DATE DUE

Demco, Inc. 38-;'93

National Bureau of Stondozds

Library

JUL 3 0 1974

750083 - ^^

f^l THE MEASUREMENT OF LUMPED PARAMETER

"ta^l' IMPEDANCE: A METROLOGY GUIDE

R. N. Jones

Electromagnetic Metrology Information Center

Electromagnetics Division

Institute for Basic Standards

(/[ ,5 . National Bureau of Standards

Boulder, Colorado 80302

i

W. J. Anson

Editor, Metrology Guides

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secreiary

NATIONAL BUREAU OF STANDARds, Richard W. Roberts, Director

Issued June 1974
Library of Congress Cataloging in Publication Data

Jones, Raymond Nelson, I928-

fhe Measurement of Lumped Parameter Impedance.

(NBS Monograph 141)

B ibliography : p

.

Supt. of Docs, no.: 013.^+^.1^1

1. Impedance (Electricity) 2. Electric measurements. I. Title. II. Series: United States.

National Bureau of Standards. Monograph ikl,

QCIOO.U556 no. li|l [TK315] 389'. 08s [621.37'^]

7I1-806O

National Bureau of Standards Monograph 141

JVat. Bur. Stand. (U.S.), Monogr. 141, 211 pages (June 1974)

CODEN: NBSMA6

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1974

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402 (Order by SD Catalog No. C13.44:141).

Price $5.50 Stock Number 0303-01289
THE MEASUREMENT OF LUMPED PARAMETER IMPEDANCE

A METROLOGY GUIDE

Abstract

The measurement of two-terminal impedance in the

30 kHz to 300 MHz range involves a variety of

different methods including null, resonance,

active and comparison. Each method is represented

by a number of instruments having specific capabilities, strengths, and weaknesses. This metrology

guide is intended to assist the scientist who is

not intimately familiar with impedance measurement,

in the selection and use of the best instrument

for a particular requirement. Information is

included on range and accuracy capabilities as

well as availability and ease of operation. In

addition to providing help in the selection of

the appropriate instrument, there are operating

tips which enhance accuracy, criteria for choosing

standards, means for extending normal measurement

range of an instrument, a discussion on generators

and detectors, and a section on the evaluation and

use of adapters. Finally, an extensive bibliography

is included to assist in pursuing a particular

problem beyond the depth of the guide.

Key Words: Adapters; capacitance; capacitors;

detectors; generators; impedance

instruments; impedance standards;

inductance; inductors; measurement

methods; reactance; resistance;

resistor; standards.

iii
EDITOR'S NOTE

This Guide is one of a series of Metrology Guides sponsored by

The Electromagnetic Metrology Information Center of the National

Bureau of Standards Electromagnetics Division designed to be

critical comparisons of measurement methods for a variety of

electromagnetic quantities. The objective is to provide guidance

in the selection, use and evaluation of methods for a particular

application. These Guides, written by measurement specialists

and based on extensive literature searches, are tailored to the

needs of technical people who may not possess specialized training

in the measurement of the quantity that is the subject of a particular guide. Therefore, these Guides will be useful to teachers,

design engineers, contract monitors, and practicing metrologists

,

as well as general engineers and scientists who need specific

measurement know-how but do not have the time or facilities to

do their own research and study on the complexities involved.

With the above objective in mind, each guide includes the following

1. A description of the physical principles underlying the

measurement technique

2. An indication of the accuracy obtainable with each method

whether by discussion of typical ranges and accuracies

or through discussion of the error equations.

3. A discussion of the technical strengths and weaknesses of

each technique. This includes a discussion of the sources

of error or, wherever possible, the error equations of

specific operating systems.

4. A discussion of the instrumentation requirements (including

standards) for each technique.

5. Operational problems, suggestions, or examples.

6. An extensive bibliography to assist the reader in

pursuing the details of methods beyond the depth of

the guide.

If the reader wishes to receive information about any future Guides

or wishes to comment on this Guide, please use the form at the back

of the book.

W. J. Anson

Editor - Metrology Guide Series

iv
ACKNOWLEVGHEUT

"hlo man li> an -ii>tand unto hA^mizt{^." Tkd tfimth tkli>

quLOtatA^on kai> buzn abundantly cto^an. to me tn tko. pKzpan.atlon

0^ tht6 manu6c^-ipt. He£p ka6 corm (^Kom 6o many iouxct^ tkzy

lOoaZd be dt{i{iZcalt to n.2,cou.nt, but pzKmtt me to exp/Le-64 my

QH-at-Ltudd to iomz Mho contK-tbuttd a gK^at ddat. iJJttbuA. J.

Anion o{^ NBS pfiovtdzd a^it^tanco. , gutdanct and Q,ncou^agzm<int

{^A.om i>tafit to ltnti>k. Mt/ ^zadd^i tue^e WttZtam E. Bo6tu)tcik,

now n,Q,tt^<id {^^om /.aw^^ence Radiation labofiaton.y , John L. Vatkn

and Rob2.n,t M. Jlcktlng o^j WBS . Glng2.H. Fea^4 and VaK(A)ln B.

Mln2.n. did tho, dK-a^tlng and ltZui>tn.atloni> , and Ma^ga^dt WootZ^y

typdd thd uikoZn thing- - -mon.z than once.. To aZZ o^ you, and

many otht^i , my ilncd^e. thanki .

V
CONTENTS

Page

LIST OF FIGURES ix

LIST OF TABLES xiii

ABSTRACT iii

EDITOR'S NOTE iv

ACKNOWLEDGMENT v

1. INTRODUCTION 1

1.1. Purpose , 1

1.2. Scope Of The Guide 1

1.3. Accuracy Limits 3

1.4. How To Use This Guide 10

1.5. From The Old To The Nevr 10

2. MEASUREMENT CATEGORIES AND EQUIVALENT SERIES

AND PARALLEL RELATIONSHIPS 12

3. MEASUREMENT METHODS AND THEIR CAPABILITIES 16

3.1. Null Method (two terminal) 17

a. Principle of the Null Method 17

b. Characteristics of ac Bridges 18

c. Error Sources 20

d. Strengths and Weaknesses 21

3.2. Null Method (three terminal) 23

a. General Comments 23

b. Strengths and Weaknesses 2 4

3.3. Resonance Methods 29

a. General Comments 29

b. Series Resonance 29

c. Parallel Resonance 31

d. Resonance Methods For Determining

Residual Impedances 33

(1) Grid Dip Meter 33

(2) Three Frequency Method 3 4

e. Error Sources 36

f. Strengths and Weaknesses of Resonance

Methods 36

vl
Contents (cont.)

Page

3.4. Active Methods 40

a. General Coinments 40

b. Vector Impedance Meters 40

c. L-C Meters 42

d. 6-Port Coupler 4 3 e. Error Sources 44

f. Strengths and Weaknesses 45

3.5. Comparators or Differential Measurements 49

3.6. Automated Measurements 51

3.7. Other Methods 52

a. Time Domain Ref lectometer 52

b. Frequency Domain Reflectometer 53

c. Swept Frequency 53

d. Slotted Line 54

e. Return Loss Bridge 54

4. INSTRUMENTS FOR VARIOUS METHODS 5 8

4.1. Null Instruments 59

a. Maxwell Bridge 59

b. Schering Bridge 6 4 c. Admittance Ratio Bridge 70

d. Transformer Ratio Bridge 7 5 e. Twin-T Bridge 82

f. Thurston Bridge 8 8

g. Young Bridge 9 4

h. Byrne Bridge 99

i. Q-Bridge 106

4.2. Resonance Instriiments Ill

a. Q-Meter Ill

b. Immittance Trans comparator 118

4.3. Active Ins truments 122

a. Vector Impedance Meter 12 2

b. L-C Meter 12 8 c. Vector Voltmeter 13 3

d. 6-Port Coupler 135

4.4. Comparator Instriiments 138

5. MEASUREMENT TIPS AND TECHNIQUES 139

vii
Contents (cont.)

Page

6. STANDARDS 142

6.1. General Comments 142

6.2. Why Are Impedance Calibrations Expensive? 144

6.3. Keeping Calibration Costs Down. . .A Tip

On Maintaining Standards 145

6.4. What To Look For In Choosing A Standard 145

6.5. Coaxial Lines 147

7. RANGE EXTENSION 148

7.1. The Series Configuration 148

7.2. The Parallel Configuration 153

8. GENERATORS AND DETECTORS 155

8.1. Phase-Sensitive Detectors 159

9. APPLICATION AND EVALUATION OF ADAPTERS 161

9.1. Introduction To The Adapter Problem 161

9.2. What Is An Adapter? 161

9.3. Usual Two- Port Representations of Adapters 164

a. Uniform Transmission Line 164

b. "tt" or "T" Network 166

c. "L" Network 166

d. Single Element Representation 169

9.4. Measurement of Open-Circuit Admittance,

Electrical Length, And Short-Circuit

Location In Non-Precision Connectors and

Adapters 171

10. APPENDIX I. DEFINITIONS, UNITS AND SYMBOLS 182

11. BIBLIOGRAPHY 187

viii
LIST OF FIGURES

Fig. No. Title Page

1-1 ± 0.1 percent uncertainty limits for two-terminal

capacitance measurement 7

1-2 ± 0.1 percent uncertainty limits for two-terminal

inductance measurement 8

1-3 ± 0.1 percent uncertainty limits for two-terminal

resistance measurement 9

3-1 (no caption) 17

3-2 Null methods for two-terminal capacitance

measurement: Instruments and their approximate

ranges in frequency and magnitude 2 5

3-3 Null methods for two-terminal inductance

measurement: Instruments and their approximate

ranges in frequency and magnitude 26

3-4 Null methods for two-terminal resistance

measurement: Instriaments and their approximate

ranges in frequency and magnitude 27

3-5 Null methods for two-terminal Q or dissipation

factor measurement: Instruments and their

approximate ranges in frequency and magnitude 28

3-6a Series resonant circuit 29

3-6b Response of series resonant circuit 29

3-7a Parallel resonant circuit 31

3-7b Response of parallel resonant circuit 31

3-8 Grid dip meter application 33

3-9 Three frequency method, equivalent method: 34

3-10 Three frequency method, data analysis 35

3-11 Resonance methods for two-terminal capacitance

measurement: Instruments and their approximate

ranges 3 8

3-12 Resonance methods for two-terminal inductance

measurement: Instruments and their approximate

ranges in frequency and magnitude 39

ix
List of Figures (cont.)

Page

3-13 Active method for measuring impedance 41

3-14 Measurement of small impedances using constant

current generator 41

3-15 Measurement of large impedances using constant

voltage generator 42

3-16 Impedance measurement using the 6-port coupler:

Relation between voltage (v) , current (i)

,

incident voltage wave (a) and reflected voltage

wave (b) 44

3-17 Active methods for two-terminal inductance

measurement: Instruments and their approximate

ranges in frequency and magnitude 46

3-18 Active methods for two-terminal capacitance

measurement: Instruments and their approximate

ranges in frequency and magnitude 47

3- 19 Active methods for two-terminal resistance

measurement: Instruments and their approximate

ranges in frequency and magnitude 48

4- 1 (no caption) 59

4-2 Maxwell impedance bridge: Range of inductance

vs frequency 62

4-3 Maxwell impedance bridge: Range of resistance

vs frequency 63

4-4a (no caption) 64

4-4b (no caption) 66

4-5 Schering bridge: Range of resistance vs frequency... 6 8

4-6 Schering bridge: Range of capacitance vs frequency.. 69

4-7 (no caption) 70

4-8 Admittance ratio bridge: Range of conductance

vs frequency 7 3

4-9 Admittance ratio bridge: Range of capacitance

vs frequency 74

X
List of Figures (cont.)

Page

4-10 (no caption) 75

4-11 Transformer ratio bridge: Range of resistance

vs frequency 79

4-12 Transformer ratio bridge: Range of capacitance

vs frequency 80

4-13 Transformer ratio bridge: Range of inductance

vs frequency 81

4-14 (no caption) 82

4-15 Twin-T bridge: Range of resistance vs frequency 85

4-16 Twin-T bridge: Range of capacitance vs frequency 86

4-17 Twin-T bridge: Range of inductance vs frequency 87

4-18 (no caption) 88

4-19 Thurston bridge: Range of conductance vs frequency... 92

4-20 Thurston bridge: Range of positive or negative

capacitance vs frequency 9 3

4-21 (no caption) 94

4-22 Young bridge: Range of conductance vs frequency 9 7

4-23 Young bridge: Range of capacitance vs frequency 9 8

4-24 (no caption) 99

4-25 Byrne bridge: Range of resistance or impedance

magnitude vs frequency 10 3

4-26 Byrne bridge: Range of capacitance vs frequency 104

4-27 Byrne bridge: Range of inductance vs frequency 105

4-28 (no caption) 106

4-29 Q-bridge: Range of Q vs frequency. 109

4-30 Q-bridge: Range of capacitance vs frequency 110

4-31 (no caption) Ill
List of Figures (cont.)

Page

4-32 Q-meter : Range of Q vs frequency 115

4-33 Q-meter: Range of capacitance vs frequency 116

4-3 4 Q-meter: Range of inductance vs frequency 117

4-35 (no caption) 118

4-36 Immittance transcomparator : Range of Q vs

frequency 121

4-37 (no caption) 122

4-38 Vector impedance meter: Range of resistance

or impedance magnitude vs frequency 125

4-39 Vector impedance meter: Range of inductance

vs frequency 126

4-40 Vector impedance meter: Range of capacitance

vs frequency 127

4-41 (no caption) 128

4-42 L-C meter: Range of inductance vs frequency 131

4-43 L-C meter: Range of capacitance vs frequency 132

4-44 (no caption) 133

4-45 (no caption) 135

4-46 Measurement uncertainty of 6-port coupler

vs directivity of hybrid junctions 136

6- 1 Derivation of NBS immittance standards 143

7- 1 (no caption) 148

7-2 (no caption) 149

7-3 (no caption) 150

7-4 (no caption) 151

7- 5 (no caption) 153

8- 1 (no caption) 155

8-2 (no caption) 159

xii
List of Figures (cont.)

Page

9-1 Adapter represented as a uniform transmission

line 165

9-2 Adapter represented as a "it" or "T" network 167

9-3 Adapter represented as equivalent "L" network 168

9-4 Adapter represented as a single element 170

9-5 Zero-length adapter for type N male connectors

(cross-section illustration) 173

9-6 Zero-length adapter for type N male connectors

(engineering cross-section) 174

9-7 Connection arrangements for measuring adapter

capacitances and open-circuit fringe

capacitances at 1 kHz 175

9-8 Connection arrangement for measuring electrical

length of adapter utilizing zero-length adapter 180

LIST OF TABLES

Table I. Instruments Measuring Equivalent Series Impedance.... 55

Table II. Instruments Measuring Equivalent Parallel

Admittance 57

• • • Xlll

1.1. Purpose

1. INTRODUCTION

In preparing this metrology guide, it has been assumed

that the potential user is broadly familiar with the field of

electrical measurement but not intimately familiar with the

methods , techniques and instrumentation for making impedance

measurements. The guide anticipates a situation where

impedance measurements are known to be necessary but the

best way to go about making them is not known. The heart of

the guide is the subject matter found in Section 3 where

various methods are covered and in Section 4 where specific

instruments, which are the embodiment of the methods covered

in Section 3, are discussed. The other sections are intended

to be supportive of the material found in Sections 3 and 4,

by providing measurement tips, information on standards, range

extension techniques , generators and detectors , and the use

and evaluation of adapters.

1.2. Scope Of The Guide

This guide is not all-inclusive of the siibject of

impedance measurement and the reader should understand at

the outset what he can or cannot expect to find. To help in

establishing the bounds of subject matter included, consider

the ideal impedance-measuring instrument as having the

following characteristics and capabilities:

(1) unrestricted frequency range

(2) unrestricted impedance range

(3) unrestricted capabilities with respect to

bias, ambience, applied power, etc.

(4) error free

(5) performs measurements instantaneously

(6) zero acquisition cost

(7) zero operating cost.

1
obviously no such instrument exists and if it did there would

certainly be no need for a metrology guide. All instruments

or methods fall short of all of these criteria, but all have

strong or weak points with respect to each. This guide is an

attempt to present a body of useful information which will

simplify the task of deciding which methods and instruments

are best suited for particular requirements. The information

presented should make possible a critical comparison of

methods and instruments with the result that the user will

be able to decide correctly upon the best method and

ultimately upon the best instrument for his application. Any

such decision must be preceded by an ordering of priorities

as to which criteria are most important, such as speed versus

accuracy, accuracy versus cost, frequency range versus parameter range, etc.

This guide will not attempt to encompass the entire

subject of impedance measurement so that some of the criteria

mentioned must be reduced to more manageable proportions.

For present purposes, the frequency range will be confined to

a lower limit of 30 kHz and an upper limit of 300 MHz,

although some of the methods and instruments to be discussed

are usable either below or above these limits. Impedance

measurement above 300 MHz is the subject of another guide of

this series.

Impedance measurement in the 30 kHz to 300 MHz range has

some unique problems and peculiarities which arise largely

because it is a transition region from open wires to coaxial

lines as the medium for propagating energy. This creates difficulties and uncertainties brought about by many different types

of connectors and the need to adapt from one to another. This

is also the frequency region where a quarter of a wavelength

begins to approach the physical size of a practical laboratory

component so that it becomes practical and desirable to use

both lumped circuit and distributed circuit theory.

2
A reduction is also necessary in the impedance range

criteria and this guide will be restricted to passive,

two-terminal measurements and passive, three-terminal

measurements. This specifically excludes negative resistance

(active devices), and balanced measurements even though some

of the methods and instruments discussed may have such

capabilities. Also excluded are measurements under bias,

high power or ambient environmental extremes

.

In Sections 3 and 4, strengths and weaknesses are

enumerated for specific methods and instruments. These

strengths and weaknesses have been determined by comparison

with the criteria chosen to represent the ideal instrument.

They are not intended as a blanket recommendation for or

against any particular method or instrument but only as an

aid to objective selection based upon the needs of a

particular user.

It is also recognized that methods or instruments exist

which are not included here. In such instances it is due

either to the fact that they were not found in the literature

search or that they were not deemed to be of wide enough

practical use to be included. It is also notable that there

are many variations on the methods and instruments that are

included. Hopefully the omissions are not of major consequence.

1.3. Accuracy Limits

When two or more methods or instruments have been identified

which can perform a particular measurement, the choice is often

made in favor of the one which is the most accurate. This is

not always an easy thing to determine and quick glances at the

percentage tolerances provided by manufacturers , although

helpful, may not tell the whole story. There are some important

questions which should be answered before a final decision is

made

3
(1) In what mathematical form does the instrument present

the measurement data?

Some instruments read out is the polar form of impedance

magnitude and phase angle (Z /£ ) , others in the rectangular

form of equivalent series impedance (R±jx) or equivalent

parallel admittance (G±jB). Still others give either capacitance or inductance for the quadrature component. Q or

dissipation factor are sometimes given and so it goes until

the variations seem almost endless. To compare the accuracy

capabilities of various instrioments , it is necessary to convert

to a common mathematical form and examine carefully the

significance of percentages as they apply to specific parameters. To make a thorough accuracy comparison it is also

necessary to consider impedances having a wide variety of

magnitudes and phase angles. This will provide a good

overall comparison as to how well the largest and smallest

components of a complex impedance vector can be measured.

(2) What is the resolution of the instriiment?

The smallest scale division on a dial or a meter becomes

very important, especially when measuring very small values,

and manufacturers often add a vernier to secure an additional

decimal place in data resolution.

(3) What about other terms in the accuracy statement?

Particularly with bridges or null instruments, accuracy

statements often include terms containing frequency and also

terms which vary depending upon the nature of the impedance

being measured. For example, the accuracy of a resistance

value may depend upon how much inductance was present in the

unknown. Such "cross products" are often very important especially when measuring the smaller component of a very high or a

4
very low Q impedance, and can greatly modify the basic percentage

accuracy capability for that particular type of measurement.

(4) What kind of connectors does the instrument have at

its unknown terminals , or how is the unknown connected

for measurement?

Connector requirements can be extremely important and should

be considered very carefully in all measurement applications.

