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Appendix I

UNITS, SYMBOLS AND CONVERSION FACTORS

The international system of units (Systeme International d'Unites - SI) has been established by international agreement to provide a logical and interconnected framework for all measurements in science and industry. It is based on six units: the metre (length), the second (time), the kilogramme (mass), the ampere (electric current), the kelvin (temperature) and the candela (luminous intensity). The majority of the world's population already use the SI system of units and it is possible that by 1975 the only major countries who have not changed will be Canada and the U.S.A.

In addition to the defining of the six basic units the SI establishes a set of factors that should be applied to all quantities so that their magnitude may always be written with less than four numerals before the decimal point, thus removing some of the difficulties associated with manipulating very large and very small numbers (see table A.l). Table A.2lists the units in the SI system.

Table A.l Multiples

Prefix Symbol Factor by which the unit is to be multiplied

tera T 1012

giga G 109

mega M 106

kilo k 103

milli m 10-3

micro JJ. 10-6

nano n 10-9

pica p 10-12

femto f 10-15

at to a 10-18

Tabl

e A

.2.

Uni

ts

Qua

ntit

y SI

Uni

ts

Sta

ndar

d -

defi

niti

on

Equ

ival

ents

C

onve

rsio

n fa

ctor

Im

peri

al

M.K

.S.

Mas

s ki

logr

amm

e (k

g)

mas

s o

f a

plat

inum

-iri

dium

po

und

(lb)

(k

g)

I lb

=

0.45

4 kg

cy

clin

der

kept

at

Sevr

es,

Fra

nce

I cw

t = 5

0.8

kg

I to

n=

101

6 kg

Len

gth

met

re (

m)

dist

ance

bet

wee

n tw

o e

ngra

ved

foot

(ft

) (m

) I

in

= 0.

0254

m

line

s on

a p

lati

num

-iri

dium

bar

I

ft

= 0.

3048

m

kept

at

Sevr

es,

Fra

nce

-al

so a

s 1

yd

= 0.

9144

m

I 65

0 76

3.73

wav

elen

gths

in

vacu

o 1

mil

e =

1.61

km

o

f th

e or

ange

lin

e (s

pect

rosc

opic

de

sign

atio

n 2

p10

5 d

5)

emit

ted

by

the

kryp

ton-

86 a

tom

Tim

e se

cond

(s)

th

e fr

acti

on 1

/31

556

925.

975

of

(s)

(s)

the

trop

ical

yea

r fo

r 19

00 J

an.

0.

Als

o as

the

int

erva

l oc

cupi

ed b

y

9 19

2 63

1 77

0 cy

cles

of

the

radi

atio

n co

rres

pond

ing

to t

he

tran

siti

on b

etw

een

the

two

hype

r-fi

ne l

evel

s of

the

grou

nd s

tate

of

caes

ium

133

Tem

pera

ture

ke

lvin

(K

) th

e de

gree

int

erva

l on

the

the

rmo-

degr

ee

degr

ee

(abs

olut

e)

dyna

mic

sca

le o

n w

hich

the

fa

hren

heit

ce

ntig

rade

te

mpe

ratu

re o

f th

e tr

iple

po

int

of

(F)

(C)

wat

er is

273

.16

K

(int

erva

l)

Cel

sius

(C

) te

mpe

ratu

re d

iffe

renc

e in

deg

rees

(F

) (C

) l°

F =

5/9°

C

Cel

sius

(= C

enti

grad

e) is

the

sam

e as

in

Kel

vins

(sca

le)

Cel

sius

(C

) te

mpe

ratu

re s

cale

in

degr

ees

Cel

sius

(F

) (o

C)

0°

C=

27

3.1

5K

is

the

scal

e va

lue

in K

elvi

n m

inus

27

3.15

Ele

ctri

c cu

rren

t am

pere

th

e cu

rren

t th

at i

f fl

owin

g in

tw

o

A

infi

nite

ly l

ong

para

llel

wir

es s

pace

d l

m a

part

in

vacu

o, w

ould

pr

oduc

e a

forc

e o

f 2

x l0

-7 N

pe

r m

etre

of

leng

th b

etw

een

the

wir

es

For

ce

new

ton

(N)

that

for

ce w

hich

, w

hen

acti

ng o

n

poun

d ki

logr

am m

e l

kgf

= 9.

8066

N

N =

kg

m/s

2 a

mas

s o

f l

kg g

ives

it

an

(lbf

) (k

gf)

l lb

f =

4.44

82 N

N

=J/

m

acce

lera

tion

of

l m

/s2

Wor

k, e

nerg

y,

joul

e (J

) th

e w

ork

done

by

a fo

rce

of

l N

ft

lbf

m

kgf

l

ft l

bf

= 1.

3558

J

quan

tity

of

heat

J

= N

m

whe

n it

s po

int

of

appl

icat

ion

is

l m

kgf

= 9

.80

66

J

J =

Ws

mov

ed t

hrou

gh a

dis

tanc

e o

f l

m

leV

=

1.60

21 X

l0

-19

J in

the

dir

ecti

on o

f th

e fo

rce.

Thi

s l

cal

= 4.

