instrument Transformers

103

Damping Vane

Three-phase

Field

(Potential)

Current Coil

Moving Vane

Figure 4-45

Polarized-vane power-factor meter (courtesy General Electric

Company

Limited).

and take up the position that the rotating field has maximum. This position is an indication of the phase angle and therefore the power factor. The instrument may be used in single-phase systems, provided that a phase-splitting network (similar to that used in single-phase motors) is used to set up the required rotating magnetic in a rotating

magnetic

field

at the instant that the polarizing flux is

field.

Both types of power-factor meter are limited to measurement at comparlow frequencies and are typically used at the powerline frequency Hz). Phase measurements at higher frequencies often are more accurately (60 and elegantly performed by special electronic instruments or techniques. atively

\

4-17 INSTRUMENT

TRANSFORMERS

Instrument transformers are used to measure ac at generating stations, trans-

former

stations,

and

at transmission lines, in conjunction

with ac measuring

instruments (voltmeters, ammeters, wattmeters, VARmeters,

etc.).

Instrument

transformers are classified according to their use and are referred to as current transformers (CT) and potential transformers (PT).

Instrument transformers perform two important functions: They serve to much as the shunt or the

extend the range of the ac measuring instrument,

multiplier extends the range of a dc meter; they also serve to isolate the measuring

instrument from the high-voltage power

line.

104

The range of a dc ammeter may be extended by using a shunt the current under is

Chap. 4

Electromechanical Indicating Instruments

that divides

measurement between the meter and the shunt. This method

satisfactory for dc circuits, but in ac circuits current division

depends not

only on the resistances of the meter and the shunt but also on their reactances. Since ac measurements are to obtain great accuracy. its

made over a wide frequency range,

A CT

it

becomes

difficult

provides the required range extension through

transformation ratio and in addition produces almost the same reading re-

gardless of the meter constants (reactance and resistance) or, in fact, of the

number of instruments (within Isolation of the

connected in the

limits)

circuit.

measuring instrument from the high-voltage power

line is

important when we consider that ac power systems frequently operate at voltages It would be impractical to bring the high- voltage an instrument panel in order to measure voltage or current, not only because of the safety hazards involved but also because of the insulation problems connected with high-voltage lines running closely together in a confined space. When an instrument transformer is used, only the low-voltage wires from the transformer secondary are brought to the instrument panel and only low voltages exist between these wires and ground, thereby minimizing safety hazards

of several hundred kilovolts. lines directly to

and insulation problems.

Many

textbooks develop in detail the theory underlying the operation of

transformers. Here these instrument transformers are merely described and their

use in measurement situations

is

shown.*

Figure 4-46 shows a potential transformer, Fig. 4-47 shows a current transformer.

The potential transformer (PT)

is

used to transform the high voltage

of a power line to a lower value suitable for direct connection to an ac voltmeter

The usual secondary transformer

or the potential coil of an ac wattmeter. is

voltage

120 V. Primary voltages are standardized to accommodate the usual trans-

mission line voltages which include 2,400 V, 4,160 V, 7,200 V, 13.8 kV, 44 kV,

66 kV, and 220 kV. The

PT

is

rated to deliver a certain

power

to the secondary

load or burden. Different load capacities are available to suit individual applications; a general capacity

The PT must

is

200

VA

at a

satisfy certain design

frequency of 60 Hz.

requirements that include accuracy of

the turns ratio, small leakage reactance, small magnetizing current, and minimal

we may be working with very high primary between the primary and secondary windings must be able to withstand large potential differences, and the dielectric requirements are very high. In the usual case, the high-voltage coil is of a circular pancake voltage drop. Furthermore, since voltages, the insulation

construction, shielded to avoid localized dielectric stresses.

or coils are

wound on

The assembly *For

is

fuller

The low-voltage

a paper form and assembled inside the high-voltage

thoroughly dried and

oil

coil coil.

impregnated. The core and coil as-

treatment of ac machines and circuits, consult textbooks like the following:

Michael Liwshitz-Garik and Clyde C. Whipple, AC Machines, 2nd ed. (Princeton, N.J.: D. Van Nostrand Company, Inc., 1961), chaps. 2-5. Russell M. Kerchner and George F. Corcoran, Alternating Current Circuits, 4th ed.

(New York: John Wiley

&

Sons, Inc., 1961), pp. 291-317.

sembly

is

then mounted inside a steel case, which supports the high-voltage

terminals or porcelain bushings.

Developments

The

in the synthetic

case

is

then

filled

with an insulating

oil.

rubber industry have introduced the molded

oil and porcelain bushings shows a rubber-molded 25-kV potential trans-

rubber potential transformer, replacing the insulating in

some

applications. Figure 4-46

former suitable for outdoor use. This unit is less expensive than the conventional oil-filled PT, and since the bushings are made of molded rubber, porcelain breakage is eliminated. A white polarity dot is placed on the proper bushing on

Two stud-type secondary terminals are enclosed removable conduit box. The power rating of a potential transformer is based

the front of the transformer. in a

on considerations other than load capacity, for the reasons previously outlined. A typical load rating is 200 VA at 60 Hz for a transformer having a ratio of 2,400/120 V. For most metering purposes, however, the burden will be significantly less than 200 VA. The current transformer (CT) sometimes has a primary and always has a secondary winding. If there is a primary winding, it has a small number of turns. In most cases, the primary is only one turn or a single conductor connected in series with the load whose current is to be measured. The secondary winding

Electromechanical Indicating Instruments

106

Figure 4-47

Current transformer (courtesy Westinghouse Electric Corporation).

has a larger number of turns and coil.

Chap. 4

Often the primary winding

is

is

connected to a current meter or a relay

a single conductor in the form of a heavy

copper or brass bar running through the core of the transformer. Such a called a bar-type current transformer.

The

CT

designed to deliver a secondary current of 5 A.

secondary winding

An

transformer would have 160 turns on the secondary

The primary winding of the load circuit.

When

the secondary winding

ratio) ings.

and could

easily

break

down

The secondary winding of

may

is

its

is

coil. is

connected directly

in

open-circuited, the voltage

be very high (because of the step-up

the insulation between the secondary wind-

a current transformer should therefore always

be short-circuited, or connected to a meter or relay

should never have

CT

usually

800/ 5- A bar-type current

the current transformer

developed across the open terminals

is

coil.

secondary open while the primary

A is

current transformer

carrying current;

it

Sec. 4-17

Instrument Transformers

107

should always be closed through a current meter, relay coil,

coil,

or simply a short. Failure to observe this precaution

wattmeter current

may

cause serious

damage to either equipment or operating personnel. The current transformer shown in Fig. 4-47 consists of a core with the secondary winding encased in molded-rubber insulation. The window in the core allows for the insertion of one or more turns of the current-carrying highvoltage conductor.

The nominal

A

single

conductor constitutes a one-turn primary winding.

ratio of the transformer

turns ratio (since

is

given on the nameplate; this

more than one turn can be used

indicates that a primary current of 500 5

A

when

limits,

the secondary coil

A

not the

secondary current of ammeter. Within practical

will cause a

connected to a

5-

the current in the secondary winding

is

is

is

as the primary) but only

A

determined by the primary

excitation current and not by the secondary circuit impedance. Since the primary

current

determined by the load in the ac system, the secondary current

is

related to the primary current

This

is

by approximately the inverse of the

is

turns-ratio.

true within rather wide limits of the nature of the secondary burden.

Figure 4-48 indicates the use of instrument transformers in a typical mea-

surement application. This diagram

illustrates the

connection of instrument

transformers in a three-wire three-phase circuit, including two wattmeters, two voltmeters,

phase lines

and two ammeters. The potential transformers are connected across B, and phase lines C and B; the current transformers are in

A and

Instrument transformers in a three-phase measurement application. Pomarkings of the potential and current transformers are indicated by black

Figure 4-48 larity

squares.

108

Electromechanical Indicating Instruments

phase

lines

A and

Chap. 4

D. The secondary windings of the potential transformers are

connected to the voltmeter

coils and the potential coils of the wattmeters; the current transformer secondaries feed the ammeters and the current coils of the wattmeters.

The polarity markings on the transformers, indicated by a dot at the transformer leads, aid in making the correct polarity connections to the measuring instruments. At any given instant of the ac cycle, the dot-marked terminals have the same polarity and the marked wattmeter terminals must be connected to these transformer leads as shown.

REFERENCES 1.

Bartholomew, Davis, Electrical Measurements and Instrumentation, chap. Allyn and Bacon,

2.

5.

Boston:

Inc., 1963.

Geczy, Steven, Basic Electrical Measurements. Englewood

Cliffs, N.J.:

Prentice-Hall,

Inc., 1984. 3.

Jackson, Herbert W., Introduction to Electric Circuits, 5th Cliffs, N.J.:

4.

Prensky, Sol D., and Castellucis, Richard chaps. 2 and

5.

ed.,

chap.

19.

Englewood

Prentice-Hall, Inc., 1981.

3.

Englewood

Cliffs, N.J.:

L., Electronic

Instrumentation, 3rd ed.,

Prentice-Hall, Inc., 1982.

Stout, Melville B., Basic Electrical Measurements,

2nd

ed.,

chap.

17.

Englewood

Cliffs,

N.J.: Prentice-Hall, Inc., 1960.

PROBLEMS 1.

Determine the

resistor value required to use a

resistance of 125 CL for a

0-1-V

0-1 -mA meter with an

internal

meter.

What value of shunt resistance is required for using a 50- uA meter movement, with an internal resistance of 250 H, for measuring 0-500 mA? V3. What series resistance must be used to extend the 0-200-V range of a 20,000-fl/V meter to 0-2000 V? What power rating must this resistor have? 4. What will a 5,000-0/ V meter read on a 0-5-V scale when connected to the circuit 2.

of Fig. P4-4?

400 r-

25

V— —

5.

Draw

k£l

WA

n

I00k&s}v =

—

Figure P4-4

the schematic, including values, for an Ayrton shunt for a meter

having a full-scale deflection of

6.

?

movement

mA

and an internal resistance of 500 Cl to cover the current ranges of 10, 50, 100, and 500 mA. Many electronic voltage measuring instruments have a fixed input resistance of 1 1

MCI. Which settings of the range switch of the multimeter shown in Figs. 4-23 and 4-24 would have a higher input resistance than the typical electronic instrument for dc measurements?

Problems

Chap. 4

7.

The

50-kH

resistance of a

Figs. 4-23, 4-24,

R X R X 8.

109

and

10,000 range

100 range

is

resistor

is

is

measured using the multimeter shown in power is dissipated in the resistor if the power is dissipated in the resistor if the

How much used? How much

4-27.

used?

Assume

that the zero control

is set

to

its

midpoint.

A series-type ohmmeter, designed to operate with a 6-V battery, has a circuit diagram shown in Fig. 4-21. The meter movement has an internal resistance of 2,000 fl and requires a current of 100 uA for full-scale deflection. The value of/?, is 49 kft. (a) Assuming the battery voltage has fallen to 5.9 V, calculate the value of R 2 as

required to zero the meter.

Under

(b)

to the

the conditions mentioned in part (a), an unknown resistor is connected meter causing a 60 per cent meter deflection. Calculate the value of the

unknown 9.

How

shown

section 10.

What

11.

Why

resistance.

low must the battery voltage of the 1.5-V is

in Fig. 4-27(a) fall before

a transfer instrument? sensitivity

is

(ohms per

Why

is

it is

cell in

the multimeter

ohmmeter

impossible to zero the meter?

an electrodynamometer a transfer instrument?

volt) of the ac scales of a

multimeter

less

than the dc

section? 12.

meant by a waveform error? Which ac meters are most likely form of error? What are the advantages of a thermocouple meter? What is the midscale point of a 10- A full-scale thermocouple meter?

What

by 13. 14. 15.

is

to be affected

this

The circuit diagram of Fig. 4-32 shows a full-wave rectifier ac voltmeter. The meter movement has an internal resistance of 250 fl and requires 1 mA for full deflection. The diodes each have a forward resistance of 50 fl and infinite reverse resistance. Calculate (a) the series resistance required for full-scale meter deflection when 25 V rms

is

applied to the meter terminals, and (b) the ohms-per-volt rating of this ac

voltmeter. 16. Calculate the indication of the

a peak value of 20 17. If

V

is

an electrodynamometer

W, what

is

meter

in Prob. 15

when

a triangular

waveform with

applied to the meter terminals. is

used to measure power with a full-scale reading of 100

the one-quarter scale reading?

CHAPTER 5

BRIDGES AND THEIR APPLICATION

5-1

INTRODUCTION

Bridge circuits are extensively used for measuring component values, such as resistance, inductance, or capacitance,

and of other

circuit

parameters directly

derived from component values, such as frequency, phase angle, and temperature. Since the bridge circuit merely compares the value of an to that of

an accurately known component

curacy can be very high indeed. This

is

unknown component

(a standard), its

measurement

ac-

so because the readout of this comparison

measurement, based on a null indication at bridge balance, is essentially independent of the characteristics of the null detector. The measurement accuracy is

therefore directly related to the accuracy of the bridge components, not to

that of the null indicator

itself.

This chapter introduces some of the basic dc bridges. Starting with the portable test instruments,

we present

the Wheatstone bridge for the measurement

of dc resistance, the Kelvin bridge for low-resistance measurements, and the test set for resistance testing field,

we

measurement of very high

5-2

of cables. In the high-precision test and calibration

introduce the principle of the guarded Wheatstone bridge and the resistances.

WHEATSTONE BRIDGE 5-2.1 Basic Operation Figure 5- 1(a)

is

bridge. Its operation

110

a photograph of a portable, self-contained Wheatstone

is

based on the fundamental diagram of Fig.

5- 1(b).

The

Figure 5-1

Laboratory-type Wheatstone bridge used for the precision measurement

of resistances ranging from fractions of an switches the ratio arms in decade steps. resistance of the standard

arm

(courtesy

ohm

to several megohms. The ratio control The remaining four step switches set the Beckman Instruments, Inc., Cedar Grove

Operations).

bridge has four resistive arms, together with a source of

emf

(a battery)

and a

null detector, usually a galvanometer or other sensitive current meter.

The

current through the galvanometer depends on the potential difference between points c

and

d.

The bridge

is

said to be balanced

when

the potential difference

Bridges and Their Application

112

across the galvanometer

V

0

is

the voltage from point

d

so that there

when

nometer. This condition occurs

is

Chap. 5

no current through the galva-

the voltage from point c to point a equals

to point a; or

by referring to the other battery terminal,

when

the voltage from point c to point b equals the voltage from point

point

b.

Hence

the bridge

I If the

galvanometer current

d

to

balanced when

is

X

R =

I2 R 2

X

(5-1)

zero, the following conditions also exist:

is

=

7 >

= r^tt,

(5 " 2)

=

(5 " 3)

and

h= Combining Eqs.

and

(5-1), (5-2),

(5-3)

R + R x

*7T^

and simplifying, we obtain

3

(5-4)

R + R4 2

from which

Equation (5-5)

is

the well-known expression for balance of the Wheatstone bridge.

from Eq.

(5-5).

Hence,

if

may

have known values, the fourth

If three of the resistances

R4

is

unknown

the

be determined

Rx

resistor, its resistance

can be

expressed in terms of the remaining resistors as follows:

Rx = * Resistor

^

3

is

called the standard

3

arm of

^

(5-6)

the bridge, and resistors

R

2

and

R

x

are called the ratio arms.

The measurement of

the

unknown

resistance

Rx

is

independent of the

characteristics or the calibration of the null-deflecting galvanometer, provided

that the null detector has sufficient sensitivity to indicate the balance position

of the bridge with the required degree of precision.

5-2.2

Measurement Errors

The Wheatstone bridge

is widely used for precision measurement of refrom approximately 1 Cl to the low megohm range. The main source of measurement error is found in the limiting errors of the three known resistors. Other errors may include the following:

sistance

(a)

Insufficient sensitivity of the null detector. This

more

fully in Sec. 5-2.3.

problem

is

discussed

Wheatstone Bridge

Sec. 5-2

(b)

Changes

113

arms due

in resistance of the bridge

to the heating effect of

the current through the resistors. Heating effect

(PR)

of the bridge

arm currents may change the resistance of the resistor in question. The rise in temperature not only affects the resistance during the actual measurement, but excessive currents may cause a permanent change in resistance values. This may not be discovered in time and subsequent measurements could well be erroneous. The power dissipation in the bridge arms must therefore be computed in advance, particularly when low-resistance values are to be measured, and the current

must be

limited to a safe value. (c)

Thermal emfs also cause

in the bridge circuit or the

problems when low-value

galvanometer circuit can

resistors are being

measured.

To

prevent thermal emfs, the more sensitive galvanometers sometimes have

copper

coils

and copper suspension systems to avoid having dissimilar

metals in contact with one another and generating thermal emfs. (d) Errors

due to the resistance of leads and contacts exterior to the actual

bridge circuit play a role in the measurement of very low-resistance values.

These errors may be reduced by using a Kelvin bridge

(see

Sec. 5-3).

5-2.3 Thevenin Equivalent Circuit

To determine whether to detect

or not the galvanometer has the required sensitivity

an unbalance condition,

it is

necessary to calculate the galvanometer

current. Different galvanometers not only

may

may have

deflection (current sensitivity), but they also sistance. It

make

is

require different currents per unit

a different internal re-

impossible to say, without prior computation, which galvanometer

more

an unbalance condition. This sensitivity can be calculated by "solving" the bridge circuit for a small unbalance. The solution is approached by converting the Wheatstone bridge of Fig. 5-1 to its Thevenin equivalent. will

Since

the bridge circuit

we

are interested in the current through the galvanometer, the

Thevenin equivalent c and d in Fig. 5-1.

The

first

sensitive to

determined by looking into galvanometer terminals steps must be taken to find the Thevenin equivalent:

circuit

Two

is

step involves finding the equivalent voltage appearing at terminals c

and d when the galvanometer

is

removed from the

circuit.

The second

involves finding the equivalent resistance looking into terminals c and the battery replaced by Fig. 5- 1(b) is

redrawn

its

For convenience, the

internal resistance.

d,

step

with

circuit of

in Fig. 5-2(a).

The Thevenin, or and we can write

open-circuit, voltage

E = E — Ead = cd

ac

is

I

]

found by referring to Fig.

R — ]

I2 R 2

5-2(a),

'

114

Bridges and Their Application

Chap. 5

1

I

WAr

AAAA/

1

od

Co-

i

'WW

.

b

AVA

—

R4

(b)

R TH AAAAr TH Figure

(g)r

5-2

Application

of

Thevenin's

theorem to the Wheatstone bridge, (a) Wheatstone bridge configuration, (b) Thev-

(

enin resistance looking into terminals c and d. (c)

Complete Thevenin

circuit,

with the

galvanometer connected to terminals c and

(0

d.

where

I

x

— R

E = — —— ~\~

i

R$

and I2

E

= R

2

H~

R4

Therefore

This

is

the voltage of the Thevenin generator.

The

Thevenin equivalent circuit is found by looking back and d and replacing the battery by its internal resistance. The 5-2(b) represents the Thevenin resistance. Notice that the internal

resistance of the

into terminals c circuit of Fig.

resistance,

Rb

,

of the battery has been included in Fig. 5-2(b). Converting this

Wheatstone Bridge

Sec. 5-2

115

more convenient form requires use of the delta-wye transformation theorem. Readers interested in this approach should consult texts on circuit circuit into a

analysis

where

this

theorem

derived and applied.* In most cases, however,

is

the extremely low internal resistance of the battery can be neglected and this simplifies the reduction of Fig. 5 -2(a) to its Thevenin equivalent considerably.

we

Referring to Fig. 5-2(b),

a and b

when

see that a short circuit exists between points

the internal resistance of the battery

Thevenin resistance, looking into terminals c and

assumed

is

to be 0 ft.

*™ = srrk + The Thevenin

by Eq.

sistance given

emf

This

(5-8).

the null detector

Thevenin equivalent

is

Example

5-1

is

described by Eq. (5-7) and an internal re-

shown

in the circuit of Fig. 5-2(c).

now connected

is

circuit, the

/

where Ig

(5 - 8 >

equivalent of the Wheatstone bridge circuit therefore reduces to

a Thevenin generator with an

When

The

then becomes

d,

to the output terminals of the

galvanometer current

=

is

found to be

^Z*

the galvanometer current and

Rg

(5.9)

its

resistance.

Figure 5-3(a) shows the schematic diagram of a Wheatstone bridge with values of the bridge elements as shown.

The galvanometer has

The

battery voltage

is

5

a current sensitivity of 10

V and its internal mm/jLiA and an

resistance negligible. internal resistance of

100ft. Calculate the deflection of the galvanometer caused by the 5-ft unbalance in

arm BC. Solution

Bridge balance occurs

BC as

if

arm

a resistance of 2,005

BC

has a resistance of 2,000

ft.

The diagram shows arm ft). The first step

representing a small unbalance (< 2,000

ft,

in the solution consists of converting the bridge circuit into its circuit.

Since

equivalent difference voltage.

we

is determined with respect to galvanometer terminals B and D. The potential from B to D, with the galvanometer removed from the circuit, is the Thevenin

Using Eq.

Eth

(5-7),

we

obtain

— EAD

= ,

The second

s

100 5Vx(,100 100 + 200 2.77

1,000

1,000

B

Herbert

and D, and replacing the battery with

W.

Jackson, Introduction

Prentice-Hall, Inc., 1981), pp. 448

jf.

+

2,005.

mV

step of the solution involves finding the equivalent

into terminals

*

Thevenin equivalent

are interested in finding the current in the galvanometer, the Thevenin

its

to Electric Circuits,

Thevenin

resistance, looking

internal resistance. Since the

5th ed. (Englewood

Cliffs,

N.J.

—

|

«

116

Bridges and Their Application

Chap. 5

lOOOft

5V

—

D

(a)

Wheatstone Bridge

(b)

Calculation of the

2005 SI

m— —vwv— —iooon 100ft

A i

I

Thevenin

Resistance

—vwv —VWv i

!

= 730 n

R TH AAAA/

o I

g

=3.34^A (c)

Thevenin Equivalent Circuit

2.77

Rg =

mV^"

I00&

Galvanometer Figure 5-3

from which we

is

the simplified Thevenin approach.

0

fi,

the circuit

is

represented by the configuration of Fig. 5-3(b)

find

100

R th = The Thevenin equivalent

—X

200

300

circuit

is

+

1,000 X 2,005 ^rzrz 3,005

given in Fig. 5-2(c).

connected to the output terminals of the equivalent

galvanometer

= IOmm/^.A

Calculation of galvanometer deflection caused by a small unbalance in

arm BC, using battery resistance

sensitivity

=

730

When

H

the galvanometer

circuit, the current

is

E TH 8

The galvanometer

R T„ +

deflection

d

2.77

= R.

730

3.34 llA

X

mV

a +

100

_

*

a

is

=

10

mm =

uA

33.4

mm

is

now

through the

Sec. 5-3

Kelvin Bridge

At

117

this point the merit of the

Thevenin equivalent

circuit for the solution

of an unbalanced bridge becomes evident. If a different galvanometer

is

used

(with a different current sensitivity and internal resistance), the computation of its

deflection

is

very simple, as

galvanometer sensitivity

is

clear

from

Fig.

5-3(c).

Conversely,

the

if

we can solve for the unbalance voltage needed mm). This value is of interest when we want to

given,

is

to give a unit deflection (say

1

determine the sensitivity of the bridge to unbalance, or in response to the question: "Is the galvanometer selected capable of detecting a certain small unbalance?"

The Thevenin method cases

is

Example

is

used to find the galvanometer response, which in most

of prime interest. 5-2

The galvanometer of Example

5-1

is

replaced by one with an internal resistance of 500

and a current sensitivity of 1 observed on the galvanometer

mm/oA.

detecting the 5-Cl unbalance in

arm

Assuming

that a deflection of

mm

1

fl

can be

new galvanometer

is

capable of

Since the bridge constants have not been changed, the equivalent circuit

is

again rep-

scale,

determine

BC of Fig.

if this

5-3(a).

Solution

resented by a Thevenin generator of 2.77

new galvanometer

is

now connected

mV

and a Thevenin resistance of 730

to the output terminals, resulting in a

The

fl.

galvanometer

current 2.77

730

The galvanometer

mA

n +

500

deflection therefore equals 2.25

n u-A

=

uA

2.25

X

1

mm/u-A =

2.25

mm,

indicating that this galvanometer produces a deflection that can be easily observed.

The Wheatstone bridge is limited to the measurement of resistances ranging from a few ohms to several megohms. The upper limit is set by the reduction in sensitivity to unbalance, caused by high resistance values, because in this case the equivalent Thevenin resistance of Fig. 5-3(c) becomes high, thus reducing the galvanometer current. The lower limit is set by the resistance of the connecting leads and the contact resistance at the binding posts. The resistance of the leads could be calculated or measured, and the final result modified, but contact resistance is very hard to compute or measure. For low-resistance measurements, therefore, the Kelvin bridge

5-3 KELVIN

is

generally the preferred instrument.

BRIDGE

5-3.1 Effects of Connecting Leads

The Kelvin bridge

is

a modification of the Wheatstone bridge and provides

greatly increased accuracy in the

measurement of low-value

resistances, generally

118

below

1

ft.

Bridges and Their Application

Chap. 5

Ry

represents

Consider the bridge circuit shown in Fig.

R

the resistance of the connecting lead from

nections are possible, to point

m

to

3

or to point

connected to point m, the resistance

Ry

n.

5-4,

where

R x Two .

When

galvanometer con-

the galvanometer

of the connecting lead

is

added

is

to the

unknown R x resulting in too high an indication for R x When connection is made to point n, R y is added to bridge arm R and the resulting measurement of R x will be lower than it should be, because now the actual value of R is .

