National Bureau of Standard'

Library, Ml Admin. Bidg.

JUN 3 1970

NBS TECHNICAL NOTE 386

A Precision, High Frequency

Calibration Facility

for Coaxial Capacitance

Standards
NATIONAL BUREAU OF STANDARDS

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UNITED STATES DEPARTMENT OF COMMERCE

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NBS TECHNICAL NOTE 386

ISSUED MARCH 1970

Nat. Bur. Stand. (U.S.), Tech. Note 386, 27 pages (March 1970)

CODEN: NBTNA

A Precision, High Frequency Calibration Facility

for Coaxial Capacitance Standards

R. N. Jones and L. E. Huntley

Radio Standards Engineering Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

*"»EAU 0«

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

a means for making available scientific data that are

of transient or limited interest. Technical Notes may

be listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C13. 46:386), Price 35 cents

,

TABLE OF CONTENTS

Section

I

.

Introduction

II. Instrumentation and Measurement Technique

III. Statistical Approach to Data Handling....

IV. Determination of Absolute Values of NBS

Working Standards

V. Adaptor Correction

VI. Calibration Uncertainties

VII

.

Conclusion

Appendix A

Appendix B

Page No.

1

4

8

17

19

20

22

24

25

LIST OF ILLUSTRATIONS

Fig. No. Caption Page No

1 Immittance Comparator Circuit Diagram 5

2 Immittance Comparator 6

3 Block Diagram of Calibration Setup 9

4 Conceptual Statistical Representation of

Calibration Data 10

5 Control Chart for Average Differences 13

6 Control Chart for Standard Deviations in

Average Differences 14

7 Equivalent Circuit for Analysis of Error Due to

Inductance in Series with Unknown... 24

8 Three-Terminal to Two-Terminal Adaptor 25

9 Transformer Ratio-Arm Bridge 26

in

A PRECISION, HIGH FREQUENCY CALIBRATION FACILITY FOR

COAXIAL CAPACITANCE STANDARDS

By

R. N. Jones and L. E. Huntley

ABSTRACT

Using high frequency impedance standards which

are fitted with precision coaxial connectors, and

limiting calibrations to specific frequencies and

impedance values, can contribute greatly toward

improving measurement agreement and standardization.

These advantages have been utilized in the development of a new and much improved calibration

service for capacitance in the high frequency

region. The service is for capacitances of 50,

100, 200, 500 and 1000 picofarads at 100 kHz,

1 MHz, and 10 MHz. This paper describes the

instrumentation used in the measurements and

the method of data handling, and gives a detailed

breakdown of the measurement uncertainties.

Key words: Calibration; Capacitance; Capacitance,

Measurement; Coaxial Capacitance Standards; Impedance,

Measurements, Capacitance; Standards; Statistical

Control

.

I . INTRODUCTION

It has been the practice of NBS to provide two-terminal

impedance calibrations at any frequency or any impedance

value which its clients have requested in the high frequency

region (30 kHz to 300 MHz). In accordance with this general

practice, there have been virtually no restraints imposed

as to the types of impedance standards accepted for calibration. The only requirements have been that the device to

be calibrated be stable to the order of about ±0.01 percent

and that the calibration frequency be far enough away from

the self resonant frequency of the device that uncertainties

in measurement frequency do not give rise to errors greater

than about 0.01 percent.
Such a practice has been a necessity because of the wide

variation in the types of impedance standards being used

throughout the country. In many situations, clients have

manufactured their own standards because appropriate commercial

standards were unavailable. A second reason that standards

vary so much has been the nonuniformity in connectors. For

example, NBS has performed calibrations of standards equipped

with banana plugs or binding posts with spacings which vary

from 5/8" to 2 1/4". This, of course, is indicative of the

variation which exists between various commercial instruments

and presents some difficult problems in correlating measurement data between instruments with dissimilar connectors.

Providing calibration services for such a variety of

standards, while it offers convenience to the client, carries

with it some serious disadvantages. The major disadvantages

are cost and difficulty in assessing measurement uncertainties.