Even though one particular instrument may appear to provide the

best accuracy, a great deal can be lost if complicated adaptors

or long measurement leads are required. This problem becomes

increasingly serious as the measurement frequency increases and

wavelengths begin to approach the physical dimensions of

practical impedance components

.

In Sections 3 and 4 of this guide are a number of graphs

showing the capabilities of various methods and instruments.

It would have been convenient for the user if some accuracy

limits could have been shown on these charts which would have

clearly indicated which methods or instruments are the most

accurate. Although the graphs were prepared showing resistance,

inductance, conductance and capacitance measuring capabilities

as appropriate for each method or instrument, no way was found

to show accuracies in individual cases which would have been

fair assessments in all cases. In lieu of this, representative

percentage uncertainty figures have been given in the short

narratives, but as stated above, these may not tell the whole

story in individual cases and should not be accepted without

careful examination.

In order to provide some feel for measurement uncertainty

a criteria of ±0.1 percent is shown on the charts to illustrate

what is attainable at the present state-of-the-art, and does not

mean that the particular instrument or method has a ±0.1 percent

capability. The ±0.1 percent criteria for uncertainty used in

5
the charts was derived under the assumption that manufacturing

tolerances of ±0.001 inch could be guaranteed for commercial

standards. Using this assumption it has been shown [A-1] that

3xl0~® Henry, 2x10"^^ Farad and 1 ohm are the smallest twoterminal values of inductance, capacitance and resistance

which can be measured to an uncertainty of ±0.1 percent

i

Figures 1-1, 1-2 and 1-3 show how these uncertainty limitations

apply to these quantities over the 30 kHz to 300 MHz frequency

range

.

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1.4. How To Use This Guide

The main purpose of this guide is to aid the user in

determining what method or instrument to use for a particular

measurement requirement. Sections 2, 3 and 4 will be of most

help in this regard. In Section 2 practical measurements

falling within the scope of the guide are categorized and the

user is provided with page numbers where appropriate methods

or instruments are discussed. Section 3 is concerned with

methods of measurement wherein some information is given

regarding the theory behind a particular method, its strengths,

weaknesses and capabilities for measuring various impedance

parameters. Also in Section 3 are graphs illustrating the

measurement capabilities of each method. These graphs can

be used for quick reference and also provide, in one location,

a summary of capabilities of all the instruments utilizing a

particular method. This will aid in critically comparing the

capabilities of specific instruments

.

Section 4 begins with a summary table showing the generalized

capabilities of all the instruments covered in that section.

Following the summary are detailed discussions of each instrument,

including circuits, equations, accuracy capabilities, strengths

and weaknesses

.

The other sections provide measurement tips and suggestions,

criteria for choosing standards, range extension techniques to

help the user make better use of an instrument, a discussion on

generators and detectors, together with some new information on

the use and evaluation of adapters.

1.5. From The Old To The New

Like most everything else, the approach to impedance measurement

has changed and continues to change . Many of the methods and

instruments included here are products of past decades and the

reader may wonder why they have been included. This is especially

10
true in the null and resonance categories where many of the

instruments have been superseded by more modern equipment.

However, just because something is old does not mean that it

isn't good or useful, and even though some of these instruments

are no longer found in the current manufacturers catalogs

does not mean that they are no longer in use. In some instances

it may be found that the newer, faster and more exotic instruments may not yet possess the accuracy, stability and

dependability characteristics of their predecessors and so it

is still wise to keep the old one for a while longer. With

this in mind a strong emphasis has been placed on those

instruments which can be said to have preceded the space age.

Newer generation equipment emphasizes speed of measurement,

broad frequency range capabilities and automatic data handling

capabilities, and is frequently interfaced with a computer

facility. Versatility is being achieved to a greater degree

and it is not uncommon to find measurement systems capable of

measuring many electrical parameters over very wide frequency

ranges. In Sections 3.6 and 3.7 the emphasis is primarily on

equipment and measurement approaches which are characteristic

of the newer generation approach to measurement.

11
2. MEASUREMENT CATEGORIES AND EQUIVALENT SERIES AND

PARALLEL RELATIONSHIPS

The lumped impedance of any device may be represented either

by a series or a parallel combination of circuit elements, whichever is more convenient, but it is often necessary to convert

from one form to the other, requiring that the following relationships be used

Series to Equivalent Parallel:

±x

+ B

Z = R±jX Y

=

G =

1 R±jX

R

= G + jB

B = +

Parallel to Equivalent Series

2 2

R +X

±8

Y = G±jB

1 G±jB

G

2 2

G +B^

R + jX

X

=

2 2

G +B^

12
As an aid to illustrating the measurement capabilities of

the various methods and instruments to be found in Sections

3 and 4, it is useful to categorize various types of impedances

and give some practical examples which are characteristic of the

various series and parallel combinations of in-phase and quadrature

components

.

By varying the signs and magnitudes of the parameters R,

X, G and B, all possible impedance or admittance values can be

obtained, but because this guide will be concerned only with

passive quantities, negative resistance (-R) and negative conductance (-G) will be excluded.

:ateSeries

R

B

D

X

gory

A Small Small (+)

Equivalent Parallel

|G| |B|

Large Large (-)

Large Large (-) Small Small (+)

Large Small (+) Small Small (-)

Large Small {-) Small Small {+)

Small Large (+) Small Large (-)

Small Large (-) Small Large (+)

Practical

Example

Short circuit or

small resistance or small

inductance

Open circuit

or small

capacitance

or large

resistance

Resistor

(large

,

inductive

,

low Q)

Resistor (large

,

capacitive

,

low Q)

Inductor

(high Q)

Capacitor

(high Q)

Pages

40,49,59,

64,75,133,

135

23,29,40,

49 ,64,70,

75,82,94,

118,133,

135

40,49,59,

64,75,82,

88,133,

135

23,40,49,59,

64,70,75,82,

88,133,135

29,40,49,59,

64,75,106,

111,118,128,

133,135

23,29,40,49,

64,70,75,82,

94,106,111,

118,128,133,

135

13
Pages

G Large Large (+) Large Large (-) Inductor 40,49,59

(low Q) 75,88,13

135

H Large Large (-) Large Large (+) Capacitor 23,40,49

(low Q) 70,75,88

133,135

I Z/e_ Y/e 40,49,99

122,133,

135

Category I, with the polar forms of impedance and admittance, is

included because it can be used to illustrate the capabilities

of instruments which utilize distributed parameter methods but

operate in the lumped parameter region.

A typical and useful example of series to parallel relationships

is the conversion of the series values of a high Q inductor to

its equivalent parallel values. Assume a 0.25 uH indicator with

a Q of 250; and a frequency of 30 MHz:

0.189fi 0.25yH

Q

= ^ WHERE CO = 2TTf

. ^

^ 2x3.14x30x10^x0.25x10"^

250

R = 0.188fi

Converting to equivalent parallel values

R n X G

2 2 2 2 R +X R'^ + X

G

= 0.188 B

= 47 .1

(0.188)^+(47.1 )^

2220

B = - 21 . 2 mS

G = 84.9yS

C

B 21.2x10"^

1 .88x10"

- llSpF

14
Therefore at 30 MHz the inductor would be an equivalent parallel

circuit of

84.7yS

nspF

It is feasible and often desirable to measure such an inductor

in terms of its equivalent parallel values through the use of

an admittance bridge. Many similar examples can be devised

which illustrate the importance and usefulness of equivalent

series and parallel relationships.

Using this example, it can be seen that if it were required

to measure such an impedance, it would come under categories E

and I. Referring to Section 3, it could be measured by either

null resonance or active methods . In Section 4 we find the

following possibilities for measuring instruments:

Null Resonance Active

Maxwell Bridge

Schering Bridge

Transformer Ratio

Bridge

Twin-T Bridge

Q-Bridge

Q-Meter L-C Meter

Immittance Transcomparator Vector Impedance Meter

Vector Voltmeter

6 port coupler

To reduce this large number of possibilities further, the capabilities,

accuracies, strengths and weaknesses given for particular instruments

in Section 4 may be consulted.

15
3. MEASUREMENT METHODS AND THEIR CAPABILITIES

Introduction

In this section the principles and characteristics of various

methods of measurement are examined. The methods considered

include null, resonance, active and comparison. Two aids are

available to assist in the selection of an appropriate method of

measurement for a particular situation. Following the description

of each method, the outstanding strengths and weakness are listed

using as criteria the characteristics of the ideal instrument

described in Section 1. Graphs are also provided to reveal

quickly the ranges of the various impedance parameters which can

be measured at a particular frequency. An attempt has been made to

show on these same graphs the capabilities of specific instruments

even though each is covered in more detail in Section 4. This has

been done as an aid to illustrating and comparing the measurement

options available within a given method.

For a particular measurement requirement there may be more than

one method which may be used. In such cases other factors such as

accuracy, cost, speed or operator skill will need to be considered.

In other instances it may be found that there is only one method

available so that the selection process is very simple, but once

the merits of various methods have been considered, Section 4

will be found useful in making detailed comparisons between

specific instruments

An exception to the foregoing is necessary in the case of the

comparator method because of the different concept of measurement

it implies as compared to the null, resonance and active methods.

Actually any null, resonance, or active instrument may be used as

a comparator providing a standard is available to use in the comparison procedure. Comparison is more of a procedure than a measurement method in this sense, although its importance is not to

be overlooked for many applications. Graphs have been omitted in

16
the discussion on comparison, even though some ins trixments are

marketed which are specifically intended for use as comparators.

3.1. Null Methods (two-terminal) Categories Measured: All^

a. Principle of the Null Method

Although there are some very notable exceptions, null

instruments most often are in the form of a Wheatstone bridge

circuit. Voltage is impressed across one portion of the circuit

and standards within the bridge are adjusted until a null

indication is obtained across some other portion of the circuit.

At the null or balanced condition, unique relationships exist

between the device placed at the unknown terminals and the other

elements of the circuit. To illustrate this principle, consider

the simple Wheatstone circuit of figure 3-1,

A

+

Figure 3-1.

with the resistance, R , connected to the unknown terminals. The

X

other three resistances can be adjusted until the galvanometer, G,

indicates a null so that the B and C corners of the bridge are at

the same potential. Under this condition

IiRi = I2R2

^Although individual null instruments have rather limited

capabilities, the null method has been applied to nearly

every type of impedance or admittance measurement.

17
and IiRs = I2R,X

Dividing these two equations gives

R 3 R

X

or R

X

(3-1)

For ac measurements the resistors can be replaced by impedances

or admittances, the battery by an oscillator and the galvanometer

by an ac detector, so that the bridge equation becomes:

which is the ac counterpart of the Wheatstone bridge,

b. Characteristics of ac Bridges

There are several significant observations to be made

about the ac bridge equation and its implications regarding

bridge characteristics and behavior:

(1) In practice usually made to be some multiple of

10, and is a variable standard. This arrangement is called a ratio-arm bridge and the unknown impedance (or admittance) in

terms of a variable impedance (or admittance) in an adjacent arm.

(2) If the product ^2^3 made to be a definite multiple

(usually some power of 10) and Z^ is a variable standard, then

the characteristic product arm bridge is obtained and an unknown

impedance will be measured in terms of an impedance in the opposite

(3-2)

18
arm. Because 1/Z^ can be replaced by its parallel equivalent, Y^^,

in the equation, the standard for impedance measurement

(Z = R + jcoL ) is invariably an admittance (conductance and

X X X

capacitance in parallel) located in the arm opposite the unknown.

This is done because variable capacitors are more suitable as

standards than are variable inductors.

(3) The basic bridge circuit may be modified in many different

ways by using various combinations of impedances and admittances.

This permits variations in circuit design to accomodate different

requirements, but no single circuit provides for all types of

impedance and admittance measurement.

(4) In actual practice all reactance standards contain some

resistance and all resistance standards contain some reactance.

These unwanted residuals may also vary with setting, causing

the resistive and reactive balance adjustments of the bridge to

be interdependent.

(5) To produce a bridge of high accuracy requires high-quality

standards and great care in shielding the internal bridge components

from one another. Despite such precautions, the effects of some

residual internal impedances cannot be completely eliminated and

this restricts the frequency range and accuracy capabilities of

any bridge

.

In operating an impedance or an admittance bridge, an

initial balance is made with either a short-circuit or an

open-circuit placed at the unknown terminals. The short-circuit

or open-circuit reference is then replaced by the unknown and

the bridge rebalanced by adjusting the bridge standards. Many

instruments are made to be direct reading so that no calculations

are necessary. Often, however, some rather involved calculations

may be required to correct for the errors caused by residual

impedances. Such calculations are necessary in order to obtain

the most accurate results.

19
In general, null instruments offer the most accurate means for

impedance measurement. Instriament accuracy depends on the quality

of internal shielding, standards, construction details and dial

resolution. Instruments are designed around some center operating

frequency where accuracy is best. Below this frequency uncertainties

may increase because of loss of sensitivity (sharpness of balance)

.

Above this frequency the major causes for increased uncertainty

are residual circuit impedances. Some null circuits are frequency

sensitive; this will be made obvious by the appearance of a

frequency term in the balance equations. If a frequency term does

not appear, then it is not an error source of first order importance

unless the bridge is being used to measure a reactance which is of

opposite sign from the normal bridge readout.^ In such applications

the frequency error will increase as the square of the frequency so

that it becomes important that the measurement frequency be accurately

known

.

For most null instruments the range for Q-measurement is from

10"^ to 10' although some admittance bridges will provide fairly

reliable results up to lO"*. Beyond these limits the accuracy is

degraded to the point where the measurement is hardly more than

qualitative. The Q-bridge is somewhat of an exception, but the

Q-measuring feature is not based strictly on the null principle.

Limitations in the purity or Q of practical bridge components

limit the extremes to which Q is measurable. Null instruments

are most accurate for measuring Q-values near 1, whereas

resonance instruments are probably most accurate for measuring

Q-values in the vicinity of 100. Of all the null instruments,

the twin-T circuit described in Section 4.1 e, provides the best

accuracy capabilities for the measurement of Q.

c. Error Sources

Major sources of error in null instruments derive from a

number of causes and limitations. Some of the more significant

of these are as follows

^See Section 7 on range extension.

20
(1) Resolution capability (the smallest measurable quantity)

.

This is significant in measuring small immittances.

(2) Inaccuracy in ratio or product arms often appears as a

percentage term in the uncertainty statement. This is significant

in measuring large immittances.

(3) Errors due to uncertainty of measurement frequency. These

are not allowed for in bridge accuracy statements so that it is

the operators responsibility to insure that frequency errors do

not appear.

(4) Especially in bridges, the expressions for measurement

uncertainty will often contain terms to allow for the effect of

residual impedances in various portions of the bridge circuit.

In high quality instruments great effort is made to reduce these

residuals or to compensate for them through the use of shielding

or compensating circuitry. It is the effect of circuit residuals

which ultimately limits the upper frequency at which a bridge is

usable

.

(5) Non-precision connectors at the interface between bridge

and unknown contribute significant uncertainties, especially to

the measurement of either very large or very small reactances.

d. Strengths and Weaknesses

In summary, some of the more noteworthy strengths and

weaknesses of two-terminal null methods are listed below:

Strengths

(1) High accuracy capability

(2) Good for low Q measurements (< 10)

(3) Excellent for use as a comparator

(4) Superior long term stability

(5) Commercially available in wide variety

21
Weaknesses

(1) The measurement procedure is relatively slow

(except for automated bridges)

(2) Limited capabilities in frequency range

and range of parameters measured

(3) Skilled operator required

(4) Difficult to calibrate

(5) Cannot be used to measure small impedances

above about 30 MHz

(6) Accuracy limitations in measuring minor

component of complex immittance become

severe for both high-Q and low-Q measurements

22
3.2. Null Method (three -terminal) Categories Measured: B,D,F,H

a. General Coininents

Two-terminal methods are frequently inadequate for extremely

small admittance measurements because capacitance to ground or

other surrounding conductors may be so large that the admittance

of interest is not detectable. As an example, interelement

capacitances of vacuum tubes and transistors may be of the order

of fractions of a picofarad. Such small capacitors are not

measurable in two-terminal situations where capacitances to

ground may be several picofarads. Such measurement problems are

solved by the use of three-terminal or direct admittance instruments,

most of which are of the null variety. Transformer bridges are used

which avoid any effects of capacitance or admittance to ground in

the bridge circuit, permitting the measurement of capacitances as

small as 10~^^ Farads at frequencies up to 5 MHz. These bridges

make use of the principle of Y to A conversion in a very ingenious

manner, so that ordinary two- terminal elements are used to provide

three-terminal standards. The entire measurement circuit is electrostatically shielded, thus eliminating unwanted admittances either

to ground or other conductors. The main use of these instruments

is for the measurement of capacitances equal to 1000 picofarads or

less , with two-terminal techniques being adequate for the larger

values .

Three-terminal techniques require a thorough understanding of

what is to be measured and the principles involved. Measurement

errors become significant at higher frequencies, again because of

the contribution of circuit residuals, ratio inaccuracies in the

bridge transformer and connection errors. Three-terminal methods

are very useful for "in situ" or remote measurements although the

inductance of leads may be an important error source for remote

measurements

.

23
b. Strengths and Weaknesses

Strengths

(1) High accuracy for small admittances

(2) Good for in situ measurement

(3) Excellent for use as a comparator to

measure small differences

(4) High resolution of small admittance values

(5) Commercially available

Weaknesses

(1) Slow

(2) Direct capacitance measurement range usually

limited to values < 1000 pF.

(3) Limited frequency range (5 MHz is maximum)

(4) Not easy to measure at different frequencies

(compared to resonance methods)

(5) Complete calibration difficult and time

consuming

(6) Requires operator training depending upon

what kind of measurements are involved

(7) Cannot be used for measurement of small

impedances

24
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28
3.3. Resonance Methods Categories Measured: B,E,F

a. General Comments

Resonance methods for impedance measurement are applicable in

instances where the ratio of reactance to resistance (Q) is large

and either series or parallel circuit arrangements may be used.

Depending upon whether series or parallel resonance is used, the

detector will either be an ammeter or a voltmeter. In either case

the unknown may be measured by varying either frequency, resistance

or reactance (usually capacitance) . Frequency variation may be

less desirable for high-accuracy requirements because the voltage

(or current) versus frequency response of the circuit may not be

symmetrical about the resonant frequency, thereby introducing

errors. Resonance methods primarily determine circuit parameters

rather than the parameters of an individual component. Determinations of the resistance and reactance, or conductance and

susceptance of a particular component can only be made when the

other circuit elements are known or their contribution to the

circuit response is determined to be of no significance. Resonance

methods are not suitable for three-terminal measurements or "in

situ" measurements, and should not be used at frequencies where

any individual circuit component is near its self-resonant frequency.

b. Series Resonance:

RESISTANCE, REACTANCE

OR FREQUENCY

Figure 3-6a. Series resonant Figure 3-6b. Response

circuit of series resonant circuit

Either a resistance variation, a reactance variation or a frequency

variation scheme may be used. In all cases: wL = l/wC.

29
For resistance variation:

R = =r- s I

R (3-3)

"r2

- 1

Here the frequency and voltage are held constant during the

measurement. The standard resistance, R, is inserted in, and

removed from, the circuit and the current levels I and I

ri ra

observed so that eq . (3-3) gives the value of the resistance,

R , of the series resonant circuit,

s

For reactance variation:

(3-4)

In this case the frequency co , and voltage are held constant

during the measurement and the values of inductance L, and

L^, (these could also be capacitances) are noted which give

current values of I, and respectively.

For frequency variation:

L(w - (jj ) (3-5)

This method is the same as the reactance variation method with

the exception that the frequency, co , is the variable quantity.

In eq. (3-4) through (3-6) the subscript r denotes values at

resonance.

Series resonant techniques have some rather serious disadvantages

and are not often used. The fact that all elements are in series

and thereby do not share a common ground increases the liability

30
of error due to undefined circuit residuals. A reliable, stable

and highly sensitive current detector (ammeter ) is a difficult

requirement to fulfill especially at high frequencies. Ideally,

of course, the ammeter should have zero impedance. Resistance,

reactance and frequency variation techniques are all equally

valid with series resonant methods , but there are some outstanding

disadvantages in each instance. Reactance variation using a

variable capacitor has the fewest drawbacks because of the relative

purity, high quality and availability of variable capacitors.

Variable resistors of infinite resolution, low and constant

reactance and low temperature coefficient are not easily procured

making the resistance variation method subject to larger errors.