,

3

3

nominal value by resistance R y If the galvanometer is connected to a point p, in between the two points m and n, in such a way that the ratio of the resistances from n to p and from m to p equals the ratio of resistors R and R 2 we can write higher than

its

.

,

,

The balance equation

for the bridge yields

R x + R np =

^(* + 3

Substituting Eq. (5-10) into Eq. (5-11),

we

R mp )

(5-11)

obtain

(5-12)

which reduces

to

Rx = Equation (5-13) bridge and

it

from point

m

is

R

the usual balance equation developed for the Wheatstone

indicates that the effect of the resistance of the connecting lead to point n has been eliminated

to the intermediate position p.

Figure

5-4

Wheatstone

showing resistance point

(5-13)

m

to point n.

Ry

bridge

circuit,

of the lead from

by connecting the galvanometer

Sec. 5-3

119

Kelvin Bridge

Figure 5-5

Basic

Kelvin double bridge

circuit.

This development forms the basis for construction of the Kelvin double bridge,

commonly known

as the Kelvin bridge.

5-3.2 Kelvin Double Bridge

The term double bridge is used because the circuit contains a second shown in the schematic diagram of Fig. 5-5. This second

of ratio arms, as

set

set

of arms, labeled a and b in the diagram, connects the galvanometer to a point

p

at the appropriate potential

the yoke resistance

R y An .

and b is the same as the The galvanometer indication

*1+ *2

when

and

n,

initially established

ratio of a

the potential at p, or

m

between

E = kl

ratio of will

R


*J

-f

yields

R

2

(a

2

+

b

+

yields

Mi + £

£

2

(a

2

+

^+ R 6

bR y

y)

(a

+

+

R,)

{a

+

b

(fl

+

H

+

so that

R Using the

+

'~-rT

(a

+

b

condition that

initially established

(5 -' 6)

{T2

a/b

b)

= R /R l

2

,

we

see that Eq.

(5-16) reduces to the well-known relationship

Equation (5-17)

the usual working equation for the Kelvin bridge.

is

that the resistance of the yoke has

no

effect

It

indicates

on the measurement, provided that

two sets of ratio arms have equal resistance ratios. The Kelvin bridge is used for measuring very low resistances, from approximately 1 ft to as low as 0.00001 ft. Figure 5-6 shows the simplified circuit diagram of a commercial Kelvin bridge capable of measuring resistances from 10 ft to 0.00001 ft. In this bridge, resistance R 3 of Eq. (5-17) is represented by the variable standard resistor in Fig. 5-6. The ratio arms (R^ and R 2 ) can usually the

be switched in a number of decade steps. Contact potential drops in the measuring circuit

and

may

cause large errors

to reduce this effect the standard resistor consists of nine steps of 0.001 ft

each plus a calibrated manganin bar of 0.0011 total resistance of the

R arm 3

ft

with a sliding contact. The

amounts to 0.0101 of 0.0011 ft by the sliding

therefore

steps of 0.001 ft plus fractions

ft

and

is

contact.

variable in

When

both

contacts are switched to select the suitable value of standard resistor, the voltage

drop between the ratio-arm connection points is changed, but the total resistance around the battery circuit is unchanged. This arrangement places any contact resistance in series with the relatively high-resistance values of the ratio arms,

and the contact resistance has

The

ratio

R /R x

standard resistance

unknown

resistance

nificant figures,

is

negligible effect.

should be so selected that a relatively large part of the

2

used in the measuring

Rx

is

circuit.

In this

way

the value of

determined with the largest possible number of

and the measurement accuracy

is

improved.

sig-

Bridges and Their Application

122

5-4

Chap. 5

GUARDED WHEATSTONE BRIDGE 5-4.1

Guard Circuits

The measurement of extremely high

resistances,

such as the insulation

on the order beyond the capability of the ordinary dc Wheatstone bridge. One of the major problems in high-resistance measurements is the leakage that occurs over and around the component or specimen being measured, or over the binding posts by which the component is attached to the instrument, or within the instrument itself. These leakage currents are undesired because they can enter the measuring circuit and affect the measurement accuracy to a considerable extent. Leakage currents, whether inside the instrument itself or associated with the test specimen and its mounting, are particularly noticeable in high-resistance measurements where high voltages are often necessary to resistance of a cable or the leakage resistance of a capacitor (often

of several thousands of megohms),

is

obtain sufficient deflection sensitivity. Also, leakage effects are generally variable

from day to day, depending on the humidity of the atmosphere. The effects of leakage paths on the measurement are usually removed by some form of guard circuit. The principle of a simple guard circuit in the R x arm of a Wheatstone bridge is explained with the aid of Fig. 5-7. Without a along the insulated surface of the binding post guard circuit, leakage current adds to current Ix through the component under measurement to produce a total circuit current that can be considerably larger than the actual device current. A guard wire, completely surrounding the surface of the insulated post, intercepts this leakage current and returns it to the battery. The guard must be carefully

Return to Battery

From Bridge

Figure 5-7

^

-

JJ

^

Leakage Current Intercepted by Guard Wire

Circuit

Simple guard wire on the

eliminates surface leakage.

Rx

terminal of a guarded Wheatstone bridge

Guarded Wheatstone Bridge

Sec. 5-4

123

Figure

Guarded

5-8

terminal

returns

leakage current to the battery.

placed so that the leakage current always meets some portion of the guard wire

and

is

prevented from entering the bridge

circuit.

In the schematic diagram of Fig. 5-8 the guard around the

Rx

binding

by a small circle around the terminal, does not touch any part of the bridge circuitry and is connected directly to the battery terminal. The principle of the guard wire on the binding post can be applied to any internal part of the bridge circuit where leakage affects the measurement; we then speak post, indicated

of a guarded Wheatstone bridge.

5-4.2 Three-terminal Resistance

To

avoid the effects of leakage currents external to the bridge circuitry,

the junction of ratio arms

RA

and

RB

is

usually brought out as a separate guard

terminal on the front panel of the instrument. This guard terminal can be used

shown

The high mounted on two insulating posts that are fastened to a metal plate. The two main terminals of the resistor are connected to the R x terminals of the bridge in the usual manner. The third terminal of the resistor is the common point of resistances R and R 2 which represent the leakage paths from the main terminals along the insulating posts to the metal plate, or guard. The guard is to connect a so-called three-terminal resistance, as

resistance

in Fig. 5-9.

is

,

x

connected to the guard terminal on the front panel of the bridge, as indicated in the

RA

,

schematic of Fig.

but since R^

is

very

This connection puts

5-9.

much

Similarly, leakage resistance

resistance of

R

2

effect is a slight

is

so

much

R

larger than 2

is

RA

in parallel

,

its

R

{

in parallel

with ratio arm

shunting effect

is

negligible.

with the galvanometer, but the

higher than that of the galvanometer that the only

reduction in galvanometer sensitivity.

The

effects

of external

leakage paths are therefore removed by using the guard circuit on the threeterminal resistance.

R and R 2 would be and the measured value of R x would be considerably in error. Assuming, for example, that the unknown is 100 Mft and that the leakage resistance from each terminal to the guard is also 100 Mft, resistance R x would be measured as 67 Mft, an error of approximately 33 per cent. If the

guard circuit were not used, leakage resistance

directly across

Rx

x

124

Bridges and Their Application

Three-terminal resistance

(a)

Three-terminal Resistance

(b)

Resistance Multiplier

Guarded bridge

circuit

Three-terminal resistance, connected to a guarded high-voltage

Figure 5-9

Chap. 5

megohm

bridge.

Megohm

5-4.3

A

Bridge

-

commercial high- voltage

megohm

bridge

the various controls can easily be identified.

instrument

is

the variable ratio

arm

RB

dial to the right of the large ratio dial

The

is

shown

in Fig. 5-10,

of Fig. 5-9.

The

resistance multiplier

corresponds to standard resistor

the circuit diagram and provides for multiplication of the ratio in a

decade 10

V

steps.

The dc supply is

is

in

adjustable over several increments from

made

to connect

an external generator. The

basically a dc amplifier with output meter

sensitivity to detect small is

is

Rc

number of

and the necessary R A and when measuring brought out as a front panel guard terminal, to be used

null detector

RB

voltage

to 1,000 V, while provision

where

large dial in the center of the

unbalance voltages. The junction of ratio arms

a three-terminal resistance.

The high-voltage megohm bridge high-resistance measurements. Other

is only one of the instruments used for methods may include the use of the well-

AC

Sec. 5-5

Bridges and Their Application

known megger

to

direct deflection

method

5-5

125

measure the insulation resistance of

method of

electrical

testing insulation samples,

machinery, the

and the

loss-of-charge

for checking the leakage resistance of capacitors.*

AC BRIDGES AND THEIR APPLICATION 5-5.1 Conditions for Bridge Balance

The

ac bridge

is

a natural outgrowth of the dc bridge and in

consists of four bridge arms, a source of excitation,

and a

its

basic

form

null detector.

The

power source supplies an ac voltage to the bridge at the desired frequency. For measurements at low frequencies, the power line may serve as the source of excitation; at higher frequencies,

Figure 5-10

an oscillator generally supplies the excitation

Commercial high-voltage megohm

bridge, used for the

resistances in the terra-ohm range (courtesy General

* Cf.

Melville B. Stout, Basic Electrical Measurement,

Prentice-Hall, Inc., 1960), pp. 126-33.

measurement of

Radio Company).

2nd

ed.

(Englewood

Cliffs,

N.J.:

Bridges and Their Application

126

Chap. 5

fa Z4 Figure

form

General

5-11

of

the

ac

bridge.

voltage.

The

null detector

must respond

and

to ac unbalance currents

in its

cheapest (but very effective) form consists of a pair of headphones. In other applications, the null detector

may

consist of an ac amplifier with an output

meter, or an electron ray tube (tuning eye) indicator.

The

general form of an ac bridge

Z Z

is

shown

in Fig. 5-11.

The

four bridge

and Z 4 are indicated as unspecified impedances and the detector is represented by headphones. As in the case of the Wheatstone bridge for dc measurements, the balance condition in this ac bridge is reached when the

arms Z„

2,

3

,

detector response null response

The

is

is

zero, or indicates a null. Balance adjustment to obtain a

made by varying one

or

more of

general equation for bridge balance

the bridge arms.

is

obtained by using complex

notation for the impedances of the bridge circuit. (Boldface type indicate quantities in

The condition

or admittances as well as voltages or currents. requires that the potential difference from

be the case

B

to C, in

when

is

used to

complex notation.) These quantities may be impedances

the voltage drop from

A B

to

C

in Fig. 5-11

A

to

for bridge balance

be zero. This will

equals the voltage drop from

both magnitude and phase. In complex notation we can write

Eba

—

or

IjZj

—

I2

Z

(5-18)

2

For zero detector current (the balance condition), the currents are

=

I,

Z,

+ Z

(5-19) 3

and

E

=

I2

Z,

+ Z

(5-20) 4

— —"

Substitution of Eqs. (5-19) and (5-20) into Eq. (5-18) yields. j

or

when

'

)

*ifiS(^ (5-21)

using admittances instead of impedances.

Y,Y 4

= YY 2

3

(5-22)

AC

Sec. 5-5

127

Bridges and Their Application

Equation (5-21)

is

the most convenient form in most cases and

is

the general

equation for balance of the ac bridge. Equation (5-22) can be used to advantage

when

dealing with parallel components in bridge arms.

Equation (5-21)

states that the

product of impedances of one pair of

opposite arms must equal the product of impedances of the other pair of opposite

arms, with the impedances expressed in complex notation. If the impedance written in the form

Z = Z

Z0, where

Z

phase angle of the complex impedance, Eq. (5-21) can be rewritten (Z, Z0.)

(Z4 Z0 4 )

is

represents the magnitude and 0 the

= (Z

in the

Z0 2 )(Z 3 Z0 3 )

2

form

(5-23)

Since in multiplication of complex numbers the magnitudes are multiplied and the phase angles added, Eq. (5-23) can also be written as

Z,Z4

+

Z(0,

0 4)

= ZZ 2

3

Z(0 2

+

0 3)

(5-24)

Equation (5-24) shows that two conditions must be met simultaneously when The first condition is that the magnitudes of the imped-

balancing an ac bridge.

ances satisfy the relationship

_____

.

Z,Z4 = or, in

ZZ 2

(5-25)

3

words:

The products of the magnitudes of the opposite arms must be

The second condition

equal.

requires that the phase angles of the impedances satisfy

the relationship

,

A Z0,

+

Z0 4

=

Z0 2

+

Z0 3

I

ge

j

(5-26)

*

Again, in words:

The sum of the phase angles of the opposite arms must be equal

5-5.2 Application of tho Balanco Equations

The two balance conditions expressed in Eqs. (5-25) and (5-26) can be when the impedances of the bridge arms are given in polar form, with both magnitude and phase angle. In the usual case, however, the component applied

values of the bridge arms are given, and the problem is solved by writing the balance equation in complex notation. The following examples illustrate the

procedure.

Example 5-3

The impedances of

the basic ac bridge of Fig. 5-11 are given as follows:

=

100

H

Z 80° (inductive impedance)

Z =

250

H

(pure resistance)

Z,

2

128

Bridges and Their Application

=

Zj

Chap. 5

c

400

fl

Z30 (inductive impedance)

Z 4 = unknown Determine the constants of the unknown arm.

Solution

The

first

condition for bridge balance requires that

= ZZ

Z,Z4

The second condition

(5-25)

3

known components and

Substituting the magnitudes of the

z< =

2

¥ — Z,Z,

X

250

=

400

i«r-

solving for

Z

4,

we

obtain

„ = U)0OQ ,

for bridge balance requires that the

sums of the phase angles of

opposite arms be equal or

e Substituting the

known phase 04

Hence

the

=

02

+

x

+

=

e,

03

-

=

0,

Z4 we

e3

(5-26)

angles and solving for 04

unknown impedance Z 4 can be

indicating that

+

e2

+

0

30

,

we

obtain

- 80= -

50°

written in polar form as

1,000

0

L -50°

are dealing with a capacitive element, possibly consisting of a series

combination of a resistor and a capacitor.

The problem becomes

slightly

more complex when

the

component values

of the bridge arms are specified and the impedances are to be expressed in

complex notation. In

this case, the inductive or capacitive reactances

be calculated when the frequency of the excitation voltage

is

known,

as

can only

Example

5-4 shows.

Example 5-4

The ac bridge of Fig. 5-11 is in balance with the following constants: arm AB, R = 450 CL: arm BC, R = 300 Cl in series with C = 0.265 uE; arm CD, unknown; arm DA, R = 200 H in series with L = 15.9 mH. The oscillator frequency is 1 kHz. Find the constants of arm CD. Solution

The general equation

for bridge balance states that

Z,Z 4 Z,

= R =

Z = R 2

450

= Z,Z

(5-21)

3

n

j/aiC

=

(300

-

;600)

f)

Comparison Bridges

Sec. 5-6

129

Z = R + jvL = 3

(200

+ ylOO)

£1

Z4 = unknown Substituting the

known

values in Eq. (5-21) and solving for the

z> _ This result indicates that Z4 at

a frequency of

obtain

5-6

L =

23.9

1

450

x

(200

+;i00)

_

(30o-y6oo)

unknown

yields

+jma

a pure inductance with an inductive reactance of 150

is

kHz. Since the inductive reactance

XL =

27r/L,

we

solve for

Cl

L and

mH.

COMPARISON BRIDGES Comparison Bridge

5-6.1 Capacitance

form the ac bridge can be used for the measurement of an or capacitance by comparing it with a known inductance or capacitance. A basic capacitance comparison bridge is shown in Fig. 5-12. The ratio arms are both resistive and are represented by and R 2 The standard arm consists of capacitor Cs in series with resistor R s where Cs is a high-quality standard capacitor and R sl variable resistor. Cx represents the unknown capacitance and R x is the leakage resistance of the capacitor. To write the balance equation, we first express the impedances of the four bridge arms in complex notation and we find that In

its

basic

unknown inductance

.

,

s

R

2;

Z = 3

R,

-

J

= Rx -

a)C/

a)Cx

Substituting these impedances in Eq. (5-21), the general equation for bridge balance,

we

obtain

0^

Unknown Figure 5-12

Capacitance comparison bridge.

Bridges and Their Application

130

Chap. 5

which can be expanded to

=

Two complex numbers

- Ri-^

R2R,

when both

are equal

(5-28)

R,R X

= RR 2

Rx =

or

S

and

their real terms

we

imaginary terms are equal. Equating the real terms of Eq. (5-28),

their

obtain

r£

(5-29)

Equating the imaginary terms of Eq. (5-28), we obtain

(5-30)

Equations (5-29) and (5-30) describe the two balance conditions met simultaneously and they also show the two unknowns Cx and

known

terms of the

in

To

satisfy

elements in

Rx

must be

expressed

bridge components.

both balance conditions, the bridge must contain two variable configuration.

its

that

Any two

chosen, although in practice capacitor

of fixed value and

is

equations shows that

of the available four elements could be

C

s

is

a high-precision standard capacitor

not available for adjustment. Inspection of the balance

R

s

does not appear in the expression for

eliminate any interaction between the two balance controls,

choice as a variable element.

We

further accept that

R

l

is

R

s

Cx is

Hence

.

to

an obvious

the second variable

element, as indicated in Fig. 5-12. Since

we

are measuring an

be very small, the

R

{

is

first

unknown

capacitor whose resistive effects could

adjustment should be

made

minimum sound

in the

therefore adjusted for

for the capacitive term,

and

headphones. In most cases,

the sound will not altogether disappear, because the second balance condition

has not yet been met. Hence the sound the

two

is

made

resistors

is

R

s

is

adjusted for balance of the resistive term and

to decrease further. It

achieve the true balance condition. clear

when we

is

found that alternate adjustment of

necessary to produce zero output in the headphones and to

realize that

The need

any change

in

for alternate adjustment

R

x

becomes

not only affects the capacitive

balance equation but also the resistive balance equation, since

R

x

appears in

both expressions.

The process of alternate manipulation of R and {

balancing procedure for ac bridges and

is

R

s

is

typical of the general

said to cause convergence of the balance

point. It should also be noted that the frequency of the voltage source does not

enter either of the balance equations and the bridge

independent of the frequency of the applied voltage.

is

therefore said to be

Comparison Bridges

Sec. 5-6

131

E

Chap. 6

Reference Section

^Meter

Section-^

dc Input

0-I000 V

Feedback

Range Selector

Block diagram of the dc standard /differential voltmeter

Figure 6-17 of operation.

The meter

in the differential

mode

section indicates the voltage balance between the reference section and

the dc amplifier section.

The range

selector

on the front panel of the instrument controls both the feedback

voltage and the voltage that

output in such a

way

is

applied in opposition to the reference divider

that the 1-V capability of the reference supply

is

never

exceeded.

In the third mode of operation, the instrument is connected as a voltmeter and the dc amplifier acts as a buffer stage to provide high-input impedance to the unknown voltage source. The input voltage is amplified, and the dc output voltage is applied directly to the meter circuit. The meter circuit incorporates a feedback-controlled amplifier and allows selection of its sensitivity by adjustment of the feedback loop through a front panel control, marked sensitivity. This feature provides for extreme sensitivity of the meter circuit, often on the order of 1 fxV full-scale deflection. Meaningful measurements at the very high

Sec. 6-7

Digital

sensitivities,

169

Voltmeters

however, are

difficult to

make because

of the problems of noise

generation and pickup.

An

ac-to-dc converter can be incorporated in the instrument to provide

the capability of ac voltage

6-7 DIGITAL

measurement by potentiometric methods.

VOLTMETERS

6-7.1 General Characteristics

(DVM) displays measurements of dc or ac voltages numerals instead of a pointer deflection on a continuous scale as in analog devices. Numerical readout is advantageous in many applications because The

digital voltmeter

as discrete

it

reduces

human

reading and interpolation errors, eliminates parallax error,

increases reading speed,

and often provides outputs

in digital

form

suitable for

further processing or recording.

The

DVM

is

a versatile and accurate instrument that can be used in

many

laboratory measurement applications. Since the development and perfection of

power requirements, and cost of the DVM have been drastically reduced so that DVMs can actively compete with conventional analog instruments, both in portability and price. The DVM's outstanding qualities can best be illustrated by quoting some typical operating and performance characteristics. The following specifications do not all apply to one particular instrument, but they do represent valid information on the present state of the art: integrated circuit (IC) modules, the size,

(a)

Input range: from ±1.000000

V

to

±1,000.000 V, with automatic

range selection and overload indication (b)

Absolute accuracy: as high as ±0.005 per cent of the reading

(c)

Stability: short-term,

0.002 per cent of the reading for a 24-hr period;

long-term, 0.008 per cent of the reading for a 6-month period (d) Resolution: (e)

1

part in 10

(1

u.V can be read on the 1-V input range)

Input characteristics: input resistance typically 10 Mft; input capacitance typically 40

(f)

6

pF

Calibration: internal calibration standard allows calibration independ-

ent of the measuring circuit; derived from stabilized reference source (g)

Output

signals: print

command

allows output to printer;

BCD (binary-

coded-decimal) output for digital processing or recording

Optional features

and voltage transducers.

may

ratios.

include additional circuitry to measure current, resistance, Other physical variables may be measured by using suitable

Electronic Instruments for Measuring Basic Parameters

170

Chap. 6

Digital voltmeters can be classified according to the following broad categories:

(b)

DVM Integrating DVM

(c)

Continuous-balance

(a)

Ramp-type

DVM

(d) Successive-approximation

6-7.2 Ramp-type

The operating ment of the time

it

DVM

DVM

principle of the ramp-type

takes for a linear

ramp

DVM

is

based on the measure-

voltage to rise from 0

V

to the level

of the input voltage, or to decrease from the level of the input voltage to zero.

measured with an electronic time-interval counter, and the number of digits on electronic indicating tubes. Conversion from a voltage to a time interval is illustrated by the waveform diagram of Fig. 6-18. At the start of the measurement cycle, a ramp voltage is This time interval

count

is

is

displayed as a

+ 12

V

—J— o

v

--12

v

Voltage Beingf

Measured

1

Gating

Time

Interval

Clock Pulses to

Counter

Figure 6-18

initiated; this voltage

ramp, shown

At

voltage.

Voltage-to-time conversion using gated clock pulses.

can be positive-going or negative-going. The negative-going

in Fig. 6-18, is

unknown input unknown voltage, a

continuously compared with the

the instant that the

ramp

voltage equals the

coincidence circuit, or comparator, generates a pulse which opens a gate. This gate

is

shown

in the

block diagram of Fig. 6-19. The

to decrease with time until

it

finally reaches

0

V

(or

ramp

voltage continues

ground potential) and a

second comparator generates an output pulse which closes the gate.

An

oscillator generates clock pulses

the gate to a

number of decade counting

which are allowed to pass through (DCUs) which totalize the number

units

Sec. 6-7

dc

Digital

171

Voltmeters

Input

Voltoge

Input

Comparator

Start Pulse

Gate

Oscillator

Counter

Stop Pulse

Readout

Ground Comparator

Figure 6-19

Block diagram of a ramp-type

The decimal number, displayed by the indicator

of pulses passed through the gate. tubes associated with the

digital voltmeter.

DCUs,

is

a measure of the magnitude of the input

voltage.

The sample-rate multivibrator determines the rate at which the measurecycles are initiated. The oscillation of this multivibrator can usually be adjusted by a front panel control, marked rate, from a few cycles per second to as high as 1,000 or more. The sample-rate circuit provides an initiating pulse for the ramp generator to start its next ramp voltage. At the same time, a reset ment

pulse

is

generated which returns

all

the

DCUs

to their

0

state,

removing the

display momentarily from the indicator tubes.

6-7.3 Staircase-ramp

The staircase-ramp is

DVM

DVM given in DVM but is

a variation of the ramp-type

is

block diagram form in Fig. 6-20.

somewhat simpler

It

in overall design,

resulting in a moderately priced general-purpose instrument that can be used in the laboratory,

on production

test-stands, in repair shops,

and

at inspection

stations.

DVM

This makes voltage measurements by comparing the input voltage an internally generated staircase-ramp voltage. The instrument shown in Fig. 6-20 contains a 10-MH input attenuator, providing five input ranges from 100

to

mV

to 1,000 V full scale. The dc amplifier, with a fixed gain of 100, delivers 10 V to the comparator at any of the full-scale voltage settings of the input divider.

The comparator

senses coincidence between the amplified input voltage

staircase-ramp voltage which its

cycle.

is

and the

generated as the measurement proceeds through

Sec. 6-7

Voltmeters

Digital

When

173

the measurement cycle

is first initiated,

ation oscillator) provides pulses to three

DCUs

the clock (a 4.5-kHz relax-

The

in cascade.

units counter

provides a carry pulse to the tens decade at every tenth input pulse.

The

tens

decade counts the carry pulses from the units decade and provides its own carry pulse after it has counted ten carry pulses. This carry pulse is fed to the hundreds decade which provides a carry pulse to an overrange circuit causes a front panel indicator to light up,

circuit.

The overrange

warning the operator that the

input capacity of the instrument has been exceeded.

The operator should then

switch to the next higher setting on the input attenuator.

Each decade counter unit is connected to a digital-to-analog (D/A) conThe outputs of the D/A converters are connected in parallel and provide an output current proportional to the current count of the DCUs. The staircase amplifier converts the D/A current into a staircase voltage which is applied to verter.

the comparator.

and the

When

the comparator senses coincidence of the input voltage

staircase voltage,

it

provides a trigger pulse to stop the oscillator.

current content of the counter

is

The

then proportional to the magnitude of the input

voltage.