1868

J

unit

is u

sed

for

ever

y ki

nd o

f l

Btu

=

1055

.06

J en

ergy

inc

ludi

ng h

eat

Pow

er

wat

t (W

) I

Jfs

Wat

t (W

) lh

p=

74

5.7

W

W =

J/s

= N

m/s

Ele

ctri

c ch

arge

co

ulom

b (C

) th

e qu

anti

ty o

f el

ectr

icit

y tr

ans-

Cou

lom

b C

=A

s po

rted

in

I s

by a

cur

rent

of

I A

(C

)

Ele

ctri

c vo

lt (

V)

the

diff

eren

ce o

f po

tent

ial

betw

een

Vol

t (V

) po

tent

ial

V=

W/A

tw

o p

oint

s o

f a

cond

ucti

ng w

ire

whi

ch c

arri

es a

con

stan

t cu

rren

t o

f I

A w

hen

the

pow

er d

issi

pate

d be

twee

n th

ese

two

poin

ts is

l W

, o

r l

J/s

Ele

ctri

c fa

rad

(F)

a ca

paci

tanc

e is

l F

if

a di

ffer

ence

fa

rad

(F)

capa

cita

nce

F =

As/

V

of

pote

ntia

l o

f l

V a

ppea

rs b

etw

een

F=

C/V

th

e pl

ates

of

a ca

paci

tor

whe

n it

is

char

ged

wit

h l

C o

f el

ectr

icit

y

Tabl

e A

.2 (

cont

.)

Qua

ntit

y S

l U

nits

S

tand

ard

-de

fini

tion

E

quiv

alen

ts

Con

vers

ion

fact

or

Impe

rial

M

.K.S

.

Ele

ctri

c oh

m (

Q)

the

resi

stan

ce b

etw

een

two

poin

ts

ohm

(Q

) re

sist

ance

Q

=V

/A

of a

con

duct

or w

hen

a co

nsta

nt

diff

eren

ce o

f po

tent

ial o

f 1

V

appl

ied

betw

een

thes

e tw

o po

ints

pr

oduc

es a

cur

rent

of

I A

in

the

cond

ucto

r. T

he c

ondu

ctor

mus

t n

ot

be t

he s

ourc

e o

f an

y el

ectr

o-m

otiv

e fo

rce

at t

hat

tim

e

Mag

netic

flu

x w

eber

(W

b)

the

flux

whi

ch,

whe

n li

nkin

g a

web

er (

Wb)

W

b=

Vs

circ

uit

of

one

turn

, an

d be

ing

redu

ced

to z

ero

at a

uni

form

rat

e in

on

e se

cond

pro

duce

s in

the

cir

cuit

an

ele

ctro

mot

ive

forc

e o

f I

V

Mag

netic

flu

x te

"sla

(T

) M

agne

tic f

lux

per

squa

re m

etre

W

b/m

2 1

gaus

s= 1

0-4

T

dens

ity

T=

Wb

/m2

Ele

ctri

c he

nry

(H)

the

henr

y is

the

ind

ucta

nce

of a

he

nry

(H)

indu

ctan

ce

H=

Vs/

A

clos

ed c

ircu

it i

n w

hich

an

elec

tro-

H=

Wb/

A

mot

ive

forc

e o

f I

V is

pro

duce

d w

hen

the

elec

tric

cur

rent

in

the

circ

uit

vari

es u

nifo

rmly

at

the

rate

of

1 A

/s

Ele

ctri

c si

emen

s (S

) re

cipr

ocal

of

resi

stan

ce

mho

(U

) co

nduc

tanc

e S

= A

/V

s = 1

/il

freq

uenc

y he

rtz

(Hz)

nu

mbe

r o

f co

mpl

ete

peri

ods

of

cycl

es p

er

Hz=

1/s

os

cill

atio

n pe

r se

cond

se

cond

(c

/s)

APPENDIX I 321

For fuller details see:

I. Symbols and Abbreviations for use in Electrical and Electronic Engineering Courses. Published by the Institution of Electrical Engineers (I 968).

2. B.S. 1991, Letter Symbols, Signs and Abbreviations. 3. B.S. 3763, International System (Sf) Units. 4. PD 5686, The Use of SI Units, BSI ( 1972).

Appendix II

DYNAMIC BEHAVIOUR OF MOVING COIL SYSTEMS

a. Equation of motion; damping magnitude

It is indicated in chapter 1 that a number of factors affect the movement of the coil of an instrument, these being:

(a) the moment of inertia J (b) the damping constantD (c) the control constant or spring stiffness C

These factors may be equated with the deflecting torque (Gl) to form the equation of motion

d2 8 d8 J ~d + D -+ C8 = GI t dt (11.1)

To obtain the transient solution of this equation consider the deflecting torque (Gl) to be removed; the moving coil then twisted through an angle and released. The equation of motion then becomes:

This equation is satisfied by a solution of the form 8 = ki e"At

differentiating equation 11.3 gives

d8_kXM dt- I e

Substituting in equation (11.2) gives

JA2e"At + DA.e"At + Ce"At = 0

or JA2 +DX+C=O if X1 and X2 are the two roots of this equation

(11.2)

(11.3)

(11.4)

(11.5)

APPENDIX II 323 2 1

AI -D + (D - 4C/)'

21 2 1

and A.2 -D- (D - 4CJ)> 21

As two arbitary constants are required in the solution of a second order differential equation, the complete solution of (II.2) is

(II.6)

where A and Bare the arbitary constants, the values of which may be obtained from the conditions of motion.

It is necessary to consider three cases:

( 1) Overdamped

D2 > 4CJ- the roots are real and unequal, the solution taking the form of the sum of two quantities both of which diminish exponentially.

that is e e _ __,_o_ {A.2e;\1t- A!eAzt} A2 - A1

(II. 7)

being the curve (a) in figure A.l.

(2) Critically damped

D2 = 4CJ- the roots being equal and real. The curve (b) in figure A.l being computed from the equation

8=80 .(1 +txt)e;\t (11.8)

(where A= -D/21). This is a special case, being termed critical damping, and is the condition in which an instrument coil will change from one position to another in a minimum of time without overshoot.

