national Bureau of Standards

Library, N.W. Bldg

NOV 2 7 1963

^ecknlcai i\ot& 92o. 201

A TECHNIQUE FOR EXTRAPOLATING THE 1 KC

VALUES OF SECONDARY CAPACITANCE STANDARDS

TO HIGHER FREQUENCIES

R. N. JONES

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress,

March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the national standards of measurement and the provision of means

and methods for making measurements consistent with these standards; the determination of

physical constants and properties of materials; the development of methods and instruments

for testing materials, devices, and structures; advisory services to government agencies on

scientific and technical problems; invention and development of devices to serve special needs

of the Government; and the development of standard practices, codes, and specifications. The

work includes basic and applied research, development, engineering, instrumentation, testing,

evaluation, calibration services, and various consultation and information services. Research

projects are also performed for other government agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's unique competence is required.

The scope of activities is suggested by the listing of divisions and sections on the inside of

the back cover.

Publications

The results of the Bureau's research are published either in the Bureau's own series of

publications or in the journals of professional and scientific societies. The Bureau publishes

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Central Radio Propagation Laboratory Ionospheric Predictions provides data for determining

the best frequencies to use for radio communications throughout the world. There are also

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Miscellaneous Publications, and Technical Notes.

A complete listing of the Bureau's publications can be found in National Bureau of Standards Circular 460, Publications of the National Bureau of Standards, 1901 to June 1947 ($1.25),

and the Supplement to National Bureau of Standards Circular 460, Jul-" 1947 to June 1957

($1.50), and Miscellaneous Publication 240, July 1957 to June 1960 (includes Titles of Papers

Published in Outside Journals 1950 to 1959) ($2.25); available from the Superintendent of

Documents, Government Printing Office, Washington D.C. 20402.
NATIONAL BUREAU OF STANDARDS

technical ^ote 201

Issued November 5, 1963

A TECHNIQUE FOR EXTRAPOLATING THE 1 KC

VALUES OF SECONDARY CAPACITANCE STANDARDS

TO HIGHER FREQUENCIES

R. N. Jones

Radio Standards Laboratory

National Bureau of Standards

Boulder, Colorado

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

£fiLC£ 1 5 CENTS
IMPORTANT NOTICE

NATIONAL BUREAU OF STANDARDS REPORTS are usually preliminary or progress accounting docu- ments intended for use within the Government. Before material in the reports is formally published it is subjected to additional evaluation and review. For this reason, the publication, reprinting, reproduction, or open-literature listing of this Report, either in whole or in part, is not authorized unless per- mission is obtained in writing from the Office of the Director, National Bureau of Stondards, Washington

25, D. C. Such permission is not needed, however, by the Government agency for which the Report has been specifically prepored if that agency wishes to reproduce additional copies for its own use.
Contents

Page

Abstract 1

1 . Introduction 1

2. Procedure for Determining High Frequency Value 3

3. Sources of Error 7

4. Conclusion J. 1

5. References ... .12

in

A TECHNIQUE FOR EXTRAPOLATING THE 1 KC VALUES

OF SECONDARY CAPACITANCE STANDARDS TO

HIGHER FREQUENCIES

A simple technique is described for extrapolating the

1 kc values of certain two -terminal capacitors to higher

frequencies without incurring serious losses in accuracy.

The method is intended for use with air capacitors having

binding post or banana plug type connectors. Because of

inherent errors, such connectors are not appropriate for

measurement where the highest accuracy is required. For

this reason, it is recommended that calibration of this

type be performed by secondary laboratories and not be

submitted to the National Bureau of Standards.

1. INTRODUCTION

With the establishment of requirements that military contractors

show traceability to the National Bureau of Standards in all areas of

measurement, increasing demands for new and improved types of

calibration services have appeared. Included in these demands is

the entire area of high frequency impedance measurements. Prior

to the increased demand for traceability there was little requirement

for impedance standards and calibration services at frequencies much

above 1 kc, and as a result there existed almost no commercially

available standards which were designed for high frequency applications. Consequently, NBS has been requested to perform high

frequency calibrations of standards which were primarily intended

for use at dc and low frequencies. Such requests have presented

difficulties because NBS does not possess appropriate standards to

use for comparison, nor is it practical to attempt to develop them.