The sample cillator triggers

second.

The

rate

and

is

controlled by a simple relaxation oscillator. This os-

resets the transfer amplifier at a rate of

two samples per

transfer amplifier provides a pulse that transfers the information

The

stored in the decade counters to the front panel display unit.

trailing

edge

of this pulse triggers the reset amplifier which sets the three decade counters to zero and initiates a

new measurement

cycle by starting the master oscillator or

clock.

The

display circuits store each reading until a

new reading

is

completed,

eliminating any blinking or counting during the computation.

6-7.4 Integrating

The

integrating

DVM

DVM measures the true average of the input voltage over DVM which samples the

a fixed measuring period, in contrast to the ramp-type voltage at the end of a measuring cycle.

A widely used technique to accomplish

integration employs a voltage-to-frequency

(V/F)

converter.

The

V/F converter

functions as a feedback control system that governs the rate of pulse generation in proportion to the

6-21.

magnitude of the input voltage.

The simplified block diagram of an integrating The dc voltage under test is applied to the input

meter circuitry from the

The attenuated input

test circuit

signal

is

DVM stage

is

given in Fig.

which

isolates the

and provides the necessary input attenuation.

applied to the

V/F converter.

This circuit consists

of an integrating amplifier, a level detector {comparator circuit), and a pulse generator.

The

integrating amplifier produces an output voltage proportional to

"O

c

'

O

CJ

1-

2§ CO

T3 co

O N OX

(J

to

"O

< o Q

O

O

Si -5

CP

>»•-

oo

o

c7)0

«

0)

.>

_

_

o 2

^

Q

N

-

?nera

o

-WW

«_

-I

o

5 i

— o CL

C

o i

en

O c

< 174

Sec. 6-7

Voltmeters

Digital

175

the input voltage, related to the input and feedback elements by the equation

(6-5)

If the input voltage is constant, the

output

is

a linear

ramp

following the equation

(6-6)

When

ramp reaches

the

a certain negative voltage level, the level detector

to the summing The sum of the input voltage and the pulse voltage is negative, causing the ramp to reverse its direction. This "retrace'* is very rapid since the pulse is large in amplitude compared to the input voltage. When the now positive-going ramp reaches 0 V, the level detector generates a reset trigger to the pulse generator. The negative pulse is removed from the summing junction of the integrating amplifier and only the original input voltage is left. The amplifier then produces a negative-going ramp again and the protriggers the pulse generator,

which applies a negative voltage step

junction of the integrating amplifier.

cedure repeats.

The voltage.

rate of pulse generation

A

is

governed by the magnitude of the dc input

larger input voltage causes a steeper

ramp and

therefore a higher

pulse repetition rate (PRR).

The major advantage of this system of A/D conversion is its ability to measure accurately in the presence of large amounts of superimposed noise, since the input

The

is

integrated.

level-detector output pulse controls the signal gate allowing the decimal

counters to accumulate a count provided by the crystal oscillator circuitry.

remainder of the circuit

is

essentially identical to

The

any conventional counter and

needs no further elaboration.

6-7.5 Continuous-balance

DVM

The continuous-balance DVM is a low-cost instrument that provides exThe accuracy of this voltmeter is usually on the order of

cellent performance.

0.1 per cent of its input range. It has

an input impedance of about 10

MH

and

acceptable resolution.

The block diagram of a servo-driven continuous-balance DVM is given in The dc input voltage is applied to an input attenuator that provides suitable range switching. The input attenuator is a front panel control that also causes a decimal point indicator to move on the display area in accordance with Fig. 6-22.

the input range selected. After passing through an overvoltage protection circuit

and ac rejection

filter,

the input voltage

is

applied to one side of a mechanical

176

Electronic Instruments for Measuring Basic Parameters

Chap. 6

Precision

Potentiometer

Range Switch Overload Protection and ac Rejection

Input

Attenuator

Filter

1

3 4

Readout

Digital

Figure 6-22

7

Functional block diagram of a servo-balancing potentiometer-type digital

voltmeter.

chopper comparator. The other side of the comparator

arm of supply.

is

connected to the wiper

the motor-driven precision potentiometer, connected across a reference

The output of

the chopper comparator, which

voltage and vibrates at the line frequency rate,

amplitude of the square wave

is

is

is

driven by the line

a square-wave signal.

polarity of the dc voltages connected to the opposite sides of the chopper.

square-wave signal fed to a

power

is

The

a function of the difference in magnitude and

The

amplified by a high-impedance, low-noise preamplifier and

amplifier.

This amplifier has special damping to minimize

overshoot and hunting at the null position.

The

servo motor, on receiving the

amplified square-wave difference signal, drives the

arm of

the precision poten-

tiometer in the direction required to cancel the difference voltage across the

chopper comparator. The servo motor also drives a drum-type mechanical indicator that has the digits 0 to 9 imprinted about the periphery of its drum segments.

The

position of the servo

motor

amount of

shaft corresponds to the

feedback voltage required to null the chopper input, and this position

is

indicated

by the drum-type indicator. The position of the shaft therefore is an indication of the magnitude of the input voltage. It is clear that this instrument does not "sample" the unknown dc voltage at regular intervals, as is the case

with more sophisticated instruments, but

continuously seeks to balance the input voltage against the internally generated reference.

Because of the different mechanical movements involved in the mech-

anism, such as the positioning of the potentiometer indicator mechanism, the average reading time

of design and low cost, however,

when extreme accuracy

is

make

not required.

this

is

arm and

the rotation of the

approximately 2

s.

Simplicity

instrument a very attractive choice

Sec. 6-7

Digital

Voltmeters

177

6-7.6 Successive-approximation

DVM

Digital voltmeters capable of 1,000 readings per second or

more

are

now

commercially available. These instruments generally use successive-approximation converters to perform the digitization (analog-to-digital conversion). A simplified block

diagram of such a

DVM

is

At the beginning of the measurement start-stop multivibrator. This sets a

control register and a 0 in register, its

all bits

1

shown

in the

most

is

significant bit

applied to the

(MSB)

of the

of less significance. Assuming an 8-bit control

reading would then be 1000 0000. This

register causes the output of the

in Fig. 6-23.

cycle, a start pulse

D/A

initial setting

of the control

converter to be one-half the reference

supply voltage (T V). The converter output is compared to the unknown input by the comparator. If the input voltage is larger than the converter reference voltage, the comparator produces an output that causes the control register to retain the 1 setting in its MSB, and the converter continues to supply its reference

output voltage of \ V.

The

ring counter next advances one count, shifting a

of the control register, and

its

1

in the

second

MSB D/

reading becomes 1100 0000. This causes the

A converter to increase its reference output by one increment, to y V + V, and another comparison with the unknown input voltage takes place. If in this case, the accumulated reference voltage exceeds the unknown voltage, the corn-J-

Input

SH

Voltage

cct

D/A Converter

Ref.

Supply

Comparator \C Gate Digital

Control Register

Delay Ring

Set

MSB

Counter

Start/

Stop

Stop Start Figure 6-23 meter.

o-

Simplified block diagram of a successive-apprxoximation digital volt-

Readout

Electronic Instruments for Measuring Basic Parameters

178

parator produces an output that causes the control register to reset

MSB

to 0.

The converter output then

returns to

Chap. 6

its

second

previous level of j

its

V

the ring counter advances another count, the third is -J-

MSB

and

When

awaits another input from the control register for the next approximation.

of the control register

and the converter output rises by the next increment, to y V + V. The measurement cycle thus proceeds through a series of successive apset to

1

shown in Fig. 6-24, retaining or rejecting the converter output manner described. Finally, when the ring counter reaches its last count, the measurement cycle stops, and the digital output of the control register represents the final approximation of the unknown input voltage.

proximations, as in the

Reject

Converter Voltage

Final

Reading

11.250 V (16 Tries)

Level

Time

Number Figure 6-24

of

Comparisons

Successive approximations are used to

make an

version. Converter reference voltages are switched to the

sequence and are rejected

if

analog-to-digital con-

comparator

in

an 8-4-2-1

the accumulated converter output exceeds the input

voltage.

With input voltages other than zation and decisions

dc, the input level

made during conversion

conversion error, a sample-and-hold (SH) circuit

following the input attenuator and amplifier, as

form, the

SH

6-25. In the

circuit

changes during

are not consistent. is

To

placed in the input, directly

shown

in Fig. 6-22. In its simplest

can be represented by a switch and a capacitor, as

sample mode the switch

is

digiti-

avoid this

in Fig.

closed and the capacitor charges to the

mode the switch is opened and the capacitor holds the voltage that it had at the instant the switch was opened. If the switch drive is synchronous with the ring counter pulse, the actual measurement and conversion take place when the SH circuit is in the hold mode. In a practical circuit the simple switch of Fig. 6-25 is replaced by fastacting transistor switches, and an operational amplifier is added to increase the instantaneous value of the input voltage. In the hold

charging current into the capacitor.

6-8

COMPONENT MEASURING INSTRUMENTS

Bridges for measuring component values of resistance, inductance, and capacitance were discussed in Chapter

5.

Bridges are potentially very accurate and

)

Component Measuring Instruments

Sec. 6-8

V; n

179

O

-TLTLTLTL Switch Drive

(a)

0"

Simple sample-and-hold circuit Figure 6-25

A

(b)

Reconstruction of the waveform

sample-and-hold circuit freezes the input voltage during digitization

so that voltage levels do not change during the successive-approximation process.

component measurements using measuring frequencies to the low megahertz region. They have some disadvantages in that they involve a variable inductor, resistor, or capacitor, depending on the type of bridge, and this usually reliable for

makes it difficult to automate or commeasurement since an actual mechanical movement is required. For

involves an operator. This adjustment puterize the

manual measurements, this tends to slow down the measurements, but computer interface, this tends to make the task nearly impossible.

6-8.1 All-Electronic

for

Component Measurements

Chapter 5 discussed the Wheatstone bridge for resistance measurements, and the simple ohmmeter was discussed in Chapter 4. This is an example of a bridge and an all-electronic instrument for measuring resistance. (In the case of the moving-coil meter, the actual meter movement is mechanical, but this could be replaced with a digital readout, making the resistance measurement allelectronic.)

There are several methods of performing an capacitance measurement where the measurement parison, as

is

all-electronic inductance or is

not performed by a com-

the case with a bridge. Figure 6-26 shows one possible

Voltage Source Figure 6-26

This circuit can measure the

value of a capacitor by measuring the current through the capacitor with a

applied voltage.

known

v

method of

v

/n

180

Electronic Instruments for Measuring Basic Parameters

Chap. 6

measuring the value of a capacitor, where a voltage is applied to the capacitor and the current through the capacitor can be measured. The relationship between the current through a capacitor and the voltage applied to the capacitor

=

Ic

where

V is

tance.

The meter

the applied voltage, is

£=

/ is

it

(6-7)

the applied frequency, and

C is

the capaci-

simply calibrated in capacitance because of the linear

lationship between the capacitance a useful circuit,

V{27TfC)

is

and the current. Although

re-

in theory this

is

not practical because of the typical values of capacitors

is

encountered in the electronics industry. Capacitors of a few picofarads are not unusual, and these capacitors typically could have working voltages of less than

RF

25 V.

current measuring devices, essentially thermocouple instruments, are

not available for currents of

less

than a few hundred milliamperes, and thus the If, as an

current expected must be greater than a few hundred milliamperes.

example, a capacitor of 10

V

applied voltage of 10

pF were

to

produce a current of 100

mA,

with an

rms, which would be safe for a 25- V capacitor, the

frequency would have to be higher than 1,600

MHz. At

this frequency,

most

capacitors have ceased to behave as capacitors and lead inductance, dissipation resistance,

and other

generator, which

impedances will dominate the measurement. In measurement is dependent on the frequency of the

parasitic

addition, the accuracy of the

would be

difficult to

control at 1,600

MHz.

Therefore, smaller

currents must be used for capacitance measurements.

An

is shown in Fig. 6-27. In this example the current sampled across a known resistance and the resultant voltage is amplified and measured. The amplifier provides the necessary gain so that the current through the capacitor can be quite small and within practicality. The voltage across the resistor can be expressed as

alternative

method

through the capacitor

is

(6-8)

R is the resistance, Vm is the generator voltage, V is the voltage across the resistor, Cis the capacitance of the unknown capacitor, and /is the frequency where

AC

Figure 6-27

and an

Amplifier

Measuring the current through a capacitor using a sampling

amplifier.

resistor

Component Measuring Instruments

Sec. 6-8

of the generator. If of the

unknown

Vm

,

f,

and

capacitance.

R

The

181

are kept constant, the voltage scale

would have

V is

a function

to be calibrated in a nonlinear

An applied frequency of a few megahertz can provide a practical system using this technique. The actual movement of the meter depends on not only the constants mentioned above, but on the gain of the amplifier. It can be difficult to maintain a constant gain in an amplifier at several megahertz, especially for the large dynamic range encounfashion because of the relationship of Eq. (6-8).

An alternative approach example the phase angle between the applied

tered while measuring capacitance using this system. is

shown

in Fig. 6-28. In this

Limiting

Phase

Amplifier

Detector

voltmeter

n-^>—i Figure 6-28

Capacitance measuring meter using the phase

of an

shift characteristics

RC circuit. voltage and the voltage across the capacitor

is

measured.

An

amplifier

is

used

scheme except that the gain of the amplifier is not a factor in the measurement. Typically, a limiting amplifier such as that found in an FM receiver would be used. The phase angle can be expressed as in this

=

0

The

angle, 0, will be read

tan-

1

A - tan- (27r/RC) I

by the meter

calibrated in capacitance since this angle tance. This

would

(6-9)

Xc

in this circuit is

and the meter can be

a function of the

unknown

capaci-

result in a nonlinear but useful display.

Using the Taylor expansion, the expression for the angle 6 can be rewritten: 0

=

=

1

tan" (27ryKC)

(Itt/RC)

-

^(27t/KC)

3

+

^(2tt/KC)

5 .

.

.

(6-10)

As can be seen from the Taylor expansion, the value of the arctangent approach the angle, in radians, if the value of (lirfRC) is small. To gain an idea of how small the arctangent must be so that just one term of the Taylor expansion may be used, that is, the first term, consider an arctangent of less than 0.1. The value of the Taylor expansion using the first term only is, of will

The actual value of the arctangent is 0.0996687, which is only 0.3% than the actual angle, in radians. If the meter in this technique were calibrated directly in capacitance and the phase angle were restricted to less than 0. 1 rad,

course, 0.1. less

the error due to

0

=

{Itt/RC) for

this less

approximation would not exceed 0.3%. Therefore,

than

0.1.

Electronic Instruments for Measuring Basic Parameters

182

The capacitance meter based on

Chap. 6

the circuit of Fig. 6-28 could be configured

by changing the value of R, such that the full-scale As an example, assume that it is desired that the lowest range

to cover several ranges

reading

rad.

is 0. 1

cover from 0 to 100 at

MHz

1

pF

1 MHz. Therefore, pF must be 0.1 rad or

with a source frequency of

full scale,

the phase shift of the resistance, R, and 100

=

0.1

(IttR

X

100 pf)

(6-11)

Solving for R,

* To

cover from 10 to 1,000

for 10

pF

scale,

and

full scale,

1

pF

ft for

6.28

(6 " 12)

x\o- w

full-scale meter, the resistors

30 pF, 159

H

for 100 pF, 47.7

could be 1,590

H

for 300

pF

H

full

pF full scale. It is difficult to measure capacitors pF using the 1-MHz source because the impedance of a capacitor

15.9 fl for 1,000

greater than 100 at

477

=

Mhz

is

too low to achieve an accurate measurement with this type of

instrument.

6-8.2 Sources of Error

The accuracy of low-capacitance measurements

is

limited by the distributed

capacitance of the measuring circuits. Figure 6-29 shows the basic measuring

Generator Resistance Limiting Amplifier

Phase Detector

Voltmeter

Amplifier Input Capacitance

Figure 6-29 ance,

Capacitance measuring meter, showing the parasitic inductance,

circuit with the parasitic capacitances added. series

resist-

and capacitance.

The

series resistance, R,

has some

inductance and the input of the amplifier will have a certain amount of

input capacitance. Primarily, the amplifier input capacitance will have the great-

on the accuracy of the measurement. It would be difficult to design an amplifier with an input capacitance low enough to allow measurements of capacitors below 10 pF without some form of compensation. Figure 6-30 shows

est effect

a modified measuring circuit allowing the effects of the input capacitance of the amplifier to be nulled out. In this example, the resistor has been placed at the

183

W 184

Electronic Instruments for Measuring Basic Parameters

amplifier input,

and the

out-of-phase component. injecting for the

some of

trimming

signal source

The

is

Chap. 6

applied to a transformer to create an

of the input capacitance are nulled out by

effects

the out-of-phase signal through a variable capacitor. Except circuits, the

operation of this capacitance measuring system

is

similar to the previous example.

Another source of error

The phase

shift

of the

is

the harmonic distortion of the signal source.

RC circuit, which is the heart of this capacitance measuring

system, will satisfy the equations presented only sine function without

any harmonic

distortion.

if

the signal source

is

a pure

For an accuracy of 0.3 per

cent,

which was the theoretical limit for the linear approximation using the Taylor expansion, the harmonic content of the signal source must be better than 50 dB down from the nominal level. A crystal oscillator is capable of supplying a signal purity of this magnitude only if the output is carefully coupled from the oscillator. In addition to the coupling point, the signal should be passed through a lowpass

filter.

By sistance.

far the largest source of error

The

to the resistance of the circuit, but the

to the capacitance but to the point join, as

is

the equivalent series or parallel re-

series resistance called equivalent series resistance, or

shown

in Fig. 6-31.

phase measurement

where the

ESR

is

and the

made

ESR, adds relative not

circuit resistance

This causes an error because the phase

shift is

not

Durce

Figure 6-31

Effects of equivalent series resistance

on capacitor measurement.

being measured accurately. Likewise, an equivalent parallel resistance, which

is

an erroneous reading because it changes the equivalent resistance as seen by the capacitor and hence changes the phase shift. This capacitance measuring method is not suitable for measuring capacitors

due to leakage

resistance, will cause

with high dissipation factors or high ESR. Corrections can be dissipation factor or

ESR

is

made

if

the actual

known, but capacitance and dissipation factor can

both be measured in a capacitance bridge. Generally, the quality of capacitors

measured by this instrument is very good with and dissipation factors, and the errors caused by these resist-

in the region of capacitance

insignificant

ESR

ances are negligible.

The same

basic system can be used to measure inductance. Figure 6-32

1

Component Measuring Instruments

Sec. 6-8

185

Limiting

R Signal

,

Source

^

~

Amplifier

Phase

r\

Detector

.

Modification of the capacitance measuring circuit described previously,

Figure 6-32

allowing the measurement of inductance.

shows a modification of the capacitance measuring instrument previously cussed to measure inductance. In this circuit the phase shift is

= tan-'^

Figure 7-6

uniform

Force

/

electric field.

on

Cathode Ray Tube

Sec. 7-3

213

we

Substituting Eq. (7-2) into Eq. (7-5),

a

=

where a

obtain

mm

= — =

acceleration of the electron, in

/= m = When

2

(7-6)'

m/s 2

N

force on the electron, in

mass of the

m/s

kg

electron, in

the motion of an electron in an electric field

is

discussed

it is

usually

customary Cartesian axes, as shown in Fig. 7-7. In discussing the concepts which follow, we shall use subscript notation for the vector components of velocity, field intensity, and acceleration. For example, the specified in respect to the

velocity

component along the

X

axis will be written vx (m/s); the

component The motion of an electron

of the force along the

Y

in a given electric field

cannot be determined unless the

axis

is

fy

written

and displacement are known. The term

(N), etc.

initial

values of velocity

initial represents the

value of velocity

or displacement at the time of observation, or time

be used to indicate these

ponent along the

X

Figure 7-7

Consider

axis

=

0.

For example, the

initial values. is

t

written as v0jc

The

subscript 0 will

initial velocity

com-

.

Cartesian coordinate system.

now an

electric field of constant intensity

with the lines of force

Y direction, shown in Fig. 7-8. An electron entering this field in the positive X direction with an initial velocity v0x will experience a force. Since the field acts only along the Y axis, there will be no force along either the X axis or the Z axis, and the acceleration of the electron along these pointing in the negative

axes must be zero. Zero acceleration means constant velocity, and since the electron enters the field in the positive it

will continue to travel

along the

Z

axis

electron along the

along the

was zero

Z

at

time

X t

X

direction with an initial velocity v0x

=

0,

there will be no

Figure 7-8

movement of

axis. ly

Path of a moving electron

a uniform electric

field.

in

,

axis at that velocity. Since the velocity

,

the

Chap. 7

Oscilloscopes

214

Newton's second law of motion, applied to the force on the electron acting in the

Y

direction, yields

f = ma

= — ee =

mm

a= —/

or

v

constant

(7-7)

Equation (7-7) indicates that the electron moves with a constant acceleration in Y direction of the uniform electric field. To find the displacement of the

the

electron due to this accelerating force, velocity

we

use the well-known expressions for

and displacement: v

=

x

=

+

v0

+

x0

(m/s)

at

+

v0 t

j at

2

(m)

(velocity)

(7-8)

(displacement)

(7-9)

Subject to the initial condition of zero velocity in the

Y

direction (v0y

=

0) Eq.

(7-8) yields vy

which, after substitution of Eq.

=

(7-7), results in

= The displacement of which

yields,

=

(m/s)

m

the electron in the

applying the

zero velocity (v0y

(m/s)

ay t

initial

Y

(7-10)

direction follows

from Eq.

conditions of zero displacement (y0

=

(7-9),

0)

and

0),

y

=

\ay t 2

(m)

which, after substitution of Eq. (7-7), results in

y

The

X

(m)

(7-11)

by the electron in the time interval and we can write, again using Eq. (7-9),

=

x which, after applying the 0),

^2m

distance, traveled

initial velocity v0x

=

=

x0

initial

+

v0x t

+

\a x t 2

conditions for the

t,

depends on the

(m)

X

direction (x 0

=

0 and a x

becomes

x

=

v0x t

or

Substituting Eq. (7-12) into Eq. (7-11),

t

we

=

—

(s)

(7-12)

obtain an expression of the vertical

deflection as a function of the horizontal distance traveled

by the electron:

Cathode Ray Tube

Sec. 7-3

215

Equation (7-13) shows that the path of an electron, traveling through an of constant intensity and entering the

field

flux, is

parabolic in the

X-Y

field at right

electric

angles to the lines of

plane.

In Fig. 7-9 two parallel plates, called deflection plates, are placed a distance

d

apart and are connected to a source of potential difference

electric field € exists

between the

plates.

The

^a

(V/m)

Ed

,

so that an

intensity of this electric field

is

given by

€

An

=

(7-14)

electron entering the field with an initial velocity v0x

is

deflected toward the

positive plate following the parabolic path of Eq. (7-13), as indicated in Fig. 7-9.

When

the electron leaves the region of the deflection plates, the deflecting

no longer exists, and the electron travels in a straight line toward point P' a point on the fluorescent screen. The slope of the parabola at a distance x = ld where the electron leaves the influence of the electric field, is defined as force y

,

=

tan 0

where y

is

=

x

ld

— dx

=

= —

The

straight line of travel of the electron

and

this tangent intersects the

X

V — m\r

(7-16)

0x

is

tangent to the parabola at x

The

axis at point O'.

=

ldi

location of this apparent

given by Eq. (7-13) and Eq. (7-16) since

m< = i ^-0 =

tan

ety ld

2

x

(m) v

. 17) (7 y

'

'

p'

Straight

Parabolic

/Path

/Path

T

y

!

x and

yields

tan 0

is

O7 " 15 )

given by Eq. (7-13). Differentiating Eq. (7-13) with respect to

substituting

origin 0'

dy

4dx

_u

Vo

~4(-

r-

_

L

-

21

—ror '

-xt

J

2

2

~

!

1

Figure 7-9

Deflection of the cathode ray beam.

p

Oscilloscopes

216

The apparent

origin O'

L from

distance

The

is

Chap. 7

therefore at the center of the deflection plates and a

the fluorescent screen.

deflection

on the screen

is

given by

D = L Substituting Eq. (7-16) for tan 0,

we

(m)

tan 6

(7-18)

obtain e

D = L -^4 The

(m)

(7-19)

kinetic energy of the electron entering the area

with an

between the deflection plates

initial velocity v0x is

eEa where

E

a is

(7-20)

the accelerating voltage in the electron gun. Rearranging (7-20),

obtain

vL

=

^

(7-21)

m

Substituting Eq. (7-14) for the field intensity ey

of the electron in the

X

where

D = L = — d = Ed — E = ld

a

deflection

,

and Eq. (7-21)

direction v0x into Eq. (7-19),

mvL

we

2dEn

distance from center of deflection plates to screen (meters) effective length of the deflection plates (meters)

distance between the deflection plates (meters) deflection voltage (volts)

accelerating voltage (volts)

Equation (7-22) indicates that for a given accelerating voltage is

for the velocity

obtain

on the fluorescent screen (meters)

particular dimensions of the

screen

we

CRT,

directly proportional to the deflection voltage

tionality indicates that the

E

the deflection of the electron

Ed

.

a

and

for the

beam on

the

This direct propor-

CRT may be used as a linear voltage-indicating device. Ed was a fixed dc voltage. However, the deflection

This discussion assumed that voltage usually

is

a varying quantity and the image on the screen follows the

variations of the deflection voltage in a linear manner, according to Eq. (7-22).

The

deflection sensitivity

S

of a

CRT

is

defined as the deflection on the

screen (in meters) per volt of deflection voltage.

