Cy = (1/2) (Cyn - Cy) 5 (oO)

where C, is the reading of air dials when C, is connected to the arm CD of the bridge, and
C,y is the reading of air dials when C, is connected to the arm AD of the bridge.

Tor capacitors of nominal valucs from higher than 0.005 pF to 0.5 pF, a certain setting of the decade
box, Cp, is needed for each nominal value, but should remain as a constant during both balances.
Also, the mica dials are needed to obtain balance when the unknown is connected to the arm CD.
The value of the unknown, C,, , can be’expressed as:

Cy = (1/2) Cy + (1/A(Cyp - Cy) 5 (8)
where C,,, is the reading of mica dials when C, is connected to the arm CD of the bridge.

For capacitors of nominal value of higher than 0.5 uF, a different measurement procedure is used.
Due to the limitation of internal mica capacitors of the Type-12 bridge, four balances, instead of two,
are needed and the decade box Cy is set to either zero or the nominal value of the unknown. Using
Cx = 1 pF as an example, the four steps of connections and settings are :

1) Connect C, to arm AD, set mica dials to zero, and Cy to 1 uF. Use air dials to obtain
balance, and record the reading as C,.

2) Disconnect C,, and leave C), at 1 uF. Use both air and mica dials to obtain balance, and
record the readings as C,,, and C,,p, respectively.

3) Connect C, to arm CD, and set C;, to zero. Use both air and mica dials to obtain balance,
and record the readings as C,, and Ciy¢, respectively.

4) Disconnect C,, set both mica dials and C,, to zero. Use air dials to obtain balance, and
record the reading as C,q.

After the above four measurements and data recordings are completed, the value of the unknown,
C,,, can be calculated from:

C= (1/2) (Cnt) + Cone) + (1/2) [Crp - Cra) + (Cro ~ Crd» 9)

Since there are no perfect capacitors, there must be some power loss, which appears as the
equivalent parallel conductance of the capacitor. Therefore, the procedure of obtaining a balance
condition of the Type-12 bridge is to balance both the quadrature and the in-phase components of
the bridge by adjusting both the capacitance and conductance dials, as shown in Fig. 3. Eqs. (5) to
(9) are used to calculate unknown capacitances, C,, of various nominal values and terminal
configurations after each balance is obtained and capacitance dial readings are recorded. As shown
in Fig. 3, Eqs. (5) to (9) can also be utilized to calculate the conductance value of the unknown
capacitor by substituting the C, and capacitance dial readings with G, and conductance dial
readings, respectively.

14


Figure 3. The NIST Type-12 Capacitance Bridge with Conductance Components.

35


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40


type standard, independently connected to arms AD and CD such that the sum of conductance of
both arms is a constant. Figure 3 is a simplified diagram of Type-12 bridge that includes the
conductance components in each arm, and a divider resistor, Ry, (see Fig. 2a), which serves as a
range shifter, Ky so that the reading of the conductance standard is divided by 1, 10, 100, 1000, or
10 000. G, is the conductance component of the unknown capacitor, C,. Specifications and
operating procedures of conductance standard of the Type-12 bridge were "Gescribed i in detail by
Wimheim [10]. As shown in Fig. 2b, (G,/ K, ) and (G,/ Ky ) are effective conductances on arm
AD and arm CD, respectively, and the quantity (G,+G, Si is equal to a constant. Both the decades
and the variable dials of the conductance standard provide readings to cover the required range and
keep the sum of G, and G, a constant.

The Type-12 system is used mainly to measure two- and three-terminal mica capacitors with
binding-post connectors from 0.001 yF to 1 pF. Accordingly, two special fixtures have been
constructed to be used for two- and three-terminal measurements, designated as P2 and P3,
respectively. These fixtures have binding post connectors, such that the capacitors can be plugged
into the bridge via either P2 or P3 directly without using cables, in order to eliminate lead
impedance. Detailed descriptions of P2 and P3 are given later in this document (sections 4.2.1 and
4.2.2).

3.3 Impedance Meters

The advantage of using impedance meters is that measurements can be performed and results can
be transferred automatically to a computer. This reduces both the measuring time and possibilities
for human errors when hand-written data are being transferred. Presently, there are two types of
commercial impedance meters being used to support the NIST capacitance calibration service.

3.3.1 Capacitance Meter

This type of Capacitance Meter employed in the ICL (hereafter referred to as the C-Meter) measures
capacitors with respect to internal temperature-controlled, fused-silica-dielectric capacitors. It has
a resolution up to one part in 10°, but operates only at a frequency of 1 kHz. It was evaluated by
carrying out two separate pilot programs [11], and is now used as the transfer standard in the NIST
C-MAP service, and to support the calibration of standard capacitors at a frequency of 1 kHz.

The C-Meter is utilized to perform measurements, at a frequency of 1 kHz, on nitrogen-dielectric
capacitors in the large uncertainty tests (25 ppm ); on air-dielectric capacitors; during the physical
tests on the nitrogen-dielectric capacitance standards to observe the changes in capacitance values;
and on two-terminal capacitance standards with HF coaxial connectors, including the standard
terminations.

The C-Meter is characterized by using it to monitor the NIST check standards of mica-dielectric
capacitors at 1 kHz. It is used to calibrate customer’s mica-dielectric capacitors at 1 kHz by using
the "substitution method" [12], as discussed in the following section (3.3.2).


The reported value of capacitance is in terms of the NIST representation of the farad. The expanded
uncertainties include allowance for both Type A and Type B uncertainties in the chain of calibration
measurements, and are assigned to the capacitance values using the coverage factor k= 2 [9]. They
do not include any components of uncertainty that may be associated with long term instability,
temperature hysteresis or changes due to stresses incurred during shipment. In addition, no
allowance is made for the variations in the capacitance of unsealed capacitors due to changes in
humidity since the magnitude of these variations is dependent upon the surface conditions of the
plates. The relative humidity in the laboratory varies but does not exceed 50%.