A limiting factor in the accuracy of impedance measurements is

associated with the connector systems which are employed as a part
of the instrumentation set-up. This is true to a varying degree at

all frequencies, but in general, as the frequency of measurement is

increased, the importance of connectors must be given added consideration. There are certain minimum requirements which should

be satisfied by any connector system in order to assure accurate

results in impedance measurements. First, the connector should

be coaxial for purposes of self-shielding so as to avoid any influence

of surrounding objects upon the measurement result. This requirement is an important one even at the very low frequencies, especially

when small values of capacitance are to be determined. Two other

requirements are a well defined plane of electrical reference and a voltage standing wave ratio (VSWR) as nearly 1 . as possible. These

are most important at the higher frequencies where short wavelengths

are encountered and measurement accuracy depends upon the degree

of impedance matching within the connector.

Many of the impedance standards submitted to NBS for calibration

at frequencies above 30 kc employ banana plug connectors and are,

therefore, subject to connection errors which render them inappropriate

for use where highest accuracy is desired. Of particular interest

here are capacitance standards which are equipped with banana plug

connectors of either the plug or jack type.

Because the calibration methods employed at NBS for standards

of this type do not depend upon any national reference standard, it is

possible for a laboratory to perform its own high frequency calibrations

of such capacitors and avoid the necessity of submitting them to NBS.

By employing accepted techniques to calibrate such secondary standards, mutual benefits can accrue both to NBS and to the laboratories

requiring calibration services. NBS, bv limiting services to only the
highest quality standards, can devote increased effort to research

and, as a result, provide better services. On the other hand, other

standards laboratories can save money and time and avoid the perils

of transporting standards by utilizing as many such self-calibration

techniques as possible.

The measurement technique to be described is not new, nor is it

complicated. It is presented as an aid to overall efficiency, and while

it does contain several sources of error, they are not out of reason

when compared with the general accuracy to which standards to this

type may be considered reliable.

2. PROCEDURE FOR DETERMINING

HIGH FREQUENCY VALUE

Let us assume that we have a two -terminal air capacitor, with

binding post or banana plug connectors, whose known low frequency

(1 kc) value in farads is CQ

, and that we have an application requiring

that we know the capacitance value, Ce

, at some higher angular frequency, oo = 2iTf, where f is in cycles per second. Inherent in any

capacitor is a certain amount of conductance, series resistance, and

series inductance. All of these contribute to the effective value of

the capacitor at any given frequency, but, in this case, it is only the

series inductance which is considered significant. This is especially

true for high Q capacitors. Consider the simplified equivalent circuit

for the capacitor as shown on the right in figure 1.

L

ce Co

o Figure 1 Simplified Equivalent Circuit
Here L is the residual series inductance of the capacitor in

henries and CQ

is the low frequency (1 kc) value of the capacitor in

farads. At some angular frequency, we wish to find the effective

value C Equating the reactances of these two circuits gives:

1 1

T u)C e uCQ

and

Ce = —

J U)

1-oa LCQ

To arrive at a value for CQ

, it is necessary to evaluate the residual

series inductance, L. This is easily done by short circuiting the terminals of the capacitor and employing a grid -dip meter to ascertain the

angular frequency, go = 2-n-f r , at which the resulting circuit resonates.

The residual series inductance of the capacitor is then given by the

expression:

r o where CQ

is again the low frequency value of the capacitor and L

is the inductance of the device used to short circuit the terminals.

The effective capacitance is then obtained by substituting the value

for L into (1). A typical set-up for determinations of this type is

shown in figure 2.

The solid line in figure 3 indicates the percentage correction, as

a function of frequency, for a 1000 picofarad capacitor having a residual series inductance of 0.050 microhenry. This is a typical

value for the inductance of a good capacitance standard and may be

expected to be nearly the same for all capacitors of the same general

type of construction and comparable physical size. With this in mind,
Figure 2

Grid -Dip Meter Arrangement Used to Determine the

Resonant Frequency of a Short-Circuited Capacitor.
100

Llj z>

_l

5

o <

UJ

£T

rrO

O

UJ

a.

o.i

1 1 Mill

L = RESIDUAL SERIES INDUCTANCE

J I

I I J/l I

100 KC/S I Mc/s 10 Mc/s PERCENT CORRECTION VERSUS FREQUENCY FOR A 1000 pf CAPACITOR

HAVING A RESIDUAL INDUCTANCE OF 0.050 MICROHENRY

Figure 3
it should be noted that the larger the value of the capacitor being

considered, the more the effective value will rise for a given frequency.