S = where

S =

deflection sensitivity

Wd = E

^W 2dE

(m/V)

a

(

By

m/v >

definition, therefore

(7 " 23)

Cathode Ray Tube

Sec. 7-3

The

deflection factor

S and

is

217

G of a CRT,

by

definition,

G=l all

the reciprocal of the sensitivity

2

=

lt

s with

is

expressed as

(V/m)

(7 " 24)

terms denned as for Eqs. (7-22) and (7-23). The expressions for deflection

sensitivity

S and

deflection factor

G

CRT

indicate that the sensitivity of a

is

independent of the deflection voltage but varies linearly with the accelerating potential. High accelerating voltages therefore produce an electron beam that requires a high deflection potential for a given excursion on the screen. A highly

beam possesses more kinetic energy and therefore produces a brighter image on the CRT screen, but this beam is also more difficult to deflect and we sometimes speak of a hard beam. Typical values of deflection factors range from accelerated

10 V/cm to 100 V/cm, mm/V, respectively.

corresponding to

sensitivities of 1.0

mm/V

to 0.1

7-3.3 Postdeflection Acceleration

The amount of light given off by the phosphor screen depends on the amount of energy that is transferred to the phosphor by the electron beam. If the electron beam is to be deflected at a rapid rate, allowing the oscilloscope to respond to fast occurring events, the velocity of the electron beam must be great; otherwise, the light output will drop to accelerate the electron

beam

other hand the greater electron deflect the It

off.

Thus, for a

to the greatest

beam

fast oscilloscope

amount

velocity will

it is

desirable

possible, while

make

it

more

on the

difficult to

beam.

can be seen that the greater the accelerating potential the more

difficult

beam. This would require higher deflection voltages, but, more important, because the voltage is higher the time change of voltage, that is, dV/dt, is also greater. This would require not only higher voltage for it is

to deflect the electron

deflection but higher currents to charge the capacitance of the deflection plates.

This becomes a very significant problem for high-frequency oscilloscopes with frequency responses greater than 100

MHz. Modern

cathode ray tubes use a

two-step acceleration to eliminate this problem. First, the electron

beam

is

accelerated to a relatively low velocity through a potential of a few thousand volts.

The beam

is

is

further accelerated to

amount of

acceleration after the

then deflected and, after deflection,

the desired final velocity. In this fashion the

deflection does not affect the deflection sensitivity. This type of cathode ray tube is

called the postdeflection acceleration tube.

Figure 7-10 shows a diagram of a postdeflection acceleration cathode ray

beam scan. manner beam is further

tube using a mesh that further increases the amount of the electron In this example the electron similar to the previous

beam

is

accelerated and deflected in a

example of the simple tube. However, the V or more, after the

accelerated through a very high potential of 10,000

deflection,

218

Chap. 7

High Voltage Acceleration Electrode

A

Figure 7-10

postdeflection acceleration oscilloscope tube using a scan expansion

mesh.

on the deflection sensitivity. A metallic mesh is beam, and acts as a magnifying lens that causes the deflection to be further increased, which improves the deflection sensitivity. With this technique, deflection sensitivity can remain on the order of 5 to 50 V/ cm even though the total electron beam acceleration is more than 10,000 V. There are several disadvantages to the mesh type of postdeflection acceleration cathode ray tube. First, the mesh tends to defocus the electron beam and make the spot broader than it would be without the mesh interfering with so

it

does not have an

suspended

effect

in the electron

the beam. Second, the

mesh conducts some of the electron beam away from the beam current and thus reduced spot intensity.

screen. This results in a reduced

Another problem with the postdeflection acceleration cathode ray tube, and this problem is not unique to the mesh, is that the electron beam tends to be defocused in the vicinity of the deflection plates owing to repulsion from charge distributions within the tube. Several recent advances in cathode ray tube design have eliminated the

mesh and

alleviated these problems, thus producing a high-perform-

ance electron gun for use in high-frequency cathode ray tubes. Figure 7-11 shows the electron gun for the meshless cathode ray tube. The electron

beam

is

generated from a conventional heated cathode surrounded by

The first accelerating anode and two focus electrodes follow and provide focus, as well as the first accelerating voltage. These focus electrodes differ from the cylindrical elements used in the conventional tube in that they are constructed from individual metal wafers with noncylindrical holes in the the control grid.

center, as can be seen in Fig. 7-12. This allows for a different focusing characteristic in the horizontal plane

one plane while being convergent

and the

vertical plane, typically divergent in

in the other.

The

holes in the center of the

Cathode Ray Tube

Sec. 7-3

219 Quadrupole Scan Expansion

Focus Element

Hrst Grid

Anode

\

\

Cathode Vertical

Defection Plates

Horizontal Deflection Plates

High-Voltage Acceleration Electrode

Figure 7-11

Diagram of

a meshless scan expansion postdefiection acceleration cath-

ode ray tube.

metal wafers can be formed with greater precision than in a formed cylinder,

and thus greater tolerances can be achieved at a lower cost. After the two focusing electrodes, the beam passes through the vertical deflection plates. The beam at this point is not fully focused, which decreases the amount of beam distortion due to the internal charge distributions. The

beam

will

be further focused after deflection to provide a fine spot.

After vertical deflection, the

then deflected in

passes through a scan expansion lens

amount of beam bending

that increases the

lens,

beam

in the vertical plane.

The beam

is

the horizontal direction and passed through another electron

which provides additional focusing.

The beam

Figure 7-12 lenses.

is

accelerated to the final velocity by a quadrupole lens, which

Modern

oscilloscope tube electron

gun showing the quadrupole electron

220

Oscilloscopes

Chap. 7

provides not only an increase in electron velocity, but adds to the scan angle (scan expansion, which

is

similar to the

distorting or defocusing the electron

The

V/cm

result of this design

mesh

an increased deflection

is

example) without

in the previous

beam. sensitivity, typically 2.3

and 3.7 V/ cm in the horizontal direction. The and horizontal deflection sensitivities is due to

for the vertical deflection

difference

between the

vertical

the fact that the vertical deflection occurs at a lower

beam

velocity.

Because the

horizontal deflection of the oscilloscope involves only a time linear sweep, while

more

the vertical deflection requires complex waveforms, the

sensitive deflection

should be reserved for the vertical direction.

Using the meshless electron gun, 100-MHz plus oscilloscopes can be conV or even less for deflection. The meshless tube, being considerably shorter, results in smaller and lighter oscilloscopes for laboratory and portable use. structed with integrated circuits using only 40 or 50

7-3.4 Screens for

When

the electron

CRTs

beam

strikes the screen of the

CRT,

produced. The screen material on the inner surface of the

a spot of light

CRT

is

that produces

this effect is the phosphor. The phosphor absorbs the kinetic energy of the bombarding electrons and reemits energy at a lower frequency in the visual spectrum. The property of some crystalline materials, such as phosphor or zinc oxide, to emit light when stimulated by radiation is called fluorescence. Fluorescent materials have a second characteristic, called phosphorescence, which

refers to the property of the material to continue light emission

even after the

source of excitation (in this case the electron beam)

The length of

is

time during which phosphorescence, or afterglow, occurs of the phosphor. Persistence for the

CRT

is

cut is

off.

called the persistence

usually measured in terms of the time required

image to decay to a certain percentage (usually 10 per cent) of the

original light output.

The

intensity of the light emitted

depends on several

from the

CRT

factors. First, the light intensity

is

screen, called luminance,

controlled by the

number beam

of bombarding electrons striking the screen per second. If this so-called current

is

increased, or the

same amount of beam current

smaller area by reducing the spot

size,

is

concentrated in a

the luminance will increase. Second,

luminance depends on the energy with which the bombarding electrons strike the screen, and this, in turn, is determined by the accelerating potential. An increase in accelerating potential will yield an increase in luminance. Third,

luminance

is

a function of the time the

beam

strikes a given area of the

therefore sweep speed will affect the luminance.

And

function of the physical characteristics of the phosphor

finally, itself.

phosphor;

luminance

Almost

all

is

a

man-

ufacturers provide their customers with a choice of phosphor materials. Table 7-1

summarizes the characteristics of some of the commonly used phosphors. As Table 7-1 shows, a number of factors must be considered in selecting

1

a

e

§

.s

1-5 C- T3

P

c

CD

c

o

3

0

_

o

If I £ 2 OnC fc

0

£

i

£ 8

3

c

t **

'P

—o

a 2

,o rrt

•c

o o

interrupted and

current charges the target in the negative direction.

The

target

voltage therefore decreases (becomes less positive), and the secondary-emission

The

ratio changes, following the curve of Fig. 7-46(b).

rate of charge decreases

A

on the curve. At this point, the secondary-emission current equals the primary beam current, and the net chargas the target voltage approaches point

ing rate

is

zero.

emission ratio

At point A,

is

the target voltage

and the

one,

called the lower stable point,

is

slightly negative, the secondary-

A

target has reached a stable condition. Point

and the target

is

is

considered to be in the erased

condition. If the initial or starting voltage of the target is to the right of crossover

+ 100 V

point C, say at

in Fig. 7-46(b), the secondary-emission ratio

than one. This means that Is

is

greater than Ip

net electron flow leaving the target surface.

When

switch S

target continues to emit secondary electrons, so that

more

positive.

Hence the secondary-emission

point

B where

the rate of discharge

is

is

greater

and there must therefore be a

ratio

it

is

now

opened, the

discharges and becomes

moves up along the curve

to

once again zero and the target obtains a

At this so-called upper stable point the secondary-emission ratio and the target is considered to be in the written condition. As long as the primary gun is on and primary electrons bombard the target, the target will always be at a stable point, upper or lower, depending on the initial voltage of the target. Crossover point C on the curve is uniquely unstable in the sense that the target voltage will always move up to point B or down to point A, depending on which way the target voltage is first shifted by stable condition.

is

one,

noise.

The

CRT of Fig.

7-46

is

an elementary bistable storage device.

Its

condition

can be interrogated by measuring the target voltage. If the target voltage "high," the target

The tube

is

written;

if

the target voltage

therefore has an electrical readout

is

and

"low," the target its

is

storage condition

is

erased. is

not

visible.

Figure 7-47(a) shows the principle of a bistable storage tube capable of

and erasing an image. This storage tube differs from the one in Fig. 7-46(a) in two aspects: It has a multiple-target area, and it has a second electron gun. The second electron gun is called the flood gun; it emits lowvelocity primary electrons that flood the entire target area. The distinguishing feature of the flood gun is that it floods the target at all times and not just intermittently as does the writing gun. The cathode of the flood gun is at ground

writing, storing,

potential, so that the target voltage will follow the secondary-emission curve

indicated in Fig. 7-47(b).

negative with respect to

+ 200

The lower

stable point of the target

the flood gun cathode, and the upper

V, the collector voltage.

The cathode of

is

a few volts

stable point

is

at

the writing gun, however,

is

at

Sec. 7-1

Special Oscilloscopes

1

253 Collector

Mesh

(a)

Storage tube with multiple targets and two electron guns

Writing

Secondary

Gun Action

Emission Ratio

Flood Gun Action

=

1

= 0

-2000

V

Writing

Target

Gun Cathode

Voltage

(b)

Figure 7-47

— 2,000 curve.

the

V, and

It is

sum

its

Storage

CRT

Secondary emissions

with multiple targets and two electron guns.

secondary-emission curve

found that the combined

effect

is

superimposed on the flood gun

of writing gun and flood gun

of the individual effects of each electron

The

flood

gun

is

on

at all times.

stable point, the erased condition.

When

Assume

beam by

that the target

the writing gun

is

is

gated on,

electrons arrive at the target with a potential of 2,000 V,

is

simply

itself.

at its its

lower

primary

which causes high

secondary emission from the target. The target voltage therefore leaves the lower stable point and starts to increase. The flood gun electrons, however, attempt to maintain the target in voltage. If the writing

its

gun

stable condition

is

and oppose the increase

in target

switched on long enough to carry the target past

gun electrons will aid the writing gun electrons and carry the target all the way to the upper stable point, so that the target is written. Even if the writing gun is now switched off, the target will be held in its upper stable condition by the flood gun electrons, thereby storing the information delivered by the writing gun. When the writing gun is not switched on the crossover point, the flood

254

Oscilloscopes

Chap. 7

long enough to carry the target past the crossover point, the flood gun electrons will

simply

move

the target back to

its

lower stable condition, and storage does

not occur.

Erasing the target simply means restoring the target voltage to the lower

can be accomplished by pulsing the collector negative, so that momentarily repels the secondary-emission electrons and reflects them back

stable point. This it

into the target. This reduces the collector current Is ratio

and the secondary-emission

drops below one. The target then collects primary electrons from the flood

gun (remember that the writing gun voltage decreases until

it

is

off)

and charges negative. The

target

reaches the lower stable point where the charging

ceases, and the target is in the erased condition. After erasure, the collector must be returned to its original positive voltage ( + 200 V in this case), and the erase pulse must therefore be returned to zero. As indicated in Fig. 7-47(a), this must happen gradually, so that the target is not accidentally driven past the crossover point and becomes written again.

The

target area of the storage tube in Fig. 7-47(a) consists of a

number

of small individual metal targets electrically separated from one another and

numbered from 1 to 5. The flood gun is of simple construction, without deflection plates, and it emits low-velocity electrons that cover all the individual targets. When the writing gun is gated on, a focused beam of high-velocity electrons is directed at one small target (number 3 in this case). This one target then charges positive and is written to the upper stable point. When the writing gun is turned off again, the flood electrons

hold target 3 at

its

upper stable point

(store). All

the other targets are held at their lower stable points (erase).

The

last step in

our development of the bistable direct-viewing storage

tube consists of replacing the individual metal targets with a single dielectric sheet, as in the typical tube of Fig. 7-48. This dielectric storage sheet consists

of a layer of scattered phosphor particles capable of having any portion of

its

surface area written and held positive or erased and held negative without affecting the adjacent areas

on the surface of the

deposited on a conductive-coated glass faceplate. the storage target backplate, and

it

sheet. This dielectric sheet

The conductive coating

is

is

called

the collector of secondary-emission elec-

is

gun and its deflection plate assembly, this has two flood guns and a number of collimation electrodes that

trons. In addition to the writing

storage

CRT

form an electron lens

to distribute the flood electrons evenly over the entire

surface area of the storage target.

After the write gun has written a charge image on the storage target, the flood guns will store the image.

bombarded by form of visible

The

written portions of the target are being

flood electrons that transfer energy to the light.

phosphor layer

in the

This light pattern can be viewed through the glass faceplate.

Since the storage target areas are either positive or negative, the light output

produced by the flood electrons There is no gray scale

brightness.

is

either at full brightness or at

in

between.

minimum

Sec. 7-1

Special Oscilloscopes

1

255

Col limating Electrodes to Shape Flood Beams

Faceplate

Layer

Storage Target

Backplate Figure 7-48

Schematic view of a bistable storage tube (courtesy Tektronix,

Inc.).

7-11.2 Sampling Oscilloscope

When

the frequency of the vertical deflection signal increases, the writing

speed of the electron speed

is

beam

increases.

The immediate

a reduction in image intensity on the

sufficient

image

brilliance, the electron

more

CRT

result of higher writing

screen. In order to obtain

beam must be

accelerated to a higher

and normal image brightness is maintained. An increase in electron beam velocity is easily achieved by raising the voltage on the accelerating anodes. A beam velocity so that

kinetic energy

is

available for transfer to the screen

with higher velocity also needs a greater deflection potential to maintain the deflection sensitivity. This immediately places higher

demands on the

vertical

amplifier.

The sampling

oscilloscope uses a different approach to improve high-

frequency performance. In the sampling oscilloscope the input waveform reconstructed from

many samples

is

taken during recurrent cycles of the input

waveform and so circumvents the bandwidth limitations of conventional CRTs and amplifiers. The technique is illustrated by the waveforms indicated in Fig. 7-49.

In reconstructing the waveform, the sampling pulse turns the sampling circuit

instant

on for an extremely short time is

measured. The

CRT

spot

is

interval.

sponding voltage input. The next sample the input

waveform

The waveform

voltage at that

then positioned vertically to the correis

taken during a subsequent cycle of

at a slightly later position.

zontally over a very short distance and

is

The

CRT

spot

is

moved

repositioned vertically to the

hori-

new

256

Sec. 7-1

1

Special Oscilloscopes

257

value of the input voltage. In this

by point, using as

many

way

the oscilloscope plots the

waveform point

as 1,000 samples to reconstruct the original

The sample frequency may be

as

waveform. low as one-hundredth of the input signal

frequency. If the input signal has a frequency of 1,000

MHz,

the required

bandwidth of the amplifier would be only 10 MHz, a very reasonable figure. A simplified block diagram of the sampling circuitry is given in Fig. 7-50. The input waveform, which must be repetitive, is applied to the sampling gate. Sampling pulses momentarily bias the diodes of the balanced sampling gate in the forward direction, thereby briefly connecting the gate input capacitance to the test point. These capacitances are slightly charged toward the voltage level of the input circuit. The capacitor voltage is amplified by the vertical amplifier and applied to the vertical deflection plates. Since the sampling must be synchronized with the input signal frequency, the signal amplifier, allowing the

a trigger pulse it

is

sweep triggering

delayed in the vertical

is

done by the input

to be

signal.

When

received, the avalanche blocking oscillator (so called because

uses avalanche transistors) starts an exactly linear

applied to a voltage comparator.

The

ramp

voltage,

which

voltage comparator compares the

voltage to the output voltage of a staircase generator. are equal in amplitude, the staircase generator

is

When

is

ramp

the two voltages

allowed to advance one step

and simultaneously a sampling pulse is applied to the sampling gate. At this moment, a sample of the input voltage is taken, amplified, and applied to the vertical deflection plates.

Input

Sampling

Vertical

Vertical

Signal

Gate

Amplifier

Signal

Sampling Pulse

P

Scanning

*

Trigger

Blocking

Input

Oscillator

Ramp

Voltage

Staircase

Generator

Comparator

Generator

Horizontal Signal

Time Scale />

Magn.

Attenuator

Figure 7-50

Simplified block diagram of the sampling circuitry (courtesy Hewlett-Packard

Com-

pany).

The

real-time horizontal sweep

is

shown

in Fig. 7-50, indicating the hor-

beam. Notice that the horizontal displacement of the beam is synchronized with the trigger pulses which also determine the moment of sampling. The resolution of the final image on the CRT screen is determined izontal deflection rate of the

by the

size of the steps of the staircase generator.

greater the horizontal distance between the trace.

CRT

The

larger these steps, the

spots that reconstitute the

Chap. 7

Oscilloscopes

258

REFERENCES Prensky, Sol D., and Castellucis, Richard L., Electronic Instrumentation, 3rd

1.

chap. 10. Englewood

Cliffs, N.J.:

van Erk, Rien, Oscilloscopes: Functional Operation and Measuring Examples.

2.

ed.,

Prentice-Hall, Inc., 1982.

New

York: McGraw-Hill Book Company, 1983.

PROBLEMS 1.

What

are the major blocks of the oscilloscope,

2.

What

are the major components of a cathode ray tube?

(3/

How

4.

the electron

is

What

beam focused

How much

voltage

is

What

7.

Why

on the

1° if

the accelerating potential {6)

on the face of the cathode ray tube?

deflection sensitivity?

required across two deflection plates separated by

an electron beam

deflect

to a fine spot

does increasing the writing rate of an oscilloscope by increasing the

effect

accelerating potential have 5.

and what does each do?

is

the effective length of the deflection plates

1,000

is

1

2

cm to cm and

V?

the velocity of electrons that have been accelerated through a potential of

is

2,000 V? are the operating voltages of a cathode ray tube arranged so that the deflection

plates are nearly

($}

How

is

ground potential?

the vertical axis of an oscilloscope deflected?

How

does this

differ

from the

horizontal axis? 9.

What

is

oscilloscope probe compensation!

noted when the compensation

is

How

this adjusted?

is

11.

Why Why

12.

What

are the advantages of dual trace over dual

How

does alternate sweep compare with chopped sweep?

10.

13.

What

effects are

not correctly adjusted?

is

an attenuator probe used?

is

a delay line used in the vertical section of the oscilloscope?

beam

for multiple-trace oscilloscopes?

When would

one method

be chosen over the other?

When

14.

What

is

15.

What

are the advantages of using an active voltage probe?

16.

How

delayed sweep?

is it

used?

are the effects of direct current

on the

flux density of the current

probe min-

imized? 17.

What is

18>

is

the relationship between the period of a

How

does the digital storage oscilloscope

differ

cilloscope using a storage cathode ray tube? 19.

waveform and

its

frequency?

How

from the conventional storage

What

What

os-

are the advantages of each?

does the sampling oscilloscope increase the apparent frequency response of an

oscilloscope? 20.

How

an oscilloscope used to determine frequency?

precautions must be taken

when

using a sampling oscilloscope?

8

CHAPTER

SIGNAL GENERATION

The generation of signals is an important facet of electronic troubleshooting and development. The signal generator is used to provide known test conditions for the performance evaluation of various electronic systems and for replacing missing signals in systems being analyzed for repair. There are various types of signal generators, but several characteristics are

common

to all types. First, the fre-

quency of the signal should be well known and stable. Second, the amplitude should be controllable from very small to relatively large values. Finally, the signal should be free of distortion.

There are many variations of these requirements, especially for specialized and sweep generators, etc.,

signal generators such as function generators, pulse

and these requirements should be considered

8-1

as generalizations.

THE SINE-WAVE GENERATOR

Because of the importance of the sine function, the sine-wave generator represents the largest single category of signal generators. This instrument covers the

many

frequency range from a few hertz to the sine-wave generator

is

as

shown

gigahertz, but in

its

simplest form

in Fig. 8-1.

The simple sine-wave generator consists of two basic blocks, an oscillator and an attenuator. The generator's performance depends on the success of these two main parts. The frequency accuracy and stability and freedom from distortion depend on the design of the oscillator, while the amplitude accuracy depends on the design of the attenuator. 259

Signal Generation

260

Chap. 8

Set Level

Set Frequency

/

/

Altenuator

RF

Output Block diagram of a simple

Figure 8-1

sine-wave generator.

Oscillator

8-1.1 Inductor-capacitor

There

is

Tuned

Oscillators

a broad class of oscillators that use the resonant characteristics

A

of an inductor-capacitor, LC, circuit to generate a stable frequency.

block

diagram of an oscillator is shown in Fig. 8-2. The oscillator consists of an amplifier and a feedback network such that the total gain of the loop, that is, the gain of the amplifier divided by the loss of the feedback network,

equal to one, and the total phase shift around the loop

is

is

exactly

zero. Oscillators are

designed such that these characteristics are met at only one frequency. This can

be achieved by using various combinations of inductors, capacitors, and

resistors.

Feedback Network Output Figure 8-2

Block diagram of an

oscillator,

showing the amplifier and feedback

net-

work.

The resonant frequency of

a circuit

is

given by

1

/=

(8-1)

2ttJZc where L is the circuit inductance in henrys, C is the circuit capacitance in farads, and / is the resonant frequency in hertz. When a resonant circuit is used in the feedback of an oscillator, the oscillation frequency is the resonant frequency of the circuit.

Figure 8-3 shows the actual circuit of a Hartley oscillator and the equivalent

showing the amplifier and feedback components. Because a common-

circuit

emitter amplifier

used as the active element of the oscillator,

is

that the circuit has a phase shift

operating frequency.

phase

shift

oscillator

be clear

is

apparent

The feedback network,

that

is,

the resonant circuit, has a

of 180° at resonance. Therefore, the phase shift requirement for the

can be met

how

at the resonant

frequency of the tuned

circuit. It

may

not

the loop gain can be equal to one, especially since the gain of a

transistor amplifier can be quite high,

For an

it

to the amplifier of 180° regardless of the

due

and there

is

no

loss in the

tuned

oscillator to sustain oscillations, the gain of the active element

reduced, and this

is

circuit.

must be

accomplished by automatic adjusting of the operating charthrough self-bias. The amplitude of the ac voltages

acteristics of the transistor

The Sine-Wave Generator

Sec. 8-1

261

+V

Noninverting Amplifier Figure 8-3

Hartley oscillator using a bipolar junction transistor.

in the oscillator build until the effective gain of the transistor is

the total loop gain

is

equal to one. This

is

accomplished

in

most

reduced so that

oscillator circuits

by increasing the transistor bias voltages so that the gain of the device is reduced. This usually results in large amplitude and distorted voltages and currents associated with the active device, which suggests that care should be taken

when

choosing the point from which to couple the oscillator output.

A

circuit similar to the Hartley oscillator

shown

is

in Fig. 8-4;

it is

called

the Colpitts oscillator. Instead of the tapped inductor, the Colpitts oscillator uses a tapped capacitance to achieve the required 180° phase

operation

is

identical. In fact, all simple transistor

shift.

LC oscillators

Otherwise, the are practically

identical.

These two basic

circuits, as well as other

simple oscillator circuits, are

used as the signal source for most radio-frequency, RF, generators from tens of 1 GHz and greater. There are practical problems with constructing an oscillator of the simple sort for frequencies above 1 GHz using these circuits,

kilohertz to

and most signal generators

for

microwave frequencies use specialized

oscillators.

Likewise, for lower frequencies the size of the inductors required for the tuned circuit

become

are used.

prohibitive,

and

oscillators using other than

LC-tuned

circuits

262

Chap. 8

Signal Generation

+V

1

X

1 Figure 8-4 (^olpitts oscillator using a

bi-

polar junction transistor.

Because both the inductance and capacitance have a similar control on the operating frequency of the oscillator, both elements can be used to set the

frequency of the oscillator. In practice, the inductor while the capacitor

is

is

changed with a switch,

used for the tuning of the oscillator. This

accomplished by switching the inductor

in

bands while the capacitor

is

is

usually

connected

to the signal generator dial.