Higher calibration costs result when special adaptation methods

must be employed to carry out a measurement procedure. It is

not infrequent that such costs exceed what the customer is

able to afford and calibrations are either sharply cut back or

left undone. In addition to higher costs, there is the

problem of being unable to perform a comprehensive assessment

of measurement uncertainties. Thus, unusual calibrations are

more expensive and less accurate than those where uniform

standards and calibration frequencies are employed.
This NBS Technical Note describes a pilot procedure which

offe"rs an alternative to the more expensive and less accurate

results obtained in calibrating nonuniform standards. As

standards equipped with precision coaxial connectors^ ^ became available commercially, it became feasible to establish

calibration services which utilize statistical data to evaluate

uncertainty limits. Employing uniform standards, and limiting

calibrations to specific impedance values and frequencies,

allows the accumulation of the data required for statistical

treatment.

The standards and calibration services to be described

in this report are the first in the area of high frequency

impedance to be treated by the statistical approach to this

extent. The service is for two-terminal, air-dielectric

capacitors having values of 50, 100, 200, 500, and 1000

picofarads. To qualify for this service, a capacitor must

be equipped with a 14 mm precision coaxial connector, and be

within ±1 picofarad of its nominal value when measured at

1 kHz. Calibration frequencies are 0.1, 1.0, and 10 MHz.

The determination of conductance or dissipation factor is

not included as part of the calibration because these quantities

are extremely small in capacitors of this type and accurate

determination at these frequencies is beyond the present

state-of-the-art.

[1] IEEE Standard for Precision Coaxial Connectors, IEEE Trans

Instr. Meas., Vol. IM-17, No. 3, pp. 204-218, Sept. 1968. Also

published as Standard Publication No. 287, available from the

Institute of Electrical and Electronics Engineers, Inc., 345

East 47 Street, New York, New York 10017.

-3-
II. INSTRUMENTATION AND MEASUREMENT TECHNIQUE

For each of the nominal values mentioned in I .

, there

are three NBS working standards. In the calibration procedure,

the difference between the unknown and each of the three

NBS standards is determined. This is accomplished by means

of an admittance ratio bridge (fig. 1), which is used in this

application as a simple comparator. AC is a coaxial incremental

capacitor with a range of two picofarads and a resolution of

0.0001 picofarad. Balance is initially established with any

one of the three NBS standards or the unknown connected at the

location indicated by C in fig. 1. Successive readings of

A

AC are then obtained by balancing the bridge with the other

standards, and the unknown, located at position C . A photograph of the comparator is shown in fig. 2. The adjustable

components are attached to the comparator externally and are

labeled in the photograph. The ratio admittances Y and

Y are mica capacitors located in the base of the instrument.

c

r These mica capacitors are easily removable so that the

condition for maximum sensitivity (i.e., all bridge arms

having equal impedance) may be provided for each unknown

being calibrated. Throughout the calibration procedure, AC

is the only item to which any adjustment is made.
Yn and Yr - Ratio immittances

Cb — Capacitor for initial bridge balance

G b — Conductance for initial bridge balance

AC— Incremental capacitor (5 -7 pF)

AG — Variable conduclance

Cx — Standard or unknown

Fig. 1 Immittance Comparator Circuit Diagram

-5-
Fig. 2 Immittance Comparator

-6-
In order to achieve a true measurement of the relative

differences between the standards and the unknown, the balance

condition of the comparator must be dependent upon the setting

of AC only. This means that the conductances, G, and AG, and

the capacitance C,, must remain at their original settings

throughout the procedure. The reason is obvious in the case

of C, , because a change in C, would change the reference

balance condition of the comparator. G, and AG must remain

at their original settings because these components have

residual reactances which may vary with setting and result in

an error in the capacitance difference measurements. The

requirement that the capacitance balance be dependent only

on the setting of AC presents a problem that is solved by the

use of a detector system which permits the separation of

the bridge output signal into its in-phase and quadrature

components

.