3. SOURCES OF ERROR

Four principal sources of error associated with this measurement

procedure are as follows: (a) inaccuracy in the determination of the

resonant frequency of the short-circuited capacitor, (b) mutual

coupling between the shorting device and the grid-dip meter coil,

(c) the inductance of the shorting device, and (d) the equivalent circuit used to represent the capacitor. In examining these sources of

error it is necessary to generalize in a number of instances because

of the absence of a convenient geometrical arrangement upon which to

base a rigorous analysis. This is especially true in the latter three

instances where current distributions in conductors and the resulting

fields are extremely complex and true representations of actual circuit conditions are almost impossible to realize.

In measuring the resonant frequency of the short circuited capacitor, the grid -dip meter indication is very distinct because the capacitor

and short constitute a high Q circuit. This condition makes in possible

to achieve repeatability which is beyond the resolution of the frequency

scale on the grid-dip meter oscillator. Either of two methods may be

employed to improve this resolution. The frequency of the radiated

signal of the oscillator may be measured with a hetrodyne frequency

meter, or the signal may be amplified and fed into a frequency

counter. In this manner, it is possible to achieve repeatability well

within one percent. Assuming that the accuracy is also of this order,

the effect on the accuracy of the total circuit inductance would be

approximately two percent. For frequency accuracies within a few
percent, the accuracy in inductance is given by the expression:

AL Ago »

OJ

where AL and Aoj represent the errors in inductance and angular frequency respectively.

The error due to mutual coupling between the short and the griddip meter coil is evidently very small because no distinct change in

the resonant frequency is caused by varying the distance between them.

Any change in the resonant frequency resulting from an increase or

decrease in the separation is probably of the same order as the stability

and setability of the grid -dip meter oscillator. In any event, the

coupling error may be minimized by maintaining a separation of an

inch or more between them.

Probably the largest source of error is in the value used to

represent the self -inductance of the short. It is possible to improve

the situation by making a judicious choice of the size and configuration

of the device used so as to permit the use of available formulas

[ Terman,1943] to calculate the self -inductance. Even so,there

remains a margin of uncertainty due to the geometry of the current

path, and such formulas may not be expected to yield accuracies

better than ten to fifty percent. However, since the inductance of

the short is usually only a small portion of the total inductance of

the resonant circuit, this does not represent a serious degradation

of the value obtained for L. in equation (2). Figure 4 is a photograph

showing two shorting bars which are convenient to use. These are

brass bars fitted with banana plugs or jacks appropriately spaced

to fit the capacitor terminals.
u

u

W>C—

1-1 o

CO 9
Finally, we must consider the equivalent circuit used to represent

the capacitor. The circuit of figure 1 may be criticized because, in

actuality, the inductance and capacitance probably do not exist as shown. Depending upon the physical details of the construction, the

capacitor may be more accurately represented by other equivalent

circuits. As an example, consider the equivalent circuit of figure 5.

Ct

Lp

Figure 5

High Frequency Equivalent Circuit

Here the inductance and capacitance, instead of being lumped together

at one point, are separated into fractional parts of the total and

arranged in a manner which more nearly approximates the actual

situation. C^. is the capacitance between the case and the high

potential lead passing through it, and C

p

is the capacitance in the

stack of plates. L., and L are the lead inductances arranged as they

ir may appear in relation to C^ and Cpo Problems arise, however,

because it is difficult to estimate the values to assign these components,

and also because complex circuits are cumbersome to handle mathematically. To illustrate the importance of the equivalent circuit,

consider a capacitor having a 1 kc value of 1000 picofarads and a

residual series inductance of 0.050 microhenry. Using the equivalent

circuit of figure 1, the value at 1 Mc is 1001.98 picofarads. The

circuit of figure 5 gives a value of 1001.96 picofarads if we let

Lj. = L = 0.025 microhenry, C. = 10 picofarads, and C = 990 picofarads. At this frequency the difference is essentially negligible,

10
but at 15 Mc the values are 1799.00 picofarads for the circuit of

figure 1 and 1786.32 picofarads for the circuit of figure 5, using

the same values for Lu., L , C,, and C . Thus it is seen that the c> p» t» p

equivalent circuit assumes increasing importance at the higher

frequencies.