The second is

part of the sine generator

to supply signals of

known

known amplitude

is

the attenuator.

known

as well as

The

signal generator

frequencies. If a signal

were applied to the input of an attenuator, the known as long as the attenuator were accurate. Signal generators are often used to supply known signal levels at very low levels for testing and evaluating receivers. It is not possible to measure and calibrate a signal at a very low level, and thus low-level signals are generated by feeding an attenuator with a higher-level signal for which the amplitude is easily measured and calibrating the attenuator steps. An attenuator is a device that will of a

fixed amplitude

output signal level would be

reduce the power level of a signal by a fixed amount. The attenuator should terminate with a fixed impedance, relative to either the input or output, regardless of the value of attenuation.

The attenuator reduces

the

input power to the output power

power of an input such is

expressed as the log of the input to

that the ratio of the

The reduction in power can be output power ratio by the following rela-

a constant.

tionship:

A

(dB)

=

10 log -i

(8-2)

o

is the attenuation in decibels, P0 is the power output, and P is power input of the attenuator. If a signal is passed through two attenuators in cascade as shown in Fig. 8-5, the output of the first attenuator is reduced by the ratio P,/P0 while the signal is further reduced by the ratio of the second

Where A (dB)

t

the

,

j

The Sine-Wave Generator

Sec. 8-1

263

Attenuator

Two

Figure 8-5

P'/P0 The

attenuator,

'.

Po

Pi

Attenuator

attenuators cascaded for increased attenuation.

total reduction

is

the product of the two attenuations,

or

A

(dB)

=

10 log

=

(J)

£+

10 log

10 log

g

Replacing each attenuation ratio with the corresponding decibel representation yields

A where A

,

and

^4

2

=

(dB)

A,

+ A

(8-3)

2

are the attenuations of each attenuator. Therefore, the total

two cascaded attenuators

attenuation, in decibels, of

attenuation of each attenuator.

is

the

sum

of the decibel

not difficult to be convinced that this can

It is

be extended to more than two attenuators to derive the general rule that the attenuation, in decibels, of any

the decibel attenuations of

number of cascaded

the attenuators.

all

It

attenuators

is

sum

the

of

should also be clear that the

order of the cascaded attenuators will not affect the end result.

The

decibel notation

convenient for a variety of reasons but needs a

is

slight modification so that

it

can represent an absolute

equation were written as

dBr whee dBr

is

W,

=

P

10

log-

a decibel notation referenced to

of decibels above or below the equation

level.

If the decibel

some

P

r

,

^

^

faA

(g

"

4)

then dBr represents the number

reference power,

P

r

.

For example,

if

P

r

were

1

would read

dBw =

10 log

-4t w l

dBw, which is a standard notation, describes an absolute power level referenced to 1 W. Another important power level is the dBm, which is referenced to 1

mW across 500 uAV.

50

dBm

CI. is

vast majority of

For example,

+3 dBm

is

2

mW,

while

—3 dBm

is

\

mW or

convenient for a 50-fl system impedance, which includes the

equipment operating

at frequencies greater

than

1

MHz.

Various attenuator types can be used in signal generators. The pi attenuator,

named

for the

Greek

one of the more

letter,

which the schematic representation resembles, is versatile types. Three resistors are required for

common and

the pi attenuator, as

shown

The

The pi attenuator can be fabricated with dB and for frequencies to about 100 MHz.

in Fig. 8-6.

standard components up to about 20

.

S,f+

B

sin o) 2 t)

3

=

K,(A 3

sin

3

o> x t

+ B

3

sin

3

a) 2 t

(9-6) sin

2

n

-

2IP

dBm, Ip is the power power of the two input

the level of the third-order product in

the third-order intercept in

To determine

the

dBm, and P

in

is

the

(9-7) level of signals.

dynamic range of the spectrum analyzer, the third-order

314

Signal Analysis

Figure 9-12

Third-order products as a function of the level of two input signals.

intermodulation products must be the same as the seen by the analyzer, that

the signal that

is,

minimum

just visible

is

is

level.

equal to the noise

Therefore, the equation can set the third-order intermodulation products

equal to the

minimum

detectable signal:

P = 3P - 21p = MDS where

MDS is the minimum detectable signal,

noise level, in

- MDS) =

The dynamic range of

minimum

signal equal to the

2(IP

- MDS)

the spectrum analyzer

is

(9-9)

the difference in level

detectable signal and the input that produces a spurious

MDS,

or

Pm ~ MDS =

is

spectrum analyzer

(9-8),

3(Pln

Example

essentially the

dBm.

Rewriting Eq.

between the

(9-8)

in

3

What

signal that can be

above the noise

For the sake of simplicity, assume that the intermodulation level.

Chap. 9

\V

P

- ME>S)

(9-10)

9-1

dynamic range of a spectrum analyzer with a third-order intercept point of and a noise level of —85 dBm?

the

+ 25 dBm

Spectrum Analysis

Sec. 9-3

315

Solution

Using the formula 2

dynamic range

= -(/,- MDS) =

and substituting the given data, the dynamic range

2

- [25

is

-

(-85)]

=

73

found to be 73 dB.

The minimum detectable signal or the noise level of the spectrum analyzer is determined by two characteristics, the bandwidth of the IF filter in use and the noise figure of the analyzer. The noise figure of the analyzer is set by the design of the front end of the unit, while the IF

from a

later stage of the analyzer.

The

filter

bandwidth

is

a parameter

noise level of the spectrum analyzer can

be related to the noise figure and the IF bandwidth by the following:

MDS = where

BW

is

-114 dBm

4-

10 log

(BW/1 MHz) + NF

the 3-dB bandwidth in megahertz of the IF

filter,

and

(9-11)

NF

is

the

noise figure in decibels.

Example 9-2

What is the minimum detectable signal dB and using a 1-kHz, 3-dB filter?

of a spectrum analyzer with a noise figure of 20

Solution

-114 dBm

The

ability of the

+10

log

1

kHz/1

MHz +

20

= -124 dBm

spectrum analyzer to separate signals

the second IF bandwidth.

To

resolve

two

is

a function of

signals that are close in frequency, a

narrow IF filter is required. In addition, signals that are close in frequency and are at two different amplitudes are even more difficult to resolve. Consider, as an example, two signals that are the same amplitude but are separated by 10 kHz. These signals could be resolved using an IF filter with a 3-dB bandwidth of 10 kHz, as shown in Fig. 9-13. The dip in the spectrum display is only 3 dB but it is clearly visible. On the other hand, if the two signals were separated not only by 10 kHz but by 10 dB, they would not be resolvable with the 3-dB, 10kHz filter. The resolution of a spectrum analyzer is defined as the 6-dB bandwidth of the second IF It

may

filter.

appear that a

filter

with sharper skirts would solve the problem of

The ratio of the 6-dB point of a filter to the 60-dB point is an indication of the steepness of the skirts of the filter. Thus, it would appear that a filter with a lower shape factor would resolve signals close in frequency, and to a certain extent it would. However, there are significant disadvantages to sharp-skirted filters in spectrum analyzers. resolving closely situated signals.

The reader should be

when

a modulated signal

to pass the entire

is

familiar with the nature of distortions introduced

passed through a

filter

with a bandwidth too narrow

modulation bandwidth. Not only

will the high-frequency

316

Chap. 9

Signal Analysis

—H

Figure 9-13

Two

signals 10

kHz

[—10

kHz

apart as displayed with an IF

bandwidth of

filter

10 kHz.

components be reduced, but the high-Q circuits of the filter will introduce ringing. Even though the signal being analyzed with the spectrum analyzer may not be modulated, the fact that the signal sweeps through the causes ringing in the

local oscillator. If

of the

first

second IF

is

bandwidth

is

filter

seen, the

cause

filters

shape called Gaussian causes the

least

rate as a function of the

given by the following equation:

maximum sweep As can be

CW input signal

too great, the amplitude of the signal out of the

amount of distortion. The maximum permissible sweep filter

center frequency

be reduced and possibly distorted. Sharp-skirted

the most distortion, and a special

Gaussian

the

is

local oscillator,

filter will

filter

filter,

modulated as a function of the sweep speed of the the sweep speed, that is, the megahertz per second rate

of the spectrum analyzer first

Relative to the second IF

filter.

rate

=

2.3

maximum sweep

(bandwidth) rate for a

can be quite slow, and usually a spectrum analyzer

is

2

Hz/s

(9-12)

narrow-bandwidth

filter

equipped with a storage

display.

9-3.1

Spectrum Analyzers

for Higher

Frequencies Spectrum analysis

at frequencies higher

than about 100

MHz

is

a very

important tool for the development of circuits and systems at these higher frequencies.

are

no

With the exception of a few higher-frequency

tools for the analysis of signals at frequencies

oscilloscopes, there

above a few hundred

Spectrum Analysis

Sec. 9-3

317

megahertz. Most signal analysis

done with the oscilloscope

is

for lower fre-

The

quencies, such as the determination of amplitude, phase, and distortion.

spectrum analyzer provides a sensitive instrument to investigate these parameters at

higher frequencies.

The frequency of the VCO for a spectrum analyzer is required to extend from a frequency higher than the highest input frequency to a frequency at least twice the highest input frequency. For spectrum analyzers operating above 1,000 MHz, this implies an oscillator from at least 1,000 to 2,000 MHz and, in practical designs, more on the order of 2,500 to 3,500 MHz. This frequency range usually requires an oscillator with a tuned circuit other than the typical coil and capacitor found in lower-frequency oscillators. An oscillator circuit suitable for this frequency range is the YIG-tuned oscillator.

YIG, yttrium

iron garnet,

is

a ferromagnetic material that has

very useful properties at microwave frequencies.

YIG,

like

many

some

ferromagnetics,

moments

has the property that the molecules of the garnet have magnetic

that

normally are randomly aligned. The magnetic moments can be aligned in one field. The moments to

direction by the application of a static magnetic

application of an

alternating magnetic field will cause the magnetic

precess

a toy top.

YIG

The

precession frequency

material and the strength of the applied static magnetic

field.

amplitude of the precession occurs when the applied alternating to the precession frequency of the

be used to create oscillators and

Q

the gigahertz region, and the

YIG about 0.25

YIG

filters.

of a

much

like

a function of the type and size of the

is

crystal. Therefore, this

The resonance frequency

YIG

The

greatest

field is

equal

resonance can is

typically in

resonator can be quite high.

made from highly polished spheres of YIG The sphere is placed in a static magnetic field of

resonators are typically

mm

field intensity

to the static

in diameter.

H, as shown in Fig. 9-14.

magnetic

and out of the

YIG

be added, which

is

field

and

sphere. In

is

A pickup coil is arranged at right

angles

used as the method of coupling energy into

some applications a second coupling coil would static field and the other coupling

orthogonal to both the

coil.

The equivalent

circuit of the

YIG

resonator

circuit with a small fixed series inductance.

is

essentially a parallel-tuned

The resonant frequency of the

parallel

can be electronically tuned by varying the current through the magnetic coils. Unlike the typical electronically tuned oscillator using a varactor,

circuit field

where the resonant frequency tuned

circuit, the

YIG

inductance. This allows for a in

is

varied by changing only the capacitor of the

resonator tunes both the equivalent capacitance and

more constant impedance of

the resonant circuit

an oscillator and also allows for a tuning range of several octaves, rather

than just the two that are typical of a varactor-tuned

oscillator.

The YIG resonant circuit can be used in an oscillator as the frequencydetermining element, as shown in Fig. 9-15. In this example the resonant circuit is

placed in the emitter, while positive feedback

the base lead.

is

introduced by the choke in

318

Signal Analysis

YIG

Figure 9-14

sphere and the associated coupling coil and static magnetic

The frequency of

Chap. 9

field.

by varying the same fashion as the

this circuit is controlled electronically

current through the static magnetic

field coils

much

in the

voltage across a varactor diode would be used to tune a conventional oscillator.

There are some

significant differences

between the YIG-tuned oscillator and the

maximum-to-minimum frequency recommended limit for varactor-tuned

varactor-tuned oscillator. First, the ratio of the

can be

much

oscillators.

greater than

2,

which

Q

Second, the high

is

the

of the

YIG

oscillator brings

improved phase

noise performance for spectrum analyzers and sweep generators.

The frequency range of

the spectrum analyzer can be extended without

resorting to a higher-frequency local oscillator by a technique called harmonic

mixing.

A

difference

mixer

will convert

between the local

also convert

an input signal to an IF by taking the sum or and the input signal. Many mixers will

oscillator

an input signal with harmonics of the local

oscillator.

RF Out

YIG Sphere

"1

+ 10 V

-10 V Figure 9-15

Oscillator circuit using a

YIG

resonator.

Spectrum Analysis

Sec. 9-3

319

An example of a simple harmonic mixer is shown in Fig. 9-16. In this example a single diode is used to mix an input RF signal with the third harmonic of the local oscillator. If the level of the local oscillator is sufficiently high, the diode can be thought of as a switch being switched at the rate of the local oscillator.

Mixing

is

essentially multiplying

two

signals together,

action of the diode can be thought of as multiplying a square

and the switch wave with an

amplitude of 1 with the input waveform. Because a square wave is made of the summation of the fundamental and all the odd harmonics of the base frequency, it would be expected that the simple diode mixer would not only mix the RF input with the local oscillator but with practical circuit, because the duty cycle just the

input

the odd harmonics as well. In a not an exact 50 per cent, more than

all

is

odd harmonics are

RF

signal with all

present, and the example diode mixer harmonics of the local oscillator.

will

mix the

To Local Oscillator

IF Output

Figure 9-16

Simple

series

diode mixer capable of mixing by harmonics.

In the spectrum analyzer described previously, the possibility of generating any spurious inputs with the harmonics of the local oscillator was eliminated by the input low-pass filter. If this low-pass filter were eliminated, or if a bandpass filter were placed at the input of the spectrum analyzer, certain harmonics

of the local oscillator could be used to extend the range of the spectrum analyzer.

As an example will

of

how

this

might work, the previous spectrum analyzer example

be used.

The

MHz. MHz,

local oscillator covers

If the

from 400 to 700

MHz

and the

first

IF

is

400

second harmonic of the local oscillator were used, 800 to 1,400

the second harmonic minus the first IF would give an input range from 400 to 1,000 MHz, while the sum would yield 1,200 to 1,800 MHz. The third harmonic of the local oscillator, 1,200 to 2,100 MHz, would allow the conversion of 800 to 1,700 MHz and 1,600 to 2,500 MHz for difference and sum, respectively. Other harmonics can be used for extending the frequency range further. One other method of gaining yet another frequency range from the same mixer and local oscillator is to simply use the sum of the first IF and the local oscillator frequency that covers the frequency range of 800 to 1,100 MHz.

320

It

should be noticed that, although the range of the spectrum analyzer

can be extended by that

is

321

Spectrum Analysis

Sec. 9-3

range of frequencies in this example from 300 to 400 MHz. When complete frequency required, the second IF is often used in lieu of the first IF to provide this technique, there is a

not covered and that

coverage

is

is

the required frequency coverage.

When harmonic

mixing

spectrum analyzer display.

is

used, several corrections are required to the

First,

when

the harmonic

mix

used, the center

is

frequency dial of the analyzer must have the correct frequency calibrations. This is

usually handled by having a mechanical dial arrangement that simply displays

the correct frequencies. Electronic dials can manipulate the ically.

Second, because a harmonic of the local oscillator

change of frequency,

relative to the

Nth harmonic, per

is

volt

numbers

electron-

used, the rate of is

N times

that at

the fundamental, so therefore the spectrum analyzer display for this. This

is

corrected in a simple fashion;

the local oscillator tuning voltage efficiency of the less

mixer

at

is

if

the

Mh

must be corrected harmonic is being used,

simply divided by N. Finally, the mixing

harmonics, especially the higher-order harmonics,

is

than at the fundamental. Therefore, the display will have to be corrected

for this loss of signal. This

number of

accomplished by simply offsetting the display by

is

and the harmonic mixer loss. A block diagram of a spectrum analyzer with harmonic mixing is shown in Fig. 9-17 with all the required correcting circuits. The chief problem in using the harmonic mixing spectrum analyzer is that the input low-pass filter is removed and all the possible harmonic mixing ranges are present at the input of the spectrum analyzer. Therefore, there is considerable ambiguity in the display as some signals can appear at more than one point on the display. Various signal-identifying techniques can discern between the correct and incorrect signals, but the best technique is to place an external band-pass filter between the system being tested and the spectrum analyzer, which will eliminate many of the spurious signals. An example of a spectrum analyzer with the

decibel difference between the fundamental mixer loss

harmonic mixing capability

is

shown

in Fig. 9-18.

9-3.2 Applications of the Spectrum Analyzer

The spectrum analyzer those

is

many applications. To applications may not be readily

a powerful tool and has

who have never used the instrument, these To illustrate some of the applications,

apparent.

descriptions,

and the spectrum analyzer

display, as

the following signals, their

shown

in Fig. 9-19, will be

presented. (a)

Pure sinusoid with no modulation or harmonic is

persion of the spectrum analyzer (b)

distortion.

This signal

characterized by a single spectral line regardless of what the disis

or the IF

filter

bandwidth.

Amplitude modulation. When a carrier is modulated with amplitude modulation, two sidebands are generated, one above the carrier fre-

322

Signal Analysis

Figure 9-18

up

to

40

Example of

GHz

Chap. 9

a harmonic-mixing spectrum analyzer covering frequencies

(courtesy Polarad Electronics, Inc.).

quency and a second below the carrier frequency. The separation frequency between the carrier and the sidebands

is

equal to the

in

mod-

The power contained in the sidebands is dependent on the percentage of modulation. One hundred per cent modulation produces sidebands that are 6 dB below the carrier. The amplitude of the carrier, on the other hand, does not change, regardless of the ulation frequency.

percentage of modulation. (c)

Frequency modulation. Frequency modulating a carrier produces

side-

bands that are centered around the carrier as in the case of amplitude modulation, except that more than one sideband is generated. The

number of sidebands and the amplitude of those sidebands is described by complex formulas based on the Bessel functions. The sidebands are all multiples of the modulating frequency, and the amplitude of the is affected by the amount of modulation supplied. The precise amount of frequency modulation can be determined if the modulation

carrier

is

adjusted so that the amplitude of the carrier or other sidebands goes

to zero. (d)

Asymmetrical

spectra.

The generation of

metrical about the carrier

is

a spectrum that

is

not sym-

usually an indication that both frequency

and amplitude modulation are occurring simultaneously. This could occur in an FM system where the passband of an amplifier is not flat and the frequency modulation is introducing amplitude modulation.

Suit Sec. 9-3

Spectrum Analysis

-4-

B /

\

i

! 1

j

i

(a)

(e)

(f

Figure 9-19

)

Applications of the spectrum analyzer.

Likewise, amplitude modulation applied to a carrier that also causes

frequency

instabilities,

which

is

a

common problem

with phase-locked

loops, will cause a similar spectrum. (e)

Harmonic

distortion.

Harmonics appear

spectrum analyzer display often required that the

the order of 60 or

as additional signals in the

at multiples of the carrier frequency. It is

harmonic content of a

more dB below

signal be kept low,

the carrier.

As an example,

on this

may be required so that a transmitter operating at an assigned frequency will not interfere

with other radio services at twice the assigned

fre-

quency that may be located near the transmitter. (f)

Pulse modulation. Examining pulse modulation was the

first

application

of the spectrum analyzer. Determining the pulse modulation of radar transmitters

was a

difficult task in the early

development of radar, and

324

Chap. 9

Signal Analysis

the spectrum analyzer

was used

to evaluate the quality of the pulse

modulation. The spectrum of a rectangular amplitude pulse in Fig. 9- 19(f).

The

structure of the sidebands shows the rise-

is

shown

and

fall-

times of the pulse modulation, and the symmetry indicates the presence

or absence of frequency modulation, which

is

a problem with modulated

such as those used with high-power radar transmitters.

oscillators

REFERENCES 1.

Engleson, Morris, and Tewlewski, Fred, Spectrum Analyzer Theory and Applications.

Dedham, Mass.: 2.

Hay ward, W.

ARTECH

House, 1974.

H., Introduction to

Radio Frequency Design, chap.

6.

Englewood

Cliffs,

N.J.: Prentice-Hall, Inc., 1982. 3.

Krauss, Herbert

L., Bostian,

Engineering, chaps. 2 and

7.

Charles W., and Raab, Frederick H., Solid State Radio

New

York: John Wiley

&

Sons, Inc., 1980.

PROBLEMS 1.

What

is

dynamic range of a spectrum analyzer

the

—80 dBm and two — 10-dBm

equal to

signals

if

the noise level of the display

is

produce third-order intermodulation

products that just appear above the noise? 2.

3.

What

is

of 30

kHz?

sideband this

if

is

amplitude modulation with only one sideband and no

modulation look

What would device

like displayed

What

be the third-order intermodulation products relative to the input of a

two input

signals of

— 10 dBm

were applied

to a device with a third-order

intercept of

+15 dBm?

What

dynamic range of a spectrum analyzer with a 30-kHz, 3-dB bandwidth,

is

the

How What

+25 dBm?

does placing a fixed attenuator ahead of a spectrum analyzer affect

order intercept, (b) the dynamic range, and 8.

carrier.

on a spectrum analyzer?

a noise figure of 15 dB, and a third-order intercept of 7.

with a 3-dB bandwidth

is the maximum sweep rate in kilohertz per second that could be used with a spectrum analyzer without introducing distortion with a 3-kHz Gaussian filter?

would

6.

filter

What

4. Single

5.

the resolution of a spectrum analyzer using an IF

(a) the third-

(c) the noise figure?

frequency ranges could be covered with a spectrum analyzer having a

of 2,050

MHz and an input of 0 to

harmonic?

1,000

MHz using harmonic

first

IF

mixing up to the third

CHAPTER

10

FREQUENCY COUNTERS

AND

TIME-INTERVAL

MEASUREMENTS

10-1 SIMPLE

FREQUENCY COUNTER

Standards of time and frequency (time and frequency being essentially the same standard) are unique in that they to another without the actual

may

be transmitted by radio from one location

movement of the

standard. Therefore,

it is

possible

have traceability to the primary standard without difficulty. Additionally, the primary standard is related to the structure of matter, and primary standards to

can be easily duplicated throughout the world to allow high-accuracy measure-

ments anywhere. Because of the

relative ease with

which frequency and time

can be measured to great accuracies, electronics systems have developed around this capability. Consider, as

an example, the tolerance expected of radio-trans-

mission equipment. The spectrum required by a voice-modulated two-way radio transmitter using frequency modulation that

if

is

on the order of

a communications channel could be assigned every 15 efficient

5

kHz. This implies

kHz and make

the most

use of the radio spectrum. Because accurate measurement techniques

are available and standards can be are assigned every 20

kHz

in the

made

available, the

communications channels

UHF (450 MHz) band.

frequency accuracy and stability of only 5 kHz, which per cent, which

is

easily achieved with

ment techniques. Although relatively

many

1

the frequency of the transmitter carrier could be held to absolute precision

task.

modern frequency

approximately 0.001 control and measure-

stable frequency standards have been available for

years, precise frequency

surement

This requires a carrier is

measurement has not always been an easy mea-

Early frequency measurement required precision standards,

fre-

325

— Frequency Counters and Time-Interval Measurements

326

Chap. 10

quency comparators and interpolation oscillators, as well as a lot of operator skill. This came to an abrupt end with the introduction of digital logic and the development of the frequency counter. Figure 10-1 shows the block diagram of a simple frequency counter. AlDisplay

Strobe

Memory Input

Input

Decade

Signal Processor 1

Counters

Reset

Time Base

1

Basic block diagram of a frequency counter.

Figure 10-1

though referred to as "simple," if

1

this basic

the parts are constructed properly.

counter

is

capable of great precision

The frequency counter operates on

the

principle of gating the input frequency into the counter for a predetermined

As an example,

time.

an exact

1

second

(s),

an unknown frequency were gated into the counter for number of counts allowed into the counter would be

if

the

precisely the frequency of the input.

an

AND

or an

OR

gate

is

to be accumulated. Figure 10-2

This example shows an similar circuit. to

A

AND gate

AND

is

AND the

AND

gate

is

zero. Thus, exactly

allowed at the output of the

input pulses

is

these pulses

and display the

AND

output

s

1,

applied

the output

pulse returns

of

unknown

gate. It is necessary to

result.

Jinjijijiririr^ |~

Gate

1

s is

1

As long as the 1-s pulse is a logic same as the unknown input. When the 1-s gate.

to logic 0, the output of the

^

shows the waveforms associated with this action. gate; however, an OR gate could be used in a

positive-going pulse having a period of exactly

one input of the

of the

The term gated stems from the fact that unknown input into the counter

used to allow the

|

_TLnjijirTJirir^^

(Figure 10-2

Waveforms

associated with the gating function of a frequency counter.

count

Simple Frequency Counter

Sec. 10-1

If the gate

is

open for exactly

average frequency of the gate was open for 10 in 0.1

Hz. Likewise,

unknown

327

1

s,

the count accumulated

input in hertz (Hz).

the accumulated count

if

the gate were open for 0.1

When

as

is

equal to the

an example, the

would be the average frequency s, the count would be the a frequency counter has more than

s,

average frequency in tens of hertz.

If,

one gate time interval available, the decimal point of the display

is

switched

with the gate time selector switch to correct the frequency display.

10-1.1 Display Counters

The

actual counting circuits are, in practice, constructed

circuit counters, but

it is

from integrated

constructive to understand the internal operation of a

digital counter.