0]

2)

B)

(4]

(5)

(6]

7

[8]

19]

3. References

RD. Cutkosky, "New NBS Measurements of the Absolute Farad and Ohm," IEEE Trans. on
Instrumentation and Measurements, Vol. IM 23, No. 4, Dec. 1974.

J.Q Shields, R. F. Dzinha, and H. P. Layer, “New Realization of the Ohm and Farad Using
the NBS Calculable Capacitor,” IEEE Trans. Instrum. Meas. Vol. 38, No. 2, pp. 249-251,
April 1989.

“TEEE Standard for Precision Coaxial Connectors," IEEE Trans. on Instr. Meas., Vol. IM-17,
No. 3, pp. 204-218, Sept. 1968.

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 Instr., Vol. I-7, No. 3 & 4, pp. 253-261, Dec. 1958.

R. D. Cutkosky and L. H. Lee, "Improved Ten-picofarad Fused Silica Dielectric Capacitor,"
Jour. of Res. NBS, Vol. 69C, No. 3, July & Sept. 1965.

R. D. Cutkosky, "Capacitance Bridge - NBS Type 2," National Bureau of Standards Report
7103, March 1961.

J. F. Hersh, “A Close Look at Connection Errors in Capacitance Measurements," General
Radio Experimenter, Vol. 33, No. 7, July 1959.

R. W. Orr, "Capacitance Standards with Precision Connectors," General Radio Experimenter,
Vol. 41, No. 9, Sept. 1967.

B.N. Taylor and C. E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty
of NIST Measurement Results," NIST Tech. Note No. 1297, Jan. 1993.

72


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APPENDIX

Al. — General Information on Fused-Silica-Dielectric Standard Capacitors.

A2. Typical REPORT OF CALIBRATION for Fused-Silica-Dielectric Standard Capacitors.
A3. — General Information on Nitrogen-Dielectric Standard Capacitors.

A4. Typical REPORT OF CALIBRATION for Nitrogen-Dielectric Standard Capacitors.

AS. — Description of Tests used to Determine the Effect of Small Mechanical Stress on High
Stability, Nitrogen-Dielectric Standard capacitors.

A6. Typical REPORT OF CALIBRATION for Test Results of the Effect of Small Mechanical
Stress on Nitrogen-Dielectric Standard Capacitors.

A7. General Information on Three-Terminal Standard Capacitors.
A8. Typical REPORT OF CALIBRATION for Three-Terminal Standard Capacitors.

A9. — General Information on Two-Terminal Standard Capacitors with Precision Coaxial
Connectors.

Al0. Typical REPORT OF CALIBRATION for Two-Terminal Standard Capacitors with
Precision Coaxial Connectors.

All. General Information on Mica-Dielectric Standard Capacitors with Binding Post
Connectors.

A12. Typical REPORT OF CALIBRATION for Mica-Dielectric Standard Capacitors with
Binding Post Connectors.

54


Pee
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Bi UNITED STATES DEPARTMENT OF COMMERCE
National Institute of Standards and Technology

Gaithersburg. Maryland 20893-0001

ant * Bey
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Mea» ot

Fares of ®
GENERAL INFORMATION ON NITROGEN-DIELECTRIC STANDARD CAPACITORS

1. Representation of the Unit of Capacitance

As a result of new absolute measurements of the farad in terms of the units of length and time, the
legal unit of capacitance was established at NIST/NBS in 1975 [1], and re-established in 1989 [2].
The reported values of capacitance since that time reflect the values assigned to NIST standards used
for the maintenance of the legal unit. Since 1989, the difference between the NIST unit, which
includes an allowance for possible drift, and the farad is believed to be no greater than +0.1 ppm.

2. Nitrogen Dielectric Standard Capacitors

Three-terminal standard capacitors of nitrogen dielectric are calibrated with a NIST transformer
bridge [3] using NIST fused-silica 10-pF capacitors [4] as reference standards. Capacitance is
measured by direct comparison with stable working standards, which are calibrated in terms of the
reference standards with the NIST transformer bridge. This is done each time they are used.

The measured capacitances are the mean of the results of two or more measurements of direct
capacitance with the capacitor connected to the NIST transformer bridge as a two-terminal-pair
admittance [5]. If the terminals of the capacitor are not two-terminal-pair, connections with
negligible impedance are made to make them so. All capacitors must be in the calibration laboratory
for 72 hours or more before measurements are performed. The average ambient temperature of the
laboratory is 23 °C + 1 °C with hourly variations of about 0.1 °C. The relative humidity in the
laboratory varies but does not exceed 50%.

During the measurements in small uncertainty calibrations, the capacitor to be calibrated is placed
ina partially insulated box and the platinum resistance probe of a digital thermometer is placed near
the capacitor. The temperature of the capacitor is obtained by direct readouts of the thermometer,
which has a resolution of 0.001 °C and limits of errors of + 0.01 °C. The capacitance and
temperature values given in the Report of Calibration are the average values of the respective
measurement results. The standard deviation of the capacitance measurements is also calculated to
assure it is within limits based on the estimated population standard deviation.

Ifit is requested, six physical tests are performed on the capacitor to detect the effects of mechanical
stress on it. If these tests are performed on a capacitor, a description of the tests and the results of
the tests for the capacitor will be given in a separate Report of Calibration.

The reported value of capacitance is in terms of the NIST unit of capacitance maintained with a
group of stable standards [4]. The expanded uncertainties include allowance for both Type A and

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The Type A standard uncertainty contains error components that can be evaluated by statistical
methods and is expressed from each known source of error as a statistical standard deviation. The
Type B standard uncertainty contains those errors that are evaluated by other means [5], and is
estimated from an "equivalent" standard deviation of each possible source of error, many times
based solely on the experience of the metrologist.

A detailed discussion is contained in [6] for each type of uncertainty for the measurement of
various standard capacitors using different measurement systems. The expanded uncertainties
assigned to these capacitors are given in Tables 7 to 10, based on the following equation:

U=2[ LEY + LT”, (12)

where s; and 5s; are the estimated standard deviations of the components of Type A and Type B
standard uncertainties, respectively.