Because of the sources of error, it is believed that the reliability

of the value obtained for the residual series inductance by the method

described is not better than ten percent. Again referring to figure 3,

the broken lines indicate the upper and lower limits of the corrections

which result from this ten percent uncertainty in the inductance value.

In general, it may be said that the effective capacitance may be determined by this method to accuracies of one percent or better up to

frequencies where the correction amounts to ten percent of the 1 kc

value

.

4. CONCLUSION

With the advent of improved rf connector systems, many standards

and instruments using the older type connectors are no longer appropriate for use at the level of primary standards. NBS has developed and

does maintain standards which are only appropriate for use with the

improved type of coaxial connectors [Jones and Nelson, 1962] . Because

it is impractical for NBS to attempt to maintain standards for a wide

variety of connector configurations, secondary standards laboratories

are urged to employ this calibration procedure where possible and

when compatible with traceability requirements.

11
5. REFERENCES

1. Jones, R. N., and R. E. Nelson (1962). "The Role of

Capacitance in the National Reference Standards of

High Frequency Impedance, " Proceedings of the

Instrument Society of America, Paper No. 18. 1. 62 .

2. Terman, F. E. (1943). Radio Engineers Handbook, First

Ed., pp. 48-51 (McGraw-Hill Book Co., Inc., New York,

N. Y.).

12

GPO837-107
U. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A.'V. Aatin, Director THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C.and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineeringin the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the

front cover.

WASHINGTON, D. C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. High Voltage. Absolute Electrical Measurements.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology. Mass and Volume.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Hadiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standard Refer- ence Materials. Applied Analytical Research. Crystal Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Polymers. Macromolecules: Synthesis and Structure. Polymer Chemistry. Polymer Physics. Polymer Characterization. Polymer Evaluation and Testing. Applied Polymer Standards and Research. Dental Research.

Metallurgy. Engineering Metallurgy. Metal Reactions. Metal Physics. Electrolysis and Metal Deposition.

Inorganic Solids. Engineering Ceramics. Class. Solid State Chemistry. Crystal Growth. Physical Properties.

Crystallography.

Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Metallic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. Operations Research. Data Processing Systems. Components and Techniques. Computer Technology. Measurements Automation. Engineering Applications. Systems Analysis.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Far Ultraviolet Physics. Solid State Physics. Electron Physics. Atomic Physics. Plasma Spectroscopy.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemisiry. Molecular Spectroscopy. Ele- mentary Processes. Mass Spectrometry. Photochemistry and Radiation Chemistry.

Office of Weights and Measures. BOULDER, COLO.

CRYOGENIC ENGINEERING LABORATORY

Cryogenic Processes. Cryogenic Properties of Solids. Cryogenic Technical Services. Properties of Cryogenic

Fluids. CENTRAL RADIO PROPAGATION LABORATORY

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services. Vertical Soundings Research. Troposphere and Space Telecommunications. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements. Tropospheric Analysis. Spectrum Utilization Research. Radio-Meteorology. Lower Atmosphere

Physics.

Radio Systems. Applied Electromagnetic Theory. High Frequency and Very High Frequency Research. Fre- quency Utilization. Modulation Research. Antenna Research. Radiodetermination. Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. High Latitude Ionosphere

Physics. Ionosphere and Exosphere Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.

RADIO STANDARDS LABORATORY

Radio Standards Physics. Frequency and Time Disseminations. Radio and Microwave Materials. Atomic Fre- quency and Time-Interval Standards. Radio Plasma. Microwave Physics.

Radio Standards Engineering. High Frequency Electrical Standards. High Frequency Calibration Services. High

Frequency Impedance Standards. Microwave Calibration Services. Microwave Circuit Standards. Low Frequency

Calibration Services.

Joint Institute for Laboratory Astrophysics- NBS Group (Univ. of Colo.).
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