The

heart of a frequency counter

constructed from four flip-flops and an

is

the decade counter, which can be

AND

gate, as

shown

in Fig. 10-3. This

Outputs

J

Input

Q

c K

Figure 10-3

Ripple binary coded decimal counter.

form of decade counter is called a ripple counter owing to the fact that the clock of one flip-flop is derived from the output of the previous flip-flop, which requires that the clock pulses ripple through the counter from the first stage to the last stage. The last stage, however, derives its clock from the first stage, which reduces the propagation delay to a certain degree.

A

method of constructing a counter is to use a synchronous shown in Fig. 10-4, requires that all the flip-flop clocks be connected together, which greatly reduces the propagation delay and allows superior

counter. This circuit,

higher counting speeds.

The output of the decade counter follows the sequence shown in Fig. and is called binary coded decimal (BCD), which implies that the normal binary code is used except that each digit is defined only for values between 0 and 9. As an example, the decimal number 138 is 0001 0111 1000 in BCD. Each BCD counter allows one decade of counting and thus the BCD counters must be cascaded. For example, three cascaded BCD counters are 10-5

328

->

O

-3

O

*

329

Simple Frequency Counter

Sec. 10-1

Clock

Counter State

1

2 3

u

c

Q D

0 0

0

0

1

1

0

0 0 0 0 0

4 5

6 7

8 9

1 1

0

IO

0 0 1

1

1

A

1

1

0 0

0

1

1

0

1

1

1

0 0 0

0 0 0

0 Figure 10-5

1

0

Binary coded decimal count-

ing sequence.

required to count from 0 to 999. There are two methods of cascading

BCD

and synchronous. Ripple cascading is usually reserved counters and, unfortunately, makes the slow ripple counter even slower.

counters, ripple cascading for ripple

With the exception of low-frequency counters, the serious frequency-measuring equipment.

The

ripple counter

is

not used in

ripple connection requires the last

output of the least significant counter to drive the clock input of the next more significant counter, as

must respond weight of

8,

shown

10-6.

in Fig.

The clock input

to the negative edge of the clock as the last bit,

goes low at the transition from 9 to

A B C D

Figure 10-6

0.

A B C D

A B C D Clock

Clock

Clock

to the next stage

which has a binary

Cascading ripple counters.

The synchronous counter has a terminal count or carry output for the purpose of cascading counters, as shown in Fig. 10-7. This output goes to a logic is

1

after the clock that

changes the state of the counter to

9.

This output

used to enable the following counter to be incremented on the next clock

pulse. This insures that the state of the next counter

is

coincident with the clock

and preserves the synchronous counter operation when the counters are cascaded. When more than two counters are cascaded, the requirement for any one counter to change state is that all of the less significant counters must be at 9. Some integrated-circuit counters have internal cascading logic that propagates the

A B C D TC

PE A B C D TC

PE A B C D ye

pE

Clock

Clock

Clock

Figure 10-7

Cascaded synchronous counters.

Frequency Counters and Time- Interval Measurements

330

"nine" state from the least significant digit through

most

to the

When

significant digit.

there

is

a large

all

Chap. 10

the intervening counters

number of cascaded

counters,

the delay can limit the count frequency of the counter. Therefore, other tech-

niques called look ahead or carry forward are used to reduce the amount of

propagation delay.

The

BCD

information available at the output of the counter must be

converted to some form of visible display. The conversion depends on the type of display desired. For example, conversion from

segment display requires a

shows a

4-bit

BCD to the very popular seven-

single, inexpensive integrated circuit.

Figure 10-8

counter including the seven-segment code conversion. Counter

Decoder/Driver

7490

7447

Display

a

Clock

b

A

c

B C D

d e f

g

Figure 10-8

Block diagram of a decade counter interfaced with a seven-segment

display.

It is

desirable in a frequency counter to display the count continuously.

Since the counter

is

reset to zero

and allowed

during this time the output of the counter

is

to count during the gate period,

would appear as a the end of the measurement period is

of the counter cannot be displayed during this period as

meaningless blur. Therefore, the count at stored in a simple

memory and

which the next count

is

required to store only 4

and

is

the entire

typically a simple 4-bit latch,

clocked together, with each

it

displayed during the next counting period, after

stored in the

bits,

The output

constantly changing.

memory and

displayed. This

memory

is

BCD word, for each decade of the counter

which consists of four D-type

flip-flop storing

1

bit

flip-flops all

of data.

Digital logic usually cannot supply the required current for driving a

Even those displays

minimal amounts of current, such as which are not readily available from the decoder output. Therefore, a display driver is included between the decade counter and the displays. For counters requiring a large number of digits, typically 10 or more, there are various techniques to reduce the required hardware, one of which is shown in Fig. 10-9. This technique is called display multiplexing and reduces the number of drivers and decoders required to implement large counters. In this example a common decoder and driver are shared between all the display digits. A multiplexer selects the BCD data from one of the latches and routes these data to the input of the seven-segment decoder. The decoded seven-segment information is applied to the proper display. The entire process is driven by an

display.

that require

liquid crystals, require special signals,

Simple Frequency Counter

Sec. 10-1

331

Scan Counter

Digit Driver

Scan Oscillator

Displays

Clock

Figure 10-9

oscillator is

done

Block diagram of a multiplexed display used

and a counter called the scan

at a rapid rate, the display

oscillator

and

in a

counter.

this

is

When

appears constant to the eye.

that the inclusion of the multiplexer, scan oscillator,

drivers

frequency counter.

It

this process

would seem

and multiplexed display

hardly worth the aggravation to save a few simple decoders. However,

technique has significant advantages

when

the frequency counter circuits

are integrated into a single silicon chip.

Consider, as an example, a 10-digit frequency counter. This scale of frequency counter could be integrated onto a single silicon chip except that 70 outputs would be required for the readouts alone if they are of the seven-segment

332

type.

Frequency Counters and Time-Interval Measurements

Add

to this the

power and ground,

and other inputs

a time-base input,

required for the frequency counter and the net result

is

Chap. 10

80 or more pins, which

does not allow for inexpensive packaging. The readout output could be multiplexed with seven outputs for the segments and a 4-bit binary output for selecting

each

digit,

which

results in only

1 1

output pins for the display interface. Adding

the other required pins results in a package size that can be handled with

conventional packaging technology.

Time Base

(10-1.2

The sequence of

events within the frequency counter

is

controlled by the

time base, which must provide the timing for the following events: resetting the counter, opening the count gate, closing the count gate, and storing the counted

frequency in the latch. The resetting of the counter and storing of the count are not critical events as long as they occur before and after the gate period, respectively.

The opening and

closing of the count gate,

on the other hand,

determine the accuracy of the frequency counter and are very

critical in its

timing.

Since the accuracy of the frequency counter depends directly on the ac-

curacy of the time-base signals, the time base

is

driven from an accurate crystal-

controlled oscillator. This element of the time base

compensated crystal

is

typically a temperature-

oscillator operating at several megahertz.

A

crystal

oven

could be used to supply a similar accuracy, except that the oven requires a relatively long period after the initial application of

power, up to 24 hours, to

The temperature-compensated oscillator does not require the appliof power to provide the correct frequency and is available for use im-

stabilize.

cation

mediately after power-on.

Figure

10-10

shows a simplified diagram of a

Varactor Diode

RFC

Temperature Sensor (Thermistor)

o

Oscillator

— RF

i

Correction

Network

Block diagram of a temperature-compensated crystal

Figure 10-10

temperature-compensated cry stal

Oul

oscillator.

A

oscillator.

conventional crystal oscillator

is

used as the basic building block of the compensated oscillator, except that a varactor diode

is

placed across the crystal. The varactor allows the frequency

of the oscillator to be changed by minute amounts.

quency error

is

The

crystal oscillator fre-

characterized over the desired operating temperature, and the

error characteristic

is

stored in the correction network. This can either be a

L 333

Simple Frequency Counter

Sec. 10-1

digital storage

technique or an analog circuit with nonlinear characteristics. The

ambient temperature

is

fed to the correction network,

which adjusts the

oscillator

frequency by varying the varactor voltage as a function of temperature.

Aside from the temperature variation of frequency of a crystal

oscillator,

quartz crystals tend to age and change frequency over a period of time. This

undesired frequency change can be reduced by special crystal fabrication techniques, but

still

it

can be as high as

5

X

10

compensated for by periodic recalibration. Many temperature-compensated crystal

"7

parts per year. This

oscillators

must be

have the capability of

being electronically adjusted. If the frequency counter has a standard frequency

output that can be compared to one of the available broadcast frequency standards, the frequency of the time-base oscillator in a frequency counter can be set to within

1

part in 10

9 .

Three outputs are required from the time base: a reset pulse, the gating pulse, and a strobe pulse, in that order. Figure 10-11 shows a simple circuit for generating the three required pulses without overlap.

The

crystal oscillator

divided by powers of ten, as the period of the frequency of the crystal shorter than the desired gate time.

counter that has 16 states.

The zero

The

final digital divider is a 4-bit

state of the counter

is

binary

decoded to provide

The 2 state is decoded to provide the was not used so as to provide a delay after the

the reset pulse for the frequency counter. gate open pulse.

The

1

state

°p en Gate

—n

Reset

4-bit Binary Counter

-_J~"|__ Close gate 1

10 Hz 100Hz1 Hz

sec

0.

1

sec

0 .01 sec |_J~~ Store

Figure 10-11

is

much

is

Logic diagram of a time base for a frequency counter.

Frequency Counters and Time-Interval Measurements

334

reset pulse to allow the counters to

be fully recovered from the

reset.

Chap. 10

The

gate

remains open for exactly 10 clock pulses, and thus the 12 state of the counter

decoded to provide the gate close pulse. The 13 state of the counter is not decoded so as to provide a delay period before the counter is stored in the latch during the 14 state. The 15 state is not decoded and provides the necessary nonoverlap between the store and reset pulses, which occur immediately after is

the 15 state of the counter.

important that the propagation delay from the input clock to the

It is

edges of the open and close pulses be the same for each so that the gate exactly equal to the correct

number of clock

pulses. This requires fast logic

is

and

careful design.

Most frequency counters have

several available gate time intervals that

can be selected by a switch. As shown in Fig. 10-11, the input of the binary counter can be selected from a choice of

These frequencies provide gate times of

10,

1

Hz, 10 Hz, 100 Hz, and 1,

0.1,

and 0.01

1

kHz.

respectively.

s,

10-1.3 Input Signal Processing

The unknown frequency input level to drive the

is

not guaranteed to be of the correct logic

frequency counter, and a processing circuit

is

required.

Typ-

an amplifier to increase the signal level, an attenuator to adjust for variations in input amplitudes, and a comparator so that the slow risetime ically, this is

of the input waveforms can be reduced to provide reliable operation of the internal logic circuits. circuit

is

shown

A schematic diagram of a typical frequency counter input

in Fig.

10-12.

Amplitudes of a few

millivolts

can be used to

trigger the frequency counter using this circuit.

Comparator

—WA

To Counter Amplifier I

VWV

Input

©

H Figure 10-12

Input circuits for a simple frequency counter.

— Simple Frequency Counter

Sec. 10-1

10-1.4 Period Measurement

.

335

^^

*

' '

If two input signals were substituted for the open and close gate signals, and one of the internal clock signals, that is, one of the available frequencies that are powers of 10 Hz, is supplied to the count gate, the time interval between the two input signals could be measured. The arrangement of this period mea-

suring

is

shown

in Fig. 10-13.

The input

measurement.

A

second identical circuit

must be processed

signals

fashion as the count input signal, and the

same

will

same

in the

can be used for period

circuit

have to be supplied for the period

measurement.

IS

Input

Signal

A

Signal

Start

Processor Counter

1

1

Input

Signal B-

Signal

Processor

IS Stop

Resolution 1

ms

o \00fxs lO/zs

1

mHz

I00 kHz

10

kHz

I

kHz

From Time Base Circuit arrangement for

Figure 10-13

making period measurements.

Another period measurement can be made using a

single input. This

would

be useful for determining the period of pulses and other signals. In this

mode

of operation, the gating signal

is

the input, and the internal frequency clocks

To measure

are used as timing sources.

the period of a pulse waveform,

it

is

necessary to open the count gate at the rising edge of the pulse and to close the gate at the falling edge of the pulse. In the case of a negative-going pulse, this

procedure would be reversed, that

is,

opening the gate on the negative edge and

closing the gate at the positive edge. If the risetimes

compared

pulse are short,

actual trigger point

is

not

and

falltimes of the input

to the resolution of the period

critical.

A

measurement, the

sophisticated frequency counter will have

independent control over the voltage level of both the rising and falling edges, as

shown

in Fig. 10-14.

measurements,

Although

this type of

method of viewing the

this results in the

most

and accurate skill and a Because most

flexible

frequency counter requires operator

trigger points, such as

period measurements involve pulses with fast

an oscilloscope. rise-

and

falltimes, a simple al-

s

Frequency Counters and Time-Interval Measurements

Chap. 10

Vref

Open

SI Frequency counter input

Figure 10-14 falling

circuits

showing the

ability to set rising

and

edges individually.

I

WW+ 5

V

© B

5 V

© 0 V

+ 2.5

Out

_L

r\ r

V

— 2.5 V

5 V

0 V Figure 10-15

waveforms.

Zero-crossing detector for a frequency counter and the associated

Measurement

Sec. 10-2

Errors

337

ternative is to ac couple the input signal and open and close the count gate at the zero crossings of the ac-coupled signal. Figure 10-15 shows a typical pulse waveform input and the resulting trigger points after ac coupling.

One

very important period measurement

is

the period measurement to

determine frequency. This measurement is not made from rising edge to falling edge but from a point in an input cycle to the same point in the next cycle,

which

is

the period of the input signal. In this case, the gate

a point of the input cycle.

This

is

waveform and closed

at precisely the

is

opened

to be

at

in the next

accomplished in the following fashion. The input signal

coupled, and a zero crossing detector triggers a crossing

is

same point

is

ac

The following zero flip-flop. The next zero

flip-flop.

of the opposite slope and does not trigger the

crossing, however, occurs after a time period equal to the period of the input

waveform and toggles the

flip-flop,

which provides a gate time exactly equal

the period of the input waveform, as

shown

to

in Fig. 10-16.

J

To

Q

frequency Counter

c

K

Figure 10-16

The

Input circuit configuration for measuring the period of a waveform.

typical laboratory counter, such as that

shown

in Fig. 10-17,

has both

input period measurement and independent control of risetime and falltime triggering selectable

10-2

from a front-panel switch.

MEASUREMENT ERRORS 10-2.1 Gating Error Frequency and time measurements made by an electronic counter are

subject to several inaccuracies inherent in the instrument

instrumental error

is

itself.

One very common

the gating error, which occurs whenever frequency and

period measurements are made. For frequency measurement the main gate

is

opened and closed by the oscillator output pulse. This allows the input signal to pass through the gate and be counted by the decade counters. The gating pulse is not synchronized with the input signal; they are, in fact, two totally unrelated signals.

Frequency Counters and Time-Interval Measurements

338

Figure 10-17

Chap. 10

Microprocessor-controlled computing counter (courtesy of Racal-Dana

Instruments, Inc.).

In Fig. 10-18 the gating interval (a)

and

is

indicated by

(b) represent the input signal in different

to the gating signal. Clearly, in

one

±

(c).

Waveforms

case, six pulses will be counted; in the other

case, only five pulses are allowed to pass

a

waveform

phase relationships with respect

through the

gate.

We

have therefore

count ambiguity in the measurement. In measuring low frequencies, the

1

gating error

may have an

appreciable effect on the results. Take, for example,

the case where a frequency of 10

equals

1

count of 10

Hz

reasonable assumption).

s (a

±

1

is

to be

measured and the gating time

The decade counters would

indicate a

count, an inaccuracy of 10 per cent. Period measurements are

therefore to be preferred over frequency measurements at the lower frequencies.

The

dividing line between frequency and period measurements

determined as follows: Let

f =

crystal (or clock) frequency of the instrument

fx =

frequency of the

c

unknown

input signal

w

JuuuLrui_rLJo_n_

«

_n_JtTLJuiJuua_n_

w

/ r«

N Gate Open

Figure 10-18

Gating

error.

»•{

may

be

Measurement

Sec. 10-2

Errors

In a period measurement the

339

number of

pulses counted equals

N = Ji

(10-1)

P

f,

In a frequency measurement with a 1-s gate time the

number of

pulses counted

is

Nf = f which N = Nf

(10-2)

x

The

crossover frequency (f0) at

p

7 =L

or

f = Q

is

(10-3)

yjfc

Jo

Signals with a frequency lower than

f

0

should therefore be measured in the

"period" mode; signals of frequencies above f0 should be measured in the "fre-

quency" mode

The

in order to

minimize the

accuracy degradation at

effect

caused by the

f

0

of the

±

1

±

1

count gating error.

count gating error

is

100/

yjfc per cent.

10-2.2 Time-base Error Inaccuracies in the time base also cause errors in the measurement. In

frequency measurements the time base determines the opening and closing of the signal gate, and

it

provides the pulses to be counted. Time-base errors consist

of oscillator calibration errors, short-term crystal stability errors, and long-term crystal stability errors.

Several methods of crystal calibration are in simplest calibration techniques

is

common

use.

One

of the

to zero-beat the crystal oscillator against the

standard frequency transmitted by a standards radio station, such as

This method gives reliable results with accuracy on the order of

1

WWV.

part in 10

6 ,

which corresponds to 1 cycle of a 1-MHz crystal oscillator. If the zero-beating is done with visual (rather than audible) means, for example, by using an 7 oscilloscope, the calibration accuracy can usually be improved to 1 part in 10 .

Several very low frequency

(VLF) radio

stations cover the

North American

continent with precise signals in the 16-20-kHz range. Low-frequency receivers are available with automatic servo-controlled tuning that can be slaved to the signal of

one of these

stations.

The

error between the local crystal oscillator and

on a strip-chart recorder. A simplified diagram of this procedure is given in Fig. 10-19. Improved calibration accuracy can be obtained by using VLF stations rather than HF stations because the transmission paths for very low frequencies is shorter than for high-frequency the incoming signal can then be recorded

transmissions.

Short-term crystal stability errors are caused by momentary frequency variations

due to voltage

transients,

shock and vibration, cycling of the crystal

oven, electrical interference, etc. These errors can be minimized by taking fre-

Frequency Counters and Time-Interval Measurements

340

Chap. 10

Phase or

Time Error

Receiver

Frequency

Phase

Multiplier

Detector

To Recorder

O

Local

Frequency Source Figure 10-19

Servomotor or Manual Adjustment

Calibration of a local frequency source.

quency measurements over long gate times (10 s to 100 s) and multiple-periodaverage measurements. A reasonable figure for short-term stability of a standard 7 crystal-oven combination is on the order of 1 or 2 parts in 10 .

Long-term

stability errors are the

more subtle contributors to the inaccuracy

of a frequency or time measurement. Long-term stability

and deterioration of the in

crystal.

As

the crystal

is

is

a function of aging

temperature-cycled and kept

continuous oscillation, internal stresses induced during manufacture are

lieved,

ness.

and minute

particles adhering to the surface are shed reducing

Generally, these

phenomena

will

its

re-

thick-

cause an increase in the oscillator

frequency.

A The

typical curve of frequency

change versus time

may

of change of crystal frequency

initial rate

is

shown

in Fig. 10-20.

be on the order of

6

10 per day. This rate will decrease, provided that the crystal

is

1

part in

maintained

at

its

operating temperature, normally about 50° to 60°C, with ultimate stabilities

of

1

part in 10

9 .

If,

however, the instrument containing the crystal

from the power source appreciably, a

new

into operation. It

slope of aging will ensue

is

is

unplugged

for a period of time sufficient to allow the crystal to cool

when

the instrument

is

put back

possible that the actual frequency of oscillation after cool

Initial

Slope

Time (Weeks) Figure 10-20

Frequency change versus time

for an oven-controlled crystal.

Extending the Frequency Range of the Counter

Sec. 10-3

341

vary by several cycles and that the original frequency will not again be

off will

reached unless calibration

To show

done.

is

the effect of long-term stability on the absolute accuracy of the

measurement, assume that the oscillator was calibrated to within 1 part in 10 9 and that a long-term stability of 1 part in 10 8 per day was reached. Assume further that calibration

time

then

is

X

1

1(T

is

60

10~ 8

X

maximum

be seen therefore that exact calibration

was done 60 days ago. The guaranteed accuracy

+

9

performed a

=

6.01

X

10~ 7 or 6 parts in 10 7 ,

.

at this It

absolute accuracy can be achieved only

relatively short time before the

can

if

an

measurement

is

taken.

10-2.3 Trigger Level Error

(j6W^n

In time-interval and period measurements the signal gate closed by the input signal. closed signal

The accuracy with which

the gate

is is

opened and opened and

a function of the trigger level error. In the usual application the input

is

amplified and shaped, and then

is

that supplies the gate with

a certain

its

it is

applied to a Schmitt trigger circuit

control pulses. Usually the input signal contains

amount of unwanted components or

noise,

which

is

amplified along

with the signal. The time at which triggering of the Schmitt circuit occurs function of the input signal amplification and of general,

we can

plitudes

and

its

is

a

signal-to-noise ratio. In

say that trigger time errors are reduced with large signal

am-

fast risetimes.

Maximum

ac curacy can be obtained

if

the following suggestions are fol-

lowed:

(a)

The

effect

of the one-count gating error can be minimized by making

frequency measurements above y[fc and period measurements below is the clock frequency of the counter. yjfci where

f

(b) Since

long-term stability has a cumulative

surement

is

effect,

the accuracy of mea-

mostly a function of the time since the

last calibration

against a primary or secondary standard. (c)

The accuracy of time measurements

is

greatly affected by the slope of

the incoming signal controlling the signal gate. Large signal amplitude

and fast risetime assure maximum accuracy.

1

0-3

EXTENDING THE FREQUENCY RANGE OF THE

COUNTER Using the

fastest logic

and the most sophisticated carry

frequency counter shown in Fig. 10-1 speed.

is

limited to about

To increase the frequency range of the counter, One technique is to use a prescaler as shown in

be used.

circuits, the

simple

100-MHz counting

several techniques can Fig. 10-21.

A prescaler

p

342

Frequency Counters and Time- Interval Measurements

Chap. 10

1MHz-IOMHz

^, 41

IO-IOO MHz Figure 10-21

is

Frequency

-10

>

Counter

Using a prescaler to extend the range of a frequency counter.

a fast digital counter that, typically, divides the input frequency by

prescaler does not drive a display,

is

10.

The

not gated, nor are the output data strobed

into the storage latch. Therefore, the propagation delay of the prescaler

is

not

important as long as the prescaler can operate at the desired frequency. If a divide-by- 10 prescaler were used ahead of a

10-MHz

counter, the counter fre-

quency would be increased by a factor of 10 and the system would be capable of counting to 100 MHz. Prescalers are available for frequencies up to 1 GHz with divisions of 10 or 100, which can extend the range of the example 10-MHz counter to

1

There

GHz. is

a penalty to be paid for the use of the prescaler.

of the frequency counter

example,

if

a

last digit,

if

10, all the digits

the counter

when

The

resolution

reduced by the same factor as the prescaler. As an

10-MHz counter were used with a prescaler,

would be multiplied by implies that

is

the frequency displayed

including the least significant. This

had a resolution of

1

Hz, which

is

the value of the

multiplied by 10 the resolution would be reduced to 10 Hz.

This can be overcome by simply using a longer time base and restoring the

become a practical problem if the prescaler has a large and very accurate frequency measurements are to be made. For example, if the divide-by- 100 prescaler were used to extend the frequency range of the 10-MHz counter to 1 GHz, and a measurement of 1-Hz resolution were desired, the gate time would be 100 s, which could be a significant problem. Typically, frequency measurements with resolution of better than 1 kHz at 1 Ghz are rare. The prescaler, as effective as it can be, is limited to frequencies below about 1.5 GHz with the current state of technology. For making frequency counter measurements at higher frequencies, heterodyning techniques are used. Figure 10-22 shows a heterodyning converter for a frequency counter. This resolution. This can

division

Input Signal

100

MHz

\

Harmonic

Tuned

Low -pass

Generator

Cavity

Filter

Figure 10-22

Manually tuned heterodyning frequency converter

frequency range of frequency counters.

To Counter

for extending the

Extending the Frequency Range of the Counter

Sec. 10-3

converter

is

used with a

50-MHz

343

counter, which requires that the converter

MHz or less, which it does with mixing Because both the sum and the differences are used, the converter frequency never exceeds 50 MHz. A 100-MHz source, which is reduce the input frequency to 50

frequencies every 100

MHz.

derived from the frequency counter's time base, feeds a harmonic generator using a step recovery diode. characteristic in that

it

The step recovery diode has a unique reverse recovery

stops conducting very abruptly, which generates har-

monics of the driving waveform to several gigahertz. The harmonic content of 5-GHz region. Harmonics from the fundamental at 100 MHz to 5 GHz are selected by a tuned cavity that tunes one of the harmonics. It is necessary to know which of the 50 harmonics is being tuned, and a calibrated dial is provided as a tuning meter to peak the desired signal. The setting of the harmonic tuner dial does not affect the accuracy of the measurement unless the incorrect harmonic is tuned. The 50 harmonics represent a 2 per cent resolution, which can be easily achieved with a mechanical the diode generator extends well into the

assembly.

The

selected

amplified,

and fed

harmonic

mixed with the input and the difference is filtered, Because there is a harmonic available every 100 MHz, the input signal is never more than 50 MHz from one of the harmonics. To select the correct harmonic, the input frequency must be known to within 10 MHz or so, which can be done with another measurement technique such as a wavemeter or spectrum analyzer. Since either the sum or difference between the selected harmonic and the input signal

may

is

to the counter.

be counted, the operator

is

required to

make

the necessary

calculations to determine the actual frequency. This involves adding or subtracting,

depending on whether the sum or difference

frequency that

is

read from the harmonic tuner

is

counted, the harmonic

dial.