7. CONCLUSION

The NIST capacitance calibration service is described in this publication, which contains material
from internal documents dated back to 1960. Over the past decade, the quality of the measurements
performed in the impedance calibration laboratory (ICL) has been improved tremendously. High-
quality commercial instruments, such as detectors and function generators, are now used in the Type-
2 system to improve its resolution. Thc usc of oil-bath type fused-silica capacitors with known
temperature corrections as reference standards in the ICL has increased the stability and consistency
of the local unit of capacitance. The development of automatic measurement procedures using
characterized commercial meters reduces measurement time and the possibility for human errors.
References [3] and [6] constitute additional, more detailed documentation for selected aspects of the
NIST capacitance calibration service.

8. REFERENCES

1. J. Q Shields, R. F. Dziuba, and H. P. Layer, "New Realization of the Ohm and Farad Using
the NBS Calculable Capacitor," IEEE Trans. Instrum. Meas. Vol. 38, No. 2, pp. 249-251,
April 1989.

2. R. D. Cutkosky, "Capacitance Bridge -- NBS Type 2, "National Bureau of Standards Report
7103, March 1961.

3. Y. M. Chang, "NIST Measurement Assurance Program for Capacitance Standards at 1 kHz,"
NIST Technical Note 1417, March 1996.

18


#121 (or other Primary Refeence)
(10 pF)
At slice Customer's
#102 (or #254) Cap Stds #131 (or #230) Fused Silica
(10 pF) P (100 pF) Cap Stds
Cyoy (1 pF) c
‘x21 (100 pF)
Cx} (10 pF)
Customer's #871 #493 & #517 #ITI7 & #1865 NBS #1615
Nitrogen (or Air) (10 pF) (100 pF) (1000 pF) (10000 pF)
Cap Stds
Cxq (10 pF)
Customer's #89790 Customer's Customer's Customer's
Air Cap Stds (1 pr) Nitrogen (or Air) | | Nitrogen (or Air) Air Cap Stds
Cxop (1 pF) Cap Stds Cap Stds Cxqy (10000 pF)
Cxp (100 pF) C3, (1000 pF)
Customers C93 (100 pF) Cx39 (1000 pF)
Air Cap Stds Cx (100 pF) Cx33 (1000 pF)
Cy, (0.1 pF)
Customer's
Air Cap Stds
Cx2 (0.01 pF)
Customer's
Air Cap Stds
Cy; (0.001 pF)

Figure 4. Block Diagram of Measurement Process and Standards being Used
In the Impedance Calibration Laboratory.

36


OF cay

‘if ‘| UNITED STATES DEPARTMENT OF COMMERCE
; | National Institute of Standards and Technology
& | Gaithersburg, Maryland 20899-0001

Fares oo"

My

wn Ota,

GENERAL INFORMATION ON TWO-TERMINAL STANDARD CAPACITORS
WITH PRECISION COAXIAL CONNECTORS

1. Representation of the Unit of Capacitance

As aresult of new absolute measurements of the farad in terms of the units of length and time, the
legal unit of capacitance was established at NIST/NBS in 1975 [1], and re-established in 1989 [2].
The reported values of capacitance since that time reflect the values assigned to NIST standards used
for the maintenance of the legal unit. Since 1989, the difference between the NIST unit, which
includes an allowance for possible drift, and the farad is believed to be no greater than +0.1 ppm.

2. Two-Tenninal Standard Capacitors with HF Coaxial Connectors

Standard capacitors with precision coaxial connectors [3] are calibrated at frequencies up to 1000 Hz
with a NIST transformer bridge [4] using working standards, which are calibrated in terms of NIST
fused silica 10 pF [5] reference standards. The general calibration procedure is described in [6].

The measured parallel capacitance is the mean of the results of four or more measurements of the
“capacitance added" [3,6,7]. Between each measurement, the capacitor is disconnected, rotated 90
degrees around the vertical axis of the connector, and reconnected. The measurements are made with
a special three-terminal to two-terminal adapter whose "zero" value to the reference plane is known
to within 0.004 pF. The “capacitance added" with this adapter is the capacitance to the reference
plane of the connector. Ifan open-ended termination (with an inner conductor preferably) is-supplied
and if it is specially requested that the change in capacitance be referenced to the termination, then
the change in capacitance is that due to disconnecting the termination and connecting the capacitor
[8]. This type of change is probably the most useful to the user since effects due to small
dissimilarities between the NIST adapter and the user's adapter will tend to cancel out.

In order to realize the stated uncertainties, the user's adapter and capacitor connectors must be kept
in good condition. These must be clean so that proper mating occurs and a uniform radial field is
maintained within the connectors. Changes in concentricity, depth of the end of the inner conductors
or damage to the leaf contacts can easily change the capacitance values by 0.01 pF or more. The use
of any non-precision or different connector with these capacitors virtually will destroy any usefulness
of the capacitance value and its uncertainty.

All capacitors must be in the calibration laboratory for 72 hours or more before measurements are
performed. The average ambient temperature of the laboratory is 23 °C + 1°C with hourly variations
of about 0.1 °C. Measurements are not made if the ambient laboratory temperature differed from the
set-point by more than 1°C during the last 24 hours.

m NIsT


Table 1.
Table 2.
Table 3.
Table 4a.
Table 4b.
Table 4c.
Table 4d.
Table 4e.
Table 4f.
Table 5.

Table 6.
Table 7.

Table 8.

Table 9.

Table 10.