(3) Underdamped

D2 < 4CJ- the roots becoming conjugate - complex

and A2 = - a: - jw

D a:= 21 and (c 2)1 w = -y- 0:

Substituting these values of A1 and A2 in Il.6 gives

324 AN INTRODUCTION TO ELECTRICAL INSTRUMENTATION

+

normalised time -

Figure A.l. Dynamic behaviour of a moving coil instrument

Since e±iwt is complt:x and 8 must be real as it represents a physical quantity, it follows that A and B must be complex.

Let A =a+ jb and B = c + jd, then if e±iwt = cos wt ± j sin wt

e = e -o:t { (a + jb) [cos wt + j sin wt] + ( c + d) [cos wt - j sin wt l} and since the imaginary part must be zero for all values oft

(b +d) cos wt +(a- c) sin wt = 0

now a = c and b = -d hence A and B must be complex conjugates. The real part of () which remains is

() = 2e-o:t (c cos wt + d sin wt) (11.9)

which may be expressed as a single trigonometric function as

() = ue-o:t sin (wt + r/>)

APPENDIX II

where and rp = tan- 1 .£ d

Showing that the transient is a damped sinusoid, of angular frequency

as shown by curve (c) in figure A. I.

325

If the instrument coil has only a small amount of damping so that D2 /4f2 may be neglected in comparison with CjJ

(C}~ Wo = TJ

giving the natural frequency of oscillation of the instrument coil as

1 (cl+ fo = 21T 7}

b. Deflection amplitude of vibration galvanometer

(II.l 0)

(II.11)

The vibration galvanometer (see chapter 1) has a narrow air cored coil oflow inertia, and a stiff suspension (large control constant). If the current in such a coil is i = Im sin wt the equation of motion is

d2B dB . J dt2 +Ddt+ CB = G/m Sill wt (II.l2)

In this case the transient solution is not of practical importance but the steady state solution will be and is obtained from the particular integral which is of the form

B = A sin ( wt - rp) where A and cp are constants.

Now

and

dB dt= Aw cos (wt- ¢)

d2 B - 2 = -Aw2 sin (wt- ¢) dt

Substituting (11.13, Il.14 and I1.15) in Il.l2 gives

(11.13)

(II.l4)

(11.15)

-AJw2 sin (wt- ¢)+A Dw cos (wt- ¢) + AC sin (wt- ¢) = G/m sin wt

(II.16)

This expression must be true for all values oft and when wt = ¢

A Dw = Glm sin¢ (11.17)


and when (wt- ¢) = n/2

-AJw2 + AC= Glm cos¢ (11.18)

As the phase angle¢ is of no practical significance- the amplitude of movement being the important quality when considering a vibration galvanometer,¢ may be eliminated by squaring and adding equations 11.17 and 11.8. Hence

or (II.l9)

A being the amplitude of the oscillation resulting from the application to the coil of an alternating current having a peak value of Im·

Now for a given frequency w, amplitude will be a maximum if w = (C/J)t which is also the angular frequency of undamped oscillation of the moving coil (equation II.ll). Thus a vibration galvanometer should be 'tuned' so that the frequency of its undamped oscillations is equal to the system frequency. The amplitude of oscillations for other frequencies being calculated using equation II.19.

c. Amplitude and phase distortion of a u.v. recorder galvanometer

Consider a current Im sin wt applied to a recorder galvanometer. Since the construction of a recorder galvanometer (see page 51) is similar to that of a vibration galvanometer in that it has low inertia, is air cored, and has a moderately stiff suspension the amplitude of vibrations will be described by the equation II.19, namely

A= GI I

[D2w2 + (C _ Jwz)j 2

Now an 'ideal' recorder galvanometer would have zero damping and i'nertia effects, that is it would respond exactly to any current variations whatever the frequency. In such a case the amplitude Ai (ideal) would be Glm/C (forD= 0 and J = 0). Now in the u.v. recorder, resonance effects and troubles due to transients are reduced by damping of the galvanometer. Critical damping would lead to a certain amount of distortion but by using less than critical damping an optimum of performance may be obtained (see chapter 2).

I

If a damping (d) is used such that d = TJD [D being critical damping= ( 4C/)2 ]

(11.20)

now

putting Wr = w/wo

APPENDIX II

= (1]2D2w2 + (!2 _ 2Jw2 + f2w4)~

! J 1 D = (4C/) 2 ; and -= -:---z

C Wo

GI A=------=--::::.:..!l"-------:----,-..,-a ( w2 w2 w4 )' c 1]2 4-2 + 1-2--2 +--4

Wo Wo Wo

or A a = C [(I - w;)2 + (2T]wr)2] f

Relative amplitude of A a to Ai is

Aa 1 Ai = [( 1 - w;)2 + (2T]w.)2 F

327

(1!.21)

(11.22)

Now Wr = w/w0 =fifo = fr the ratio of the frequency of the signal to the resonate frequency of the galvanometer.

. Aa 1 .. Ai = [(I - fi) 2 + (2rif.)2 F (11.23)

To estimate the amplitude distortion in any recorded wave it is necessary to calculate Aa/Ai for the fundamental and for each harmonic.