Modern frequency counters are capable of tuning the harmonic and making the necessary calculation automatically. Figure 10-23

shows a block diagram of

an automatic heterodyning unit for converting frequencies up to 4 GHz to extend the range of a 500-MHz counter. A 100-MHz signal from the frequency counter

is

multiplied using a bipolar transistor frequency multiplier to 500

This signal multiplier.

is

MHz.

amplified and used to drive a step recovery diode frequency

The output of the

MHz

step recovery diode multiplier

is filtered

to recover

and 3.5 GHz. The input signal is fed to an amplifier, which feeds the mixer and a level detector. When the presence of an input signal is detected with the level detector, the six possible mixing frequencies, that is, 1, 1.5, 2, 2.5, 3, and 3.5 GHz, are electronically sequenced in ascending order, while the presence of an output signal below 500 MHz is determined by a level detector at the mixer output. When it has been determined that a difference exists below 500 MHz, the selected mixing frequency is transmitted to the frequency counter and added to the counted frequency. Because there is a mixing frequency every 500 MHz, and these frequencies are sequenced from the lowest to the highest, the first detection signals at 1,000

and

1.5, 2, 2.5, 3.0,

Frequency Counters and Time-Interval Measurements

344 1

1.5

Chap.

10,

GHz

GHz Switch

Harmonic 2.0

Generator r+-

GHz

x5

a

2.5 GHz

IOO MHz from Frequency Counter

3.0

GHz

3.5

GHz

Input

500 MHz

4 GHz Level Detector

Figure 10-23

Automatic heterodyning unit

frequency counters to 4

for extending the frequency range of

GHz.

of an output from the mixer less than 500

MHz represents the difference between

the input frequency and the selected mixing frequency.

an output using the next-higher mixing frequency, but the

first

It is

this is

mixing frequency to supply an output below 500

It is

possible to obtain

avoided by selecting

MHz.

informative to calculate the effects on the accuracy of both the pre-

and the heterodyning methods of frequency extension. For the case of the prescaler, assuming that the prescaler does not miss counts, and this is generally true, the output frequency is simply the input frequency divided by N, the prescaler ratio. The displayed frequency is the input frequency to the counter times the gate time, which is scaler

displayed frequency

Because

N

is

fin

(10-4)

N

a constant, the accuracy of the display

is

simply a function of

the gate time. Thus, the accuracy of the counter with a prescaler

same

is

t,

exactly the

as the accuracy of the counter without a prescaler.

Consider the case when using the heterodyning frequency converter where the mixing signal

is

derived from the same clock as

base within the counter.

The

gate time

is

is used to derive the time an integer number of cycles of the

time-base clock, or gate time

= ? Jc

(10-5)

Automatic and Computing Counters

Sec. 10-4

Q

where

is

345

the division of the time base and fc

The mixing frequency

in the converter

output frequency of the converter

A

is

the time-base clock frequency.

is

derived from the same source, and the

is

= A' ± Nf

(10-6)

c

where fm is the frequency into the counter, fj is the frequency into the converter, is the multiplication between the internal time-base clock and the hetand

N

erodyning

signal.

The displayed frequency of the counter is times the gate time, which

displayed

The is

the input frequency of the counter

is

frequency

= fm = *t£. (|)

relationship between the actual input frequency

a function of

f

c

QN

+

(10-7)

and the displayed frequency QN, is a

only, as the second term of relationship (10-7),

constant.

Therefore, neither the heterodyning nor the prescaling

method of increasing

the frequency range of a counter affects the accuracy.

10-4

AUTOMATIC AND COMPUTING COUNTERS

The frequency

counter, being an intensely digital machine,

didate for automating and computerizing.

One

is

an excellent can-

measurement that can be handled by a calculating counter is the measurement of low frequencies with accuracy. One significant problem with the frequency counter is the measurement of low frequencies. If a signal of less than 1 Hz was to be measured with a resolution of 0.01 Hz, the time required would be 100 s if the conventional gatecontrolled counter were used. An alternative measurement technique is to measure the period of the input waveform and calculate the frequency from the excellent

relationship:

frequency

=

—— \

(10-8)

-

period

The time required

to display the frequency

is

the period of the

unknown

input plus the computation time. For the example of a frequency on the order is on the order of 1 ms any waveform can be measured within the time of one period plus a small increase for the computation. However, the determination of frequency from a single period measurement has a statistical

Hz, the period

of

1

or

less.

is

1

s,

while the computation time

Essentially, the frequency of

is very great. A second frequency calculation made from a second period measurement would improve the probability of error, while a third calculation would further improve the error. The calculating frequency

probability of error that

Frequency Counters and Time-Interval Measurements

346

counter would continue to

make frequency

calculations

Chap. 10

from the period of the

input as long as the input were present and display the arithmetic

mean

of the

calculations.

Not only ability of a

are low-frequency measurements improved from the calculating

frequency counter; the measurement of pulsed carriers can be im-

proved by the calculating counter.

often necessary to determine the frequency

It is

of bursts of energy that do not last for long periods of time. consider a

1-jlls

burst of a

1-GHz

carrier.

To measure

As an example,

the frequency of the burst,

only 1,000 complete cycles are available that can be counted.

counter has an ambiguity of

an error of is

1

+

or

—

one count which in

part in 1,000, or 0.1 per cent. If the accuracy of the

measurement

more than one burst has to be counted and ultimately frequency calculation. The calculating frequency counter can make

to be better than this,

used for the

several measurements, average the result of each measurement, statistically

and display a

determined frequency.

In the section on frequency counter accuracy, is

The frequency

this case represents

it

was discussed that there

a point where measuring the period of an input with a certain clock frequency

produces improved accuracy over the measurement of the input frequency for a fixed gate time.

A block

capability of automatically

diagram of an automated frequency counter with the making period or input frequency measurement and

then performing the necessary mathematics to display the correct frequency

is

shown in Fig. 10-24. In this counter, rather than a conventional gate, there are two gated counters. One counter is used to accumulate the input frequency, while the second counter accumulates a precision clock. Both counters are gated Matched Gates Input

>-

A Counter

van

>

B Counter

Gate

Time Base

Computer

Precision

Clock

Period/Frequency Display

Figure 10-24

Precision computing counter using dual counters.

347

Problems

Chap. 10

simultaneously, such that the

counter B.

number of input

A while a precision clock,

cycles has been accumulated in

or the elapsed time

The frequency of the input can be determined from input frequency

count in

=

:

count in

The opening and

is

accumulated

counter

in

the following relationship:

A (10-9)J

B

closing of the gate are controlled from either the input

if the gate is controlled by measurement will be made, and if the gate is controlled by the input signal, a period measurement is being made. As previously explained, the frequency where the accuracy changes from a period measurement to a frequency measurement is (fc ) l/2 where fc is the clock frequency from which the time base is derived and the clock used for the period measurement. In this example the precision clock used for the period measurement is 500 MHz, which places the changeover point at 22 MHz. From the setting of the input switches, which can select the number of significant digits and the resolution, the automatic frequency counter will select the method of measure-

signal or the internal precision clock. Essentially,

the internal clock a conventional frequency

,

ment.

REFERENCES 1.

Prensky, Sol D., and Castellucis, Richard

Englewood 2.

Cliffs, N.J.:

Tocci, Ronald

Englewood

J.,

L.,

Digital Systems: Principles

Cliffs, N.J.:

Electronic Instrumentation,

3rd ed.

Prentice-Hall, Inc., 1982.

and

Applications, chaps. 4,

5,

and

7.

Prentice-Hall, Inc., 1980.

PROBLEMS 1.

A

frequency counter capable of measuring an

unknown frequency

to within

1

Hz

by measuring frequency rather than period would require what minimum gate time? (2}

To what

accuracy can a frequency counter determine an

kHz, using a 3.

How many

1-s

unknown frequency

of 450

time base and a time-base accuracy of 0.01 per cent?

displays (total decades) should a frequency counter have

and resolution are

if its

accuracy

to be 0.001 per cent?

(5plf the internal time base of a frequency counter is 10.000 MHz, what frequency range is best measured by a period measurement, and what frequency range is best

measured by a conventional frequency measurement? 5.

What

effects

on accuracy, resolution, etc., does the addition of a on a frequency counter?

fixed

modulus

prescaler have

^pWhat method can be used to increase the frequency range of a frequency counter? How can this be achieved without degrading the accuracy of the counter?r 7.

What problems

are associated with the

measurement of pulsed

signals?

^4

CHAPTER

1 1

TRANSDUCERS AS INPUT ELEMENTS TO INSTRUMENTATION SYSTEMS

11-1 CLASSIFICATION

An

OF TRANSDUCERS

number of components which measurement and record the result. An instrumentation system generally consists of three major elements: an input device, a signal-conditioning or processing device, and an output device. The input device receives the quantity under measurement and delivers a proportional electrical signal to the signal-conditioning device. Here the signal is amplified, filtered, or electronic instrumentation system consists of a

together are used to perform

a'

otherwise modified to a format acceptable to the output device. device

may

The output

be a simple indicating meter, an oscilloscope, or a chart recorder

for visual display. It

may be a magnetic tape recorder for temporary or permanent it may be a digital computer for data manipulation

storage of the input data, or

or process control.

how

The kind of system depends on what

the measurement result

The input quantity

for

is

is

to be

measured and

to be presented.

most instrumentation systems

is

nonelectrical. In

order to use electrical methods and techniques for measurement, manipulation, or control, the nonelectrical quantity device called a transducer.

One

when actuated by energy

in

same form or transmission

in

may

is

converted into an electrical signal by a

definition states "a transducer

is

a device which,

one transmission system, supplies energy

in the

another form to a second transmission system." This energy be

electrical,

mechanical, chemical, optical (radiant), or ther-

mal.

This broad definition of a transducer includes, for example, devices that convert mechanical force or displacement into an electrical signal. These devices

348

Sec. 11-2

Selecting a Transducer

349

form a very large and important group of transducers commonly found in the and the instrumentation engineer is primarily concerned with this type of energy conversion. Many other physical parameters industrial instrumentation area,

(such as heat, light intensity, humidity) may also be converted into electrical energy by means of transducers. These transducers provide an output signal when stimulated by a nonmechanical input: a thermistor reacts to temperature variations, a photocell to changes in light intensity, effects,

and so on. In

all cases,

an electron beam to magnetic

however, the electrical output

measured by

is

standard methods, yielding the magnitude of the input quantity in terms of an analog electrical measure.

Transducers may be classified according to their application, method of energy conversion, nature of the output signal, and so on. All these classifications usually result in overlapping areas. A sharp distinction between, and classification types of transducers is difficult. Table 11-1 shows a classification of transducers according to the electrical principles involved. The first part of the table lists transducers that require external power. These are the gassive transducers, proof,

ducing a variation in some electrical parameter, such as resistance, capacitance, and so on, which can be measured as a voltage or current variation. The second category are transducers of the self-generating type, producing an analog voltage or current when stimulated by some physical form of energy. The self-generating transducers do not require external power. Although it would be almost impossible to classify all sensors and measurements, the devices listed in Table 1 1- 1 .represent a good cross section of commercially available transducers for application in instrumentation engineering.

Some

of the more

common

trans-

ducers and their application are discussed in the following sections.

11-2 SELECTING

A TRANSDUCER

In a measurement system the transducer

function of transforming

signal. Selection of the appropriate

most important step

is

the input element with the critical

some physical quantity transducer

is

to a proportional electrical

therefore the

in obtaining accurate results.

A

first

and perhaps

number of elementary

questions should be asked before a transducer can be selected, for example,

(a)

4/* J (b) (c)

The

first

What is the physical quantity to be measured? Which transducer principle can best be used to measure What accuracy is required for this measurement?

this quantity?

question can be answered by determining the type and range of the

measurand.

An

appropriate answer to the second question requires that the

input and output characteristic of the transducer be compatible with the recording

or measurement system. In most cases, these two questions can be answered readily,

implying that the proper transducer

is

selected simply

by the addition

1

"

C £ u a

a

H &

3 £

>

£ 3

.ti

>

«J

.3

-a

o o

'3

H

U

—

0)

1

§

5

£

o ^ C C D

c/5

o 13

"o

G U

O

Si

c 3

g 1)

£?

o .2 a >

si

^

4>

2 ° '5 s

ed

2 *? D C

« £

~

^

i3 6JD

c

I

"S

g

> * £ o 03

C •s.

2

5

C

8 o c

«

I

00

| 4= 00

3

> g o '-3

.2

s

«

3

-

2

-a

3 43 a C Cu O 03 c O _ 43 o a E « 2

T3

w c 5/5

a.

°

TZ

^ o

3 C O

T3

-a

o

S5g 3

T3 t« (S

03

O

§ .2 8 2 3 O 03

Comparator Outputs

Figure 12-13

and j V;

if all

than } V. In

1

Analog

Reference Voltage

V

Chap.

^V {V

to-^V to

|v

Simultaneous analog-to-digital converter.

the comparators are on, the analog voltage must be greater

four different output conditions

total,

parators on to all comparators on.

may

The analog input

exist:

from no com-

voltage can therefore be

resolved in four equal steps. These four output conditions can be coded to give

two binary

bits

of information. This

is

shown

in the table alongside the

diagram

of Fig. 12-13. Seven comparators would give three binary bits of information,

comparators would give four bits, etc. The advantage of the simultaneous system of A/D conversion is its simplicity and speed of operation, especially when low resolution is required. For a high-resolution system (a large number of bits), this method requires so many fifteen

comparators that the system becomes bulky and very

12-5.3 Counter-type

A/D

If the reference voltage to variable, the

Converter

which the analog input

number of comparators could be reduced

the reference voltage

is

costly.

is

to be

to only one.

a linearly increasing voltage (a ramp) that

compared were If,

is

for instance,

continuously

applied to the comparator input, coincidence of the reference voltage and the

unknown voltage could be determined in terms of the time elapsed since ramp started. But a digitally controlled variable reference already exists in form of the simple

D/A

converter of Fig. 12-12. This

used to convert a digital number in

which can be compared

to the

its

DAC

unknown analog

D/A

register into

the the

converter can be

an analog voltage

input by a comparator circuit.

Sec. 12-5

If the

Analog-to-Digital Conversion

411

two voltages are not equal, the digital number in the DAC register is its output is again compared. This is exactly the operation of the

modified and

circuit of Fig. 12-14.

The

A/D

generalized

converter of Fig. 12-14

is

feedback system, where the main components are the and some control logic circuitry.

D/A

the comparator,

may be used to control the conversion that takes place One of the simplest ways is to start the DAC at zero

Various methods in the

actually a closed-loop

DAC,

converter.

and count the number of input pulses required to give an output voltage that equals the analog input. Analog Input

Reference Supply

DAC Feedback Loop

Digital

Output

Gating

and

Flip-flop Register

Control

D/A Converter Figure 12-14

A/D

converter using a

DAC

to provide the

comparison voltage. The

contents of the flip-flop register provide the digital output.

The

counter-type

A/D

converter of Fig. 12-15 contains a

D/A

converter

(DAC), the reference supply, the DAC register of Fig. 12-14. The

section consisting of the resistive divider network

and a six-stage counter which replaces comparator again receives the unknown analog input the generated

DAC

for

comparison against

output voltage. The control circuitry consists of a pulse

generator or clock, a signal gate that steers the clock pulses to the counter, and a control flip-flop for starting and stopping the conversion.

When

a start signal

start-stop flip-flop

is reset.

is

given, all the counter flip-flops are cleared

This

flip-flop

and the

provides a gating level (positive logic)

to the signal gate, allowing the clock pulses to be applied to the counter register.

The clock

pulses are propagated through the counter, and the

DAC

output increases in steps toward the top of the reference voltage. divider output

is

the

equal to the analog input, the comparator switches, delivering

an output signal to the start-stop

flip-flop.

This

flip-flop sets

to zero, blocking the clock pulses at the signal gate.

stores the

divider

When

number of clock

At

and

its

output drops

this instant, the

counter

pulses that were required to raise the reference

voltage to the level of the analog input voltage.

then the binary equivalent of the analog input.

The contents of

the counter are

412

Sec. 12-5

Analog-to-Digital Conversion

The

413

measured from the moment a request is given to is available. For the counter-type A/D converter the conversion time depends on the magnitude of the analog voltage and is conversion time

moment

the

is

a digital output

therefore not constant. If the input signal

know when

is

variable,

uncertainty of this time measure

is

is

also important to

The

called the aperture time (sometimes also

window or sample time). The aperture occurs shown in the waveform diagram of Fig. 12-16.

called as

it

the input signal had the value given by the digital output.

at the

end of the conversion,

Volts

Analog Voltage

Figure 12-16 of coincidence

The bits (extra

Waveform diagram of analog when readout occurs.

input and divider output showing points

resolution of the counter-type converter

is

improved by adding extra

counter stages). This addition can be done at small extra cost. The

conversion time, however, increases rapidly with the number of bits used, since

an

jV-bit

converter needs time for 2

A

counts to accumulate. Higher resolution

therefore obtained at the cost of increased conversion time.

is

One method into sections.

of

five bits each.

the counter

of decreasing the conversion time

For instance, a is

At

10-bit converter

to divide the counter

the start of the conversion, the least significant section of

preset to all ones

significant section.

is

could be divided into two sections

When

and counts are inserted only into the most

the comparator indicates that the analog input level

has been exceeded, the least significant section of the counter the

until the correct value

complete a conversion

is

6

)

cleared, reducing

reached.

The maximum number of

steps required to

5

is

2 for the most significant counter and 2

significant counter, giving a total of 2

(2

is

DAC divider output. Pulses are then inserted into the least significant section

versus 1,024 counts (2

10

)

6

steps.

This

is

a

for the standard counter.

maximum

5

for the least

of 64 counts

Analog and

414

The

section counter technique

where the output

is

is

Digital

Data Acquisition Systems

Chap. 12

frequently used in digital voltmeters,

to be in decimal notation.

Each

section of the counter then

represents a sectional digit.

12-5.4 Continuous

The

A/D

Converter

big disadvantage of the counter converter

is

that the entire comparison

process starts from the beginning each time a coincidence has been detected by the comparator. This

A

means low resolution and low speed. counter method involves replacing the simple

slight modification of the

counter with a reversible counter, or up-down counter. This allows the converter to continuously follow the analog input voltage this voltage changes.

Once the converter

whatever the direction

in

which

starts running, the digital equivalent

of the input voltage can be sampled at any time, and an extremely rapid readout is

possible.

The

simplified logic block

converter.

The

D/A converter,

(b) the

diagram of

Fig. 12-17 represents the continuous

up-down counter,

illustration contains four basic parts: (a) the (c)

the comparator, (d) the synchronization and control

logic.

An

ordinary binary counter counts in the forward direction (up)

trigger input of the succeeding binary

is

connected to the

1

when

the

output of the

preceding binary. The count will proceed in the reverse direction (down)

if

the

made instead to the 0 output of the preceding binary. The two methods may be used simultaneously to produce an up-down counter. In Fig. coupling

is

12-17 additional

make

AND

nization of the count

D/A

The Fig.

gates are used in the trigger circuits of the binaries to

moment; synchro-

sure that counts are accumulated only at the desired

and the comparison must take

converter section

is

place.

identical to the basic resistive divider of

12-11; the reference supply provides the required precision voltage for

accurate conversion.

DAC,

but

it

The 0 outputs of the

binaries are connected directly to the

should be understood that appropriate level conversion takes place

between the binaries and the

DAC

input terminals.

The comparator again compares

the analog input voltage with the

output voltage, providing two possible output voltage is larger than the feedback voltage comparator output terminal is connected to the

input voltage

a gating element. Similarly,

when

(DAC

When

levels.

output), the appropriate

set input

of the up flip-flop via

the analog input voltage

is

feedback voltage, the comparator provides an output voltage at

which

The flops

is

then connected, via a gate, to the

is

smaller than the its

terminal of the

actual transfer of the comparator output signals to the

other terminal

down

flip-flop.

up and down

flip-

controlled by gating pulses from the clock, which controls the synchro-

nization of the entire flops are exclusive

both

set

DAC

the analog

measurement

OR 'd

cycle.

together to

make

The outputs of

the up and

down flipwhen

sure that no count takes place

flip-flops are set (a safety precaution).

r

Digital

Outputs

Up-down Counter

D/A Conversion

° FF

0

t

0

1

FF

—

0

FF

FF

1

1

c

i

0

T.

1

FF

1

Down

Up Synchronization /Control

Comparator

re

Feedback Voltage

0

1

C

3

1

Analog Input o

2 Figure 12-17

Down Flip-Flop

Up Flip-Flop]

0

1

q

s

i

Delay

n

Clock

Simplified logic block diagram of the continuous converter.

415

Analog and

416

At the

measuring

start of a

Data Acquisition Systems

Digital

cycle,

when

all

Chap. 12

the flip-flops are cleared, the

clock generates a pulse that samples the comparator output. If the analog input is

it usually is when a measurement first The delayed clock pulse is then allowed to trigger the same time, it conditions the trigger gate of the

larger than the feedback voltage (as

starts),

the

the up flip-flop

first

is set.

binary, while at

succeeding binary. The 0 output of the

and the resulting

DAC output

analog input

If the

is still

is

first

compared

binary

and also

at

The procedure

DAC

output

is

this at the

pulse

up

flip-flop again,

binary back to

original

its

used for comparison against the analog

repeats until the feedback voltage equals the analog input,

which time the comparator output If the

by the comparator.

The count then has advanced by one

to trigger the next binary.

and the corresponding input.

first

DAC,

connected to the

larger, the next clock pulse sets the

allowing the delayed clock pulse to trigger the state

is

to the analog input

is

zero and the count

stopped.

is

analog input changes to a lower value, the next clock pulse detects

comparator output and

sets the

down

Now

flip-flop.

the delayed clock

allowed to enter the binary counter at the trigger input of the

is

binary, but the count

is

first

carried from stage to stage at the 0-output side of the

binaries of Fig. 12-17 so that the contents of the counter are reduced by one.

DAC

The

output then also drops the appropriate amount and the next com-

parison determines whether the up flip-flop or the

down

flip-flop will

be

set.

The

counter therefore continuously follows the analog input voltage.

The waveform diagrams of Fig. The aperture is the time

converter.

12-18 illustrate the action of the continuous

The assumption more than ± 1 LSB (the

for the last step.

that the analog input voltage does not change

increment of the the

DAC)

between conversion

steps.

To meet

maximum range of change of the input voltage must

rate of

made

smallest

this requirement,

not exceed the

maximum

change of the converter.

12-5.5 Successive-approximation

The successive-approximation to a

is

DAC

reference voltage that

illustrated in Fig. 12-19,

where a

A/D

is

A

Converter

converter compares the analog input

repeatedly divided in half.

four-digit binary

the full reference supply voltage V,

corresponding to - V.

A/D

is

number

The process

divided in half (binary

comparison between

is

(1000), representing

number

this reference voltage {\

100),

V) and

is made. If the result of this comparison shows that this first approximation was too small (y V is smaller than the analog input), then the next comparison will be made against j V (binary number 1 10). If the comparison showed that the first approximation was too large ( T V larger than the analog

the analog input

input), then the next

comparison

will

be

made

against \

After four successive approximations, the digital

number

will

V

number

(binary

is

number

resolved.

A

010).

six-digit

be resolved in six successive approximations. This compares very 6 with a conventional ) comparisons needed

favorably with the sixty-four (2

counter-type converter.

Final

Compa rison Third

Comparison Second Comparison First

HE

Comparison

1

f V

RTO

Ton 1

\ V

10

fTOQ

oo

oTTl [011

oTol

iV 1010 DAC

001

Output Voltage

ov

ooo

Contents of Control Register Figure 12-19

Operation of the successive-approximation

A/D

converter.

417

Analog and

418

Digital

The successive-approximation method previous methods since

it

is

a

little

more

Chap. 12

elaborate than the

requires a special control register to gate pulses to the

bit, and so on. The additional cost of the control and the converter can handle continuous and diswith large and small resolutions at moderate speed and

first bit,

then to the second

register,

however,

is

continuous signals

moderate

Data Acquisition Systems

small,

cost.

The generalized block diagram of Fig. 12-20 shows the basic successive approximation converter. The converter uses a digital control register with gateable

and 0

1

comparison

tribution register

which step

inputs, a digital-to-analog converter with reference supply, a

timing loop, and a distribution register. The dis-

circuit, a control

is

is

like a ring

counter with a single

1

circulating in

it

to determine

taking place.

Analog Input

9 Digital

Reference Supply

-to-Analog Converter

Digital

Output Control Register

Time Delay Set

MSB

Startstop Distribution Register

Flip-flop Start

o

End Figure 12-20

of

Conversion

Simplified block diagram of the successive-approximation

A/D

con-

verter.

At the beginning of the conversion distribution register are set with a in all bits of less significance.

The

1

.

.

.

,

both the control register and the

most significant

bit

(MSB) and

a 0

distribution register therefore registers that

the cycle has started and that the process

which now reads 1000

cycle,

in the

is

in its first phase.

The

control register,

causes an output voltage at the digital-to-analog

converter section of one-half of the reference supply. At the same instant, a pulse enters the timing delay chain.