The detection system employs a two-phase, lock-in

amplifier wherein the output signal from the bridge is compared

f 21 with a reference signal of the same frequency. j Both signals

are derived from the bridge oscillator. The heart of the

lock-in amplifer is a phase sensitive detector which permits

the operator to differentiate between bridge unbalance due

[2] R. D. Moore, "Lock-in Amplifier for Signals Buried in

Noise," Electronics, June 8, 1962, McGraw-Hill Publishing

Co., New York, New York.

-7
to conductance as opposed to that due to capacitance. This

eliminates the need to adjust the bridge conductance standard in order to achieve a good capacitance balance. The

detector scheme is shown in fig. 3. At present, lock-in

amplifiers are available which operate up to only about

0.1 MHz. To permit the use of this method of detection up to

10 MHz, a dual-channel converter containing a local oscillator

is used to beat the reference and bridge output signals down

to a frequency within the range of the lock-in amplifier.

This detector system is capable of very high sensitivity

and enables the capacitance differences to be resolved to

±0.0001 picofarad over the 0.1 to 10 MHz range.

III. STATISTICAL APPROACH TO DATA HANDLING

In the measurement procedure described in the previous

section, let us assume that we initially connect NBS standard

No. 1 and obtain a reading C,, on the incremental capacitor,

AC. Successive readings for AC are then obtained with NBS

standard No. 2, NBS standard No. 3 and the unknown capacitor

located at position C (fig. 1). These operations produce

balance readings of C,,, C,-, C.., and C, respectively. By

these four measurements we can establish the differences in

the capacitance of the four capacitors, each relative to the

other three. The process just described is repeated n times

(n is usually 6) . The data (AC readings from each of the n

8-
r

"

ADMITTANCE

COMPARATOR

SIGNAL

CHANNEL

»

i \

SIGNAL

GENERATOR

LOCK-IN

AMPLIFIER

LOCAL

OSCILLATOR

i

1

REFERENCE CHANNEL

Dual Channel —

Frequency Converter

L J

Fig. 3 Block Diagram of Calibration Setup

9-
runs) may be arranged as follows:

C ll C 12 C 13 C lx

C

21

C

22

C 23 C 2x

C 31 C 32 C

33 C 3x

nl n2 n3 nx

A statistical procedure is used to obtain the reported calibration results and also to obtain control chart information.

Let us proceed to the explanation of this statistical procedure

by first considering the following diagram, (fig. 4)

c ix c is AC Reading -

12 13

Fig. 4 Conceptual Statistical Representation

of Calibration Data

Here C,,, C,

2

> c i? and C, are the AC readings, for the

three NBS standards and the unknown for the first run. The

-10-
curves of figure 4 suggest that each value falls within some

distribution which we will assume for the moment to be normal,

or Gaussian.

For each run of data an average C reading is obtained

for the NBS standards

C. = (C,+C.,+C.-)/3; i=l-««n. (1) is ^ ll i2 i3 ; ' ' v * Using the differences:

D--, = C.,-C. , (2) ll il is' * '

D

i2

- C i2 -C is> (3)

D.

3

- C.

3

-C is , (4)

obtained from each of the n runs of data, average differences

are computed:

°1 5 X D il' C5)

1=1

n

D

2 ' H J,

D

i2> («J

°3 5 .!. D

i3- C ? ) 1-1

One reason for using differences between observed readings,

instead of just the observed readings themselves, is to reduce the effects of any drift or change in the bridge network. A second reason is that in this part of the procedure

the measurements are used to determine the values of the

standards, each relative to the others, as opposed to making

-11-
absolute measurements of individual capacitors. The estimated

variances about these average differences are given by:

n

v

l sl 5PT .L ( D ir Di) • C8)

1 = 1

V

2 " s2 " iTT .1 ( Di2- D

2)

2

' W

1=1

V

3

s

3 * iTT ;I. ( D

i3- D

3)

2

- ( 1Q ) 1=1

In addition to the average differences D, , D- , and D.,

obtained in (5) , (6) , and (7) , we also compute average

differences which include all previous runs m in number.