Frequency variation also places very stringent requirements on

the signal source. It not only must be tunable, but must also

be highly stable in both frequency and output level and have

relatively high power output capabilities in order for high

accuracy measurements to be obtained.

References on Series Resonance see [3, 69].

c. Parallel Resonance:

RESONANCE

GEN DET

0

CONDUCTANCE

,

SUSCEPTANCE

OR FREQUENCY

Figure 3-7a.

circuit

Parallel resonant Figure 3-7b. Response of

parallel resonant circuit

Either a conductance variation, a susceptance variation or a

frequency variation scheme may be used. In all cases:

ooL = 1/coC (3-6)

31
For conductance variation:

ri - 1

(3-7)

Here the frequency and current are held constant during the

measurement. Voltages V^^ and V^^ are observed with the standard

conductance, G, in and out of the circuit. G is the conductance

P

of the parallel resonant circuit.

For susceptance variation:

(3-8)

In this case the frequency, co, and current are held constant

and the capacitance values , C and are noted which give

voltages of V and respectively.

For frequency variation:

(3-9)

This method differs from susceptance variation only in that the

frequency is the variable quantity instead of capacitance. In

eqs.(3-7) through (3-9) the subscript, r, indicates values at

resonances

.

32
Parallel resonance methods find application in the measurement

of dielectric constant and loss tangent or conductance of

dielectric materials. Parallel arrangement of circuit elements

is easier to implement and introduces fewer errors because each

circuit element shares a common ground. High impedance detectors

with good sensitivity which do not introduce significant circuit

loading are available.

The frequency variation method has been used at high frequencies

(up to 100 MHz) and involves the measurement of Q by the technique

of varying the frequency on each side of the resonance voltage peak,

V^, until the voltage seen by the detector falls to /2 /2 V^, the

half-power points. Q is then given by f/Af, where f^ is the

resonant frequency and Af is the difference in frequency between

upper and lower half-power points. A 3 dB attenuator can be used

for the initial setting and then removed, thereby increasing

by 3 dB. The circuit is then detuned in frequency to the

original value. A similar procedure can be used with capacitance as the variable quantity in which case Q is given by

C^/AC. See references [6] and [14].

d. Resonance Methods For Determining Residual Impedances:

The following two paragraphs describe useful measurement

techniques which utilize the resonance method to determine the

residual impedances associated with capacitors and inductors.

(1) Grid Dip Meter: (for determining the residual

inductance of capacitors)

GRID

DIP

METER

Figure 3-8. Grid dip meter application

33
In high Q circuits a grid dip meter may be used for determining

either inductance or capacitance where two reactive elements are

connected in parallel as shown in figure 3-8. The coil of the grid

dip meter is loosely coupled inductively to the circuit and the

frequency of the grid dip meter is varied until a dip occurs

.

This locates the resonant frequency of the circuit and either

L or C is then calculable from the resonant relationship

wL = 1/wC provided the other parameter is known. This method is

useful for measuring the inductance of capacitors and with care

can yield inductance values accurate to well within ±10%. The

use of a heterodyne frequency meter as a frequency counter and

corrections for the value of the shorting inductance increase

the accuracy of the results. See references [3, & 15],

(2) Three Frequency Method (for determining the residual

capacitance of inductors)

Figure 3-9. Three frequency method, equivalent method

It is occasionally necessary that the distributed or

residual capacitance of an inductor be measured, and this can

be accomplished to a reasonable accuracy, ±10%, by measuirJing

the capacitance required to resonate the inductor at three

different frequencies . A Q-meter is usually the most appropriate

instrument for the purpose although a grid dip meter and three

capacitors of known value could also be used. For best accuracy,

the frequencies must be sufficiently far from the self-resonance

of the coil so that l/oo^^ is approximately linear with capacitance,

This can be assured by measurements at three frequencies

instead of two. By plotting l/oo ^ versus C on linear graph

34
paper, a straight line will result, and the equation for the

line is = (1/L^) d/oj^") - (3-10)

where = the capacitance in Farads necessary to

resonate the inductor at the angular frequency

0) rad/sec.

r = the true inductance of the inductor in henrys

= the distributed capacitance of the coil in Farads.

Equation (3-10) is of the form y = mx+b which is the slope-intercept

form of the equation for a straight line where the slope is

and the y intercept is C . See reference [3] or [19].

THE SQUARE OF THE SELF-RESONANT

FREQUENCY OF THE INDUCTOR

Fi_gure 3-10. Three frequency method, data analysis

Resonance methods offer a distinct advantage in resolving small

losses in the presence of large reactance (high-Q components)

because Q may be resolved to two or three significant figures.

This is in contrast to bridges where the resistance dial calibration near the zero setting may be rather coarse and provide

no more than a one significant figure readout.

35
For details on the derivations of the equations of resonance

methods, see especially reference [4].

e . Error Sources

The following are some of the more important sources of error

occurring in resonance measurements

(1) Frequency inaccuracy or instability during the measurement

procedure

(2) Generator voltage level instability

(3) If an element of the resonant circuit is nonlinear with

frequency or power level it will produce an unsymmetrical

detector response and result in erroneous measurements. (See

fig. 3-6b and fig. 3-7b)

.

(4) In any resonance measurement it is very difficult to

separate the resistance of the measured component from the

resistance of the remainder of the resonant circuit. This causes

the percentage error in Q to increase as the measured Q becomes

larger. (In other words the optimum accuracy for measuring Q

is obtained for Q = 1 with the uncertainty increasing as Q becomes

either larger or smaller)

(5) Non-precision connectors at the measurement interface

between instrument and unknown contribute significant uncertainties

especially to the measurement of very large or very small reactances.

f . Strengths and Weaknesses of Resonance Methods

Strengths

(1) Good for high-Q measurements

(2) Fast compared to null methods (when Q-meter

is being used)

(3) Broad frequency range

(4) Easy to use with external standards for

extending impedance range

(5) Versatile in that frequency is easy to vary

in the measurement procedure

36
(6) Calibration less difficult than for most

null instruments

(7) Good resolution of minor compoent in high-Q

impedances

Weaknesses

(1) Not usable for low-Q measurements

(2) Accuracy generally not as good as null method

in impedance ranges where the two methods have

overlapping capabilities

(3) Frequency must be closely controlled to avoid

large errors

(4) Operator experience is essential for good results

and to avoid instrument damage

(5) Reactance range is relatively narrow at a given

frequency when compared to null instruments

(this is especially true for Q-meters)

(6) Residual circuit losses introduce large errors

in measurement of high-Q values

Other references: [5, 8, 9, 10, 11, 12, 13, 14, 15, 19, 68]

37
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39
3.4. Active Methods Categories Measured: All

a. General Comments

The active definition of impedance is, by ohms law, the

ratio of complex voltage to complex current

Z = V/I (3-11)

Following this definition, active methods of impedance

measurement are defined or distinguished as being those which

measure the ratio of complex voltage to complex current.

Expanding the above equation

where |z|, |v|, |l| are absolute magnitudes and G, (f)^ are

the phase angles of impedance, voltage and current respectively.

b. Vector Impedance Meters

Many different schemes have been devised which embody the

active method with the vector impedance meter being the one

most often encountered, and all have basic and common characteristics. A source of energy, either current or voltage, is

impressed across the unknown impedance and the resulting voltage

drop is measured by a voltmeter which may be calibrated to read

directly in impedance magnitude. In addition some means must be

provided whereby the phase of the detected voltage is compared to

the phase of the input signal and the difference displayed. These

concepts are illustrated by the following diagrams.

Z = Z (3-12)

40
Figure 3-13. Active method for measuring impedance

The impedance magnitude is the ratio of the magnitudes of the

voltage and the current and the impedance phase-angle is the

phase difference between the voltage and the current. The

principle is quite simple, but the instrumentation necessary

to accomplish it can become rather complicated and elaborate

especially as accuracy requirements and measurement

frequencies are increased.

For measuring small impedances, a constant current

generator is required and for measuring large impedances , a

constant voltage generator is ideal and practical. To examine

this more closely consider the following diagram

Figure 3-14. Measurement of

small impedances using constant

current generator

41
where a large impedance, , is placed in series with the

oscillator. As long as the unknown impedance Z , is much

smaller than Z^ , then the current, i, will remain essentially

constant, and the measurement can be made accurately. However,

when the measurement of large values of Z is required, it

becomes necessary to alter this circuit arrangement to provide

a constant voltage source as shown in the next diagram, where

the large series impedance, Z^ , is replaced by a small shunt

impedance, Z . Under these conditions large values of Z

Figure 3-15. Measurement of

large impedances using constant

voltage generator

do not seriously alter the generator voltage, and the

measurement error can be kept small. Through the proper

selection of circuit parameters and source voltages, the

detector can be calibrated to read directly in impedance

magnitude, regardless of whether the source is operated on a

constant current or a constant voltage principle.

c. L-C Meters

To perform phase measurement there is also a variety of

available methods, and these too require either a constant

current or constant voltage source in accordance with the

magnitude of the unknown impedance. Measurements on inductors

and capacitors may be made directly at angular frequencies

which are integral powers of ten. For example, if the source

42
is a constant current generator, the voltage, E, across an

unknown inductor, L, is given by

E = I CO L (3-13)

where o) = 27Tf radians/second. In a similar manner capacitance

measurements are made possible by the use of a constant

voltage source and the relationship

I = E to C . (3-14)

In general such methods as illustrated by equations (3-13)

and (3-14) are usable only at lower frequencies, although

useful measurements are possible somewhat above the audio

frequency region provided sufficient source voltages and/or

adequately sensitive voltmeters are available,

d. 6-Port Coupler

The six port coupler may take a number of forms, but basically

it is an arrangement of hybrid junctions and directional couplers.

It provides a unique and highly versatile measurement system with

the capability of measuring several electrical parameters over

wide ranges. The parameters it can measure include impedance,

voltage, current, power and phase.

The voltage V and the current i in a transmission line are

related to the complex amplitude, a, of the incident voltage wave

and the complex amplitude, b, of the emergent voltage wave by the

diagrams shown in figure 3-16, where is the real characteristic impedance of the line at the reference plane.

43
Measuring the magnitude of any 3 of the 4 vectors (complex

numbers) v, iZ^, a, and b completely determines all parts of

the parallelogram including phase angles. Phase angles are

calculated using the law of cosines. If the magnitudes of all

four vectors are measured, the sensitivity in measuring angles

near 0 and 180° is greatly increased, many calculations are

simplified, and the resulting redundancy provides a check on

the measurement accuracy.

a i z 0

Figure 3-16 . Impedance measurement using the

6-port coupler: Relation between voltage (v)

,

current (i) , incident voltage wave (a) and

reflected voltage wave (b)

e. Error Sources

Active methods in general are not capable of the high accuracies

that can be obtained by other methods, but it is also worth noting

that active methods are the newest additions and a great deal of

innovation and improvement can be expected. Chief error sources

are the following:

References on active methods: [57, 71, 6]

Reference on 6-port coupler: [71].

44
(1) Inability to locate the measurement interface between the

measuring instrument and the unknown. This is especially

true where probes are used at high frequencies and it

becomes very uncertain as to what is actually being measured and the meaning of the results. (The 6-port coupler

is an exception to this limitation)

(2) Meter resolution

f. Strengths and Weaknesses

Strengths

(1) Fast

(2) Operator experience relatively unimportant

(except for 6-port coupler)

(3) Broad frequency ranges available in some instruments

(4) No calculations required (except for 6-port coupler)

(5) Often adapted for use with automatic dataprocessing equipment

(6) Broad impedance measurement range

(7) Instruments are commercially available

(except for 6-port coupler)

Weaknesses

(1) Low accuracy

(2) Frequency range must be sacrificed to obtain

accuracy comparable to null instruments

(3) Measurements very difficult to verify in terms

of high-quality impedance standards, especially

at high frequencies . Measurement reference

plane not well defined (except for 6-port coupler)

45
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48
3.5. Comparators or Differential Measurements

Categories Measured: All

The measurement of impedance by comparison may involve null

methods , resonance methods , or active methods and thereby is not

distinguishable as a different measurement method. It is included

here because the approach offers some unique advantages , and also

because it is widely used. Comparator measurements are of most

value where it is necessary to measure a large number of nearly

identical items, quickly and accurately.

The comparator approach may utilize any impedance instrument

such as a bridge or a meter capable of resolving small differences

between a standard and an unknown. This means that the instrument

should be both sensitive and stable, but it does not mean that it

must be capable of high absolute accuracy. Often it is found

that an instrument in the ±5 percent accuracy class, together

with a good standard, is capable of producing ±0.1 percent

measurements. For this reason comparator techniques may be

extensively used in standards and calibration laboratories. The

comparator concept may be illustrated by the equation

= Zg ± AZ (3-15)

where the value of the unknown, Z , is equal to the value of

the standard, Z^, plus or minus some small increment, AZ,

observed on the instrument serving as the comparator.

Listed below are some^ of the main advantages and

disadvantages associated with comparator measurements.

Advantages

(1) High precision and high accuracy (little effect from

large systematic errors)

(2) Speed and economy (measurements can be made quickly

by unskilled personnel)

4^
(3) High-accuracy instrumentation not required (only

stability and sensitivity are needed)

(4) Excellent for production, quality control and

calibration lab applications , sorting of

components within tolerance limits, go-no-go

testing

Disadvantages

(1) Low versatility usually capable of measurements only

for specific values, specific types of components

and specific frequencies)

(2) Different standards required for each additional

measurement application

References pertaining to Comparator methods: [16, 17]

50
3.6. Automated Measurements

A great deal of emphasis has been devoted to the automation

of all types of measurement. Automated instrumentation can greatly

reduce measurement time and make possible the accumulation of

large amounts of data which would otherwise be impractical. Also,

measurement data is made available in digital form for fast

processing, and inexperienced personnel may be used so that

very little training is required. In lumped parameter impedance

measurement, automation has come into extensive use in several

ways .

At the lower frequencies (around 10 kHz and below) a number

of bridges have been manufactured which fully automate the measurement procedure for resistance, inductance and capacitance.

These may be found very valuable for inspection or quality

control purposes where measurements at lower frequencies may be

used to monitor the behavior of devices whose values are either

not frequency dependent or where a highly predictable correction

factor may be applied to give higher frequency values. It is not

always necessary to perform measurements on components at the

exact frequency where they are to be used so long as the values

bear a predictable difference between the frequency of measurement and the frequency of application.

At intermediate frequencies (mainly 100 kHz and 1 MHz)

automated bridges are available and most are for the measurement

of capacitance and either dissipation factor or conductance.

These bridges may also be used for component selection or quality

control in place of measurements at other frequencies. These

bridges, as well as those operating at lower frequencies, are

self-balancing so that the only requirement of the operator is

the attachment of the device to be measured. Balance is reached

in a fraction of a second and the value is displayed in the form

of an in-line numerical display or through a digital innerface

for computer handling of measurement data.

51
At higher frequencies (100 MHz and above) automated systems

appear in the form of network analyzers capable of performing

a wide variety of measurements. These are often large systems

operating in conjunction with a computer that controls a preprogrammed measurement procedure in addition to processing the

data. Such systems are now appearing with operating capabilities

down to very low frequencies. Network analyzers can be used in a

swept frequency or a stepped frequency operating mode and can also

utilize an oscilloscope display for the measurement data. These

find extensive use in the analysis of multiport devices, attenuators, filters and various system components where input/output

response characteristics and measurements of S parameters,

attenuation, and return loss are of interest.

3.7. Other Methods

There are a number of ways for obtaining impedance infoirmation

pertinent in the 30 kHz to 300 MHz range which do not fall under

the previous methods but will be briefly described here for the

sake of completeness.

a. Time Domain Ref lectometer - This has been described

as a closed circuit radar system, and is used mainly

in connection with coaxial equipment where a uniform

characteristic impedance is of interest. Pulses with

very fast rise time are transmitted down a line and

when impedances are encountered which are different

from the characteristic impedance, energy is reflected

back and a scope trace can be made to show, within

less than a centimeter, the location of a discontinuity.

Information regarding the magnitude of the reflection

as well as whether the discontinuity is inductive or

capacitive is also determined. Time Domain reflectometry has many uses, among them being the design

References on Time Domain Reflectometry [75, 76]

52
and construction of adapters, loads and mismatches.

The information obtained with a reflectometer is broadband in the sense that it is an integrated response

covering frequencies up to about 12 GHz. The resolving

power of the reflectometer is dependent upon the risetime of the transmitted pulses with 30 picoseconds being

the approximate limit

.

Frequency Domain Reflectometer - With the development of

directional couplers which are capable of operating down

as low as 1 MHz with directivities of the order of 50 dB

for coupling ratios of 30, 40 and 50 dB, the way has opened

for the use of frequency domain ref lectometers in the

lumped parameter region. The approach is much the same

as for higher frequency reflectometers and the capabilities

and limitations are also very similar. These methods

produce only impedance magnitude measurements normalized

with respect to the characteristic impedance of the system

and the range is typically only for voltage standing wave

ratios of about 4. Accuracies of three to five percent

are typical. Such devices are also very useful in high

power measurements in the 1 to 30 MHz frequency range.

Swept Frequency - A very popular method for studying the

response characteristics of a circuit or component over a

wide frequency band is through the use of swept frequency

techniques. For one-port devices a slotted line may be

used which is terminated by the one-port. The line is

energized by a generator emitting a constantly varying

frequency between preset upper and lower limits . A

broadband detector attached to the slotted line probe

is used to record the voltage response as the frequency

changes. Two-port devices such as filters are quickly

Reference for Freq-Domain Reflectometer : [77]

Reference for Swept Freq: [78]

53
analyzed in this manner by simply placing them between a

sweep generator and a broad band detector. X-Y plotters

are usually employed to graph the swept frequency response

for detailed study.

d. Slotted Lines - A majority of the impedance measurements

made with slotted lines are made above 300 MHz, but much

work may also be done at lower frequencies , especially down

to 100 MHz. Much lower than this, either the phase angle

range becomes too restricted or extremely long lines must

be used so that other methods are better. Proper use of

a slotted line requires a highly trained person and

uncertainties of 1 or 2 percent are typical. Voltage standing

wave ratios up to 10 and phase angles from -90° to +90°

are attainable for frequencies where the length of the

slotted line is at least one-quarter wavelength. One

unique and interesting application for a slotted line

is in the measurement of the residual series inductance

of a two-terminal capacitor.

e. Return Loss Bridge - This instrument might be classified

as a null method because the measurement process does

involve a nulling procedure and the equivalent circuit

resembles a Wheatstone bridge. The lowest frequency

versions operate down to around 2 MHz with uncertainties

in the 2 to 5 percent range. These bridges measure

voltage standing wave ratio only and do not provide phase

information. Operating range covers a bandwidth of

several octaves with some bridges being usable as high

as 12.4 GHz. Operating procedures are not complicated

and are quickly learned.

References on Slotted Line Measurement: [76, 79]

Reference for Return Loss Bridge [80]

54
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57
4. INSTRUMENTS FOR VARIOUS METHODS

Introduction

The material presented in this section is intended as an

aid in critically comparing various instruments which operate

under the methods identified in Section 3. Following the

same order of presentation of Section 3, nine instriiments

are described and evaluated which are of the null variety,

three of the resonance variety and two which utilize the

active method. The format is also similar, in that specific

comments regarding technical characteristics, strengths,

weaknesses and graphs of measurement range versus frequency

are provided. Most of the instruments discussed are

commercially available. However, some are not manufactured

for sale and those in existence have been constructed for

specific needs by individual laboratories. There is still

another group of instruments that should not be overlooked.

This group includes those instruments which were once commercially available, but for one reason or another have

disappeared from the catalogs of instrument manufacturers.

Many of these remain in service, or may be found available

in surplus or used equipment inventories. Examples of this

group include the Twin-T and the Byrne Bridge. The

information on frequency ranges , measurement ranges and

uncertainties, is an attempt to generalize what is found

in the referenced literature, and in the catalogues of

instrument manufacturers. In the upper right hand corner

of the initial page describing a particular instrument, an

item "categories measured" will be found followed by one

or more capitalized letters which allude to the categories

identified in Section 2.