By

the time the

D/A

converter and the

comparator have settled, this delayed pulse is gated with the comparator output. When the next most significant bit is set in the control register by the action of

Sec. 12-5

Analog-to-Digital Conversion

419

the timing chain, the most significant bit either remains in the

1

-state or

it is

depending on the comparator output. The single 1 in the distribution register is shifted to the next position and keeps track of the number of comparisons made. reset to the 0-state,

This procedure repeats, following the diagram of Fig. 12-19, until the

final

approximation has been corrected and the distribution register indicates the end of the conversion. Synchronization

is

not required in this system because the

comparator controls only one flip-flop at a time. For a successive-approximation converter, the

some value

digital

output corresponds

had during the conversion. Thus the aperture time is equal to the total conversion time. This is illustrated in the waveform reconstruction of Fig. 12-21. Aperture time of this converter can be reduced by using redundancy techniques or by using a sample-and-hold circuit. to

that the analog input

Analog

Read Read Read Read Read Read Read Read Read Read Read Read Read Out 1

Out 2

Out

Out

3

4

Out 5

Out

Out

Out

Out

6

7

8

9

Out 10

Out II

Out 12

Voltage

Figure 12-21

proximation

Waveform diagrams

A/D

converter.

illustrating the operation of the successive-ap-

Out 13

Analog and

420

Digital

Data Acquisition Systems

Chap. 12

12-5.6 Sample-and-hold Circuit

A

sample-and-hold circuit

used with an

is

necessary to convert a high-frequency signal that

The sample-and-hold

an accurate conversion.

is

A/D

circuit

amplifier that charges a capacitor during the sample

converter

is

it

is

basically an operational

mode and

retains the charge

The sample-and-hold

of the capacitor during the hold mode.

when

varying too rapidly to allow

circuit

can be

represented by the simple switch and capacitor of Fig. 12-22.

(b)

(a) Circuit

Input

waveform

Hold

Sample

/

/

Al

1

1

I

I

1

i

1

I

i

1

t

(c)

Figure 12-22

When

the switch

Output waveform

Operation of the sample-and-hold

is first

circuit.

closed, the capacitor charges to the value of the

input voltage and then follows the input (assuming a low driving source impedance).

When

at the

time the switch was opened (assuming a high-impedance load).

The

the switch

is

opened, the capacitor holds the voltage that

acquisition time of the sample-and-hold

is

The aperture time

and the uncertainty time

is

in the

is

is first

the time required for the switch to change state

time that this change of state occurs. The holding

the length of time the circuit can hold the charge without dropping

than a specified percentage of It is

had

the time required for the

capacitor to charge up to the value of the input signal after the switch shorted.

it

its initial

possible to build a sample-and-hold circuit exactly as

12-22. Often, however, the circuit

is

more

value.

built

shown

in Fig.

with fast-acting transistor switches

and an operational amplifier to increase the available driving current into the capacitor or to isolate the capacitor from an external load on the output. However the sample-and-hold circuit is built, it always acts as the simple switch and capacitor shown.

Sec. 12-6

421

Multiplexing

—VWV-

V\AAr-

|Okn

Input

9.5

11%

1

kH

1

kn

7


-

20

dB

-

20

dB

2.884

X

10

X

10

=

100

X

100

dB

Number

9.2

dB

2.884

288.4

8.318

8.318

X

=

of decibels negative (-).

number of

to the given

=

decibels until the

sum

83180

Add + falls

20 decibels successively

within the range of Table

1

For the voltage ratio, divide the value from the left-hand voltage-ratio column by 10 for each time 20 dB was added. For the power ratio, divide the value from the left-hand power-ratio column by 100 for each time 20 dB was added. Example Given: -49.2

dB -49.2 dB

Voltage

ratio:

-9.2 dB

—»

+

ratio:

-9.2 dB

—>

dB + 20 dB = -9.2 dB

0.3467

0.3467

Power

20

x

X

i-

= 000 34 67

0.1202

0.1202

X

—X—= 100

0.00001202

100

453

Voltage Ratios to Decibels: Table

For ratios smaller than those by 10 successively

by

Table

2.

Multiply the given ratio

product can be found in Table

until the

of decibels thus found, subtract tiplied

in

457

2, p.

+20

2.

From

number was mul-

the

decibels for each time the ratio

10.

Example Given: Voltage ratio

=

0.0131

X

0.0131

From Table

2:

1.31

—»

2.345

10

=

1.31

dB

dB -

2.345

X

10

20

dB - 20 dB

For ratios greater than those

in

=

-37.655 dB

Table

2.

Divide the given ratio by

10 successively until the remainder can be found in Table decibels thus found,

add

+20 dB

for each time the ratio

2.

Example Given: Voltage ratio

=

712 712

From Table

2:

7.12

—

>

17.050

17.050

454

x

To

x To

=

7 12

dB

=

-

dB

dB + 20 dB

+

20

57.050

To

the

number of

was divided by

dB

10.

1

1

TABLE To account (a)

Conversion of Decibels to Power and Voltage (or Current) Ratios

1

for the sign of the decibel:

For positive

+ ) dB

(

values use the

two right-hand columns. The voltage and power

ratios

are greater than unity. (b)

For negative

(

— dB )

values use the two left-hand columns.

The

voltage and

power

ratios

are less than unity.

-dB+ Voltage

Hal 10 1.0000 .9886 .9772 .9661

.yoou .9441

.9333 .9226 .9120 .yui o

flower Ratio

1.0000 .9772 .9550 .9333 9 1 20

dB 0 .1

.2 .3

A

.8913 .8710

.5 .6

.8511

.7 .8

.8318

Q .y

.8913 .8810 .8710 .8610 851

.7943 .7762 .7586 .7413

.8414 .8318 .8222 .S12K .SUoO

.7079 .6918

.7943 .7852 .7762 .7674

o8b

.6310 .6166 .6026 .5888 .0/ 04

.7499 .7413 .7328 .7244 .7161

.5623 .5495 .5370 .5248 .5129

2.5 2.6 2.7 2.8 2.9

.7079

.5012 .4898 .4786 .4677

3.0

.

/

.6998 .6918 .6839 .6761

7244

.6761 .6607 KA ^7

-dB+ Voltage Ratio

Power

1.000 1.012 1.023 1.035

1.000

1

047

1.059 1.072 1.084 1.096 1

1

no

Voltage Ratio

Power Ratio

3.41

10.655

dB

(voltage) X

Voltage Ratio 1.0 1.1

1.2 1.3 1.4

.00 .

000

.828 1.584

2.279 2.923

.02

.01

.086 .906 1.656 2.345 2.984

.03

.172 .984 1.727

=

dB X -

10.655

dB (power)

5.328

.05

.04

.06

.07

.424 1.214 1.938 2.607 3.227

.506 1.289 2.007 2.671 3.287

.588 1.364 2.076 2.734 3.346

.668 1.438 2.144 2.798 3.405

2.212 2.860 3.464

3.637 4.190 4.711 5.201 5.666

3.694 4.244 4.761 5.249

3.750 4.297 4.811 5.296 5.756

3.807 4.350 4.861 5.343 5.801

3.862 4.402 4.910 5.390 5.845

3.918 4.454 4.959 5.437 5.889

3.973 4.506 5.00S 5.483 5.933

4.028 4.558 5.057 5.529 5.977

6.319 6.729 7.121 7.495 7.854

6.361 6.769 7.159 7.532 7.889

6.403 6.809 7.197 7.568 7.924

8.199 8,530 8.850 9.158 9.455

8.232 8.563 8.881 9.188 9.484

8.266 8.595 8.912 9.218 9.513

9.771 10.049 10.317 10.578 10.832

9.799 10.076 10.344 10.604 10.857

2.41

3.046

5.621

6.064 6.486 6.888 7.272 7.640

6.

107 6.527 6.927 7.310 7.676

6.

150 6.568 6.966 7.347 7.712

6.

2.2 2.3 2.4

6.021 6.444 6.848 7.235 7.604

193 6.608 7.008 7.384 7.748

6.235 6.649 7.044 7.421 7.783

6.277 6.689 7.082 7.458 7.819

2.5 2.6 2.7 2.8 2.9

7.959 8.299 8.627 8.943 9.248

7.993 8.333 8.659 8.974 9.278

8.028 8.366

8.062 8.399 8.723 9.036 9.337

8.097 8.432 8.755 9.066 9.367

8.131 8.465 8.787 9.097 9.396

8.165 8.498 8.818 9.127 9.426

3.0

9.542

9.939 10.211 10.475 10.731

9.686 9.966 10.238 10.501 10.756

9.743

9.883 10.157 10.423 10.681

9.629 9.911 10.184 10.449 10.706

9.714

9.827 10.103 10.370 10.630

9.571 9.855 10.130 10.397 10.655

9.657

3.1

9.994 10.264 10.527 10.782

10.021 10.291 10.553 10.807

10.931 1 1 174

10.955 1 1.198

10.980

1.41

1K434

1L457

1

1.481

1L504

.5

1.6 1.7 1

.8

1.9

to 2.1

3.2 3.3 3.4

3.580 4.137 4.660 5.154

8.691 9.005 9.308

9.600

5.71

.053 1.293

11.078

1

11

1L527

1L573

11.754 11.976

11.550 11.777 11.998

12.770 12.967

12.171 12.382 12.588 12.790 12.987

12.192 12.403 12.609 12.810 13.006

12.213 12.424 12.629 12.829 13.026

12.234 12.444 12.649 12.849 13.045

13.141 13.330 13.516 13.697 13.875

13.160 13.349 13.534 13.715 13.892

13.179 13.368 13.552 13.733 13.910

13.198 13.386 13.570 13.751 13.927

13.217 13.405 13.589 13.768 13.945

13.236 13.423 13.607 13.786 13.962

14.031 14.202 14.370 14.535 14.696

14.049 14.219 14.387 14.551 14.712

14.066 14.236 14.403 14.567 14.728

14.083 14.253 14.420 14.583 14.744

14.100 14.270 14.436 14.599 14.760

14.117 14.287 14.453 14.616 14.776

14.134 14.303 14.469 14.632

14.855 15.010 15.163 15.313 15.461

14.870 15.026 15.178 15.328 15.476

14.886 15.041 15.193 15.343 15.490

14.902 15.056 15.208 15.358 15.505

14.917 15.072 15.224 15.373 15.519

14.933 15.087 15.239 15.388 15.534

14.948 15.102 15.254 15.402 15.549

11.596 11.821

11.387 11.618 11.844

11.641 11.866

11.664 11.888

11.687 11.910

11.709 11.932

11.732 11.954

4.9

12.041 12.256 12.465 12.669 12.869

12.063 12.277 12.486 12.690 12.889

12.085 12.298 12.506 12.710 12.908

12.106 12.319 12.527 12.730 12.928

12.128 12.340 12.547 12.750 12.948

12.149

4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

13.064 13.255 13.442 13.625 13.804

13.084 13.274 13.460 13.643 13.822

13.103 13.293 13.479 13.661 13.839

13.122 13.312 13.497 13.679 13.857

5.0

13.079

5.1

5.2 5.3 5.4

14.151 14.320 14.486 14.648

13.997 14.168 14.337 14.502 14.664

14.014 14.185 14.353 14.518 14.680

5.5 5.6 5.7 5.8 5.9

14.807 14.964 15.117 15.269 15.417

14.823 14.979 15.133 15.284 15.432

14.839 14.995 15.148 15.298 15.446

4.1

1 1

1

50

1

1

11.102

1 1

1

10.906

1L364

3 6

.749 1.511

1 1

10.881 1 1.126

3.7 3.8 3.9

3.5

.09

.341 1.138 1.868 2.542 3. 167

3.522 4.082 4.609 5. 105 5.575

1

.08

.257 1.062 1.798 2.477 3. 107

1 1

.222

11.005 1 1 .246

12.361 12.568

.029 1.270

317

1

1.341

11.799 12.019

14.791

457

TABLE

2

Conversion of Voltage (or Current) and Power Ratios to Decibels (cont.)

T

V olX(XQt Ratio

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

6.0

15.563 15.707 15.848 15.987 16.124

15.577

15.592 15.735 15.876 16.014

15.606 15.749

15.635

778

15.649 15.792

15.918 16.055 16.191

15.931 16.069 16.205

15.664 15.806 15.945 16.083 16.218

15.678 15*820 15.959 16^096 16.232

15.692 15.834 15.973 16^1 10 16.245

16.258 16.391 16.521 16.650 16.777

7.2 7.3 7.4

16.151

16.028 16.164

15.621 15.763 15.904 16.042 16.178

16.272 16.404 16.534 16.663 16.790

16.285 16.417 16.547 16.676 16.802

16.29S 16.430 16.560 16.6S8 16.815

16.312 16.443 l6.57o 16.701 16.827

16.325 16.456 16.586 16.714 16.840

16.338 16.468 16.598 16.726 16.852

16.351 16.483 16.612 16.739 16.865

16.365 16.496 16.625 16.752 16.877

16.378 16.509 16 637 16.764 16.890

16.902 17.025 17.147 17.266 17.385

16.914

16.927 17.050

16.939 17.062 17.183

17.290 17.408

17.302 17.420

16.951 17.074 17.195 17.314 17.431

16.964 17.086 17.207 17.326 17.443

16.976 17.098 17.219 17.338 17.455

16.988 17.110

17.171

17.231 17.349 17.466

17.001 17.122 17.243 17.361 17.478

17.013 17.135 17.255 17.373 17.490

7.5 7.6 7.7 7.8 7.9

17.501 17.616 17.730 17.842 17.953

17.513 17.628 17.741 17.853 17.964

17.524 17.639 17.752 17.864 17.975

17.536 17.650 17.764 17.875 17.985

17.547 17.662

17.570 17.685

17.886 17.996

17.559 17.673 17.786 17.897 18.007

17.908 18.018

17.582 17.696 17.808 17.919 18.029

17.593 17.707 17.820 17.931 18.040

17.605 17.719 17.831 17.942 18.051

8.0

18.062 18.170 18.276 18.382 18.486

18.073 18.180 18.287 18.392 18.496

18.083 18.191 18.297 18.402 18.506

18.094 18.202 18.308 18.413 18.517

18.105 18.212 18.319 18.423 18.527

18.116 18.223 18.329 18.434 1H.537

18.127 18.234 18.340 18.444 18.547

18.137 18.244 18.350 18.455 18.558

18.148 18.255

18.159 18.266

8.2 8.3 8.4

18.361 18.465 18.568

18.371 18.475 18.578

8.5 8.6 8.7 8.8 8.9

18.588 18.690 18.790 18.890 18.988

18.599

18.609 18.710 18.810 18.909 19.007

18.619 18.720 18.820 18.919 19.017

18.629 18.730 18.830 18.929 19.027

18.639 18.740 18.840 18.939 19.036

18.649 18.750 18.850 lh.949 19.046

18.660 18.760 18.860 18.958 19.056

18.670 18.770 18.870 18.968 19.066

18.680 18.780 18.880 18.978 19.075

.0

19.085

9.1

19.181 19.276 19.370 19.463

19.094 19.190 19.285 19.379 19.472

19.104 19.200 19.295 19.388 19.481

19.114 19.209 19.304 19.398 19.490

19.123 19.219 19.313 19.407 19.499

19.133 19.228 19.323 19.416 19.509

19.143 19.238 19.332 19.426 19.518

19.152 19.247 19.342 19.435 19.527

19.162 19.257

9.2 9.3 9.4

19.351 19.444 19.536

19.171 19.226 19.360 19.453 19.545

9.5 9.6 9.7 9.8 9.9

19.554 19.645 19.735 19.825 19.913

19.564 19.654 19.744 19.833 19.921

19.573 19.064 19.753 19.842 19.930

19.582 19.673 19.762 19.851 19.939

19.591 19.682 19.771

19.600

19.609 19.700 19.789 19.878 19.965

19.618 19.709 19.798 19.886 19.974

19.627 19.718 19.807 19.895 19.983

19.636 19.726 19.816 19.904 19.991

6.1

6.2 6.3 6.4

6.5 6.6 6.7

6.8 6.9

7.0 7.1

8.1

Voltage Ratio

15.721 15.862 16.001 16.137

17.037 17.159 17.278 17.396

IN. 700

18.K00 1K.900 18.998

15 890

17 775

19.860 19.948

15

17 797

19.691

19.780 19.869 19.956

0

1

2

3

4

5

6

7

8

9

20 30 40

20.000 26.021 29.542 32.041

20.828 26.444 29.827 32.256

21.584 26.848 30.103 32.465

22.279 27.235 30.370 32.669

22.923 27.604 30.630 32.869

23.522 27.959 30.881 33.064

24.082 28.299 31.120 33.255

24.609 28.627 31.364 33.442

25.105 28.943 31.596 33.625

25.575 29.248 31.821 33.804

50 60 70 80 90

33.979 35.563 36.902 38.062 39.085

34.151 35.707 37.025 38.170 39.181

34.320 35.848 37.147 38.276 39.276

34.486 35.987 37.266 38.382 39.370

34.648 36.124 37.385 38.486 39.463

34.807 36.258 37.501 3S.588 39.554

34.964 36.391 37.616 38.690 39.645

35.117 36.521 37.730 38.790 39.735

35.269 36.650 37.842 38.890 39.825

35.417 36.777 37.953 38.988 39.913

100

40.000

10

To the

458

'

convert voltage and power ratios outside the range of this table, use

method

illustrated

on page 454 of the introduction to these

tables.

SELECTED ANSWERS

CHAPTER

1

mV

2.

I

4.

75.0

6.

82

8.

(a) 147.5 ft, (b) 0.21 ft, (c) 0.3 ft, (d) 0.2 ft

±

jLtF

0.1

mV

10. (a) (c)

36

± ±

ft

24.32

1.8 ft,

75

ft

±

3.75

ft,

(b) 111

±

5.55

ft,

111

± 5%

3.65 ft

3.7% ±7.55%, ±0.57%

12. (a) 435.3 ft, (b) 14. (a)

CHAPTER

2

GHz,

1.

1.5

3.

X 10~ 2.85 X 10 4.6

5.

180

9.

35.7

19

cm m/s

X 200 V

10

15. 4.6875

X

11. 3.6

13.

12,500 Hz, 0.125 jnH, 346,400 V, 0.0053 A, 5,000 9 13 12 hr, 14 X 10" /lis J, 0.0014 ms, 8.89 X 10~

17. (a) 8,930

6

10

15

kg/m

3 ,

(b)

557 lb/ft

3

mH,

ft,

Selected Answers

460

CHAPTER 6.

10.

3

0.999993 1.0190

fl

V

CHAPTER 4 n

1.

875

3.

36

MCI

6.

50

V

7.

(a)

0.094

9.

1.25

15.

900

17. 25

and higher

mW,

(b) 4.29

mW

V

n/v

W

CHAPTER 5 i.

o.oi

3.

6

v 5. 7.

X

n 10- 7

R = 34.3 ft, L = (a) R = 1,000 O, s

29 (b)

mH R = s

250

H

CHAPTER 6 mV,

2.

15

4.

26.6

6.

2+ pF

CHAPTER 6.

2.65

10,000

m,

X

H/V

2.66 kn, 266

O

7 10

7

m/s

CHAPTER 8 1.

2.65

3.

+35 dBm, -30 dBm, +26 dBw,

VtV+ 15.

15.9

Hz

1

N-

\

1

V,

+3 dBw, -17 dBw,

0.22

Selected Answers

461

CHAPTER 9 dB

1.

70

5.

-60 dBm

7.

(a)

(b) (c)

amount equal to the attenuation. dynamic range. Increases the noise figure by an amount equal to the attenuation. Increases the third-order intercept by an

Does not

affect the

CHAPTER 10 1.

Is

3.

Five digits

CHAPTER 4.

%

694

11

kg/cm

2

25 iiV

6,

4.16

7.

2.5

mm X

10" 3

mm

INDEX

463

1

464

AC

Index

Digital /analog conversion, 407

voltmeter, 151

ATE, 429

Direct frequency synthesis, 273

ATN, 434 Accuracy,

Distortion analyzer, 300

Distributed-parameter delay

1

Acquisition time, 420

Droop

Alternate sweep, 234

Dynaloy, 356

(pulse),

line,

232

284

Alternating-current instruments, 85

Analog /digital conversion, 409 Arithmetic mean, 4, 10 Atomic definition, 38 Atomic standard, 38

EDI, 435

Attenuator, 262

Electrostatic deflection, 212

piston,

266

Electrodynamometer, 86 Electromagnetic system, 22 Electronic multimeter, 156

Electrostatic system, 22

Average deviation, Ayrton shunt, 63

1

English system, 27

Environmental

errors, 9

Errors, 2

CRDX,

55

Campbell standard, 46 Capacitance comparison bridge, 129

FM

Capacitance standards, 45

Fluorescence, 220

Cathode ray

Form

tube,

210

Chopped sweep, 234

recording, 401

Falltime, 283

factor, 91

Chopper-stabilized amplifier, 149

Frequency divider signal generator, 274 Function generator, 291

Colpitts oscillator, 261

Fundamental-suppression analyzer, 303

Compensated attenuator, 225

Fundamental

Component measuring instrument, 178 Computing counter, 345 Constantan, 355

A/D

Continuous

DVM,

175

Conversion time, 413

Counter

Gating

error,

337

Gauss, 25 Gilbert, 25

Giorgi system, 22

327

Graticule, 222

frequency, 326

Guarantee

synchronous, 328

Counter-type Critical

Galvanometer, 50 Gas-filled phototube, 386

converter, 414

Continuous-balance

BCD,

units, 21

A/D

damping,

Guarded

errors, 16

bridge, 122

converter, 410

53, 55

Current transformer, 104

Hard beam, 217 Harmonic analyzer heterodyne, 302

DAV,

tuned

433

Delay

line,

Derived

230

units,

circuit,

Harmonic

Damping, 54 20

Detector, crystal, 281

Hay

301

converter, 342

bridge, 134

Heterodyne wave analyzer, 297 Horizontal deflection, 235

Deviation from the mean, 10 Differential voltmeter, 163

IEEE, 488, 433, 443

Digital recording, 402

IEEE

Digital voltmeter, 169

IFC, 435

standards, 47

Index

IM

465

Potential transformer, 104

distortion

second-order, 312

Potentiometer, 144

third-order, 312

automatic, 376

Indirect frequency synthesis, 270

Power-factor meters, 101

Inductance comparison bridge, 46

Precision,

Inductance standards, 46

Prescaler, 341

2

1,

Inductor-capacitor oscillator, 260

Primary standard, 35

Input resistance, 161

Probe, oscilloscope, 239

Instrument,

Pulse generator, 282

1

Instrument transformer, 103

Q

Instrumental errors, 9 Integrating

DVM,

meter, 186

173

International standard, 35

REN,

435

RF

power measurement, 203 Ramp-type DVM, 170

Josephson junction, 42

Random Kelvin bridge, 117

errors, 9, 186

Reciprocal mixing, 308 Rectifier-type instruments, 89

LORAN-C, LVDT, 362

39

Repetition rate, 284

Resistance thermometer, 369

Limiting errors, 16

Resolution, 2

Lumped-parameter delay

MKSA

line,

231

system, 22, 27

Risetime, 283

SI system, 22, 27

Magnetic tape recorder, 394

SINAD,

Maxwell

bridge, 132

SRQ, 435

Megohm

bridge, 124

Sag

Modulation, signal generator, 277 Multimeter, 80, 92

431

(pulse),

284

Sample-and-hold

circuit,

420

Sampling oscilloscope, 255

Multiplexing, 330, 421

Saturated

Multiplier phototubes, 386 Multiplier resistor, 65

cell,

42

Schering bridge, 136 Scientific notation, 3

Secondary standard, 35

NDAC, NRFD,

434

Self-balancing potentiometer, 403

433

Sensitivity, 2

Nichrome V, 355 Normal distribution,

voltmeter, 42 12

Significant figures, 3

Ohmmeter, 74

Spatial encoder, 424 Spectrum analyzer, 306 Square-wave generator, 282, 285

Oscilloscope, 208

Stability

Ohm,

25

long-term, 340

PIN

diode, 268

short-term, 340

Passive transducer, 349

Stabiloy, 356

Phosphorescence, 220

Staircase-ramp

Photoconductive

cell,

388

DVM,

171

Standard deviation, 12

Pi attenuator, 263

Statampere, 24

Postdeflection acceleration, 217

Storage oscilloscope, 248

466

Index

Transducer (cont.)

Strain gage, 353

Successive-approximation

A/D

oscillation,

converter, 416

Successive-approximation

365

photoelectric, 366

DVM,

177

Sweep-frequency generator, 277 Systematic errors, 9

piezoelectric, 367

potentiometric, 368

Trigger level error, 341

True

RMS

voltmeter, 155

Taut-band suspension, 59

Temperature compensation (meters), 60 Thermistor, 377 Thermocouple, 374 Thermoinstruments, 94

Vacuum

Third-order intercept point, 313

Vertical deflection, 224

phototube, 384

Variable differential transducer, 362

Vector impedance meter, 195 Vector voltmeter, 199

Three-terminal resistance, 123

Time Time

base, 332

solar,

Wagner ground, 142 Watthour meter, 99

37

universal, 37

Transducer displacement, 359

Wattmeter, 97

Wave

analyzer, 296

Weston

cell,

42

THIRD EDITION

ELECTRONIC INSTRUMENTATION

AND MEASUREMENT TECHNIQUES WD COOPER A.D HELFRICK

This new Third Edition traces test and measurement systems from the simplest basic parameter measurement through the latest computercontrolled test system. Mathematical derivations are given for basic measurement to help you understand these measurements.

Among • •

• •

this

book's many special features:

improved material on digital measurements. expanded discussion of spectrum analysis. entire chapter on computer-controlled measurements. updated material on oscilloscopes and on recent advances

in

CRT

construction.

Of special interest: In-depth discussion of basic measurements systems; worked-out examples and review questions; broad range of measurement systems.

PRENTICE-HALL,

INC.,

Englewood

Cliffs, N.J.

07632

ISBN 0-13-250721-5