List of Tables

Summary of Standard Capacitors Acceptable for Calibrations ............. 20
Summary of Reference and Check Standards of the Type-2 Bridge ......... 21
NIST Calibration Design for Fused-Silica-Dielectric Standard Capacitors ...22
NIST Calibration Design for 10 pF Nitrogen-Dielectric Standard Capacitors . . 23
NIST Calibration Design for 100 pF Nitrogen-Dielectric Check Standards . . . 23
NIST Calibration Design for 1000 pF Nitrogen-Dielectric Check Standards. . . 23
NIST Calibration Design for One 100 pF (or 1000 pF)

Nitrogen-Dielectric Standard Capacitors «2.02... 00.00. c eee e cece eee 24
NIST Calibration Design for Two 100 pF (or 1000 pF)

Nitrogen-Dielectric Standard Capacitors ............ 0. cece e eee nee eee 24
NIST Calibration Design for Three 100 pF (or 1000 pF)

Nitrogen-Dielectric Standard Capacitors .........0. 00sec seen eee eee ee 24

NIST Large Uncertainty Calibration Design for Nitrogen-
and Air-Dielectric Standard Capacitors
Summary of Check Standards of the Type-12 Bridge . .
Calibration Uncertainties of Fused-Silica- and Nitrogen-Dielectric

Standard Capacitors 2.1.6... e een eeee 27
Calibration Uncertainties of Air-Dielectric and Two-Terminal

HF Coaxial Connector Standard Capacitors ..
Calibration Uncertainties of Capacitance Values of ‘I'wo- anc

Three-Terminal Mica- Dielectric Standard Capacitors ................005 29
Calibration Uncertainties of Conductance Values of Two- and
Three-Terminal Mica- Dielectric Standard Capacitors .............0.0005 30


4,

04,
8 ay

a4 UNITED STATES DEPARTMENT OF COMMERCE
National Institute of Standards and Technology
Gaithersburg, Maryland 20899-0001

a

yt © Peay
Oh

Fares of

GENERAL INFORMATION ON MICA-DIELECTRIC STANDARD CAPACITORS
WITH BINDING POST CONNECTORS

1. Representation of the Unit of Capacitance

As aresult of new absolute measurements of the farad in terms of the units of length and time, the
legal unit of capacitance was established at NIST/NBS in 1975 [1], and re-established in 1989 [2].
‘The reported values of capacitance since that time reflect the values assigned to NIST standards used
for the maintenance of the legal unit. Since 1989, the difference between the NIST unit, which
includes an allowance for possible drift, and the farad is believed to be no greater than +0.1 ppm.

2. Mica-Dielectric Capacitors with Binding Post Connectors

Two- and three-terminal standard capacitors with plug and binding post connectors are calibrated
with a resistance ratio-arm bridge, as described in (3]. This bridge is calibrated with working
standards that are calibrated in terms of NIST fused silica 10 pF [4] reference standards.

The measured parallel capacitance and conductance are the means of two or more measurements
obtained by connecting the capacitor into the bridge via the binding posts of the terminal plate with
the plugs supplied by the customers. If no plugs are supplied, measurements are performed by using
standard connectors model GR274. The binding posts of the capacitor are never used for this
measurement.

The uncertainty for the measured capacitance contains a 0.01 pF systematic component for binding
posts and plate geometry [5]. The measured capacitance of any capacitor with exposed connectors
is dependent upon the mechanical and electrical geometry of the connections to the capacitor, the
stability of this geometry and of the surroundings [6]. For example, changes in plug type and
heights, hole depths, center to center distance of the binding posts can cause changes of 1 pF or
more. In some cases, connectors other than binding posts and a plate can cause changes of 0.1 pF
or more. In order to realize the stated uncertainty, the user must compare his/her geometry with that
used in the calibration of the capacitor and make appropriate calculations and/or measurements for
the differences. If this cannot be done, it is reasonable to assume that the addition of 1 pF to the
stated uncertainty would be adequate for most geometries.

All capacitors must be in the calibration laboratory for 72 hours or more before measurements are
performed. All measurements are made in a laboratory where the temperature control set-point is
23°C. Measurements are not made if the ambient laboratory temperature differed from the set-point
by more than 1 °C during the last 24 hours.

7 NIsT


UNITED STATES DEPARTMENT OF COMMERCE
National Institute of Standards and Technology
Gaithersburg, Maryland 20899-0001

REPORT OF CALIBRATION

Standard Capacitor

General Radio Company
Type 1406-A, Serial No. ####

Submitted by:

Expanded
Frequency Capacitance Uncertainty
(Hz) (PF) (2)
1000 1000.123 60

For additional information regarding the calibration of capacitors of this type at NIST, the user should
consult the information sheet(s) enclosed with this report.

Temperature: 23°C +1°C
Date of Calibration: October 2, 1997

Measurements performed by:

Summerfield B. Tillett
Electricity Division

Test No. 811/

Reference:

Date: January 6, 1998

Telephone Contact: 301-975-4221

73

For the Director,

Barry A. Bell, Group Leader
Electricity Division

NUsT


2X0 OF co,

ee “4
f ‘4 % | UNITED STATES DEPARTMENT OF COMMERCE
£ : | National Institute of Standards and Technology
%, y Gaithersburg, Maryland 20899-0001
“Stare of

REPORT OF CALIBRATION

Standard Capacitor

General Radio Company
Type 1409-Y, Serial No. ####

Submitted by:
Type of Capacitance Conductance
Measurement Frequency Capacitance Uncertainty Conductance Uncertainty
(iz) @F) (2) (uS) (uS)
2-Tenninal 1000 0.99878 0.018 05 0.4

For additional information regarding the calibration of capacitors of this type at NIST, the user should
consult the information sheet(s) enclosed with this report.

Temperature: 23° C + 1°C

Date of Calibration: December 1, 1997

Measurements performed by: For the Director,
Summerfield B. Tillett Barry A. Bell, Group Leader
Electricity Division Electricity Division

Test No. 811/

Reference:

Date: January 5, 1998

Telephone Contact: 301-975-4221

1 NUsT


Table 9. Calibration Uncertainties of Capacitance Values of Two- and Three-Terminal
Mica-Dielectric Standard Capacitors

Expanded Uncertainties of Capacitance (ppm)

Configuration Two-Terminal Three-Terminal
Frequency (Hz) 66, 100, 400, and 1000 10.000 | 66, 100, 400, and 1000 10 000
Nominal Value (iF)
0.001 180 180 120 120
0.002 120 120 100 100
0.005 120 120 100 100
0.01 120 120 100 100
0.02 120 120 100 100
0.05 120 120 100 120
0.1 120 150 100 150
0.2 120 250 100 250
0.5 120 500 100 500
1 120 1000 120 NA

29



5. QUALITY CONTROL IN THE IMPEDANCE CALIBRATION LABORATORY

In order to achieve high quality in the measurement results, it is important to establish procedures
to assure that the measuring systems and reference and check standards are in a state of statistical
control. In the ICL, the unit of capacitance is transferred from the PSL, and maintained via primary
reference standards to perform calibrations of customer’s standards. Quality control procedures have
been established in many parts of the calibration process, including maintaining the farad,
developing control charts of reference and check standards, observing the variations in
measurements, and examining the calibration data history of the customer’s standard.