58
4.1. Null Instruments Categories Measured:

A,C,D,E,G

a. Maxwell Bridge

(product arm)

B

BALANCE EQUATIONS:

^ = •^2^3^^ (4-1)

Figure 4-1.

Range and uncertainty for resistance:

0.2 xa^ to 110 kf^ at 30 kHz decreasing to 11 kQ at 500

kHz and 30 at 30 MHz.

Basic uncertainty of the order of ±3% for unknowns with

low Q, and increasing as Q of unknown impedance becomes

larger

.

59
Range and uncertainty for inductance

0.2 nH to IIH at 30 kHz decreasing to 10 mH at 1 MHz and

60 yh at 30 MHz.

Basic uncertainty of the order of ±0.25% at lower frequencies

and increasing to +5% at higher frequencies.

Comments

This bridge measures series inductance and series

resistance in terms of capacitance standard, , and

conductance standard, , and is about the only method

available for accurately measuring low impedances at high

frequencies except for the Schering bridge. Initial balance

is made with respect to a short circuit placed at the unknown

terminal. A complete calibration of a Maxwell bridge is

extremely difficult so that it is best to calibrate or check

at spot frequencies and values as needed. Accuracies are very

difficult to verify because of different connector

configurations at unknown terminals. Internal shielding

requirements are stringent, making the circuit impractical for

use much above 30 MHz. Most commercial versions have a

self-contained oscillator and detector. Resistance and

inductance measurements do not contain first order errors due

to inaccuracy of oscillator frequency because frequency terms

do not appear in balance equations. When measuring large

values of inductance, the capacitance from the "C" corner of

the bridge to ground becomes an important source of error.

These errors also increase with frequency. Measurements made

with the Maxwell bridge are relatively slow and operator

should be aware of, and know how to minimize, connection

errors when attaching the unknown to the bridge . Leads should

be kept short, in all cases. Graphs showing frequency and

magnitude measurement ranges do not represent any one

instrument. Several commercial versions of the Maxwell bridge

60
are available, of both domestic and foreign manufacture, and

there are many areas of overlap in frequency and measurement

range.

Strengths

(1) High Accuracy

(2) Best of all instruments for measuring small

values of series resistance and series inductance

(3) Commercially available

(4) Broad measurement range for resistance

Weaknesses : or Limitations

(1) Maximum upper frequency 30 MHz

(2) Difficult to calibrate

(3) Slow

(4) Complex internal shielding requirements make

the bridge difficult to construct

Reference pertaining to Maxwell Bridge: [18, 19]

61
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63
b. Schering Bridge

(ratio arm bridge)

Categories Measured: A,B,C,D,E

General Coitunents :

The basic Schering bridge has been modified to perform

many specialized measurement functions and in one form or

another is probably the most widely used of the rf bridge

circuits. This bridge appears in several forms and variations

with the two circuits shown above being the ones most

frequently encountered. The bridge can be used either for

admittance or impedance measurements and in the latter

instance will cover ranges which partially overlap the

Maxwell bridge. The most nearly ideal standards are variable

air capacitors and the main advantage of the Schering bridge

is that it employs them as internal standards for both the

real and imaginary components of the unknown. Other advantages

include small circuit residual impedances permitting operation

over wide frequency ranges. Some commercial versions of this

bridge contain oscillator and detector and some do not and

therefore must be provided. The Schering bridge is often

used for measuring components under dc bias conditions.

Circuit (a)

B BALANCE EQUATIONS:

±C

4 (4-3)

(4-4)

(4-5)

X

Figure 4-4a.

64
Range and uncertainty for parallel resistance:

15 n to 100 kfi from 500 kHz to 250 MHz

Basic uncertainty of the order of ±2%.

Range and uncertainty for parallel capacitance:

0 to -100 pF or 0 to + 20 pF from 500 kHz to 250 MHz.

Basic uncertainty ±0.5%.

Conunents :

This bridge measures admittance in terms of equivalent

parallel resistance and either positive or negative

equivalent parallel capacitance, thus either capacitive or

inductive impedances can be measured. Balance is made

initially with respect to an open-circuit and first order

errors due to oscillator frequency are not present.

Measurements can be made in a few minutes and no computations

are necessary because the readout is direct at all frequencies.

Operator skills are important in making proper connections of

the unknown to the instrument because improper procedures

may seriously degrade the accuracy of the results.

Strengths

(1) Broad frequency range

(2) Broad range for parallel resistance measurement

(3) Uses variable air capacitors as internal standards

for both real and imaginary components

(4) Good accuracy

(5) No calculation required

(6) Commercially available

Weaknesses or Limitations

(1) Minimum frequency 500 kHz

65
(2) Range for inductance and capacitance measurement

small

(3) Slow

(4) Not usable below 500 kHz

(5) Some operator training required

Circuit (b)

(4-6)

(4-7)

Figure 4-4b.

Range and uncertainty for series resistance:

0 to 1000 ^ from 50 kHz to 60 MHz-. This requires two

instruments with overlapping frequency ranges. Basic

uncertainty of the order of ±1%

Range and uncertainty for series reactance

0 to ±5000 Q at 1 MHz for one model having a basic

uncertainty of ±2% with range varying inversely as

frequency

.

66
Comments

Although the same basic circuit is used, two instruments have

been used to cover the entire frequency range from 50 kHz to 60

MHz. These instruments overlap in frequency range as shown

in the graphs for circuit (b) . These bridges measure impedance

in terms of equivalent series resistance and either positive or

negative reactance meaning that either inductive or capacitive

unknowns can be measured. Initial balance is made with respect

to a short-circuit. Because the readout of the imaginary or

quadrature component is in terms of reactance, the measurement

accuracy is limited to the accuracy to which the frequency

is known. Measurement time is of the order of a few minutes,

and operator skill and knowledge are important, especially in

making the best connections of the unknown to the bridge.

Strengths

(1) Can measure either inductive or capacitive unknowns;

readout in terms of reactance

(2) Uses variable air capacitors as internal standards

for both real and imaginary components

(3) Broad frequency range

(4) Commercially available

(5) Good accuracy

Weaknesses or Limitations:

(1) Good accuracy depends on accurate frequency control

(2) Usable only up to 60 MHz

(3) Requires trained operator

(4) Some calculation required for each measurement

References pertaining to Schering bridge: [19]

circuit (a)

circuit (b)

[24,25,26]

[20,21,22,23]

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c. Admittance Ratio Bridge Categories Measured:

D,F,H,B

(4-8)

(4-9)

Figure 4-7.

Range and uncertainty for conductance

0 to 1000 mS from 30 kHz to 5 MHz. Range extendable with

external standards connected in parallel with standard

arm. Basic uncertainty ±5% at lower frequencies.

Range and uncertainty for capacitance:

0.1 to 1100 pF from 30 kHz to 5 MHz. Range may be

extended to 0.1 uF with external standards connected in

parallel with standard arm. Basic uncertainty ±0.25%

at lower frequencies increasing to +1% at 1 MHz and

above 1 MHz increasing as square of frequency in MHz.

Lower frequency versions operating up to 200 kHz have

capacitance capabilities up to 1.11 yF.

Comments

This bridge has its application in the low frequency

range and extending upward to 1 MHz. Difficulty in pro70
viding accurate resistive ratio arms having small corrections

over a wide frequency range are the main reasons restricting

its use at higher frequencies. The basic circuit is usable as

a comparator where external standards are available. Initial

balance is made with respect to an open-circuit. Readout is

in terms of conductance and capacitance, and the unknown is

measured directly in terms of internal standards in the adjacent arm of the bridge. External standards added in parallel

with the standard arm of the bridge may be used for range

extension purposes. Resistors are used as ratio arms providing

ratios of 0.1, 1.0, 10 and 10 0. Errors appear at high frequencies for ratios other than unity because of the effects of

reactive residuals in the ratio arms

.

A high frequency version of this bridge employing a unity

ratio and an electrically symmetrical circuit has been

developed for accurate and precise measurements to 20 MHz.

See [29]

.

For the measurement of a wider range of admittances at

frequencies up to 200 kHz, both capacitance and conductance

standards are provided respectively by capacitors and

resistors arranged in a Y-network configuration and connected

to the A, C and D corners of the bridge.

This circuit may be used either for capacitance or

inductance measurements, but the internal standards must be of

the same kind as the unknown to be measured, i.e., the bridge

compares like reactances, which is a characteristic of ratio

bridges

.

Few commercial versions of this bridge are available.

Measurements require a few minutes to make with no difficult

computations usually required. For maximum accuracy, some

rather involved frequency corrections must be used. Good

operator skill is desirable.

71
strengths

(1) Wide capacitance range

(2) Good accuracy capabilities

(3) Convenient for use with parallel range extension

techniques or as a comparator

Weaknesses or Limitations:

(1) Does not measure small impedances

(2) Generally limited to frequencies below 5 MHz

(3) Some operator training required

(4) Few commercial models available

References pertaining to Admittance ratio bridge: [2,17,28,29]

72
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74
d. Transformer Ratio Bridge Categories Measured:

A,B,C,D,E,F,G,H

When used as an impedance bridge

Range and uncertainty for resistance:

0.1 mO, to 100 up to 10 MHz. Basic uncertainty ±1 to ±2

percent depending on frequency

Range and uncertainty for inductance

Generally 10"^^ H to 10 H up to 10 MHz. Reduced ranges

above 10 MHz. See chart. Basic uncertainty ±1 to ±2 percent

depending on frequency

NOTE: On the accompanying resistance range charts no

distinction is made between series or parallel resistance

because they would be equal if the reactance or susceptance

of the unknown being measured were equal to zero. These

ranges require several instrixments for coverage.

75
when used as an admittance bridge

10"^ S to 10'* S up to 10 MHz decreasing to 10"^ S to 10"^ S

above 10 MHz. Basic uncertainty ±1 to ±2 percent depending

on frequency.

Range and uncertainty for capacitance:

Generally 10"^^ F to 10"^ F up to 10 MHz. Reduced ranges

above 10 MHz. See chart. Basic uncertainty ±1 to ±2

percent depending on frequency.

Comments

This is a very versatile bridge circuit which offers some

unique features including a wider measurement range than the

conventional Wheatstone type circuits. The transformer ratioarm bridge, capable of either two- terminal , three-terminal

or balanced measurements, is less difficult to calibrate. The

effects of internal residual impedances are easier to eliminate

than in product-arm bridges so that internal shielding requirements present less of a problem.

Primary and secondary transformer turns-ratios in both the

input and detector locations may be tapped to provide the

effect of a variable internal standard. This eliminates the

need for adjustable resistors and capacitors although they

may be added for higher resolution. Principal error sources

are the ratio transformers and degradation of ratio accuracies

at high frequencies . The amount of degradation is highly

dependent upon the design and construction of the transformers.

Additional measurement applications include "in situ"

measurements, the measurement of transistor parameters, and the

transfer impedances of two-port devices

.

76
Several domestic versions of this bridge are available for

lower frequency use, say up to 1 MHz, but higher frequency

versions are not currently available except from foreign

manufacturers . This bridge principle is the one most frequently

used in automated measurements. Automated versions operate at

specific fixed frequencies utilizing electronic switching,

logic circuits , and digital readout or binary coded decimal

(BCD) equipment. Go- no-go circuits are used to indicate whether

or not an unknown falls above, below or within certain preset

limits. Self-balancing admittance bridges also use this circuit.

A sophisticated version of this bridge with a unity

transformer ratio has been built in the Soviet Union for measuring

dielectric constant and loss tangent of solid dielectric materials

up to 300 MHz. They have also used ratio transformers in bridge

circuits for measuring permeability and its temperature coefficient,

plus losses and various other characteristics of ferrites. [34]

In use the bridge is typical of manual impedance bridges in

that the measurement process requires a few minutes to complete.

Measurement time is somewhat shorter than with most null type

bridges because a zero or initial balance is not required unless

the bridge is being used as a comparator where the difference

between two components is being determined. Calculations required

are usually minimal.

Some of these instruments include an internal source and

detector, especially those which operate at specific fixed

frequencies; however most of the rf versions require an external

source and detector.

Strengths

(1) Wide frequency range

(2) Wide measurement range for resistance, inductance or

capacitance

77
(3) Relatively easy to calibrate

(4) May be automated

(5) Can measure grounded, balanced or unbalanced

impedances or make in situ measurements

(6) Commercially available

Weaknesses or Limitations

(1) Requires skilled operator

(2) Slow

References pertaining to Transformer Ratio Bridge: [2,5,27,30,

31,32,33,34,35]

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81
e. Twin-T Bridge Categories Measured: C,D,E,F,B

(4-12)

(4-13)

Figure 4-14.

Range and uncertainty for resistance:

1 kf2 to 50 m at 30 kHz decreasing to 5fi to 300kf2 at

5 MHz. A high frequency version measured from 20 Q. to

300kf2 at 5 MHz decreasing to 20^ to 6kf2 at 300 MHz.

Uncertainty ±0.1 to ±0.2 percent.

Range and uncertainty for capacitance

0.1 to 5000 pF at 30 kHz decreasing to 0.1 to 50 pF at

300 MHz. Uncertainty ±0.1 to ±0.2 percent.

82
Range and uncertainty for inductance

Inductance range is from 5 mH and up at 30 kHz and widens

to 0.2 ijH and up at 5 MHz. For a higher frequency version

the range is from 20 yH and up at 5 MHz, with the lower

limit decreasing to 50 nH at 300 MHz. Uncertainty ±0.1

to ±0.2 percent.

Comments

The twin-T bridge is basically an admittance bridge and

initial balance is made with respect to an open-circuit. It

appears to have found its place in the standards laboratory in

the role of performing measurements of high accuracy as

opposed to being used as a field instrument or a general

purpose tool for impedance measurement. There are a number of

good reasons for this which are due to the characteristics of

the bridge. Most notable is the fact that the bridge balance

is frequency sensitive in that the factor, w^, appears in the

balance equations. This requires that the generator be highly

stable and accurate in frequency to avoid error and virtually

precludes the use of easily portable oscillators. Other

features of the bridge include some unique advantages which

make it very desirable for standards work. Generator, detector,

unknown and standards share a common ground in the bridge

circuit which makes for ease of shielding and helps in the

elimination of error-causing ground loops. This bridge is

used at high frequency for measuring resistance (or conductance)

directly in terms of a capacitance change. Capacitance and

inductance are also measured directly in terms of a capacitance

change. This is the most accurate method for determining Q

because at a particular frequency, Q is given as simply the

ratio of two capacitance increments. The principle disadvantages

of the bridge are that it is not simple to use, measurements

are somewhat tedious and an experienced operator is mandatory.

83
No domestic version of the twin-T bridge is currently being

manufactured and the one foreign version, though excellent,

is expensive.

Strengths

(1) Versatile - Wide frequency range and wide impedance

range for conductance, capacitance and inductance

(2) Excellent accuracy capabilities

(3) Utilizes variable capacitors as standards for both

real and imaginary components

(4) Can measure conductance directly in terms of a

capacitance increment

(5) Most accurate method for measuring Q

Weaknesses or limitations:

(1) Requires highly skilled operator

(2) Commercial procurement difficult

(3) Expensive

(4) Slow

(5) Cannot measure small resistances

References pertaining to the Twin-T Bridge: [5,36,37,38,39,40]

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87
f. Thurston Bridge Categories Measured: C,D,G,H

SLIDING

SHORT

LOOPS GENERATOR

Figure 4-18.

Range and uncertainty for conductance

10 yS to 4000 mS from 40 to 1500 MHz. Basic uncertainty

±3% to 1000 MHz increasing to ±5% at 1500 MHz.

Range and uncertainty for susceptance:

± (10 yS to 4000 mS) from 40 to 1500 MHz. Basic uncertainty

±3% to 1000 MHz increasing to ±5% at 1500 MHz.

88
Comments

Although the Thurston bridge is classified as a microwave

bridge, its capabilities extend down into the frequency range

covered by this metrology guide so that its inclusion here is

appropriate even though it is not a liimped parameter device.

The voltages are induced into the junction of the bridge

branches by means of the inductive coupling loops and are

proportional in magnitude to the angle of orientation of the

plane of the loops with the center conductors of the respective

branches of the bridge. The bridge is balanced when the detector voltage is at zero or null. This occurs when the current

in the unknown branch, the real branch and the imaginary branch

sum to zero.

where V is the generator voltage which is common to all three

loops, Y is the branch admittance and k is the coupling

coefficient which is proportional to the angle of orientation

of the loop. If the real branch is terminated in a reflectionless admittance and the imaginary branch adjusted to an

electrical distance of 45 degrees at the generator frequency,

then the transformeed admittance, y' , of the unknown seen at the X

junction is given by

+ I. = 0 (4-16)

Each induced current in each loop is

I = kVY (4-17)

(4-18)

89
Thus the normalized admittance, Y , can be deduced by transforming

Y ' through the length of line separating the unknown from the

junction, or it may be read directly by using a lossless half

wavelength line section between the unknown and the junction.

Calibrated scales which read out directly in conductance, susceptance and multiplying factor are provided for the real,

imaginary and unknown branches respectively.

In addition to limited resolution, the most significant errors

arise from the fact that the loops are physically located a

slight distance from the junction point. [46]

The bridge finds application in coaxial systems for

impedance matching and adjustment, antenna measurements and

as a comparator. Through its use, voltage standing ratios or

reflection coefficients may be obtained.

Work has been done which in theory extends the range of

the Thurston bridge to ]/40 0 Z to 400 Z , Z being the ^ o o o

^ characteristic impedance about which the bridge standards

and readout is normalized. [4 7]

A modification of this instrument includes a built-in

constant-impedance, adjustable-length lines in the form of a

loop through the imknown and back to the junction permitting

the measurement of transfer impedance and admittance on both

active and passive four terminal networks.

Strengths

(1) Suitable only for measurements above 40 MHz

(2) Versatile - can be used to measure transistor

parameters and has a broad admittance range

(3) Commercially available

(4) Relatively inexpensive

(5) Broad susceptance range including both positive

and negative susceptance capability

90
Weaknesses or Limitations

(1) Relatively low accuracy and resolution

(2) Not usable at lower frequencies

(3) Requires experienced operator

(4) Slow

References pertaining to the Thurston Bridge: [42,43,44,45,46]

91
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93
g. Young Bridge Categories Measured: B,F

BALANCE EQUATIONS:

Gj^ = k(G^-G(.) (4-19)

Cx = k(C^-C(,) (4-20)

Figure 4-21.

94
Range and uncertainty for conductance

0.01 ijS to 1000 yS at fixed frequencies of 100 kHz, 465

kHz and 1 MHz. Basic uncertainty ±10%.

Range and uncertainty for capacitance:

0.00002 to 1000 pF at fixed frequencies of 100 kHz, 465

kHz and 1 MHz. Basic uncertainty ±0.25%.

Comments

The Young bridge circuit was devised especially for

measurement of extremely small values of capacitance. The

operating principle is based on the conversion of the wye

configuration of admittances between bridge corners A,B and

C to the equivalent delta and the use of differential

capacitance and conductance standards to maintain constant

and equal admittances in arms AB and BC. Bridge multipliers

from 1 to 10" are obtained by switching various admittance

combinations between points E and B. The unknown is inserted

across AB after an initial balance has been established.

The bridge is then rebalanced and is direct reading in

conductance and capacitance. Because of the wye to delta

conversions, the circuit is restricted to operation only

at fixed design frequencies. Domestic versions of the

modified Young bridge are commercially available and contain

built-in oscillator and detector. Provisions are available

for measurement of unknowns with external bias applied.

The bridge may be used for either three- terminal (direct)

or grounded admittance measurements. Operation is relatively

simple; although the original Young bridge was restricted

to measurements only at fixed frequencies, modifications

have been incorporated in modern commercial versions which

permit its use over a range of frequencies extending as

high as 1 MHz.

References pertaining to the Young Bridge: [47]

95
strengths

(1) Excellent for measuring very small admittances

(2) Capable of in situ measurement or measurements

of remotely located components

(3) Good accuracy capabilities

(4) Commercially available

(5) Versatile - may be used for either two-terminal

or three-terminal measurements

Weaknesses or Limitations

(1) Usable only at fixed frequencies

(2) Upper frequency limit approximately 1 MHz

(3) Cannot be used for small impedance measurement,

i.e., resistance and inductance

(4) Requires experienced operator

(5) Slow

96
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98
h. Byrne Bridge Categories Measured: I

SIGN

SOUR

Figure 4-24.