These are called D. , D

?

, and D, where:

_' l 5

D, = i I D.,

,

(11)

i = l

_, 1 m

D

2 -5 .1. D i2> C12)

1=1

1 £

D z = - I D. -. (13)

3 m . L, 1

' 1 = 1

i » ? The variances about D, , D

?

, and D, are also computed:

V

l = s

l = m^T .UD ir D

l) (14)

i = l

t t 2 1 m _' 2 V

2 = s

2 " i^T .1, ( D i2- D

2) ' CIS)

i 1 2 i m _, 2 V

3

" s

3 =5PT J JD

i3- D

3) • C16J

1 = 1

-12-
In the expressions (11) through (16) , m does not include the

n runs of the most recent series of measurements.

Using the results of the foregoing computations, control

charts are constructed, and updated after each series of

comparisons. 101 Control charts aid in determining whether or

not the measurement system and standards are behaving in

a predictable manner. When this is the case, the measurements are said to be "in control," and well- justified bounds

of measurement uncertainty may be determined.

10 — o

c c O Q> o|

"?

<u Q

= a> o o> 04

Upper Control Limit (U.C.L.)= D,' +1.22 s',

Center Line (C.L.) = D,

Lower Control Limit (L.C.L.)= Dj - i .22 s\

Total Number of Observations (m)

Fig. 5 Control Chart for Average Differences

Figures 5 and 6 are indicative of the types of control

charts in use. In fig. 5 the average difference D, is

[3] M. G. Natrella, "Experimental Statistics," NBS Handbook

91, August 1, 1963.

13
plotted each time a new run of 6 observations is obtained.

i The center line on the control chart is the grand mean D,

of all the previous average differences D, . Upper and lower

t control limits are based upon the standard deviation s, in

i the average differences (D.-D,) of all previous runs. The

factor 1.22 comes from evaluating the expression — where

k is the factor by which the standard deviation is multiplied

to give a particular confidence level, and n is the number

of observations. In this instance k = 3 for 99.7% confidence

level and n = 6. In fig. 6 the controlled quantity is the

standard deviation of the average differences and, as in

fig. 5, the upper and lower control limits are based upon

' k

s , with the multiplier now being = 0.948. The

•2(n-l)

factor c used in connection with the center line is a correction term which is used to allow for the fact that

values of s, are biased estimates of the value for the

population standard deviation. For n = 6, c = 0.952.

jantity i

in

Average

s.) Upper Control Limit (U.C.L.)= sj + 0.948sj

Dlled

Qi

Deviatioi ference Center Line (C.L.) = s',

Contn

mdard

1 Dif

Lower Control Limit (L.C.L.)= sj - 0.948 s|

en Total Number of Observations (m)

Fig. 6 Control Chart for Standard Deviations in

Average Differences

-14-
With the center line and upper and lower control limits

determined, the results of each set of six determinations

are plotted to determine whether or not they fall within the

predicted control limits. Because the limiting mean and

standard deviations in the average difference are initially

unknown, the center line and control limits may require

adjustment until sufficient data is obtained to arrive at

stable values based on a large number of observations over

a long time interval.

Section IV. contains a discussion of the absolute values

of the three NBS working standards and how they were obtained

but, for the moment, assume that the absolute values are

known at a particular frequency and call them C., , C.

2

and C., . In this calibration process, the standard, C , is

the average of the absolute values of the three capacitors

or

C

- CA1 * CA2 * CA3

^ (17)

Thus the standard is embodied by the three individual NBS

working standards.

Up to this point nothing has been said about the unknown

capacitor being calibrated. The next step is to obtain relationships between the unknown and the NBS standards, thereby

permitting the determination of the value of the unknown.