5.1. Transfer and Maintenance of the Farad

The primary reference of the ICL is a group of four NIST-made, 10 pF oil-bath type, fused-silica-
dielectric capacitors, which are maintained in an oil bath at a temperature of 25 °C and are traceable
to the calculable capacitor via another NIST-made, 10 pF air-bath type, fused-silica capacitor used
as the transfer standard. Each of the reference standards, including the transfer standard, has a
known temperature coefficient at its reference temperature, which is measured in terms of a resistive
temperature sensor. Therefore, besides the capacitance value, it is necessary to measure the
resistance of the copper wire wrapped around the individual capacitor, to determine the temperature
of the capacitor during measurements. Thus, a temperature correction that corresponds to the
measured deviation from the reference temperature (or reference resistance value) can be applied to
the reference capacitance value when performing calibrations.

The above procedure for maintaining the farad has been developed and used in the ICL since 1993.
According to the data history, all of the primary references are stable to within 0.02 ppm/year with
an average drift for the group of less than 0.005 ppm/year. Figure 11 is a plot of the average value
of the four primary reference standards in the oil bath of the ICL corrected to their respective
reference temperatures.

The transfer standard is normally situated in the PSL and measured, against a bank of reference
standards in the PSL, weekly to monitor the stability of the transfer standard. It is brought to the ICL
to transfer its value to the primary references in the oil bath of the ICL every two to three months.
Figure 12 is a block diagram illustrating the procedure used to maintain the farad obtained from the
PSL and transfer it to the customer workload.

In the ICL, the primary references are used to calibrate customer’s fused-silica-dielectric capacitors
and to measure ICL’s secondary reference standards, which are two commercial temperature-
controlled air-bath type, fused-silica capacitance standards, one 10 pF and one 100 pF. The exact
temperature coefficients of these standards are unknown, but the temperature variations of each
enclosure during measurement periods of two weeks are within 0.004°C, with a drift rate of less than
0.002 °C/year. Since 1988, a data history of each secondary reference has been maintained by staff
in the ICL with control charts to observe their stabilities. Figures 13 and 14 are examples of the
histories of secondary reference standards #102 and #131 (with control limits at the 95 percent

15


Table 2. Summary of Reference and Check Standards of the Type-2 Bridge

Serial No. Values (pF) Dielectric Control Temperature (°C)
Primary #121 10 Fused-Silica | Oil-Bath 25
Reference #181 10
#183 10
#184 10
Secondary #102 10 Fused-Silica Air-Bath 30
Reference #131 100
#254 10
#230 100
Check #89790 1 Nitrogen Stable 23
Standards #871 10 Laboratory
#493 100 Environment
#517 100
#1717 1000
#1865 1000
#202201 10 000
#NBS1615 10 000 Air

21



Type-12 bridge. Data obtained from these measurements show that the differences in measurements
among these three systems vary in accordance to the nominal values of the capacitors. Figure 19 is
an example illustrating the data from measurements using all three systems. Both the C-Meter and
the DIM are utilized to perform calibrations on mica capacitors at 1 kHz by using the "substitution
method" [12], and the average of the calculated values from both meters is used in the NIST
calibration reports. The range of these two measurements is used to observe the variation in
measurements to check the measurement uncertainty.

5.4 Customer’s Standards

As mentioned previously, standard capacitors received by NIST must be in good working condition,
and the calibration process begins after these are in the ICL for more than 72 hours. After the
calibration process is completed, the final value is compared with the data history of the customer’s
standard to determine if any inconsistencies occurred. In the case where the standard has not been
calibrated by NIST previously, two separate calibrations are performed on the standard at an interval
of several days to check for consistency. The average value of these two measurements is reported.

6. REPORTED VALUE AND MEASUREMENT UNCERTAINTY

The capacitance value along with its uncertainty is stated on the calibration report issued by NIST.
The reported values are determined as discussed in Section 3. General information relevant to the
capacitance measurement is given in the Appendix, which also contains a few Report of Calibration
examples.

The uncertainty given in the Report of Calibration is the expanded uncertainty, U, of the assigned
value, and expressed as :

U=kug, (10)

where 1, is the combined standard uncertainty and & is the coverage factor to be chosen on the basis
of the approximate confidence level desired. The coverage factor used at NIST to calculate U is
generally K = 2, which is consistent with current international practice [5,15] and having a level
of confidence of approximately 95 percent.

The combined standard uncertainty, u, , is the combination of estimated values of two types of
uncertainties, the Type A and Type B standard uncertainties, and is defined as the "RSS" (root-
sum-of-squares) of both types as :

Ug= [u,? +My? 1”, (1)

where u, and u, are Type A and Type B standard uncertainties, respectively.