Range and uncertainty of resistance or impedance magnitude

measurement:

2 to 2000 ^ from 50 to 500 MHz. Basic uncertainty ±5%,

useful over an extended range of from 5 to 700 MHz at

higher uncertainties

.
Range and uncertainty of phase angle measurement:

-90° to +90° from 50 to 500 MHz. Basic uncertainty ±3°.

Can be used from 5 to 700 MHz at reduced range and higher

uncertainty. Phase angle range +9° to -9° at 5 MHz.

Range and uncertainty of inductance measurement:

From 7nH to 7yH at 5 MHz decreasing to 0.7nH to 0.7yH

at 500 MHz. Accuracy limited mainly by the uncertainty

in measuring magnitude of impedance which is a function

of frequency.

Range and uncertainty of capacitance measurement:

From 1.5 pF to 1500 pF at 5 MHz decreasing to 0.15 pF at

500 MHz. Accuracy limitation the same as for inductance.

Comments

Although the Byrne bridge reads out in terms of impedance

magnitude and phase angle, and thereby should not be classified

as an instrument for lumped parameter measurement, it is included

here because its operating frequency extends well down into what

has been designated as the lumped parameter frequency range.

Strictly speaking this instrument is not a bridge although it

does rely upon a null principle. In practice the actual

operation is exactly the same as a bridge with two adjustable

controls and dials which are read directly.

In operation a square wave modulated sinusoidal signal of

the desired measurement frequency is fed directly down a short

section of coaxial line into the unknown to be measured.^

^Caution: In the usual arrangement of generator, bridge and

detector, all of the generator power goes directly into the

unknown. Care should be exercised to avoid damage to unknowns

having low power capacity. It is also possible to reverse the

generator and detector connections to avoid this problem, but

such a manner of connection results in reduced sensitivity.

100
The impedance characteristics of the unknown are determined

i from the resulting standing wave pattern at a specific reference point in the line. This, of course, is no different from

the way a slotted line operates. The differences arise in the

means for obtaining the measurement information . In the Byrne

bridge this is done directly and automatically so that time

consuming calculations and tedious measurement procedures,

characteristic of slotted line measurements, are avoided.

Hence, operator skill is much less important. Ganged capacitive and inductive probes located at the point of reference

are calibrated to read directly in impedance magnitude at all

frequencies, and a detector probe in the slotted section

provides a direct readout in phase angle at some fixed frequency,

usually 00 MHz. At other frequencies the phase angle is obtained

by multiplying the dial reading by the ratio of the measurement

frequency to the fixed frequency at which the dial is calibrated.

Principal error sources are the uncertainty of the

measurement reference point location, probe loading or

coupling, mismatch of terminations, non-uniformity in the

slotted section and stray pickup in the null detector. Stray

pickup in the null detector is easily detectable by the fact

that leads become "hot. " The remedy for the problem is more

elaborate shielding. Ultimate measurement accuracy is poorer

than that obtainable by slotted lines when used at the same

frequency. Voltage level stability is not as important for

the Byrne bridge as it is with slotted lines because of the

different approach to the measurement of impedance magnitude.

Although neither foreign nor domestic models are now

available, a domestic version was manufactured, and no doubt

many are still in use. This instrument has probably been

superseded by automated vector impedance meters.

Calibration of this instrument is quite simple compared

to most null type instruments and is carried out by measuring

101
a 50 ohm load, an open-circuit, and a short-circuit at as many

frequencies as desired in the range of operation. This provides

only a partial calibration however, and more elaborate procedures

must be followed for further error reduction.

Strengths

(1) Wide range of capabilities for impedance magnitude

and phase angle

(2) Operation and data interpretation simple compared

to slotted line

(3) Few calculations required

Weaknesses or Limitations

(1) Reduced measurement capabilities below 50 MHz

(2) Relatively low accuracy

(3) Slow

(4) No longer commercially available

(5) Recommended only for measurement of devices with

coaxial connectors

References pertaining to Byrne Bridge: [48,49]

102
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Q-Bridge Categories Measured

106
Range and uncertainty for Q:

5 to 10,000 from 100 kHz to 50 MHz. Basic uncertainty

±10% increasing with frequency and value of Q being

measured

Range and uncertainty for capacitance

20 pF to 1000 pF from 100 kHz to 50 MHz. Basic uncertainty

±0.5%, increasing with frequency.

Comments

The Q-bridge actually embodies two measurement principles;

a situation made possible through the use of a phase sensitive

detector. The bridge elements and the unknown are arranged in

the traditional Wheats tone configuration, and the detector

separates the unbalance voltage between points A and C into its

in-phase and quadrature components , the in-phase component being

due to reactance unbalance. The reactance balance is made by

adjusting the in-phase voltage to a maximum, using the Q balance

control, the Q of the unknown is read directly as the ratio of

the in-phase unbalance voltage e^ to the generator reference

voltage, e^ . Measurement accuracy is apparently somewhat lower

than a Q-meter but there are other advantages , especially in

the versatility of the instrument for measuring capacitance

beyond its direct reading range. With all four bridge corners

brought out to accessible terminals either capacitance or inductance may be measured through the use of ratio arm, product

arm or substitution methods. The range for Q measurement also

goes beyond the Q-meter although the uncertainty increases to

the order of ±20% at 1 MHz for Q of 10,000. Through the connection of external capacitors, the capacitance measuring capability may be extended to cover 0.002 pF to 0.25 yF. External

standards can also be used to provide inductance measuring

capabilities as follows

107
Range and uncertainty for Q:

5 to 500 from 100 kHz to 50 MHz. Basic uncertainty ±10

increasing with frequency and measured value of Q.

Range and uncertainty for inductance

0.1 \iF to 100 mH. Basic uncertainty ±5%.

Strengths

(1) Has high Q-measuring range

(2) Versatile - can be used to measure a wide variety

of impedances and admittances

(3) Commercially available

Weaknesses or Limitations

(1) Relatively low accuracy for Q-measurement

(2) Requires experiences operator

(3) Slow

(4) Measures only components with Q of 5 to 500

Reference pertaining to Q-Bridge . [41]

108
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110
4.2. Resonance Instriiments

a. Q-Meter Categories Measured, E,F

(4-21)

(4-22)

Figure 4-31.

Range and accuracy of Q measurements

10 to 1000 from 30 kHz to 300 MHz. Uncertainty of Q

depends upon measurement frequency and value of Q being

measured but generally varies from ±5% to ±15% with

Q-meters usually reading low.

Range and accuracy of capacitance measurement:

20 to 500 pF up to 50 MHz and 10 to 100 pF from 20 MHz

up to 300 MHz. Uncertainty ±1%

111
Range and accuracy of inductance measurement:

50 mH to 1.4 H at 30 kHz decreasing to 20 nH to 0.6 \iE

at 50 MHz for lower frequency versions. Higher frequency

versions measure from 0.5 yH to 9 yH at 20 MHz decreasing

to 2.5 nH to 40 nH at 300 MHz. Uncertainty basically ±1%.

Comments

The Q-meter has long been one of the most versatile and

widely used instruments available for impedance measurement.

It is used in many forms and is available from a number of

sources both foreign and domestic. The most common version

reads directly in Q and resonating capacitance, and at

certain frequencies a direct reading inductance scale is

provided. Measurements can usually be made quickly (more

quickly than with a conventional, manually operated impedance

bridge) because no initial balance is required. Because of

the extra set of terminals in parallel with the internal

Q-meter capacitor, it is very easy to achieve measurements

of components whose values fall outside the direct reading

range of the instrument. This, of course requires the use of

external standards, and most manufacturers provide such

standards together with ample instructions in these procedures

as a part of the instruction manual for the Q-meter. It should

be noted, however, that such procedures almost invariably

bring new error sources into the picture which must be

carefully evaluated and compensated for best results.

The fact that both capacitance and frequency may be varied

easily by means of simple external controls greatly enhances

the versatility of the Q-meter. This feature is not available

in other instruments, and makes the Q-meter an especially

useful tool for design or trouble shooting applications.

112
Q-meters which utilize a resistance in the circuit for the

insertion of the test signal voltage should not be used for

making measurements on components with external dc bias

applied because of the risk of damage either to the insertion

resistor, the associated thermocouple unit, or the fact that

such a bias would seriously alter the calibration of the Q

scale of the detecting voltmeter. The Q-meter is not suitable

for "in situ" measurements.

Q-meters may be used directly or indirectly for the

following: 1) Q of inductors and capacitors 2) Self-capacitance

of inductors 3) Inductance 4) Capacitance 5) Power factor

6) Dielectric constant 7) Permeability 8) Low and high rf

resistance and impedances.

A more recent version of the Q-meter has appeared where

the measurement principle is based upon the logarithmic

decrement of an oscillation in a parallel resonant circuit

composed of the unknown inductor and a standard capacitor

contained within the instrument. An initial square wave

pulse is applied to the resonant circuit which may contain

any preset capacitance between 50 pF and 0.01 yF. The

measuring circuitry displays the resonant frequency of the

circuit and also displays the Q which is derived from a

counter circuit in accordance with the time required for the

signal to decay to e"^ of the original voltage amplitude. The

frequency range of measurement is from 1 kHz to 12 MHz. The

instrument provides a digital readout for Q and for the

resonant frequency which results for the various capacitance

values which must be preset at the beginning of the measurement

procedure. Measurements are performed in a few seconds and

basic accuracy for Q is of the order of 10 percent.

113
strengths

(1) Versatile - easy to perform measurements at

various frequencies

(2) Fast compared to manually operated bridges

(3) Measures high-Q devices

(4) Broad frequency range

(5) Good accuracy capabilities

(6) Commercially available

* Weaknesses or Limitations

(1) Uncertainty in Q increases for higher Q values

and higher frequencies

(2) Frequency monitoring required for best accuracy

(3) Cannot be used to measure low-Q devices directly

(4) Operator experience required

References pertaining to the Q-meter

[12,13,50,51,52,53,54,55,56]

114
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b. Inutiittance Trans comparator Categories Measured: B,E,F

OR C

0 0

FREQUENCY OR

CAPACITANCE

MEASUREMENT EQUATIONS:

q

=!o

^ AC Af

(jOC

(4-24)

(4-25)

Figure 4-35.

Range and accuracy for Q measurements

50 to 10,000 from 1 to 250 MHz with accuracies of the

order of ±1 to ±10% under most ideal conditions

Range and accuracy for capacitance and inductance measurement:

These are entirely dependent upon the external standards

available for use in the resonant circuit. The

118
standards are connected externally and are not an integral

part of the trans comparator

.

Coioments :

The operation of this instrument is based upon the principle

of parallel resonance or anti-resonance. It is mainly used in

standards work and provides for the accurate intercomparison of

inductors and capacitors and the measurement of high valued

resistances in the 1 to 250 MHz frequency range. Such an

instrument is also useful for the measurement of dielectric

constant and loss tangent of dielectric materials. The instrument, which has been constructed in many forms by various

experimenters, can utilize either the frequency variation or

the capacitance variation technique for measuring Q or bandwidth

of a parallel resonant circuit. Q is determined by increasing

the input voltage by 3 dB after the circuit has been brought to

resonance and then detuning either in frequency or capacitance

to the original reference voltage level. Q is then

C^/AC or f^/Af where AC or Af are the difference between upper

and lower half-power points in either capacitance or frequency

respectively. and f^ are the capacitance and frequency

settings at resonance.

This instrument is not available commercially. Its use is

probably limited to very specialized applications where other

resonance instruments, such as the Q-meter are inadequate. At

the National Bureau of Standards a version has been used to

intercompare inductors and capacitors with precision sections

of coaxial transmission line.

This is definitely not a field instrument. It requires a

highly stable and tunable source with more than average power

output capability, without which it is no better than a

Q-meter. Very high detector sensitivity and stability is also

119
required. As the Q of the circuit decreases and the response

curve flattens, the accuracy of measurement is impaired,

thus limiting the application to high-Q situations. An

advantage is that Q values much above the capabilities of the

Q-meter circuit are measurable, because of the capabilities

for high resolution, using either a frequency counter or a

very high quality incremental capacitor.

The coupling of the oscillator to the circuit is inductive

and largely limits the lower operating frequency to

approximately 1 MHz. The detector is capacitively coupled to

the circuit to avoid interaction between input and output.

Strengths

(1) High accuracy

(2) Versatile - capable of measurements over wide

frequency range and can measure either positive

or negative reactance

(3) Can utilize either frequency variation or reactance

variation method

Weaknesses or Limitations:

(1) Requires highly skilled operator

(2) Very slow

(3) Only capable of measuring high-Q devices

(4) Not available commercially 7

References pertaining to the Immittance Trans comparator

[4,8,9,10,11,14]

120
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121
4.3. Active Instruments

a. Vector Impedance Meter Categories Measured: I

I e

ALC

MEASUREMENT EQUATIONS

Z = E/T (4-26)

Figure 4-37.

Range and uncertainty of impedance magnitude measurement:

10. to 10 M.9, from 30 kHz to 500 kHz decreasing to 10 to

100 kO from 500 kHz to 100 MHz; basic uncertainty ±5%.

Range and uncertainty of phase angle measurement:

0 to ±90 degrees from 30 kHz to 100 MHz; basic uncertainty

±6 degrees up to 500 kHz and ±3 degrees from 500 MHz to

10 0 MHz. For higher frequencies additional uncertainties

must be added which are functions of frequency and

impedance magnitude of the unknown.

122
Range and uncertainty for resistance measurement:

Same as for Impedance magnitude.

Range and uncertainty for inductance measurement:

5 yH to 1 H at 30 kHz decreasing to 1 nH to 10 yH @ 100

MHz with basic uncertainty of the order of ±7 percent

over entire frequencies for inductances with Q>10.

Range and uncertainty for capacitance measurement:

0.5 pF to 5 yH (3 30 kHz decreasing to 0.03 pF to 0.3 yF

@ 500 kHz with basic uncertainty of ±7%. From 500 kHz

to 100 MHz the range limits also decrease with frequency.

Over this range the capabilities are 3 pF to 0.3 yF at

500 kHz and 0.02 pF to 2000 pF at 100 MHz. Basic

uncertainties about ±7%.

Comments

These are among the more recent instruments to appear and

no foreign versions have yet been introduced. The main

advantages are much increased speed and convenience over more

conventional instruments such as bridges. However, gaining

these advantages requires some sacrifice in accuracy. A

coaxial probe is used to connect the unknown to the measuring

circuit/ and impedance magnitude and phase angle are directly

read on panel meters. The main applications are in design

work, or perhaps in production testing, but not in standards

work where highest accuracy is required. The vector impedance

meter is also useful for "in situ" measurements. Calibration

of these instruments is made difficult because of the ambiguity

in defining the measurement reference plane. Depending upon

whether a low impedance or a high impedance is being measured,

123
either a constant current or a constant voltage is introduced

into or across the unknown and the resulting voltage or current

detected. Complex impedance is displayed in polar form. No

initial balancing is required and no calculations are necessary

unless the measurement results are desired in rectangular form.

Measurements at different frequencies are quickly made because

only one dial adjustment is required. This is in contrast to a

bridge measurement where both generator and detector tuning are

required at each frequency. In this sense then the vector

impedance meter is a broadband instrument. The measurement range

mentioned here is covered by two instruments, one operating below

500 kHz and the other above 500 kHz. For measurements with the

lower frequency instrument, measurements must be performed with

the unknown isolated from ground potential.

Strengths

(1) Fast

(2) Very little operator experience required

(3) Versatile - excellent for investigating behavior

of an unknown over a range of frequencies

(4) Commercially available

(5) Wide frequency range; wide range of measurement

Weaknesses or Limitations

(1) Low accuracy

(2) Accuracy difficult to verify especially at higher

frequencies

Reference pertaining to the Vector Impedance Meter: [57]

124
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b. L-C Meter Categories Measured

AMP 0 SENS

DET

REFERENCE VOLTAGE

MEASUREMENT EQUATIONS:

(4-27)

« C (4-28)

Figure 4-41.

Range and uncertainty for inductance

10 yH to 10 mH at 100 kHz with basic uncertainty of

±0.5%; 1 liH to 1 mH at 1 MHz with basic uncertainty

of ±0.5%.

128
Range and uncertainty for capacitance:

10 pF to 0.01 yF at 100 kHz with basic uncertainty of

±0.5%; 1 pF to 1000 pF at 1 MHz with basic uncertainty

of ±0.5%.

Comments

The L-C meter is limited to measurement at fixed frequencies

and does not provide information as to the resistance or conductance of the tested reactance. However, the convenience of

the meter readout combined with its relatively good accuracy,

speed and the additional capability for either two-terminal or

three- terminal capacitance measurements fulfills many measurement

requirements, especially in quality control or component selection. This instrument also permits measurement under bias

conditions and "in situ" measurements. The L-C meter is often

equipped to provide a linear dc output which is proportional

to the measured inductance or capacitance and therefore it may

be used to drive an X-Y plotter. No initial balancing operations

are required and minimal operator skill is required. The instrument

is capable of serving well in the role of a comparator and is

relatively inexpensive when compared to other impedance instruments.

Strengths

(1) Fast

(2) Little operator experience required

(3) Relatively good accuracy

(4) Relatively inexpensive

(5) Easily portable

(6) Easy to calibrate

(7) Has linear d.c. output for automatic data processing

applications

129
Weaknesses or Limitations

(1) Operates only at fixed frequency

(2) Does not measure resistance or conductance; limited

to capacitance and inductance

Reference pertaining to the L-C Meter: [5]

130
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c. Vector Voltmeter Categories Measured:

A,B,C,D,E,F,G,H,I

Although not specifically designed for the measurement of

impedance, this instrument can occasionally provide unique

solutions to impedance measurement requirements which might

otherwise be awkward and difficult by more conventional means.

OSC

R

A/VAr

R±jx

Figure 4-44.

The measurement principle is illustrated by the figure where

current from the oscillator flows through a resistor of some

known value, R, to the unknown load impedance, Z . A vector

voltmeter is used to measure the complex quotient of the

voltages, E2/E1 . This data may be plotted on a Smith chart

which has been normalized to the value of R, and thus

information on VSWR and complex impedance of an unknown may

be determined very quickly over wide frequency ranges

.

The vector voltmeter has also been used in conjunction with

directional couplers to perform measurements on remotely

located or inaccessible loads. These methods are usable over

a frequency range from 1 MHz to 1 GHz. Uncertaintities vary

widely over such a range but ±5% in impedance magnitude and

133
±2 degrees in phase angle are typical. Best results are obtained

when the unknown impedance is near the value of R.

Strengths

(1) Fast

(2) Wide frequency range

(3) Wide range of impedances measurable

(4) Good for field measurements

(5) No special equipment required (all components

usable for wide variety of applications)

Weaknesses and Limitations:

(1) Low accuracy

(2) Operator experience and training necessary '

References pertaining to the Vector Voltmeter: [6,7]

134
d. 6-Port Coupler Categories Measured:

&

k a

a

DIRECTIONAL

X

COUPLER

k . i

1

k. V

HYBRID JUNCTIONS

X

UNKNOWN

DIRECTIONAL

COUPLER

a

i

V

2

Figure 4-45.

The six port is probably the most recent approach to the

measurement of impedance. It offers many exciting possibilities not realizable by other methods or instruments. The

concept is based upon the law of cosines and all necessary

information to determine the unknown impedance is obtained

through the measurement of magnitudes of output voltages.

The diagram above is only one of several different configurations which may be used to form a six port network. The

principal limitations on the six port are the directivities

which can be achieved in directional couplers and hybrid

junctions and the bandwidths over which the directivity of

these devices can be sustained. Figure 4-46 shows the

measurement accuracy attainable as a function of directivity.

135
^ 30 40 50 60 70

DIRECTIVITY IN db

Figure 4-46. Measurement of

6-port coupler vs directivity of

hybrid junctions.

Higher directivities are attainable by the use of tuning but

this of course slows the measurement process. Directional

couplers and hybrid junctions are most frequently thought of

as being distributed parameter elements designed for use at

frequencies above the normal range where lumped parameter

measurements are made . In recent years these devices have

been developed for use at lower frequencies making the 6

port feasible for lumped parameter impedance measurement.