-15
For this purpose define

B

i - c ix - c is ; i=1 "-

n < 18 )

and

B = I I B . (19) n

i = l

1

The value of the unknown capacitor, C , is then given by:

C = C + B (20)

x s

v *

and the variance about this value is

B~, of itself, is either positive or negative depending upon

whether the unknown capacitor is greater or less than the

average of the three NBS working standards.

Because of the relatively small sample of data obtained

for each unknown capacitor, (n=6) , we have used the student's-t

distribution in determining uncertainty limits . Therefore

the standard deviation, s , is multiplied by 1.65* to arrive

A

at a value of the 99 percent confidence level. The term

1.65s is included as a part of the "Comparison Uncertainty"

in the Report of Calibration.

Student's t for 99 percent confidence level and 5 degrees

of freedom is 4.03. Dividing this by /6 gives 1.65 as the

multiplier for s to yield confidence limits for the mean of

6 measurements.

-16
IV. DETERMINATION OF ABSOLUTE VALUES OF NBS WORKING STANDARDS

Having described the comparison procedure and statistical

operations associated with the maintenance of the NBS working

standards, there remains to be described the technique used

in determining the absolute values of the NBS working standards

The process begins with a measurement of the absolute

value of the capacitor at 1 kHz, This is done by means of

a transformer ratio arm admittance bridge 1 J and a special

adaptor which enables absolute two-terminal capacitance

measurements to be made on a three- terminal bridge.*

The high frequency value, C , of an NBS working standard

is calculated from the expression

C

C = _ 2 (22)

e

l-a) 2 L C

r o where to = the angular frequency in radians per second

C = the capacitance in farads measured at 1 kHz.

o

r

L = the residual inductance of the capacitor in

r

r

r 5

1

henries . L J

[4] M. C. McGregor, J. F. Hersh, R. D. Cutkosky, F. K. Harris

and F. R. Kotter, "New Apparatus at the National Bureau

of Standards for Absolute Capacitance Measurement," I.R.E.

Trans, on Inst., Vol. 1-7, Nos . 3 $ 4, Dec. 1958, pp. 253-261.

* See appendix (B) for a description of the two-terminal

to three- terminal adaptor.

[5] R. N. Jones, "A Technique for Extrapolating the 1 kc

Values of Secondary Capacitance Standards to Higher Frequencies," NBS Tech. Note No. 201, November 5, 1963.

17
Reference [5] is used here to direct the reader to a resonance

method used to measure the residual inductance of a capacitor.

The reference also contains a discussion of some of the uncertainties involved. In the present situation, the residual

inductance determination was performed in an all coaxial

circuit configuration using shorted sections of precision

coaxial line to resonate the capacitor. These inductance

determinations were made at a number of different frequencies

by resonating the capacitors with different lengths of

shorted coax line and the resonant frequencies were determined

to a few parts in 10 7 or better. Resonance experiments

performed at a number of different frequencies provided

assurance that no appreciable errors were incurred by assuming

that the capacitors could be represented by a single series

L-C equivalent circuit. These resonance experiments were

performed over a frequency range from 10 to 100 MHz and in

no case did the values obtained for residual series inductance

vary by more than ± 10 percent. Agreement of this order

has also been achieved by an alternate method which utilizes

a slotted line . • '

[6] J. Zorzy and M. J. McKee, "Precision Capacitance Measurements with a Slotted Line," General Radio Experimenter,

Vol. 41, No. 9, pp. 10-11, September 1967.

-18-
V. ADAPTOR CORRECTION

In the actual measurement situation, it is necessary to

utilize a coaxial adaptor between the unknown terminal of the

immittance comparator and a standard or unknown capacitor

equipped with a 14 mm precision coaxial connector. This introduces a systematic error or bias in the difference measurements which is a function of the error in the value used for

the inductance of the adaptor, and the measurement frequency.

This bias which is denoted as B is given by:

*B = AC(1 + 2w 2 L

A C) where AC = capacitance difference

between unknown and

standard at 1 kHz.

w = angular frequency of

measurement.

