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92c. 57

VARIABLE CAPACITOR CALIBRATION WITH

AN INDUCTIVE VOLTAGE DIVIDER BRIDGE

BY THOMAS L. ZAPF

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS

technical ^Ttote

57

May, I960

VARIABLE CAPACITOR CALIBRATION WITH AN

INDUCTIVE VOLTAGE DIVIDER BRIDGE

by

Thomas L. Zapf

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

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CONTENTS

Page

ABSTRACT li

1. INTRODUCTION 1

2. EQUIPMENT 1

3. THE BRIDGE CIRCUIT 2

4. TWO -TERMINAL CAPACITANCE MEASUREMENTS 3

5. CONCLUSION 4

REFERENCES 5

LIST OF ILLUSTRATIONS

Figure 1. A simple transformer capacitance bridge for

direct capacitance measurements 6

Figure 2. A modification of the bridge shown in Figure 1 6

Figure 3. Connections for two -terminal capacitance

measurements 6

Figure 4. Connections to a dual-range, two-terminal

variable air capacitor showing guard

cap over unused terminal 6

ii VARIABLE CAPACITOR CALIBRATION WITH AN

INDUCTIVE VOLTAGE DIVIDER BRIDGE

Thomas L. Zapf

ABSTRACT

The use of an inductive voltage divider bridge for the calibration of three -terminal and two -terminal variable air capacitors is

discussed.

VARIABLE CAPACITOR CALIBRATION WITH AN

INDUCTIVE VOLTAGE DIVIDER BRIDGE

by

Thomas L. Zapf

1. INTRODUCTION

The accurate calibration of variable air capacitors can be accomplished by several methods, one of which has been described as

a step-up or step -substitution method (1). Another method, that is

particularly useful for the calibration of three -terminal capacitors,

is presented in this paper.

Very simple inductive ratio arm bridges may be assembled for

the calibration of direct capacitance of three -terminal capacitors or

capacitance differences of two -terminal variable air capacitors using

fixed three -terminal capacitors as reference standards.

2. EQUIPMENT

Commercially available inductive voltage dividers can be used

as inductively-coupled ratio arms of a capacitance bridge. The

accuracy of ratio of the arms thus formed often far exceeds that

needed for the calibration of variable air capacitors, even if the

nominal ratio is used without correction.

Because of the inherent freedom from variations of their direct

capacitance, it is desirable to use three -terminal capacitors (now

commercially available) as fixed standards, particularly with

bridges having inductively -coupled ratio arms. The stray capacitances to ground are then across either the detector or the ratio

arms. A small capacitance across the detector generally does no

2

more than reduce the sensitivity, and the effect on accuracy of

loading the closely coupled ratio arms, which have very small

equivalent series impedance, is negligible.

3. THE BRIDGE CIRCUIT

Figure 1 shows an oscillator -amplifier power supply connected

to the extremities of an inductive voltage divider, to one terminal

of the fixed standard capacitor, Cs , and to one terminal of the

variable capacitor under test, C. The other terminal of each of

the capacitors is connected to one input terminal of a sensitive ac

detector by means of well-shielded cable with shielded connectors.

The shields of these cables, the other terminal of the detector, and

the variable tap on the inductive voltage divider are connected

together and to ground. The variable capacitor is set to the calibration point and the inductive voltage divider adjusted until the

bridge is balanced. If A is the reading of the inductive voltage

divider, C = ( -r - 1 ) Cs

. For best precision it is suggested that

Cg be approximately equal to the maximum capacitance of C.

In Figure 2, a modification is shown in which the inductive

voltage divider is grounded at a fixed tap, A-p, by means of a separate wire connected to one contact of the first decade switch.

When the bridge is balanced, C = ( 1 ) Cs , and if A-p = 0. 5,

\AT /

C = 2(A - 0. 5)C g

. This particular modification is rather convenient

for routine calibrations because computations are simplified.

If good quality air capacitors are used in the above bridge circuit, it may not be necessary to provide for the conductance balance

of the circuit. If better resolution is desirable, however, a small

adjustable resistor of several hundred ohms or less may be placed

3

in series with one or the other (as needed) of the capacitors in the

unshielded leads to the inductive voltage divider as shown in Figure

2. Resistors, so placed, may permit a considerable improvement

in the precision of the balance.

It should be evident that one three -terminal variable capacitor,

set to a known capacitance by means of a larger fixed standard,

serves excellently as a temporary standard to extend measurements

to smaller values. Several orders of magnitude can be covered by

this means. If extension of measurements to larger capacitance is

contemplated, consideration must be given to the effect of inductance

in the leads and in the resistor mentioned above.

4. TWO -TERMINAL CAPACITANCE MEASUREMENTS

The electrical connections to a single -range, two -terminal,

variable air capacitor are shown in Figure 3. It is evident that the

case of the capacitor is not grounded. The admittance from case to

ground is merely a load on the inductive voltage divider and is generally of no consequence. If the voltage applied to the extremities

is kept low, there is no danger to the operator, but to avoid small

but disconcerting changes in the balance of the bridge resulting from

changing capacitance at the terminals, the observer should avoid

touching the case of the capacitor during the balancing operation,

and should keep away from the terminals. The uncertainties of

capacitance at the terminals of two -terminal capacitors is discussed

in detail in reference (2). If the unused terminal of a dual-range,

two -terminal, variable air capacitor is normally left unconnected,

then, when calibrating the capacitor by this method it will be necessary to place a guard cap over, but not touching, the unused terminal,

The guard cap must be electrically connected to the case of the

4

capacitor as shown in Figure 4. Capacitance differences corresponding to two settings of a variable air capacitor can be measured

with excellent accuracy by this method.

5. CONCLUSION

Inductive voltage dividers can be used as ratio arms of a transformer capacitance bridge for two -terminal capacitance difference

measurements as well as three -terminal capacitance measurements,

REFERENCES

(1) T. L. Zapf, Capacitor calibration by step-up methods,

J. Res. NBS. 64C, 75 (I960)

(2) J. F. Hersh, A close look at connection errors in capacitance

measurements, General Radio Experimenter. 33, (No. 7) ,

3 (1959)

The two following papers contain references to prior literature

on bridges having inductively-coupled ratio arms.

(3) A. M. Thomson, The precise measurement of small capacitances, IRE Trans, on Instrumentation. 1-7 , 245 (1958)

(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, IRE Trans,

on Instrumentation. 1-7, 253 (1958)

Ib'-H-i)

Figure 1. A simple transformer capacitance bridge for direct

capacitance measurements.

a«-a-')

Figure 2. A modification of the bridge shown in Figure 1

Dp

Figure 3. Connections for

two -terminal capacitance

measurements

.

Figure 4. Connections to a dual -range, two -terminal

variable air capacitor show^

ing guard cap over unused

terminal.

I .S. DEPARTMENT OF COMMERCE

Frederick H. Mueller, Secretary NATIONAL BUREAU OF STVNDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

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