Because of its relative simplicity, the availability of

component parts, its potential for automation, and the

fact that impedances from short-circuit to open-circuit

are measurable over broad frequency ranges the 6 port

appears to have the best potential for approaching the

ideal instriament.

Strengths

(1) Broadband

(2) Versatile

136
(3) Can be assembled from commercially

available components

(4) Redundancy of measurement facilitates

calibration and self-checking

(5) Adaptible to automated measurement

(6) No requirement to measure phase directly;

all parameters determined by measurement

of voltage magnitudes

(7) Capable of measuring both active and

passive impedances

(8) Usable for measuring other quantities

such as voltage, current, power and phase.

Weaknesses

(1) Accuracy capability limited by directivity

of hybrid junctions

(2) Requires experiences and knowledgeable

operator

References pertaining to the 6-port Coupler: [71]

137
4.4. Comparator Instriaments

As mentioned in 3 D, almost any null or resonance or

active type instrument may serve as a comparator. For specific

and detailed examples of the use of instruments in the role of

a comparator (see reference 13) in which a Q-meter is used as

a comparator in the calibration of Q-standards, or see

reference 17 wherein the use of an admittance ratio bridge is

used as a comparator for calibrating capacitance standards at

100 kHz, 1 MHz and 10 MHz.

References pertaining to the Comparator method: [13,16,17]

138
5. MEASUREMENT TIPS AND TECHNIQUES

The following are a few simple steps and precautions which

can be observed to produce better measurement results.

(1) Use precision coaxial connectors wherever and whenever

possible, especially in standards work. If it is not

possible to use precision coaxial connectors, the next

choice should be a non-precision coaxial connector.

Unshielded connector arrangements such as banana jacks

and plugs should be avoided except in circumstances where

there is no other choice.

(2) Leads should be kept as short as possible because of the

residual impedances they add to the measurement or to the

measured circuit. When it is necessary to utilize

unshielded leads and connectors, the high potential

leads should be kept as far from grounded objects as

possible in order to minimize stray capacitance effects.

(3) Depending upon whether an impedance or an admittance

measurement is being made, the impedance of the shortcircuit reference or the admittance of the open-circuit

reference should be kept as small as possible to avoid

errors in measurement of absolute values

.

(4) Keep generator voltages as low as possible while

preserving adequate detector sensitivity. This reduces

the possibility of thermal drift or damage either to

instruments or components being measured. Most impedance

and admittance bridges operate very well on two volts

or less.

(5) Tuned detectors should be used for maximum sensitivity

and also to avoid the need for large generator voltages

to produce adequate sensitivity.

(6) Impedance matching between signal source and bridge, or

between bridge and detector can be a significant factor

in improving sensitivity. Input and output impedances

139
of generator detectors and bridges may vary widely so

that impedance matching may produce substantial

improvements in measurement system operation.

(7) Use a frequency counter to check the frequency of the

source voltage. This is especially important where the

readout of the bridge is a function of frequency, or

where the impedance of the device being measured is

frequency dependent. (for example a device which is

at or near self-resonance at the measurement frequency)

.

(8) Keep contact surfaces clean through the use of low-residue

solvents. Cleanliness is always good practice.

(9) Store and operate instruments in a clean, dry environment.

Treat the instrument right and it will return the favor.

Avoid exposure to environmental extremes , and allow time

for temperatures of instriaments and components to reach

equilibrium conditions.

(10) Do not assume that the effect of a long lead between

bridge and unknown can be balanced out by the bridge

circuit. Such an assumption can result in large

measurement errors. Make all measurements as near to

the bridge terminals as possible, and then correct for

lead effects. A long lead or cable can be considered as

an adapter, and corrections can be made for it by using

the equations to be found in Section 9

.

(11) Consider the alternative of performing measurements at

other frequencies . With the exception of inductors and

capacitors which are operating at frequencies near

self-resonance, many components are not frequency dependent

to the first order. As a result, it is often satisfactory

to perform measurements at frequencies quite far from

actual application frequencies . Such an alternative is

sometimes useful when measuring instruments which operate

at the actual application frequencies, are not available.

140

I

I
As an example suppose that capacitors with low dissipation

factor are needed at 30 MHz. Although capacitance bridges

which measure dissipation factor accurately at that frequency are not available, it may be entirely satisfactory

to use bridges which operate at 1 MHz or even 1 kHz.

141
6. STANDARDS

6.1. General Comments

Impedance standards for the lumped parameter range are

highly developed and directly relatable to the prototype units

of length and time (reciprocal frequency) . Accuracies of the

order of 0.01 to 0.1 percent are feasible over a wide range

of frequencies and values as seen by the graphs which accompany

Section 1. Unfortunately it is very difficult to utilize these

standards without appreciable loss of accuracy because of

connector or interface problems. Impedance standards, in order

to possess the best accuracy, must be equipped with precision

coaxial connectors. Most measuring instriaments on the other

hand are not equipped with such connectors so that the best

standards cannot be connected directly to them. This requires

the use of adapters with a resulting loss of accuracy which

varies with frequency, impedance magnitude and phase angle.

It follows then that the proper evaluation and use of adapters

is an important part of accurate impedance measurement. See

Section 9

.

142
BASIC QUANTITIES |

LENGTH Mo TINE 1

PRECISION COAXIAL

AIR DIELECTRIC TRANSMISSION LINES

Cfi)

®

THOMPSON- LAMPARD

ABSOLUTE CAPACITANCE STANDARD 0

HI6H ®

FREQUENCY

INDUCTANCE ^0lMH

®

WORKING STANDARDS

CAPACITANCE > 50 pF

THREE - TERMINAL CAPACITANCE

<IO0O pF

CAPACITANCE ^50 pF

0® INDUCTANCE

>O.I/iH

.0 ,0 0 ,

QOR

DISSIPATION FACTOR

RESISTANCE THREE - TERMINAL CONDUCTANCE G< 1000 fiV

0 0

RESISTANCE R<

^

« oj DENOTES ANGULAR FREQUENCY IN RADIANS/SECOND

® COMPUTATION ® DIRECT COMPARISON ® EXTRAPOLATION 0 MAXfELL IMPEDANCE BRIDGE

0 NEGATIVE CAPACITANCE EQUIVALENT

0 RESONANCE TECHNIQUE

0 SERIES TECHNIQUES

0 TilN-T CIRCUIT

Figure 6-1. Derivation of NBS

immittance standards.

143
Figure 6-1 shows how the NBS standards for high frequency

iininitance are derived. These standards together with various

null and resonance instruments are used to provide calibration

services which can be found listed in Reference 60.

Good standards may be purchased from a number of companies

both domestic and foreign. Some of these commercial standards

are equipped with precision coaxial connectors. The best

accuracies may be achieved for those having precision coaxial

connectors but even in such cases some accuracy degradation

must be accepted when a transition is made to non-precision

connectors

.

6.2. Why Are Impedance Calibrations Expensive ?

In order to establish the most efficient, inexpensive and

accurate calibrations, it is necessary to adhere to some basic

initial requirements . For lumped parameter impedance this means

that specific calibration frequencies, impedances and connector

types would have to be chosen initially, to the exclusion of

all others. Comparator techniques and statistical control can

then be used to best advantage in providing calibrations. Such

an ideal situation does not exist in the case of impedance

standards in the lumped parameter range. Attempts to establish

calibration services for specific items have not received sufficient use to be termed successful. In the calibration requests

received by NBS , frequencies , impedance values and connector

types vary so widely that almost every calibration must be

treated as a special problem. When a standard, received for

calibration, must be treated as unique rather than as a member

of a large group of like standards, calibration is more expensive.

Therefore it is desirable to extend the time between recalibrations

of a particular standard.

144
6.3. Keeping Calibration Costs Down —

Standards

A Tip On Maintaining

While it is true that a resistor, an inductor, or a capacitor

may change in value as the frequency is varied, it is also true

that if a good impedance standard is stable at one frequency, it

can be expected to be stable at all other frequencies , so long

as it is not subjected to adverse conditions. This fact can be

used to avoid overfrequent need for calibrations . Once an impedance

standard is calibrated at a high frequency, and its absolute value

determined, it can be monitored at lower frequencies periodically

to determine whether or not its value has remained constant.

Measurements at dc or audio frequencies are capable of higher

accuracies than are higher frequency measurements because the

effects of residual impedances such as the series inductance

of a capacitor or the shunt capacitance of an inductor are much

less significant. Consequently, measurements at lower frequencies

frequently can be made more quickly than those at higher frequencies while still maintaining equivalent accuracies. Thus it

is useful to monitor high frequency impedance standards at low

frequencies, or at dc in the case of resistors, as a test to

determine high frequency stability. If the dc or low frequency

value is unchanged, and if no signs of physical damage or mistreatment are present, it is a good indication that the high

frequency value is also unchanged. These are not infallible

rules, however, so that occasional recalibration at high frequencies is desirable.

6.4. What To Look For In Choosing A Standard

Presented here are some general criteria regarding the

characteristics necessary in a good standard. In choosing those

characteristics it is assumed that the standard will be sent

to NBS for calibration with the objective of transferring the

145
maximum practical accuracy and reliability from NBS to the user.

Not all of these characteristics are to be found in commercially

available standards, a notable case being inductance standards

which are equipped with precision coaxial connectors. Although

standards falling short of these criteria are accepted for

calibration, it is merely good measurement practice and economy

to use the best standards available. NBS does not check the

items it receives to ascertain their conformance to all of these

requirements, and rejections are only made in extreme cases of

obvious instability or unreliable performance.

Characteristic Resistor Capacitor Inductor

Temp Coeff. <10 ppm/° C <20 ppm/° C <30 ppm/°C

Q <10-^ - >10^

Dissipation Factor <10 - 3

Residual Impedance for R<lkf2 ^<10nH Lg<10 nH ^p'^-'-^

for R>lkn,C <5 pF

p

Long term stability 0.05%/year 0.01%/year 0.01%/year

Power Rating 1 watt min.

In all cases, standards should be well shielded, of rugged

mechanical construction and preferably equipped with precision

coaxial connectors.

All impedance standards and impedance components exhibit

changes in value with changes in frequency because of the

presence of residual impedances. Capacitors show an increase

because of the series inductance in the leads , and inductors

do likewise because of the shunt capacitance. Resistors

also vary with frequency but in a more complicated way

depending upon whether it is a large or a small resistor,

whether it is considered in a series or a parallel sense and

which residuals predominate. As a general rule regarding the

upper frequency limit at which a standard should be used, it
is not advisable to rely on any standard to an uncertainty

better than 1 percent at any frequency above that where the

value departs from the nominal (dc or low frequency) value by

more than 10 percent.

6.5. Coaxial Lines

In choosing standards or designing measurement procedures,

the use of precision coaxial, air-dielectric transmission

lines should not be overlooked. When terminated in a short

circuit they provide excellent standards for small inductance

values or when terminated with an open-circuit of well known

characteristics, they may be used for small value capacitors

standards. In either of these applications the inductance and

capacitance values are calculable from physical dimensions and

known material properties

.

Excellent use can be made of these lines at higher

frequencies in the role of an impedance transformer to extend

the usefulness of other impedance standards. See equations

9-1 and 9-2 under Section 9 for appropriate equations for use

in such circumstances.

References pertaining to Standards: [15,40,58,59,60,61,62,63,

64,65,66 ,67,68]
7. RANGE EXTENSION

The frequency ranges over which impedance measuring

instruments are designed to operate are usually not extendable

for a number of reasons, but it is very often possible and

desirable to extend the ranges for impedance parameters

through the use of external standards. This is done by

combining an unknown with some standard or other well known

impedance in a manner such that the resulting impedance or

admittance falls within the measurement range of an available

instrument. In general there are two range extension techniques

which may be used. One is to combine the unknown and some

known impedance in a series configuration. The other scheme

is to combine the unknown and some known impedance in a

parallel configuration.

7.1. The Series Configuration

The basic characteristic of a series circuit is that all

of the current passes through each circuit element. Such a

circuit is shown in figure 7-1.

Figure 7-1.

148
Here the voltage across the circuits is from Kirchoffs Law:

V

ab

= iZ. = (7-1)

X

where is the total input impedance and Z^, and Z^ are the

impedances of the standard and the unknown respectively. From

this relationship it follows that

Z^ = Z. - Z^. (7-

If Zrp is the upper limit of the impedance measuring range of

a bridge and Z^ is an imknown impedance which is larger than

Z^, it would appear to be a very simple matter to insert some

known value, Z^, in series with Z^^ to make the combination fall

within the range of the instrument.

This could be the case where it is required to measure an

inductance too large for a bridge and a capacitor of known

value is inserted in series. Considering only the reactances

this would give

X— — X • x_ L X A

(7-3)

in the circuit of figure 7-2,

a b

Figure 7-2.

149
the capacitor, represented by X^, would have a reactance less

than that of the unknown inductance , X , at the measurement

j-i frequency

.

Another situation which lends itself to the use of an

external series impedance element of known value for range

extension purposes, is the measurement of large capacitances

out of the normal range of an admittance bridge. Figure 7-3

illustrates this case, where C^^ is the unknown whose value

is to be determined and, C , is the capacitor of known value.

Here the series approach of Equation (7-1) yields the expression:

Figure 7-3.

C. =

1 (7-4)

which when solved for yields

(7-5)

150
The foregoing two simple examples do not tell the whole

story however because the series circuits from which the

relationships were derived do not accurately represent the

true picture that exists with grounded two-terminal measurements.

Now that the principle has been illustrated, a closer examination

is in order. A more valid circuit than figure (7-1) would be the

following

The series element must be shown as an equivalent-pi or

equivalent-tee network because of the shunting capacitances

which are present in the actual circuit. Failure to treat the

series elements in this manner can seriously degrade the measurement accuracy of the procedure. Evaluating the elements

of the equivalent pi or tee-network for the series element

is done by making impedance and admittance measurements at

each port of the series element with the opposite end opencircuited and short-circuited. Once this is done, the equations

of 9-3a and 9-3b may be used to arrive at the desired result.

References: [59] A discussion of the use of series techniques

and transformer techniques for range extension.

[69] An exhaustive treatment of the use of series

elements in immittance measurement.

151
For convenience, equation 9-3 is repeated here:

(9-3)

Equation 9-4

Z . =

1 (9-4)

Note that if the shunt admittances are set equal to zero,

equations (9-3) and (9-4) reduce to (7-2).

The most nearly ideal type of series element which can be

employed for range extension is a section of precision coaxial

air dielectric transmission line placed between the bridge and

the unknown to be measured. These procedures become especially

versatile at higher frequencies where a relatively short section

of coax line represents an appreciable portion of a wavelength.

Figure (9-1) and equations (9-1) and (9-2) are appropriate for

applications of this type.

Before leaving the subject of the use of series elements in

range extension, several additional comments are in order:

(1) Because precision coaxial connectors and improved

methods for evaluating the open-circuit admittances

of various connectors (see 9-4) are now available,

improved accuracy with series elements is realizable.

(2) Where the reactance of the series element is of

opposite sign to that of the unknown, frequency

should be accurately known and controlled.

(3) Unless coaxial elements are used, the highest

measurement accuracy cannot be assured.

152
(4) Even under ideal circumstances, the accuracy resulting

from the series technique will be poorer than the basic

accuracy of the bridge used in making the required

measurements

.

7.2. The Parallel Configuration

In contrast to the series circuit it is the input voltage

which is common to each of the elements in a parallel circuit:

b

Figure 7-5.

From Kirchof f s Law the total circuit current is

V , V , V , = ab _ ab ^ ab

Z. Z^

1 A L

Dividing through by and replacing impedances by admittances

,

this becomes

= Y. - (7-6)

There are a number of applications for range-extension through

the use of parallel components. Here are some examples:

(1) When performing measurements using parallel resonance

methods a capacitor of known value can be placed in

153
parallel with an iinknown inductor to extend the range

of the instrument.

Q-meters, with their extra pair of teirminals are

well adapted to such applications and it is

thereby possible to effect considerable extension

of the measurement range with very little difficulty.

(2) Impedance bridges may be used to measure resistors

out of their normal range by placing them in parallel

with other known resistors whose values fall within

the normal range of the bridge

.

Measurement accuracy is reduced with the use of parallel range

extension techniques because of impedance uncertainties introduced

by the connection. Coaxial tees introduce mutual impedances at

their junctions and also add undesirable residuals to the components connected to them. In general the same comments

regarding accuracy in the use of series elements for range

extension also apply to parallel range extension.

154
8. GENERATORS AND DETECTORS

A typical setup for measuring impedance is illustrated by

the following diagram:

UNK

[

EA

ST

GEN Z MEAS

DET INST

Figure 8-1.

In many instances the entire system will be an integrated

package so that no decisions or selections with respect to

the generator and detector need be made. In still other

situations the impedance measuring instrument is a separate

chassis requiring that a generator and detector be supplied

externally. Either situation has advantages and disadvantages

relative to the other which bear careful consideration. First,

consider the separate impedance measuring instrument which

does not include a generator and a detector; and the following

advantages and disadvantages

Advantages

(1) Generator and detector are not "tied up" in one

system so that they are available for use in

other measurement applications . This is economical

from the standpoint of maximum utilization of

equipment.

155
(2) Impedance measuring instriament may be acquired for

less expense if suitable generator and detector are

otherwise available.

Disadvantages

(1) More setup time required because generator and

detector must be procured and connected.

(2) More operator experience required because the

metrologist must be informed as to generator and

detector requirements; be able to recognize system

problems such as leakage inadequate sensitivity,

etc

.

Next consider the packaged system and its inherent advantages

and disadvantages

Advantages

(1) Very short setup time

(2) Little or no operator experience necessary to

assemble the measurement system

(3) Generator, detector and impedance measuring

circuit all especially arranged to provide

optimum performance, i.e., generator and

detector well-shielded, providing adequate

frequency stability, sensitivity, etc.

Disadvantages

(1) Higher aquisition cost for packaged system

(2) Generator and detector "tied up" and unavailable

for use elsewhere.

156
The generator and detector subject may be pursued from a

slightly different aspect which is mainly concerned with

requirements of null and resonance methods for measuring

impedance. For a null method the following general requirements are important

(1) Generator frequency stability - Should be stable

and accurate to 1 part in 10 but particular

attention should be paid to this requirement where

the unknown being measured is frequency sensitive

or where a frequency term appears in the balance

equations for the instrument.

(2) Generator output - Usually an output of 2 volts

into 50 ohms or something in the vicinity of 100

milliwatts is adequate and this may be considerably less where good detector sensitivity

is provided. It is good practice to use the

minimum generator voltage possible to avoid the

possibilities of damage or thermal drift in either

the instrument or the unknown. Voltage level

stability is very rarely important except where

the unknown may be current or voltage sensitive

as in some dielectric or magnetic materials

measurements

.

(3) Shielding - Coaxial leads should be used between

generator and bridge and between bridge and

detector in all cases. Inadequate shielding can

be detected if a difference in the detector null

indication is noticeable with the generator off

or on.

157
(4) Harmonic content of generator - The importance of

generator harmonics depends upon the selectivity

of the detector in rejecting signals at other than

the measurement frequency. Most good signal generators will have harmonics 30 dB below the fundamental

frequency. The use of band pass or low pass filters

will help to reject unwanted frequency components.

(5) Detector sensitivity - Should be adequate to resolve

the minimum calibration interval on the dials of

the measuring instruments. This is typically a

sensitivity of the order of 1 uV.

(6) Logarithmic detector response is desirable because it

avoids the necessity of switching ranges as the null

is approached.

Communication receivers provide excellent detectors for

null measurements because they provide the combination of

selectivity, sensitivity, good shielding and logarithmic

response. They are also capable of covering a wide frequency

range

.

For resonance methods, many of the same requirements exist

for generator and detector as for null methods with a few

very notable exceptions, most of which apply to the generator.

Generator requirements for resonance measurements include:

(1) Frequency stability and accuracy - should be of the

order of 1 part in 10^. This requirement is difficult

to fulfill in the case where frequency variation

method is being used, because tunable generators

with such capabilities are expensive.

158
(2) Output voltage - Because it is desirable from the

standpoint of accuracy to decouple the input and

output probes to the maximum extent possible in a

resonant type measuring instriiment, it is an advantage to have a generator capable of an output

of one or two watts at the measurement frequency.

This requirement, coupled with the simultaneous

requirement for output level stability is a significant reason why resonance techniques are not

widely used except in the case of the Q-meter,

which utilizes a different insertion technique

together with a calibrated detector.