To assess the possible phase distortion of harmonics or the time displacement error between channels using different galvanometers it is necessary to reconsider equations 11.17 and 11.18 from which:

G. Im sin¢ tan ¢ = --:::-~'-------'--G. Im cos¢

Adw =AC-AJw2

_ 1] (4CJ)'~ w - C- Jw2

2yw

= (5?- (F= Wo w ---w Wo

(11.24)


Note. This expression gives the phase displacement of the recorded frequency with respect to its true position, measured on its own time scale of angular frequency. To estimate the distortion produced in a recorded wave it is necessary to calculate the phase displacement of the fundamental and each harmonic, and to allow for the different angular frequency scales of the various harmonics. For example a 25° displacement of a 5th harmonic on its own time scale represents 5° displacement on the angular frequency scale of the fundamental or vice versa.

For further analytical work see: E. Frank. Electrical Measurement Analysis, McGraw-Hill, New York ( 1959).

Appendix Ill

EQUATIONS TO DETERMINE THE COMPONENTS OF A RESISTIVE 'T' ATTENUATOR PAD

R, R2 o-----~~-----.----~ ---IL

~--------------*---------------~

Figure A.2. Resistive attenuator pad

Consider the resistive attenuator pad shown in figure A.2 for which

Is R3 + R2 + RL = K h R3

For correct matching (see page 150)

R =R 1 +R3(R2+RL) s R2 + R3 + RL

and

From equation Ill.l

or

now from equations Ill.l and III.2

R + (R2 + RL) I K Rs

(III. I)

(III.2)

(III.3)

(III.4)

(111.5)


Substituting equation III.4 in III.5 gives:

or

R 3 (K ~ 1) Rt + K Rs

R3(1-K) R K + s

Now substituting equations Ill.4 and III.6 in III.3 gives:

or

and 2K R 8 RL

R3 K2Rs~RL

Now from equations III.1 and 5.11 (page 168)

k =(-;~r =(::: ~~t =K(~~t

or

Substituting equation III.8 in lll.7 gives .j_

R = 2k (RsRd 2

3 k2 - 1

Substituting equations 111.8 and 111.9 in Ill.4 gives

R =R [k2 +1l 2k(R 8 Rdi 2 L k2 - 1J k2 - 1

and substituting equations 111.8 and III.9 in III.6 gives

Note. k = (P8/Pd1; and attenuation, A = 10 log10 (P8/Pd dB

Hence k = 1 oA 120 or e0 ·llSl3A where A is in dB.

(III.6)

(UI.7)

(III.8)

(III.9)

(III.10)

(111.11)

absolute values 208 acceleration 231 accelerometer 231, 245, 264 accidental error 219 accuracy (see errors) 1, 208, 297 acquisition of data 27 5 actuating mechanisms 236 admittance, measurement of 102 ageing of equipment 218 airborne data recorder 284 air tlow measurement 249 air vane damping 5, 14, 16 alternate mode 70 alternating current, measurement of,

by c.r.o. 72 by d.vm. 206 by differential vm. 189

alternating current bridges 91 alternating current carrier system 244 alternating current potentiometer 83

applications of 86 features of 86

alternating current to d.c. converter 23 alternating current standard 83 ammeter, electrodynamometer 16

electronic 3 2 moving coil 9 rectifier 21 thermocouple 23

ampere 319 amplifier, charge 17 5

chopper 29 computing 174 d.c. 190 differential 67, 143, 177 gain 99, 106, 172 galvanometer 61 operational 171 phase shift 106 power 315

amplifier, contd screening 141 strain gauge 1 7 6 summing 173 testing 315 vertical 66

Index

voltage reference 188, 203 amplitude, detlection 53

error 55 modulation 181 recorder galvanometer vibration galvanometer

analog instruments 4 ff. calibration of 221

53, 326 12, 325

comparison of, graphical 74 pointer 40

graphical 43ff. pointer 4 ff.

analog to digital conversion 181, 279 analysers, data 290 analysis, of attenuators 329

of errors 214 of moving coil instrument 322 of specifications 300

anemometer, hot wire 249 angular measurement 25 3 apparent inductance 37 apparent strain 241 approximation errors 217 atomic clock 212 attenuated feedback 1 73ff. attenuators 167

analysis of 329 balanced 16 9 range 170

attenuator input 136 attraction, moving iron 13 atto 317 audio tape recorder 283 autocorrelation function 292

332 INDEX

automated instrumentation system 315 autotransformer 95, 156 autotransformer transducer 261 automatic monitoring 275

back gap 287 balanced attenuator 169 bandwidth 2

of instrument, see comparison tables of operational amplifier 172 of ratio transformer 100

bandwidth system 240 barium titanate 264 battery operation 28, 298 bench instrumentation 312 binary coding 180, 191 bridge, a.c. 90

calibration of 223 d.c. 88 De Sauty 91 double ratio transformer 100 errors 218 Heaviside 91 inductive ratio 249 Kelvin double 89 Maxwell 91 MtJller 249 Owen 91 Schering 91, 144 simple transformer 94 self balancing 11 0 Smith 249 strain gauge 112, 241 unbalanced 112 universal 1 07 Wheatstone 88, 112, 143, 241, 248 Wien 91

bridged T 11 0 British Calibration Service 221 Brownian Movement 148,219 Burden 157, 165

cable capacitance 132, 140 caesium oscillator 212 calculation errors 217 calibration 62, 82, 87, 214, 221 calibration history 212 calibration systems 226 calibrator ( c.r .o.) 7 0 calibrators 2 25 cameras 71 capacitance 319

effective 126 electric 319 measurement, by Q meter 37

by Schering bridge 91 by transformer bridge 103, 98

capacitance standard 211, 213 capacitive divider 155 capacitive transducer 254 capacitor, compressed gas 155

frequency characteristics of 127

high voltage 144 properties 37, 125

capacitor voltage transformer 157 capstan 288 carrier frequency 283 cascade voltage transformer 158 cathode ray oscilloscope 62