17


Table 10. Calibration Uncertainties of Conductance Values of Two- and
Three-Terminal Mica-Dielectric Standard Capacitors

Expanded Uncertainties of Conductance (1S)

Frequency (Hz) 66 & 100 400 & 1000 10 000
Nominal Value (uF)
0.001 0.0003 0.0005 0.001
0.002 0.0003 0.0007 0.002
0.005 0.0003 0.0007 0.005
0.01 0.0004 0.0009 0.01
0.02 0.0005 0.003 0.02
0.05 0.0009 0.005 0.1
0.1 0.002 0.015 0.2
0.2 0.005 0.04 0.7
0.5 0.008 0.13 5
1 0.02 0.3 15
(two-terminal only)

30



reference adapter used for HF coaxial capacitor measurements. The capacitance of the reference
adapter was determined by using another adapter with an inner terminal connected to ground.
Measurements were performed by mating the adjustable adapter, which also has a GR900 connector,
with the reference adapter in five positions of 0°, 90°, 180°, 270°, and back to 0°. The average value
of these five measurements is then used as the capacitance value of the reference adapter. Therefore,
calibrations of HF two-terminal coaxial standard capacitors are also performed using five
measurements by connecting the unknown to the reference adapter, as shown in Fig. 6, in the above
five positions. The average value of these measurements is then the capacitance value of the sum
of the unknown capacitor and the reference adapter. The capacitance of the unknown can be
determined by subtracting the known capacitance value of the reference adapter from the measured
value.

4.2 Type-12 Capacitance Measurement System

The Type-12 capacitance bridge is mainly used to measure mica capacitors with banana plugs and
binding post conncctors in two- or threc-terminal configurations from 0.001 pF up to 1 pF. The
basic equations of balance for each configuration at various nominal values given below are
discussed in detail by Chang [6]. Depending on the terminal connections, measurement procedures
are slightly different as described in the following sections.

4.2.1 Two-Terminal Measurements

The two-terminal configuration of mica capacitors is achieved by connecting the low terminal
binding post to the ground terminal of the capacitor and removing its ground terminal-plug.
Therefore, there are only two terminal-plugs, HIGH and LOW, of the capacitor connected to the
bridge, via the HIGH and LOW double insulated binding posts of a metal plate - fixture P2 (sec
Fig. 7). The HIGH terminal of P2 is connected to the bridge corner "D" and the LOW terminal is
connected to the bridge comer "C", via the metal plate and a copper bushing, which is used to mount
the plate to the bridge, as shown in Fig. 7. For rigidity, a piece of rectangular Teflon is mounted on
top of the plate to support the capacitor being measured, and four Bakelite standoffs are mounted
underneath the plate to support the plate on the bridge, also shown in Fig. 7. The procedure for the
two-terminal measurements is to balance the bridge twice, once with the unknown capacitor, Cy
connected to the arm CD of the Type-12 bridge and once with C, disconnected entirely, as shown
in Fig. 8. The two-terminal capacitor can plug into the bridge directly, via the special fixture P2,
without using any cables.

Theoretically, the difference of the balance readings represents the capacitance value of the
unknown, given by:

Cy= (Cm'- Cmo) + (Cy - Go)» (4)

where C,,' is the reading of mica dials when C, is connected to the bridge,
Cyo is the reading of mica dials when C, is disconnected from the bridge,

12


The reported values of capacitance are in terms of the NIST representation of the farad. The
capacitance calibration uncertainties are expanded uncertainties and include allowances for both
Type A and Type B uncertainties in the chain of calibration measurements, and are assigned to the
capacitance values using the coverage factor k=2 [7]. The standard deviation is estimated to be less
than 40 ppm for all nominal values and frequencies except for 1000 pF at 66 Hz where it is estimated
to be 55 ppm.

The uncertainties of the measured conductances also include both Type A and Type B uncertainties
and these are usually of secondary importance. However, it should be mentioned that series
resistance in the connections, leads, etc., to the larger nominal capacitance values at the higher
frequencies can cause large increases in the measured conductance. Such increases are proportional
to the square of the frequency and to the square of the capacitance.

The uncertainties do not include any allowance for long-term instability, temperature hysteresis or
changes due to stresses incurred during shipment.
3. References

{yg R.D. Cutkosky, "New NBS Measurements of the Absolute Farad and Ohm," IEEE Trans. on
Instrumentation and Measurements, Vol. IM 23, No. 4, Dec. 1974.

22] J. Q Shields, R. F. Dziuba, and H. P. Layer, “New Realization of the Ohm and Farad Using
the NBS Calculable Capacitor,” IEEE Trans. Instrum. Meas. Vol. 38, No. 2, pp. 249-251,
April 1989.

[3] W. D. Voelker, “An Improved Capacitance Bridge for Precision Measurements," Bell
System Record, Jan. 1942.

[4] R. D. Cutkosky and L. H. Lee, "Improved Ten-picofarad Fused Silica Dielectric Capacitor,"
Jour. of Res. NBS, Vol. 69C, No. 3, July & Sept. 1965.

[5] J. F. Hersh, "A Close Look at Connection Errors in Capacitance Measurements," General
Radio Experimenter, Vol. 33, No. 7, July 1959.

[6] R.D. Cutkosky, "Capacitance Bridge -- NBS Type 2," National Bureau of Standards Report
7103, March 1961.

[7] B.N. Taylor and C. E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty
of NIST Measurement Results," NIST Tech. Note No. 1297, Jan. 1993.

76


standard deviation of the measured capacitance by an order of magnitude or more.

The reported value of capacitance is in terms of the NIST unit of capacitance maintained with a
group of stable standards [4]. The expanded uncertainties include allowance for both Type A and
Type B uncertainties in the chain of calibration measurements, and are assigned to the capacitance
values using the coverage factor k = 2 [6]. These do not include any uncertainties that may be
associated with long term instability, temperature hysteresis, changes due to stresses incurred during
shipment, and long term drift of the temperature of the enclosure of the air-bath type, fused-silica
capacitors.

Measurements of three-terminal coaxial standard capacitors are not made at frequencies exceeding
1 kHz because of limitations in the present NIST measurement apparatus. Depending upon the
construction and presence of films, the frequency dependence of the capacitors considered here
ranges from 1 ppm to about 10 ppm for a frequency change from 100 Hz to 1 kHz. The principal
factor causing such changes is usually the variation in dielectric constant with frequency of insulating
material located so that it changes the electrostatic field associated with the direct capacitance.
Frequency dependence due to series inductance and resistance can be estimated from manufacturer's
data or by resonance methods [7].

3. References

1] RD. Cutkosky, "New NBS Mcasurcments of the Absolute Farad and Ohm," IEEE Trans. on
Instrumentation and Measurements, Vol. IM 23, No. 4, Dec. 1974.