8.1. Phase-Sensitive Detectors

Phase-sensitive detectors are an addition to impedance

measuring systems which have made possible new applications,

the most notable of which is the vector impedance meter.

Figure 8-2 is a diagram to illustrate the principle of the

phase-sensitive detector.

UNK

REFERENCE SIGNAL

Figure 8-2.

159
The arrangement is similar to the setup of figure 8-1 except that

a reference signal is fed directly to the detector, bypassing

the bridge circuit. The detector has the capability of comparing

the reference signal with the output or unbalance signal of

the measurement instrument and separating the unbalance signal

into an in-phase and a quadrature component. At balance of a

bridge, both components become zero. However, instruments such

as the Q-bridge, the L-C meter and the vector impedance meter

all utilize the capabilities of the phase-sensitive detector

to achieve a direct reading impedance instrument which does

not require the customary balancing operations characteristic

of bridges or null instruments. Phase-sensitive detectors

also provide greater sensitivity because much smaller signals

can be detected in the presence of noise.

160
9.1.

9. APPLICATION AND EVALUATION OF ADAPTERS

Introduction To The Adapter Problem

In a majority of situations where an impedance measurement

is required, there is an interface or connector problem which,

if not correctly handled, can contribute serious errors. In

the ideal situation, an instrument equipped with a precision

coaxial connector at its unknown terminals is used to measure

a component which is also equipped with a precision coaxial

connector. This, however, is a rare occurrence which probably

only happens in standards laboratories. Although efforts have

been made to extend the use of precision coaxial connectors

[58] , [59] , the eventual need to use connectors of different

diameters (including non-precision ones) remains. Usually

the component to be measured cannot be directly attached to

the instrument and some sort of a mechanical adaptation is

required. The more knowledgeable metrologist will recognize

the adapter as a source of error and take steps to compensate

as best he can. Others may either ignore the problem entirely,

compensate incorrectly, or dismiss it as being of negligible

importance which may or may not be true. To make measurements

more accurate, and hence more meaningful and useful, there is

a need for a better understanding of the problem as well as for

better techniques and procedures for dealing with the many and

varied types of adapters.

9.2. What Is An Adapter ?

Let an adapter be defined here as any mechanical arrangement

of conductors used to connect two or more electrical devices.

This definition of course includes all interconnecting devices

such as terminal strips, tube or transistor sockets and many

others, and is, therefore, too broad for our present purposes.

The only types of adapters to be considered here will be those

used for interconnecting two devices , each having a grounded

terminal and an ungrounded terminal. Such adapters may range

161
from the crudest arrangement of interconnecting wires to a

sophisticated device carefully designed and manufactured to

high tolerances

.

Besides the simple mechanical interconnection, an adapter

must meet certain electrical requirements. These requirements

depend on the intended use of the adapter, the working

frequency range and the precision needed in fulfilling

various operating conditions. Adapters used in high frequency

applications must have good efficiency (small losses) and

produce low reflections. For any kind of adapter, the precision

of physical dimensions, repeatability of connector parameters,

leakage and certain other electrical parameters represent gener

performance figures

.

It is useful to identify adapters by classifying the types

of connectors they are used to join. The following is a list

of connector types, together with identification symbols and

some typical examples of commercial types which are used.

Symbol Connector Type Examples ** A *Precision coaxial 14 mm, 7 mm, 3.5 mm

B Coaxial symmetrical

(sexless

)

General Radio Type 874

Rohde & Schwartz Dezifi

Coaxial unsymmetrical

(sexed)

Type N, BNC, TNC, SMA,

etc

.

Non-coax (unshielded) banana plugs , banana

jacks, interconnecting

wires, etc.

Precision Coaxial Connectors as defined by IEEE Specifications

162
This connector classification permits adapter identification

follows

Symbol Example **

A to A GR900 to APC-7

A to B GR900 to GR874

A to C GR900 to Type N (male or

female)

A to D GR900-Q9

B to B GR87 4 to R and S Dezifix

B to C GR874 to BNC (male or female)

Symbol Example *

B to D GR874 to banana plug or jack

C to C Type N (male or female) to

BNC (male or female)

C to D BNC to banana jack

D to D 3/4" binding posts to 1"

binding posts

*The mention of specific manufacturers is only intended for

purposes of illustration and does not constitute endorsement

by NBS of any product.

163
Not only are there many different classifications (10 listed

here) but there is a wide selection of adapters either available

commercially or potentially available within each classification.

It is also true and perhaps somewhat disconcerting, that with every

new connector introduced comes the need for another family of

adapters

.

9.3. Usual Two-Port Representations of Adapters

In any situation involving adapters, where impedance is

a critical parameter, it may be necessary to take into account

the effect of the adapter. This in itself is not difficult

and can be done by a number of well known procedures as follows

;

a. Uniform Transmission Line (Distributed parameter

The adapter can be described in terms of the characteristic

impedance Z^, propagation constant y, and the electrical length

i , if Z and y constant throughout the length of the adapter

(see fig. 9-1)

.

In this situation the adapter can be taken into account by

the following relationships (neglecting losses):

(a) Load impedance known and input impedance required:

representation)

Z. =

1

z z,. + jz ^ o L otan Bil (9-1)

(b) Input impedance known and load impedance required:
T

q:

UJ

hQ.<< <zoozo<Z

X

o z

EN LE

_i

»- z z

1- q: z UJ < UJ Q.

Q.

(/) UJ z UJ o o o z o z < < »- LU Q »- UJa o<

II II II II

UJ

o

en

m

ui

(rUJX

oHW

cn HguPo

•H

to

(d

0) -pc

<DW

0)

5^

(UUU

<U

4-> & <U

J-i

•H

165
When it is more convenient to work, with admittances, the same

equations may be used by replacing , Z^, and Z^ by , Y^

,

and Y , respectively.

b. "it" or "T" Network (Lumped parameter representation)

See figure 9-2. Because it is usually more convenient to use

a TT-network representation when working with admittance, the

expression for admittance is used:

^B + Y = Y + ? ^ . (9-3)

Because it is usually more convenient to use a T-network

representation when working with impedances, the expression

for impedance is used:

^B +

Z. = Z + (9-4)

In these and succeeding equations, series elements are

represented as impedances and shunt elements are represented

as admittances because it is most convenient to evaluate them

in that form.

c. "L" Network (Lumped parameter representation)

With the adapter described as an equivalent L-network,

in a "direct" or a "reversed" arrangement fiqure 9-3. the

relationships are:

Y Y Z Y. = Z. = Z + (9-5)

' ^A^^A ^l) 1' Va +

1

166
-J

rij

AA/V

U

O

a

C!

U

O

ril

LJ

h-

<

<

AA/V

AA/v

ffi

AAV

* •

01

(U +)

c:

0)

(U

o

+>Qa

I

u

&>

167
rw

AA/V
Y. = Y + Z. = (9-6)

These equations can be used as a test of the validity of

using an L-network representation for a particular adapter.

For the same measurement, if the equations (9-5) and (9-6) yield

results which are different by an unacceptable amount then a more sophisticated equivalent network such as a tt or a T

would be required. On the other hand if for the same

measurement equations (9-5) and (9-6) yield results which do

not differ by a significant amount, then it may be adequate to

simplify the adapter equivalent circuit to a simple single

element representation.

d. Single Element Representation (Lumped parameter

representation)

With the adapter described as a single element equivalent

as in fig. 9-4:

^i = ^A \ ^i = ^A (9-7)

Some general statements can be made about the equivalent

network and representations in the foregoing three cases

(1) Increasing the measurement frequency will

generally require increasingly complex equivalent adapter

networks to maintain a given limit of uncertainty (for a

constant value of Z^. or Y ) .

(2) As measured impedance, Z , becomes larger, the

Xj value of the shunt elements in the adapter network become

increasingly important (for a constant frequency)

.

169
UJ

a

0)§H

0)

<D H

c: •H

CO

CO

a)

-O

<U +>

C!

(0

CO

0)

ft

(1> V4

I

<UU

&4

170
(3) As measured admittance, Y_ , becomes larger, the

value of the series elements in the adapter network becomes

increasingly important (for a constant frequency)

.

The foregoing cases presuppose that an appropriate

equivalent circuit can be representative of a particular

adapter and that the immittance elements comprising it are

known. Numerous techniques relying either upon low frequency

capacitance measurements , electrical length determinations or

resonance methods can be employed which aid in determining

the approximate values of series or parallel elements of

adapter equivalent circuits. These methods, however, are

often cumbersome and the uncertainty of the results is

difficult to assess. Improvement is needed both in evaluating

adapters and in the computational procedures used to correct

for them.

9.4. Measurement of Open-Circuit Admittance, Electrical

Length, and Short-Circuit Location in Non-Precision

Connectors and Adapters

One criterion distinguishing a precision coaxial connector

from a non-precision one is that the precision connector has

a precisely defined reference plane or plane of cleavage. An

alternative interpretation of this criterion is that the open

and short-circuit impedances of the precision connector are

known accurately. If the open-circuit and short-circuit impedances of non-precision connectors could be determined then

this important difference would be eliminated and it would

become possible to change or adapt from one connector system

to another with practically no added uncertainty due to

reference plane location. Such a capability would prove useful

in improving traceability between various levels or echelons

of measurement and calibration.

171
Accurate determination of the open-circuit fringe capacitance

of various non-precision connectors can be accomplished by a

procedure which utilizes a "zero length" adapter. a "zero length"

adapter can be used to mate two two-precision connectors of the

same sex without adding any significant impedances at the interface, thereby preserving the same electrical conditions that

exist when male and female connectors are mated in the usual

manner. The technique is useful for most, if not all, of the

more common connector systems. For purposes of describing the

technique, specific reference will be made to the type-N connector,

The use of a zero length adapter to join two type-N male

connectors is illustrated by figures 9-5 and 9-6. In a paper by

Millea [70] a "connector pair" technique is described which

permits the exact measurement of precision three- terminal to

two- terminal adapters. As a preliminary step in the measurement

of the open-circuit capacitance of non-precision connectors,

the evaluation of two auxiliary three-terminal to two-terminal

adapters must be made. Let the capacitance of the two threeterminal to two-terminal adapters be C^^ and G^^. ..These are

located in position 1 shown in figure 9-7a, which is the isetup

to be used in measuring open-circuit capacitances :of non^,-

precision connectors. Three separate two- terminal to two^'

terminal adapters are needed to carry out this experiment.

Two of these adapters will have type-N male connectors and a

third will have a type N female connector, and all three will

be alternately inserted at position 2 of figure 9-7a, at the

opposite end of each of these adapters, either a sexless or a

hermphroditic type of connector is required initially to mate

with the adapters in position 1.

With the two adapters having type-N male connectors joined

by means of a zero length adapter and located in position 2,

we can determine the capacitance value

172
173
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-I

0.

LjJ oz

LU

01

UJ

IL. UJ

oro

h-o

UJoooo

UJoo

UJ

_Jo

a:

UJN

uo

+Joc

SI! oo

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-p

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•H

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CO

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Em

174
5 ?

r

5

POSITION

POSITION 2

POSITION 2

POSITION I

POS. POS.

I 2

• r

' u _m

•

H

G •

Figure 9-7. Connection arrangeraents for measuring adapter

capacitances and open-circuit fringe capacitances at 1 kHz

175
Combining the adapter with the female type-N with the two type-N

male adapters gives

+ = C2 (9-9)

and

C3 + = C3 (9-10)

The arrangement of figure 9-7b is then utilized to give the

following

CfmA = ^4 (5-11)

S ^ ^fmB = S (9-12)

^ffC = ^6 (9-13)

where C^^, C^^g, and C^^^ are the open-circuit (fringe) capacitance of the two type-N male and the type-N female connectors

respectively. These equations may then be solved simultaneously

to give values for the open circuit capacitances of the type-N

connectors and also values for C, , C„ , and C^. A B C

Equations (9-8) through (9-13) may be put into the general

form

^nl^A ^n2^B ^n3^C ^n4^fmA ^nS^fmB ^ns'^ffC ~ ^n

where a , ... a , are coefficients equal to 1 or 0

.

nl n6 ^

176
Using determinants

fmA

1± n u ^1 u u

X

1X n p^2 1Xnu

u u

1X ^3 u X

1

_i_ 1

U U u ^5 X X

A

u u u ^6 1 u

T

J. U u X U u

nu X

n

u nu

1X u

u u X nu u

1X

0 0 0 1 0 1

0 0 0 0 1 1

0 0 0 1 1 0

(9-14)

and in a similar manner the values for Cj- „, C^j-^, C, , C„

,

fmB ffC A B

and are obtained. Upon siibtracting C^^ or C^^ as

appropriate from , C„ , and C„, the capacitance from the

reference plane at one end of the adapter to the reference

plane at the other end of the adapter is obtained. This

information can be used together with the electrical length,

determined with reference to a short circuit, to deduce the

characteristic impedance, or conversely, to determine the

inductance of an adapting device if its characteristic

impedance is known. Although these capacitive adapter

parameters are determined at 1 kHz they are useful at much

higher frequencies because they are almost invariant to

frequencies up to 1 GHz.

There are a number of items pertaining to this measurement

technique which require additional discussion. First it is to

be noted that the coupling collars of the type N male connectors

177
extend beyond the end of the outer conductor. In order to join

the two type-N male connectors in the manner shown in figures 9-5

and 9-6, it is necessary to cut back one or both of the outer

coupling collars by a small amount. The same is true for the

BNC, TNC and other connectors, but slightly different approaches

are required in making a zero- length adapt r for each connector

type. In most instances it is better to make a zero- length

adapter for two male connectors rather than for the female

connectors because one extra piece would be required in the

case of the females and also because some difficulties are

encountered in arranging an outer coupling device.

The open-circuit fringe capacitance of a connector is

apt to be more repeatable if some sort of cap is used instead

of merely leaving the end of the connector uncovered. This

is due to the possibility of capacitance to surrounding

objects. However, because such caps are not available for

the male and female connectors in all types, it may be

necessary to make the fringe field determinations with the

connector ends uncovered. In using the method described by

Millea [70] , it is advisable to surround the end of the

connector by a fairly large (one cubic foot) conducting

shield driven at the same potential as the "Hi" electrode of

the three- terminal capacitance bridge being used to perform

the measurements. This condition most nearly simulates the

actual situation encountered when performing two-terminal

capacitance measurements

.

There are several types of commercially available

non-precision coaxial connectors which are sexless. In these

instances the zero-length adapter is not necessary for

the determination of adaptor capacitance or open-circuit

capacitance. In some instances there may be no reference plane

which is mechanically identifiable, but it is interesting

to note that the foregoing measurement procedure yields a

178
unique value for open circuit capacitance and thereby defines

an electrical reference plane. The extent to which this reference plane is repeatable from one connector to another or from

one connector pair to another is determined by the mechanical

precision to which they are manufactured. This is true for

all connectors

.

Once the open-circuit capacitance of one half of a connector

pair of any two-electrode connector system is known, it is then

possible, by the technique described, to measure the open circuit

capacitances of all other connectors of that system whether they

be male or female. In other words, the zero- length adapter need

only be used once to provide the key to these determinations

.

With sexless connector systems the zero- length adapter is not

required

.

In addition to its use in determining open-circuit capacitances

of various connector types the "zero length" adapter has additional

applications. When evaluating the electrical length of a particular precision-to-non-precision adapter, by slotted line methods,

it is convenient to utilize the back-to-back technique and to

join identical adapters in the manner shown in figure 9-8.

Using a short-circuit at the outer end of the adapter, unique

values of electrical length can be determined for individual

adapters taken in any one of the following combinations

1. Three precision to non-precision male

2. Two precision to non-precision male and one

precision to non-precision female

3. Three precision to non-precision female

4. Two precision to non-precision female and one

precision to non-precision male.

179
UJ

a:UJo

UJo<o

a:

£5

oX

cn ? o

a: < lij ^ ^ 2 ^ ^ O t ? Q g

CO ^ o: ^ < 0 liJ O o I S < liJ ^ o

Qd CO z ^ S i y y 1 ^ g < o ^ lij

o

•H

+>O •

0)

M

rH <U

0) -PO. erf

-Hm

CO +>

0)

c

g 0) M I og d

<U-H O^N O Q) -H -P

-P

a

U nJ CDT3

(«

c:O 4-) U O

UJQ

UJ

\-

cn zo

a:

o z UJ 3

00

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01 -H

180
Such methods can be further extended to include adapters

from one non-precision connector type to another, because once

a reference plane is determined for a particular non-precision

connector, it can be treated as though it were a precision

connector. In such cases the essential differences are in the

repeatability of the interconnection of individual connector

halves within each different connector system, with the

repeatability of precision connectors being superior to the

non-precision types. Once electrical lengths are determined

in this manner, it is then possible to determine the precise

location of the short-circuit with respect to the reference

plane of a non-precision connector.

181
10. APPENDIX I. DEFINITIONS, UNITS AND SYMBOLS

The definitions which follow are intended as an aid in the

use and understanding of this metrology guide, and may be found

to differ from definitions found elsewhere. This is done

deliberately because of the need to emphasize certain concepts

important to understanding the material in the guide. Some

elaboration is done in the hope of adding clarity to the term

or concept. The terms are arranged alphabetically for quick

reference.

Admittance

Bridge

Symbol, Y /e_ = G + jB; Unit: mho (U) - The

reciprocal of impedance; usually used for

describing parallel arrangements of circuit

elements; associated with measurements made

with respect to an open-circuit reference.

A network of immittance elements including

standards and an unknown immittance to be

measured. When the network is energized by

a source of voltage the standards may be adjusted until a null or zero transmission

condition exists across some portion of the

network. At null a unique mathematical relationship exists between the immittance of the

unknown and the bridge standards.

Capacitance Symbol, C;

circuit or

electric f

voltage by

a positive

circuit or

a series c frequency

Unit Farad (F) - That property of a

component of storing energy in an

ield causing the current to lead the

90°. Capacitance is represented by

susceptance (+ja)C) in a parallel

by a negative reactance (-j/wC) in

ircuit where o) = 2-nf is the angular

in radians per second.

Conductance

Detector

;

Symbol, G; Unit: Siemens (S) or mho (y) - That property of a conductor or circuit which

causes electric energy to be dissipated in the

form of heat. It is the real portion of a

passive complex admittance and is ordinarily

used in the context of parallel arrangements

of circuit elements . Conductance is the equivalent of reciprocal series resistance only

when the circuit has no reactance. Conductance

is the reciprocal of parallel resistance in all

cases, and the two terms are used interchangeably.

A device used to sense a null or other response

in a measurement circuit enabling the operator

to determine the existance of a particular

relationship between the standards and the unknown

being measured.

182
Symbol, 6 - The reciprocal of quality factor, Q

and used to indicate capacitor quality. It is

the ratio of conductance to susceptance in a parallel circuit; also known as loss tangent and

sometimes stated in percent.

Implies that circuit dimensions are large enough

or that frequencies are high enough so that all

circuit elements may be considered as being present

in uniform amounts at all locations throughout the

circuit as opposed to being concentrated at a single

point. Distributed parameter methods are the most

exact means of describing a circuit but do not become

practical from the standpoint of physical analytical application until circuit dimensions are

significant compared to a quarter wavelength of the

operating frequency. Uniform circuit geometry is

also necessary for the application of distributed

parameter analysis

.

A source of sinusoidal voltage at a particular

frequency used to energize a circuit or network

for the purpose of performing an impedance

measurement.

Symbol, L; Unit Henry (H) - That property of a circuit

or component of storing energy in a magnetic field and

causing the voltage to lag the current by 90°.

Inductance is represented by a positive reactance

(+ja3L) in a series circuit or by a negative susceptance

(-j/coL) in a parallel circuit where co is the angular

frequency in radians per second.

A contraction of the words impedance and admittance

used to convey the concept of all magnitudes and

phase angles of any impedance or admittance and

encompassing both series and parallel circuit

representations

.

Symbol, Z = R + jX; Unit: Ohm {Q) - The most

commonly used definition is the one derived from

Ohm's law, namely the ratio of voltage to current

(Z = E/I) . This is called the active definition

of impedance. Another definition is also appropriate. This is the passive definition that

impedance is a geometrical configuration of materials whose magnitude depends upon a length and

the electromagnetic properties of free space (1).