applications of 71 calibration of 222

cathode ray tube 64 cell, standard 118, 210, 212, 307 Celsius 318 characteristics, capacitor 127

galvanometer 53 instrument 298 see also comparison

tables. of insulating materials 122 seismic transducer 232

charge, electric 319 charge amplifier 17 5 charts 46 chopped mode 7 0 chopper, electromagnetic 29

electromechanical 17 8 photoconductive 29 photoresistive 29, 178

chopper amplifier 29 chopper bar recorder 44 circular chart recorder 46 classification, of current transformers 166

of transducers 234 of voltage transformers 160

clock spring suspension 8 clocks, atomic 212

digital 196 closed loop system 311 code, Gray 267 cold cathode numerical indicator 185 cold junction 22, 267 common mode rejection 146 comparators 107 comparison, of analog (pointer) instruments

41 analog (graphical) instruments 74 comparison (null) methods 115 data recorders 294 digital instruments 206 instruments 310 recording instruments 294 scaling methods 182 specifications 306 transducers 272

INDEX 333

comparison (null) methods 77 comparison of 115 of calibration 221

compensated wattmeter 20 compensating thermocouple 241 compensation, of lead resistance 243, 248

of strain gauge 241 of thermocouple 268

component impurities 118ff. effects on signals of 128

computer, mini 278 computer controlled system 315 computing amplifier 174 conductance 102, 320 conducting shield 145 confidence levels 218 connection errors 218 connections, screened 139 constructional errors 215 constant temperature oven 192 contact errors 218 control constant 5 control torque 5, 8, 16, 322 conventional true value 1 conversion, A to D 181, 279 conversion factors 317 coordinate potentiometer 84 correlator 290 coulomb 319 counters 190ff.

calibration of 225 critical damping 6, 53, 56, 323 cross-correlation function 29 3 cross talk 148, 287 crystal oscillators 192, 212

piezoelectric 264 current error (ratio error) 164

measurement of 81, 107 current measurement, by a.c. potentiometer

86 by c.r.o. 72 by d.c. potentiometer 82 by differential voltmeter 189 by digital voltmeter 206 by electronic instrument 32 by electrodynamometer 16 by moving coil ammeter 9 by moving iron ammeter 14 by rectifier instrument 21 by thermocouple instrument 23

current probe 137 current shunts 9, 161 current transformer 137, 163

classification of 166 high voltage 165

Curie brothers 264

damping 323 air vane 5, 14, 16

damping, contd critical 56, 323

fraction of 53 eddy current 5 electromagnetic 5, 12, 53, 58 fluid 53 fractional 53 magnitude of 323 of recorder galvanometers 53 pneumatic 5

damping resistance 5R damping torque 5 data analysers 290 data logger 276 data recorders 27 5

comparison of 294 dead resistance 238 decade resistance box 8 8, 216 deflection, of vibration galvanometer 325

of recorder galvanometer 326 deflection amplitude 53 deflection plates 64 deflection torque 4, 14, 15 De Sauty bridge 91 detectors 32, 90

phase sensitive 32, 258 determination error 217 demodulator 137 deviation, standard 220 d.c. potentiometer, see potentiometer dielectric loss 122 dielectric, polarisation of 123

variable, transducer 25 5 differential amplifier 67, 143, 177 differential transformer 258 differential voltmeter 188, 306


differentiator 130, 175 diffraction (optical) grating 265 digital clocks 196, 276, 277 digital counter, applications of 192 digital displays 185 digital encoder 266 digital instrument 185 ff

calibration of 224 comparison of 206

digital recorders 27 5 digital tape recording 284 digital transducers 265 digital voltmeter (d.vm.) 197, 275ff.

applications of 203 calibration of 225 dual slope 200 features of 203 multimeter 206 specifications for 300, 306

diode switching 277

334

direct coupled voltmeter 27 direct current bridges 88 direct current potentiometer 77


direct current tachometer 253 direct current voltmeter 309

digital 203 electronic 2 7 electro dynamometer 17 electrostatic 25 moving coil 10 moving iron 14 thermocouple 23

direct recording 281 dispersion 122 displacement 230, 233, 272

phase 54, 164

INDEX

electromagnetic chopper 29 electromagnetic damping 5, 12, 53, 58 electromagnetic interference 145ff. electromagnetic transducer 252 electromechanical instruments 4 electrometer instrument 25

valve 27, 120 electron gun 64, 70 electronic ammeters 32 electronic instruments 27 electrostatic instruments 24


electrostatic interference 137 electrostatic stylus 44 emitter follower 136, 148 encoder, digital 266 energy 319

displacement transducers, autotransformer energy meters 26 environment 221, 289, 298 environmental errors 21 7 ephemeris time 212 equalisation 281

260 capacitance 254 differential 2 58 digital 265 electromagnetic 252 inductive 256 resistive 234 strain gauge 244

display 3, 298 digital 185 multiple trace 70 X-Y 47, 67,72

drift 148, 288 dropouts 282 Drysdale potentiometer 83 dual beam oscilloscope 70 dual slope d.vm. 200 dummy strain gauge 241 dynamic behaviour, of moving coil

system 5, 322 dynamic skew 289 dynamometer, see electrodynamometer

earphones 91 earth connections 139 earth loop 139, 146 eddy cuHent 34 eddy damping 5 effective capacitance effective inductance effective resistance electric capacitance electric charge 319 electric current 319