L. = inductance in series with A

unknown or standard.

C = C «C Absolute capacix s

r tance of unknown or

standard.

The adaptor used for these calibrations has a value for

-9 L.~15xl0 henries. This value is used in evaluating B, but

at these calibration frequencies, there is a wide range of

uncertainty and actual measurement is extremely difficult.

* See appendix (A) for derivation.

-19-
In the estimates of systematic error a 100 percent uncertainty

was allowed in L.. For the worst case, which is the calibration of a 1000 pf capacitor at 10 MHz, the uncertainty due

to B would be equal to 0.12% of C, if AC = 1 pf.

VI. CALIBRATION UNCERTAINTIES

The method of reporting the uncertainties associated with

these calibrations is based upon the premise that repeatability

or measurement agreement throughout the nation is often of

greater importance than absolute accuracy. While it is

desirable to have both precision and accuracy, the fact remains

that it is often possible to make measurements which are

much more precise than they are accurate. With this in mind

the uncertainty statement has been separated into two categories; one called the "Comparison Uncertainty" and the other

called "Uncertainty in Absolute Value of NBS Standard." With

this approach, measurement agreement need not be limited by

the state of the art as far as knowledge of the absolute value

of an item or measurand is known.

Table 1 is a tabulation of the magnitudes of uncertainties

from five sources designated a, b, c, d and e. In addition

the tabulation separates the errors as a function of frequency

and nominal value of the capacitor calibrated. Factors a and

b are added to give "Uncertainty in Absolute Value of NBS

Standard." Factors c, d and e are added to give the "Comparison Uncertainty." The explanation of the meaning of

each of these factors is as follows:

-20-
TABLE 1.

MEASUREMENT UNCERTAINTIES

Nominal Capacitance of

Unknown Capaci- Uncertainties in (±) % tor at 1 kHz in

picofarads Factor 1 kHz 100 kHz 1 MHz 10 MHz

(a) 0.009

(b) <0.0001 0.0002 0.02

50 (c)

(d) 0.01

0.001 0.001 0.002

(e) <0.0001 <0.0001 0.006

(a) 0.006

(b) <0.0001 0.0004 0.04

100 (c)

(d) 0.01

0.002 0.002 0.003

(e) <0.0001 0.0001 0.01

(a) 0.004

(b) <0.0001 0.0008 0.08

200 (c)

(d) 0.01

0.003 0.002 0.002

(e) <0.0001 0.0002 0.02

(a) 0.004

(b) <0.0001 0.002 0.2

500 (c)

(d) 0.01

0.005 0.003 0.004

(e)

(a) 0.004

<0.0001 0.0006 0.06

(b) <0.0001 0.004 0.4

1000 (c)

(d) 0.01

0.05 0.03 0.04

(e) <0.0001 0.001 0.12

21
(a) The uncertainty of the value of the NBS standard as

measured at 1 kHz.

(b) The uncertainty in the high frequency value of the NBS

standard resulting from a ±10% uncertainty in the

residual inductance.

(c) The imprecision in the intercomparison of the unknown

with the NBS standard based upon 99 percent confidence

limits and the Student's t distribution for a sample

size, n = 6. See footnote at bottom of page 13.

(d) A factor of 0.01 percent to allow for a long term

drift in the NBS standard.

(e) The uncertainty associated with the inductance of the

adaptor used in the calibration setup. This is a bias

uncertainty which is calculated for each calibration

assuming a 100 percent uncertainty in the inductance,

V

VII. CONCLUSION

By the techniques described, an attempt has been made

to inject a degree of sophistication into impedance measurement and standardization which have not been either practical

or possible heretofore. The fact that this is now possible

is primarily because precision coaxial connectors are now

widely available.

-22
This approach to calibration is dependent upon wide

acceptance of specific frequencies and capacitance values

around which the standards, equipment, and measurement

techniques are designed. The advantages are many fold and

include the ability to use a high speed digital computer for

data handling, the incorporation of statistical methods in

the treatment of data and improvements in accuracy and precision.