The active definition is the one appropriate in

most practical measurement applications whereas

the standards laboratory must concern itself with

the passive concept also. Impedance is most

commonly used to describe series arrangements of

circuit components and is associated with measurements made with respect to a short-circuit reference.

183
Impedance

(Active)

An impedance whose resistance is negative which

means that an energy emitter or an energy generating

source is present and that for that portion of the

circuit which the impedance represents more energy

is being emitted than is being dissipated in heat.

Impedance

(Passive)

;

An impedance containing only positive resistance.

Either no energy sources are present or the circuit

can dissipate more energy in the form of heat than

the amount being generated.

In situ

Measurements

Measurements made on components which are in place

in a circuit.

Implies that circuit dimensions are small enough

or that frequencies are low enough so that the

circuit elements may be considered as being

concentrated or lumped at a single location as

opposed to being distributed over some finite

distance in a circuit. Lumped parameter concepts

are never perfectly realizable in practice but

are necessary where physical circuit dimensions

are small with respect to a wavelength or where

the circuit geometry is nonuniform.

An arrangement of elements in a way such that all

of the energizing voltage appears across each one.

Symbol, 4), for admittance and 6, for impedance;

Units degrees or radians - The angle of lead or

lag of current with respect to voltage in a

parallel circuit, cf) , or the angle of lead or lag

of voltage with respect to current in a series

circuit, 6

.

()) = tan"-' ^ ; 6 = tan"-' ^

Quality Factor: Symbol, Q - The ratio of the maximum amount of

energy stored to the energy dissipated over a

unit of time corresponding to one cycle multiplied by 2 TT. This is also commonly called the

energy storage factor of a component. The most

common usage is in connection with inductors or

capacitors and it indicates the degree of purity

of the component. It is also very commonly used as a

measure of bandwidth or sharpness of tuning or

selectivity of a resonant circuit. Voltage

multiplication factor is also a commonly used

name for this phenomena because the voltage across

the output of a tuned circuit is Q times the input

voltage.

Lumped

Parameters

Parallel

Circuit

Phase Angle

184
Range

Reactance

Resistance

(series)

Resistance

(parallel) ;

Resonance

(series) :

Resonance

(parallel)

The extremes of values of a parameter such as

frequency or impedance between which an instrument

such as a generator, detector or bridge is usable.

Symbol, X; Unit: ohm {U) - The imaginary component

of a complex impedance which is positive

(+jX = + jwL) if the impedance is inductive and

negative (-jX = -j l/wC) if the circuit is

capacitive. Reactance is most commonly used in the

context of series circuit arrangements and is the

equivalent of reciprocal susceptance only if the

circuit is lossless.

Symbol, R ; Unit: ohm (fi) - That property of a

conductor^or circuit which causes electric energy

to be dissipated in the form of heat. It is the real

portion of a passive complex impedance and is

ordinarily used in the context of series circuits.

It is the equivalent of reciprocal conductance or

parallel resistance only when the circuit has no

reactance or susceptance.

Symbol, Rp," Unit: ohm {^) - The reciprocal of

conductance and also equal to series resistance in

circuits with no reactance or susceptance.

The condition in a series circuit where the positive

and negative reactances are equal , the current and

voltage are in phase and current is at a maximum.

The circuit at series resonance is purely resistive

and the impedance is at a minimum.

The condition in a parallel circuit where the positive

and negative susceptances are equal, the current and

voltage are in phase and the voltage is at a maximum.

The circuit at parallel resonance is purely resistive

and the admittance is at a miniraiim.

Self-resonance

:

Susceptance

Three-Terminal

The frequency at which an inductor reaches parallel

resonance with its own distributed capacitance or a

capacitor reaches series resonance with its own

series inductance.

Symbol, B; Unit: Siemens (S) or mho (U) - The

imaginary component of a complex admittance which

is positive (+jB) if the circuit is capacitive and

negative (-jB = - j l/coL) if the circuit is inductive.

Susceptance is used in the context of parallel

circuits

.

A measurement made in such a way that the results

include only the admittance between two conductors

with the effects of other conductors in the vicinity

185
being excluded. Primarily used in the evaluation

of very small capacitances.

Two-Terminal; The impedance or admittance of a point in a circuit

to ground. Such measurements include the effects

contributed by all other conductors or objects in

the vicinity of the measurement, i.e., near enough

to be detected.

186
11. BIBLIOGRAPHY

High Frequency Impedance Standards at The National Bureau

of Standards

Powell, R. C, R. M. Jickling and A. E. Hess

IRE Trans. Instrumentation

Dec. 1958, Vol. 1-7, Nos . 3 & 4, 270-274

Alternating Current Bridge Methods

Hague and Ford

Pitman, (BATH) 6th Edition

1971

Radio Frequency Measurements by Bridge and Resonance

Methods

Hartshorn, L.

John Wiley & Sons, New York

1943

Parallel-Resonance Methods for Precise Measurements of

High Impedances at Radio Frequencies and a Comparison

With the Ordinary Series-Resonant Methods

Sinclair, D. B.

Proceedings IRE

Dec. 1938, Vol. 26, No. 12, 1466-1497

Electronic Measurements and Instrumentation

Oliver, B. M. , J. M. Cage, and

Clyde F. Coombs, Jr. (editors)

Inter-University Electronics Series

(McGraw-Hill Book Company)

1971, Vol. 12, Chapter 9, 264-318

Measure Impedance the Easy Way, Use A Vector

Voltmeter

Heck, J. R.

Electronic Engineer

Dec. 1970, Vol. 29, No. 12, 54-57

Measurement of Complex Impedance 1-1000 MHz

Hewlett Packard Application Note 77-3

Apr. 1, 1967, 11 pages

The Measurement of the Permittivity and Power Factor of

Dielectrics at Frequencies from 10 "* to 10® Cycles Per

Second * Hartshorn, L. and W. H. Ward

J. lEE (London)

Nov. 1936, Vol. 79, 597-609

187
9 . Impedance Measurements at High Frequencies With Standard

Parts

Sinclair, D. B.

G. R. Experimenter

Sept. 1939, Vol. XIV, No. 4, 1-8

10. Precise Measurement of Dielectric Properties at Radio

Frequencies

Reddish, W. , Mrs. A. Bishop and P. J. Hyde

Proceedings lEE (London)

Jan .1971, Vol. 118, No. 1, 255-265

11. Analysis and Experimental Evaluation of the Immittance

Transcomparator

Agy , D . L

.

University of Colorado Library (Masters Thesis)

1970

12. Digital Q-Meter WDM

Durbeck, B.

News from Rohde & Schwarz (Germany

)

1970, Vol. 10, No. 45, 20-22

13. Standards For the Calibration of Q-Meters - 50 kHz

to 45 MHz

Jones, R. N.

NBS Journal of Res. Sec. C. Eng. & Inst.

Oct. -Dec. 1964, Vol. 68C, No. 4, 243-248

14. A Transcomparator for High-Q Immittance Measurements

Agy, D. L. and R. E. Nelson

Electronic Instrument Digest

Jan. 1971, Vol. 7, No. 1, 37-40

15. A Technique for Extrapolating the 1 Kc Values of

Secondary Capacitance Values to Higher Frequencies

Jones, R. N.

NBS Tech. Note No. 201

Nov. 5, 1963, 12 pages

16. Electrical Measurement Analysis

Frank, Ernest

McGraw-Hill, New York

1959

17. A Precision, High Frequency Calibration Facility for

Coaxial Capacitance Standards

Jones, R. N. and L. E. Huntley

NBS Tech. Note No. 386

Mar. 197 0, 27 pages

18. Impedance Bridges for the Megacycle Range

Wilhelm, H. T.

Bell System Technical Journal

Sept. 1952, Vol. 31, 999-1012

188
19 . Handbook of Electronic Measurements

Wind, M. (editor)

Polytechnic Institute of Brooklyn, Brooklyn, N. Y.

1956, Vol. 1, Ch. 4, 4-8 to 4-56

20 . A Radio Frequency Bridge for Impedance Measurements from

400 Kilocycles to 60 Megacycles

Sinclair, D. B.

Proceedings IRE

Nov. 1940, Vol. 38, No. 11, 497-503

21. A 1-Megacycle Schering Bridge

Easton, I. G.

G. R. Experimenter

Feb. 1952, Vol. XXVI, No. 9, 1-4

22. New R-F Bridge Features Small Size and Added Operating

Convenience

Soderman, R. A.

G. R. Experimenter

June 1955, Vol. 30, No. 1, 5-9

23. A Wide Range VHF Impedance Meter

Mennie , John H.

The Boonton Radio Corporation Notebook

Summer 1964, No. 2, 1-4

24. Some VHF Bridge Applications

Reimenschneider , N. L.

Boonton Radio Corporation Notebook

Summer 1955, No. 6

25. A Coaxial Adaptor for the RX Meter

Gorss , C. G.

Boonton Radio Corporation Notebook

Fall 1954, No. 3

26. Transmission Line Measurements With the RX Meter

Reimenschneider, N. L.

Boonton Radio Corporation Notebook

Fall 1954, No. 3

27. The Transformer Ratio-Arm Bridge

Calvert, R.

Wayne-Kerr, Philadelphia, PA.

Monograph No. 1, 11 pages

28. An Improved Bridge for Precision Measurements

Voelker, W. D.

Bell Laboratories Record

Jan. 1942, 133-137

189
29. Accurate Immittance Measurements at Frequencies up to

20 MHz

White, Lowell D.

IEEE Trans. Instrumentation & Measurement

Nov. 1970, Vol. IM-19, No. 4, 331-336

30 . A New Technique in Bridge Measurements

Calvert, R.

Electronic Engineering

Jan. 1948, Vol. XX, 28-29

31. AC Bridge Methods for the Measurement of ThreeTerminal Admittances

Thompson, A. M.

IEEE Trans. Instrumentation & Measurement

Dec. 1964, Vol. IM-3, No. 4, 189-197

32. The Measurement of Lumped Immittance at RF

McCartney, T.

Joint Conference on R.F. Measurements

and Standards

Nov. 1967

33. Standard High-Frequency Meter for IPDO-3 Solid

Dielectrics

Abrosimov, E. A.

Measurement Techniques

June 1971, Vol. 14, No. 6, 844-898

34. Measurements of Electrical and Magnetic Quantities

Bikulov, A. P. and P. M. Frolov

Izmeritel ' naya Tekhnika

May 1968, No. 5, 643-647

35. The Measurement of Transistor Parameters on WayneKerr RF Bridges

Scarlet, R. M.

Wayne-Kerr, Phila. , PA. 3-9

36. Bridged-T and Parallel-T Null Circuits for

Measurements at Radio Frequencies

Tuttle, W. N.

Proceedings IRE

Jan. 1940, Vol. 28, 23-29

37. The Twin-T A New Type of Null Instrument for Measuring

Impedance at Frequencies up to 30 MHz

Sinclair, D. B.

Proceedings IRE

July 1940, Vol. 28, 310-318

190
38. A Self-Calibrating Instrument for Measuring Conductance

at Radio Frequencies

Huntley, L. E.

NBS Journal of Res. Sec. C. Eng. & Instr.,

Apr. -June 1965, Vol. 69C, No. 2, 115-126

39. A Precision Dual Bridge for the Standardization of

Admittance at Very High Frequencies

Woods, D.

Proceedings lEE (London)

June 1957, Vol. 104C, Mono. 244R, 506-521

40. Standards for Electrical Circuit Properties at Radio

Frequencies: A Survey of some U.K. Developments

Harris, I. A.

Radio Electronic Engineer (Great Britian)

Apr. 1968, Vol. 35, No. 4, 189-198

41. Method and Apparatus For Measuring Q of a Reactive

Element in a Bridge Circuit

Bara , S

.

U.S. Patent No. 3,523,242

Issued Aug. 4, 1970

42. Handbook of Coaxial Microwave Measurements

Gray, D. A.

General Radio Company

West Concord, Mass. 01781, 163 pages

43. A Direct- Reading Impedance-Measuring Instrument

for the UHF Range

Thurston, W. R.

G. R. Experimenter

May 1950, Vol. 24, No. 12

44. Improved Accuracy and Convenience of Measurements

With Type 16 02B Admittance Meter in VHF and UHF Bands

Soderman, R. A.

G. R. Experimenter

Aug. 1953, Vol. 28, No. 3

45. Wide-Range Transfer-Function and Immittance Device

for Measurements in the VHF/UHF Ranges

Buhn, U.

Electronic Engineering (Great Britian)

July 1968, Vol. 40, 394-396

46. Impedance Measurement in the 50 to 2000 Mc Range

Soderman, R. A.

Radio Electronic Engineering

July 1951, 3-6

191
47. Measuring Inter-Electrode Capacitances

Young, C. H.

Bell Labs Record

Dec. 1946, Vol. XXIV, No. 12, 433-438

48. A Null Method for Determination of Impedance in the

100-400 Mc Range

Byrne , J . F

.

Proceedings of the Natl. Elec. Conf. (Chicago)

1947, Vol. 3, 603-614

49. Direct Measurement of Impedance in the 50-500 Mc

Range

Fong, A.

Hewlett-Packard Journal

Apr. 1950, Vol. 1, 4 pages

50. A Versatile Instrument - The Q-Meter

Cook, L.

Boonton Radio Corporation Notebook

Winter 1954, No. 4

51. Circuit Magnification Meter

Parkyn, J. M.

Marconi Instrumentation

March 1959, Vol. 7, No. 1, 8-16

52 . The Development of Q-Meter Methods of Impedance

Measurement

Briggs , A. J. and J. E. Houldin

Proceedings lEE (London)

July 1949, Vol. 96, Pt. Ill, 295-305

53. The Story of Q

Green, E. I.

American Scientist

Oct. 1955, Vol. 43, No. 4, 584-594

54. The Q-Meter and Its Theory

Rao, V. V. L.

Proceedings IRE

Nov. 1942, Vol. 30, 502-505

55. The Nature of Q

Moore, W. C.

Boonton Radio Corporation Notebook

Spring 1954, No. 1

56. Measurement of Dielectric Materials and Hi-Q Capacitors

With the Q-Meter

Reimenschneider , N. L.

Boonton Radio Corporation Notebook

Winter, 1956, No. 8

192
57. Direct- Reading, Fully-Automatic Vector Impedance Meters

Alonzo, G. J., R. H. Blackwell and H. V. Marantz

Hewlett-Packard Journal

Jan. 1967, Vol. 18, No. 5, 12-18

58. Lumped Parameter Impedance Measurements

Huntley, L. E. and R. N. Jones

Proceedings IEEE

June 1967, Vol. 55, No. 6, 900-911

59. Precision Coaxial Connectors in Lumped Parameter Immittance

Measurement

Jones, R. N. and L. E. Huntley

IEEE Trans. Inst. & Meas

.

Dec. 1966, Vol. IM-15, No. 4, 375-380

60. Calibration and Test Services of The National Bureau of

Standards

NBS Special Publication 250

Dec. 1970, 209 pages

61. Electrical Parameters of Precision, Coaxial, Air Dielectric

Transmission Lines

Nelson, R. E. and M. R. Coryell

NBS Monograph 96

June 30, 1966, 103 pages

62. Errors in the Measurement of Capacitance and Inductance

Dabrowski, G.

News from Rohde & Schwarz

1967, Vol. 1, No. 28, 48-49

63. Coaxial^ Impedance Standards

Kempf, R. A.

Bell System Technical Journal

July 1951, Vol. 30, 689-705

64. Iimnittance Transformation Using Precision Air-Dielectric

Coaxial Lines and Connectors

Woods , D

.

Proceedings lEE (London)

Nov. 1971, Vol. 118, No. 11, 1667-1674

65. The Realization of High Frequency Impedance Standards

Using Air-Spaced Coaxial Lines

Harris, I. A. and R. E. Spinney

IEEE Trans. Inst. & Meas.

Dec. 1964, Vol. IM-13, 265-272

193
66. Air-Filled Coaxial Lines as Absolute Impedance Standards

Weinschel, B. 0.

Microwave Journal

Apr. 1964, Vol. 17, No. 4, 47-50

67. Skin-Effect Corrections in Immittance and Scattering

Coefficient Standards Employing Precision Air-Dielectric

Coaxial Lines

Zorzy, J.

IEEE Trans. Instr. & Meas

.

Dec. 1966, Vol. IM-15, No. 4, 358-364

68. Radio Engineers Handbook

Terman, F. E.

McGraw-Hill Book Co.,

New York & London

1943, 1019 pages

69. Some Applications for Series Impedance Elements in Radio

Frequency Immittance Measurements

Huntley, L. E.

NBS Journal of Res. Sec. C. Eng. & Inst.,

July-Dec. 1970, Vol. 74C, Nos . 3 & 4, 79-85

70. Connector-Pair Techniques for the Accurate Measurement

of Two-Terminal Low-Value Capacitances

Millea, A.

NBS Journal of Res. Sec. C. Eng. & Inst.,

July-Dec. 1970, Vol. 74C, Nos. 3 & 4, 111-116

71. The 6-Port Coupler; A New Approach to Measuring Voltage,

Current, Power, Impedance and Phase

Hoer, C. A.

IEEE Trans. Instrumentation & Measurement

Nov. 1972, Vol. IM-21, No. 4, 466-470

72. Five-Terminal, 1 MHz Automatic Capacitance Bridge

Sette, R. F.

General Radio Experimenter

Nov. /Dec. 1969, Vol. 43, Nos. 11 & 12, 6-7

73. Microwave Theory and Applications

Adam , S

.

Prentice-Hall Inc., Englewood Cliffs, N. J.

1964, 513 pages

74. Choosing An Automated Test System

Ewy, M. 0. and S. C. Shank

Hewlett-Packard Journal

Aug. 1969, Vol. 20, No. 12, 7-10

194
75. Time Domain Ref lectometry

Oliver, B. M.

Hewlett-Packard Journal

Feb. 1964, Vol. 15, No. 6, 1-7

76. Impedance Measurements in Coaxial Waveguide Systems

Jesch, R. L. and R. M. Jickling

Proceedings IEEE

June 1967, Vol. 55, No. 6, 912-923

77. Broadband Resistive-Divider-Type Directional Coupler

Hoer, C. A. and D. L. Agy

IEEE Trans . Instrumentation & Measurement

Nov. 1970, Vol. IM-19, 336-343

78. Swept-Frequency Techniques

Ely, P. C. Jr.,

Proceedings IEEE

June 1967, Vol. 55, No. 6, 991-1001

79. Precision Capacitance Measurements With a Slotted Line

Zorzy, J. and M. J. McKee

G. R. Experimenter

Sept. 1967, Vol. 41, No. 9, 10-11

80. Present Day Simplicity In Broadband VSWR Measurements

Oldfield, W. W.

Wilton Technical Review

July 1970, Vol. l,.No. 1, 1-8

<

i) U.S GOVERNAAENT PRINTING OFFICE : 1974 O-547-804 195
FORM NBS-114A (1-71)

U.S. DEPT. OF COMM. 1 . PUBLIC ATION OR REPORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA NBS-MONOGR. 141

5n c c T

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

The Measurement of Lumped Parameter Impedance;

A Metrology Guide

5. Publication Date June 1974

6. Performing Organization Code

7. AUTHOR(S)

R. N. Jones

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

10. Project/Task/Work Unit No.

^ / ^ X I) -5 11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same as 9 above

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13. Type of Report & Period

Covered

Final

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15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 74-8060

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The measurement of two-terminal impedance in the 30 kHz to 300 MHz

range involves a variety of different methods including null, resonance,

active and comparison. Each method is represented by a number of

instruments having specific capabilities, strengths, and weaknesses.

This metrology guide is intended to assist the scientist who is not

intimately familiar with impedance measurement, in the selection and

use of the best instrument for a particular requirement. Information

is included on range and accuracy capabilities as well as availability

and ease of operation. In addition to providing help in the selection

of the appropriate instrument, there are operating tips which enhance

accuracy, criteria for choosing standards, means for extending normal

measurement range of an instrument, a discussion on generators and

detectors , and a section on the evaluation and use of adapters

.

Finally, an extensive bibliography is included to assist in pursuing

a particular problem beyond the depth of the guide.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Adapters; capacitance; capacitors; detectors; generators; impedance instruTients; impedance standards; inductance; inductors; measurement methods;

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