126 125

123 319

electric potential 319 electric stress 121 electrodynamometer 15, 84


equation of motion 5, 3 22 equivalent circuit capacitance 126 equivalent circuit resistance 123, 125 errors, amplitude 55

analysis of 214 ff connection 218 contact 218 correction (wattmeter) 17 current (ratio) 164 determination 217 d.vm. 300 environmental 217 instrument transformer 87, 103,

160, 166 lead resistance 218 phase 54, 160, 166 potentiometer 7 8, 80 probable 219 random 219 ratio 159, 164 summation of 218 systematic 214 thermoelectric 83, 218 timing 289 voltage ratio 159

eventrecorder 47

farad 319 Faraday cage 143 feedback 1 72 femto 317 fiducial value 1, 48 field effect transistor 27 filter, high pass 130

low pass 131

INDEX 335

fixed reference transducer 230 flow measurement 247, 249 fluid damped galvanometer 58 fluid damping 53 flutter 288 flux meter 39 flyback 64 foil strain gauge 23 7 force 319 force measurement 247 form factor 30 four-terminal resistance 161 frequency 320. See also bandwidth

resonant 53 frequency-based data logger 278 frequency bias 282 frequency characteristics, of capacitor 127

of insulating materials 122 of recorder galvanometers 53 of strain gauges 239 of transducers 232

frequency effects 14, 122 frequency equalisation 281 frequency limit 282

of differentia tor 17 5 frequency measurement, by counter 193

by c.r.o. 72 by twin T 109

frequency modulation 181 frequency-modulated recording 283 frequency selective detector 32, 91 frequency standard 211

by transmissions 213 front gap 287

gain, amplifier 99, 106, 172 galvanometer 120, 162

amplifier 61 analysis 3 26 calibration 62 characteristics of 53 electromagnetically damped 58 fluid-damped 58 lightspot 11 moving coil 11 optimum performance from 58 pencil 51 recorder 51

deflection amplitude of 326 selection 61 vibration 12, 85, 90, 325

deflection amplitude of 325 galvanometer matching 59 gauge factor 239, 262 guard ring 143 guard circuits .139 gaussian distribution 219 gauss meter 39

giga 317 graphical instruments 43

calibration of 222 Gray code 267 grid lines 49

Hall efect 39, 137 heads, record 279, 287

reproduce 280, 287 heated stylus recorder 44 Heaviside bridge 91 hemy 320 hertz 320 high frequency screening 145 high impedance source 59 high pass filter 130 high resistance measurement 119 high voltage capacitor 144 high voltage current transformer 165 histogram 220, 290 hot wire anemometer 249 humidity, effects on standards of 219

measurement of 24 7 humidity gauge 251 hygroscopic salt 251 hysteresis, indication 14

measurement 14

ideal rectifier 1 7 6 ideal transformer 94 impedance, effects of 128, 148

input 298 instrument 2 instrument input 128 matching 150 measurement of 88, 105 Tbevenin 113

impurities, component incandescent displays indication hysteresis inductance 3 20

effective 125 indicated 37

118 186

14

measurement of, by a.c. bridge 92 by bridged T 11 0 by Q meter 36 by transformer bridge 1 04

standard 213 inductance change transducers 256 inductive divider 94,156 inductor properties 124 infrared light 26 3 infrared thermometer 271 'in house' standards 213 input attenuator 136 input characteristics 29fs input conditioning equipment 276 input impedance, instrument 38, 128

336 INDEX

'in situ' measurement 105 instruments, analog 4

comparisons between 31 0 cost of 299 digital 185 ff. electromechanical 4 electrometer 25 electronic 27 electrostatic 24

applications of 25 graphical 43 Hall effect, features of 41 impedance effects of 2 mean sensing 21, 30 moving coil 6

features of 9 moving iron 13

features of 14 ranges of 297 recording 295 r.m.s. responding 15, 21, 24, 31 selection of 297

instrument system, 311 instrumentation tape recorders 279 integrators 132, 174 interference 118ff.

electromagnetic 145 electrostatic 13 7

isolation 298 isolating transformer 139

joule 319

Kelvin 318 Kelvin-Varley divider 153 Kelvin double bridge 89

errors of 217 kilo 317 kilogramme 318

L attenuator 169 lead resistance, compensation of 243, 248 lead resistance errors 218 lead resistance strain gauge 243 lead twisting 145 leakage resistance 38, 39, 118, 256 length 318 life expectancy 235, 299 light spot galvanometer 11 limit detector 27 8 linear mixing .282 linear velocity transducer 25 2 lineariser 277 liquid crystal displays 186 liquid level 255 Lissajous figures 67, 73 load cells 24 7 logarithmic converter 177

logger, data 276 loop, earth 13 9, 146 loss angle 38, 127 loudspeaker 253 low impedance so.urce 58 low pass filter 131, 283 low resistance measurement 89, 97, 82

magnetic flux 320 magnetic heads 287 magnetic recording 279 magnetic shield 145 magnetic tape 280 magnetisable medium 280 magnetostriction transducers 254 main gate 192 manual system 313 mass 318 mass spring transducer 230 matching, of impedances 150 matching transformer 152 matching u.v. galvanometers 59 material standards 209 materials, thermocouple 269 Maxwell bridge 92 mean sensing instrument 21, 30 measurand 27, 230, 278, 311 measurement hysteresis 14 measurement systems 31lff. mechanical displays 185 mega 317 Megger 120 meter calibration 82, 87, 99, 222 meter calibrators 225 metre 318 micro 317 micro strain 2 3 8 milli 317 minimum impurity (of resistance) 124 mini computer 278 modulator 178 Moire pattern 265 moving coil instrument 6 ff, 25 3

applications of 9 moving coil recorder 43 moving iron instrument 13 ff

applications of 14 Muller bridge 249 multi-channel recorder 46 multi-function d.vm. 206 multi-function meter 312 multimeter. electronic 30

moving coil 10 rectifier 21

multiple earths 146 multiple period averaging 195 multiple trace displays 70 multiples 317