Similar endeavors in the dissemination of high frequency

impedance standards could well be undertaken for other values

of capacitance, for inductance, and for resistance. How

soon this will be done is not certain, but it will depend

upon the number of calibration requests received for the new

high frequency capacitance facility.

23-
APPENDIX A

ERROR DUE TO INDUCTANCE, L. , IN SERIES WITH C OR C 'A' x s

«IOpF IZ. ASC 0.3

I

Bridge Corner

U—Adaptor—A

I c x orC s ^— —

<v-nr*—A

npppL

1

Fig. 7 Equivalent Circuit for Analysis of Error Due

to Inductance in Series with Unknown

From the bridge corner looking toward C or C :

*C = C (l+w 2 L A C ) = C + u) 2 L A C

2 e x

v A x

J x Ax

C

e e = C (l+a) 2 L A C ) = C + a) 2 L.C 2 s s

v A s^ s A s AC ~ " C« - C = C + u> 2 L A C

2 - C - o) 2 L A C eeex 2 Ax s As

C - C + o) 2 L A (C 2 -C 2 AC. ) e x s A

v x s AC = C - C + w

2 L A (C -C )(C +C ) e x s A

v x s x s'

let AC = (C -C ) AC = AC + (o 2 L A (C +C )AC

for C w C

X s AC = AC(l+2w 2 L.C ) which is denoted as B in the

e

v As 7 text.

The error due to L in series with ASC0.3 is negligible because the capacitance is only about 10 pF.

*C

e ' l-„*LC ! but C

e

o resonance.

C + o) 2 LC 2 oo at frequencies n well below

-24-
APPENDIX B

ABSOLUTE TWO-TERMINAL CAPACITANCE MEASUREMENTS

USING A TRANSFORMER RATIO ARM BRIDGE

The most accurate capacitance measurements which it is

possible to make, at the present state of the art, are performed using a transformer ratio arm bridge. * These are

usually three- terminal capacitance measurements and are performed at a frequency of 1 kHz. When a good two-terminal

capacitor is equipped with a precision coaxial connector, it

can be evaluated to uncertainties of the order of ten parts

per million using a three- terminal to two-terminal coaxial

adaptor and a transformer ratio arm bridge. This technique

is used extensively in the high frequency impedance laboratory

at NBS Boulder.

To understand the technique, examine first the adaptor

which must be used. The diagram of the adaptor is shown

in fig. 8.

Mica Washer 0.0005" Thick

(THICKNESS SHOWN GREATLY EXAGGERATED)

Fig. 8 Three-Terminal

to Two-Terminal

Adaptor

Dielectric

Dielectric Sleeve

-25-
A 0.0005" thick mica washer and a dielectric sleeve, insulate

the two parts of the center conductor from each other, and the

center conductor is also insulated from the outer conductor.

The adaptor is connected to the transformer ratio bridge as

indicated by fig. 9.

Fig. 9 Transformer Ratio-Arm Bridge

The bridge measures only the direct capacitance which is

connected between the "Hi" and "Lo" terminals, thus the

effective capacitance of the adaptor is only that amount

of adaptor capacitance appearing between the top section of

the center conductor and the outer conductor (fig. 8).

Because this is a uniform coaxial section, we can calculate

its capacitance very accurately if we know the length of

the section, and the diameters of the inner and outer conductors. The presence of the thin mica washer, and the fact

that the ground and "Lo" terminals come to the same potential

at bridge balance, assure that there will be no electric

26-
field across the gap occupied by the thin mica washer, and

a practically uniform field from the inner conductors to the

outer conductor in the vicinity of the gap. This, in turn,

provides assurance that the capacitance measured by the

bridge is identical to that calculated for the outer coaxial

section of the adaptor. By this means absolute capacitance

measurements can be made with respect to the top surface

of the adaptor by merely subtracting the adaptor capacitance

from the bridge reading.

-27

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