[2] J.Q. Shields, R. F. Dziuba, and H. P. Layer, “New Realization of the Ohm and Farad Using
the NBS Calculable Capacitor,” IEEE Trans. Instrum. Meas. Vol. 38, No. 2, pp. 249-251,
April 1989.

[3] 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 Instr., Vol. I-7, No. 3 & 4, pp. 253-261, Dec. 1958.

[4] | R.D. Cutkosky and L. H. Lee, "Improved Ten-picofarad Fused Silica Dielectric Capacitor,"
Jour. of Res. NBS, Vol. 69C, No. 3, July & Sept. 1965.

[5] A.M. Thompson, “The Precise Measurement of Small Capacitances," IRE Trans. on Instr.,
Vol. I-7, No. 3 & 4, pp. 245-255, Dec. 1958.

[6] _B.N. Taylor and C. E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty
of NIST Measurement Results," NIST Tech. Note No. 1297, Jan. 1993.

[7] RN. Jones, "A Technique for Extrapolating the 1 kC Values of Secondary Capacitance
Standards to Higher Frequencies," NBS Tech. Note No. 201, Nov. 1963.

56


2.3 Three-Terminal Air-Dielectric Capacitance Standards

A typical example of a three-terminal air-dielectric capacitance standard is the model GR1403 with
nominal values that range from 0.001 pF to 1000 pF. Another example, the model GR1615-P1, has
a nominal value of 10 000 pF. GR1403 capacitors are accepted for calibration and tested at a
laboratory temperature of 23 °C + 1 °C, and at frequencies of 100 Hz, 400 Hz, and 1 kHz, while
GR1615-P1 capacitors are calibrated only at 1 kHz. The total uncertainty of calibration ranges
between 100 ppm and 2000 ppm, according to the nominal value of the capacitor and the nominal
measurement frequency. The calibration uncertainties are described in detail in [6], and summarized
later in this document (section 4.1.3).

2.4 Two-Terminal Capacitance Standards with HF Coaxial Connectors

This category of two-terminal capacitance standards is mainly used for the calibration of high-
frequency bridges and other impedance measuring instruments. These normally have GR900 coaxial
connectors, which have a known reference plane to separate the bridge and the standard capacitor
to improve the performance of the standards up to radio frequency range. Models GR1405 (with
capacitance values from 1 pF to 20 pF), GR1406 (with capacitance values from 50 pF to 1000 pF),
and GR1407 (with capacitance values from 0.001 pF to 0.1 pF) are all accepted for calibration at
a frequency of 1 kHz.

In addition, ICL staff provide calibration services for capacitors with standard terminations such as
the open-circuit-termination models GR900-WO and GR900-W04, at a frequency of 1 kHz.

The total uncertainties of calibration for the above standards range from 75 ppm to 1000 ppm, and
are described in detail in [6], and summarized in a later part of this document (section 4.1.4).

2.5 Two- and Three-Terminal Mica-Dielectric Capacitance Standards with
Binding Post Connectors

The most common examples of this type of capacitance standard are the models GR1409 and
GRS509, which can be measured at frequencies of 66 Hz, 100 Hz, 400 Hz, 1 kHz, and 10 kHz, in two-
or three-terminal configurations, according to the appropriate terminal connections. Capacitance and
conductance values are given in the Report of Calibration for this type of capacitor and represent the
equivalent parallel capacitance and conductance values of the capacitor.

When the capacitor is shipped to NIST, it is important that the customer specifies whether the
capacitor is to be measured in two- or three-terminal configuration.

Measurements of other models of mica-dielectric capacitors with different types of connectors, or
at frequencies higher than 10 kHz, would be considered for calibration as "Special Test" by
prearrangement.


Table 7. Calibration Uncertainties of Fused-Silica- and Nitrogen-Dielectric Standard Capacitors

Expanded Uncertainties (ppm)
Dielectric Type Fused-Silica Nitrogen
Test Type Small Uncertainty Large Uncertainty
Frequency (Hz) 100 400 1000 100 400 1000 | 100, 400, & 1000
Nominal Value (pF)
1 8.5 4S 3.8
10 4 2.5 1.7 6 5 4 25
100 4 2.5 17 6 5 4 25
1000 6 5 4 25

27



ih F Cog

< | UNITED STATES DEPARTMENT OF COMMERCE
: | National Institute of Standards and Technology
¢ | Gaithersburg, Maryland 20899-0001

REPORT OF CALIBRATION
Standard Capacitor
General Radio Company
Type 1404-A
Serial No. ####

Submitted by:

Small Knock Knock
Orientation Angle ‘Tilt Soft Hard Drop
(Maximum) (Range) (Range) (Range) (Range) (Range)
0.74 0.13 0.11 0.13 0.21 0.06

The results of the six tests are used to determine the effects of small mechanical stresses on high-stability,
nitrogen diclectric standard capacitors arc given above, in units of parts per million (ppm). Thcy arc not
included in the expanded uncertainty given in the accompanying report of calibration (NIST SP250
Service ID No. 52140C). Therefore, except for the results of the orientation test, the above values should
be included in the expanded uncertainty of the calibration as the Type B uncertainty, especially if any of
them are larger than 0.5 ppm. Unless the standard is carefully hand-carried back to the user's laboratory
and then left in the upright position at all times, the expanded uncertainty in the other report should be
increased by one half of the sum of all the ranges.

For additional information regarding the calibration of capacitors of this type at NIST, the user should
consult the information sheet(s) enclosed with this report.

Date of Calibration: April 3, 1997

Measurements performed by: For the Director,
Summerfield B. Tillett Barry A. Bell, Group Leader
Engineering Technician Electricity Division

Test Report No.: 811/

Reference:

Date: January 5, 1998

Telephone Contact: 301-975-4221

6s NUST


Measurements of three-terminal coaxial standard capacitors are not made at frequencies exceeding
1 kHz due to limitations in the present NIST measurement apparatus. Depending upon the
construction and presence of films, the frequency dependence of the capacitors considered here
ranges from 1 ppm to about 10 ppm for a frequency change from 100 Hz to 1 kHz. The principal
factor causing such changes is usually the variation in dielectric constant with frequency of insulating
material located so that it changes the electrostatic field associated with the direct capacitance.
Frequency dependence due to series inductance and resistance can be estimated from manufacturer's
data or by resonance methods [7].