INDEX 337

multiplexer 277, 284 multiplier 1 7 8 multipoint recorder 46 multipoint strain measurement 242 multirange milliammeter 16 3 multitrack heads 287 mutual inductance 258

nano 317 National standards 208 neon tube displays 185 nepers 167 network characteristics 106 newton 319 noise, acoustic 219

. electrical• 148, 219 no1se level 287 normal distribution 219 null detector 12, 3 2 null methods 77

ohm 320 open loop system 311 operation criteria 299 operational amplifiers 141, 171ff.

bandwidth of 172 optical grating 265 oscilloscope 6 2 ff

dual beam 70 storage 69

output characteristics 298 output devices 278 overdamping, analysis of 323 overshoot 56 overspecification 299

peak acceleration 231 peak responding voltmeter 30 Peltier 267 pencil galvanometers 51 pen recorders 43

calibration of 222 period measurement 194 permanent installations 27 8, 313 permanising 51 permittivity 122 phase angle measurement, by c.r.o. 67, 72

by transformer bridge 99 by u.v. recorder 62 phase angle of a resistor 124

phase displacement 54, 164 phase error 54, 160 phase modulation 181 phosphors (c.r.t.) 68 photoconductive chopper 29 photodevelopment 51 photodiodes 263, 271 photoresistance 251

photoresistive chopper 29, 17 8 phototransistors 263 pico 317 pickup 137 piezoelectric transducer 264 plate seperation, in capacitive transducer

256 platinum resistance thermometer 213, 247 playback 289 plotters, X- Y 47 pneumatic damping 5 pointer instrument 4

calibration of 221 Poisson strain 239 polarisation of dielectric 123 polar potentiometer (a.c.) 83 potentiometer, d.c. 77, 306

Drysdale 83 potentiometric recorder 45 potentiometric transducer 235 power 319 power amplifier, testing of 315 power density spectrum 293 power factor meter 15, 20 power measurement, by a.c. potentiometer

87 See also wattmeter Poynting vector wattmeter 41 practical sampling rate 279 pressure gauge 245 probes 31. 70, 135ff. process temperature control 45 processing u.v. sensitive paper 51 production line instrumentation 315 production line standard 214 programmed calibration 228 programmed instrumentation 313 programme pin board 277 pulse amplitude modulation 180 pulse code modulation 180 pulse duration 133 pulse duration modulation 284 pulse height analysers 290 pulse position modulation 180 pyrometer 271

Q meter 34 applications of 36

Q of a coil 34 quartz crystal thermometer 266 quartz oscillator 192, 212

radiation pyrometer 271 ramp d.vrn. 198 range attenuators 170 rated transformation ratio 159, 164 ratio errors 159, 164

338 INDEX

ratio measurement, frequency 195 resistance 190 standard 214

ratio transformer 94 reactance, effective 124

standard 211 reactance transducers 254 recirculating remainder d.vm. 202 recorder galvanometers 51, 3 26

frequency of 53 recorders, calibration of 222

chopper bar 44 circular chart 46 comparisons between 7 5 digital 27 5 electrostatic stylus 44 event 47 heated stylus 44 moving coil 43 multipoint 46 pen 43 potentiometric 45 tape 279 temperature 45 ultra violet 49

recording head 279 recording instrumentation 311

comparison of 294 records 228 rectifier, ideal 1 7 6 rectifier instrument 20


reed relays 277 reference amplifier 203 reference standard 212 relative humidity 251 reliability 299 reproduce head 280 repulsion, moving iron, instrument 13 residuals 218 resistance 3 20

attenua tor 167 -capacitance divider 156 chain 153 damping 58 dead 238 effective 123 four terminal 161 high, measurement of 119 leakage 38, 39, 118, 256 measurement of, by d.c. potentiometer

82 by Kelvin double bridge 89 by loss of charge 121 by multimeter 1 0 by self-balancing bridge 110 by transformer bridge 96, 101

resistance, measurement of, contd by Wheatstone bridge 88

minimum impurity of 124 noninductive 123 series 10 standard 210, 213 standardising 7 9 temperature coefficient of 240

resistance change transducers 234 resistance dividers 15 3 resistance ratio measurement 190 resistance strain gauge 236 resistance strain gauge transducer 244 resistance thermometer 213, 247 resistor impurities 123 resistor, phase angle, reactance 124 resonant frequency 53 response characteristics 29 8 see also

frequency characteristics ribbon suspension 8 rise time 69, 133

measurement of 7 5 r.m.s. responding instrument 15, 21, 24, 31 rotary speed 25 3 roulette patterns 7 5

sag 133 sampling devices 185 sampling oscilloscope 68 sampling theory 279 saw tooth waveform 64 scaling, current 161

voltage 153 scanning switch 27 7 Schering bridge 93, 145 screen phosphors 68 screened isolating transformer 141 screening 2, 118, 298 second 318 Seebeck 267 segmented display 185 seismic transducer 230

characteristics of 2 3 2 self-balancing bridges 11 0 self-balancing potentiometer 30, 45 self-capacitance 37 semiautomatic system 313 semiconductor transducers 261 sensitivity 3, 12, 61 series resistance 10

of an inductor 104 shaft position encoder 266 shield, electrostatic 13 7

magnetic 145 shunt 9, 161

universal 16 2 siemen 320 signal conditioning 150ff., 311

INDEX 339

simple transformer bridge 94 SI units 317 skew 288 skin effects 34 slewing speed 4 7 Smith bridge 249 solid state display 186 specification analysis 300 speed measurement 252 spectrum analyser 294 stability 298 standard cell 78, 118, 210, 212, 218, 307 standard deviation 220 standard of temperature 213, 24 7 standards 208 ff

'in house' 213 laboratory 213, 249

standardisation 78, 84 statistical analyser 290 steady state solution 5 storage oscilloscope 69 strain gauge 236 ff

amplifier 176 applications of 243 attachment of 238 bridge 112, 241 compensation of 241 dummy 241 foil 237 frequency of 239 lead resistance 243 resistance 236 semiconductor 262 transducer 244 unbonded 244 vibration 239 waterproofing of strain gauge 238

strain sensitivity 238 strays and residuals 122, 218 stretching (tape) 289 strip chart 46 successive approximation d.v.m. 197 summing amplifier 173 suspension, clock spring 8

ribbon 8 symbols 317 synchro 261 system, instrumentation 311 ff system bandwidth 240 systems calibration 226

tachometer 253 take-up reel 288 tan li (loss angle) 38, 122, 127 tape recorders 279ff.

features of 289 tape transport 288 T attenuator 167

temperature 318 temperature coefficient 240, 24 7, 302 temperature compensation 263, 268 temperature effects 83, 148, 305

in strain gauges 240 temperature measurement 82, 247, 261,

267ff. temperature recorder 45 temperature standards 213 tera 317 testing (of power amplifier) 315 thermal converter 23 thermal e.m.f. 83, 148 thermal radiation pyrometer 271 thermistors 261 thermocouple, application of 45, 267

circuit for 22, 267 compensating 241 compensation of 268 materials in 269

thermocouple instrument 21 features of 22

thermoelectric transducers 267 thermometer, platinum resistance

213, 24 7 quartz crystal 266 resistance 24 7

thermopile 270 Thevenin impedance 113 Thompson, William 267 three dB point 130 time 318 timebase (c.r.o.) 64 time constant 124, 129, 130 time interval measurement 195 time shift 291 timing error 289 timing lines 49 timers (counters) 190

features of 192 tooth rotor tachometer 253 toroidal core 95 torque, control 5

damping 5 deflecting 4, 14, 15

torsion head dynamometer 85 torsion measurement 247 totalising 192 trace identification 51 transducer 230 ff

capacitive 254 classification of 234 comparison of 272 dielectric variation 25 5 electromagnetic 252 features of 272 fixed reference 230 frequency of 232

340 INDEX

transducer, contd linear velocity 25 2 magnetostriction 254 mas~rspring 230 piezoelectric 264 potentiometric 235 reactance 254 resistance change 234 resistance strain gauge 244 seismic 230 semiconductor 261 thermoelectric 267 ultrasonic 254 variable capacitance variable inductance variable resistance velocity 25 2

255 257

234

transfer instrument 16, 23, 24, 83, 85, 228 transfer standard 212 transformation ratio 159, 164 transformer, auto 95

bridge 94, 100, 218 applications of 96, 1 00 features of 1 07

current 163 differential 258 ideal 94 isolating 139 matching 152 phase shift of 1 06 phase shifting 84 ratio 95, 99, 106

features of 1 00 screened isolating 141 voltage 1 00, 156

transient measurements 62, 128, 28r transient response 56 transient solution (moving coil instrument.)

5, 322 transistor parameters 1 06 transverse strain 23 9 trigger, counter 192

c.r.o. 64 true value (conventional) 1 tuned amplifier detector 32, 91 twin T network 1 07


twisting of leads 145

ultrasonic transducer 254 ultraviolet recorder 49ff.

applications of 62 calibration of 222 galvanometer analysis of 326

unbalanced bridge 112 applications of 116 features of 116

unbonded strain gauge uncertainty (tolerance) underdamping 53, 323

244

units 317 unity integrator universal bridge universal shunt

175 107 162

1, 208, 214ff.

variable capacitance transducer 255 variable inductance transducer 257 variable resistance transducer 234 variations of environment 298 Varley vernier 80 velocity transducer 25 2 vertical amplifier (c.r.o.) 66 vibration galvanometer 12, 85, 90, 325 vibration strain gauge 239 virtual earth 139, 173 viscosity measurement 24 7 volt 319 voltage divider 15 3 voltage measurement, by a.c. potentiometer 86

by c.r.o. 71 by d.c. potentiometer 82 by differential voltmeter 189 by digital voltmeter 203 by electrodynamometer 1 7 by electronic instrument 27 ff by electrostatic voltmeter 25 by moving coil voltmeter 1 0 by moving iron voltmeter 14 by rectifier instrument 21 by thermocouple instrument 23

voltage reference amplifier 188, 203 voltage standard 209, 212 voltage to frequency converter 180, 199 voltage transformer 100, 156

capacitor 157 cascade 158 classification of 160

voltmeter, see voltage measurement

watt 319 wattmeter, compensation 20

correction 19 electrodynamometer 1 7 electronic 3 2 electrostatic 25 Poynting vector 41 thermocouple 24

waveform, effects on moving iron instrument of 14

waveform purity 3 waveform recording 62, 71 weber 320 weight measurement 247 Wien bridge 91 Weston standard cell 210, 212

Wheatstone bridge 88, 112,218, 262 calibration of 223 errors in 217

work 319 working standards 213 wow 288 writing speed 4 7, 7 0

INDEX

X- Y display 67, 72 X- Y plotter 47

Y (vertical) amplifier

zener diode Z modulator

188, 213 67

341

66

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