For best accuracy in the use of this type of capacitors, corrections for the capacitance values may
be required if the temperature is changed significantly. If it is not possible to apply corrections for
the temperature differences, the magnitude of the errors usually can be estimated from information
supplied by the manufacturer, and the uncertainty in the measurement increased accordingly.

1.5 References

{1] _ R.D. Cutkosky, “New NBS Measurements of the Absolute Farad and Ohm," [EEE Trans. on
Instrumentation and Measurements, Vol. IM 23, No. 4, Dec. 1974.

[2] J. Q. Shields, R. F. Dziuba, and H. P. Layer, “New Realization of the Ohm and Farad Using
the NBS Calculable Capacitor,” IEEE Trans. Instrum. Meas. Vol. 38, No. 2, pp. 249-251,
April 1989.

[3] 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 Instr., Vol. I-7, No. 3 & 4, pp. 253-261, Dec. 1958.

[4] R. D. Cutkosky and L. H. Lee, "Improved Ten-picofarad Fused Silica Dielectric Capacitor,"
Jour. of Res. NBS, Vol. 69C, No. 3, July & Sept. 1965.

[5] A.M. Thompson, "The Precise Measurement of Small Capacitances," IRE Trans. on Instr.,
Vol. I-7, No. 3 & 4, pp. 245-255, Dec. 1958.

[6] B.N. Taylor and C. E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty
of NIST Measurement Results," NIST Tech. Note No. 1297, Jan. 1993.

[7] RN. Jones, "A Technique for Extrapolating the 1 kC Values of Secondary Capacitance
Standards to Higher Frequencies," NBS Tech. Note No. 201, Nov. 1963.

68


ott Feo

Ww,

<

s; ws
ares of

av * Dep,
*

UNITED STATES DEPARTMENT OF COMMERCE
National Institute of Standards and Technology
Gaithersburg, Maryland 20899-0001

REPORT OF CALIBRATION

Standard Capacitor

General Radio Company
Type 1403-D, Serial No. ####

Submitted by:

Expanded

Frequency Capacitance Uncertainty
(iz) (pF) (%)
1000 100.013 100

For additional information regarding the calibration of capacitors of this type at NIST, the user should
consult the information sheet(s) enclosed with this report.

Temperature: 23°C 41°C
Date of Calibration: December 1, 1997

Measurements performed by:

Summerfield B: Tillett
Electricity Division

Test No. 811/

Reference:

Date: January 6, 1998

Telephone Contact: 301-975-4221

69

For the Director,

Barry A. Bell, Group Leader
Electricity Division

Ntsr


Table 4d. NIST Calibration Design for One 100 pF (or 1000 pF) Nitrogen-Dielectric Standard Capacitor

Standards Working Standards One Customer's Capacitor
Used (.GR-1404 without trimmers ) (GR-1404 & ESI SC-1000 )
Serial No. #493 (or #1717) | #517 (or #1865) Cx» (or Cx31)
Nominal
Value 100 (or 1000) pF {100 (or 1000) pF 100 (or 1000) pF
Group of +1 -1
3 Standards -1 +1
-1 tT +1
— “l +H SY
+1 -1 fo
es -1

Table 4e. NIST Calibration Design for Two 100 pF (or 1000 pF) Nitrogen-Dielectric Standard Capacitors

Standards Working Standards Two Customer's Capacitors
Used (.GR-1404 without trimmers ) (GR-1404 & ESI SC-1000 )
Serial No. #493 (or #1717) | #517 (or #1865) Cx22 (or Cx31) Cyy3 (or Cx32)
Nominal
Value 100 (or 1000) pF {100 (or 1000) pF {100 (or 1000) pF {100 (or 1000) pF
Group of +1 -1
4 Standards +1 -1
pd +1 C~<Cit«‘zU;*‘(‘iéSCOS
OO | +1 -1
+1 -1
-1 +1
-1 +1
-1 +1

Table 4f. NIST Calibration Design for Three 100 pF (or 1000 pF) Nitrogen-Dielectric Standard Capacitor

Standards Working Standards Three Customer's Capacitors
Used (GR-1404 without trimmers ) (GR-1404 & ESI SC-1000 )
Serial No. | #493 (or #1717) | #517 (or #1865) Cyn (or Cx31) Cyo3 (or Cx39) Cyn (or Cx33)
Nominal
Value 100 (or 1000) pF {100 (or 1000) pF |100 (or 1000) pF {100 (or 1000) pF _| 100 (or 1000) pF
Group of +1 -1
5 Standards +1 an ee -1
Po 4—~Cti‘R;’!’SS”S”Sd |
-l rs +1
-1 +1 |
+1 -1
oO +1 el
-1 +1
-l +
Zz -I +1

24


NIST Calibration Service for Capacitance Standards at Low Frequencies

Y. May Chang and Summerfield B. Tillett

ABSTRACT - This document describes the capacitance calibration service provided by NIST,
including measurement procedures and systems used to calibrate capacitance standards of nominal
values in the range of 0.001 pF to 1 pF, at frequencies up to 10 kHz. Discussed are the process to
transfer the unit of capacitance from the NIST capacitance primary laboratory, which maintains the
USS. representation of the farad, realized by the calculable capacitor, and the quality controls of
reference standards and check standards in the calibration laboratory. Also included are summaries
of calibration uncertainties of capacitors of various dielectric materials, such as fused-silica,
nitrogen, air, and mica.

1, INTRODUCTION

Most standards laboratories use one or a group of capacitance standards as a reference to maintain
the unit of capacitance and to compare to unknown capacitors. NIST provides a calibration service
for capacitance standards of various dielectric materials, including fused-silica, nitrogen, air, and
mica, and of nominal values in the range between 0.001 pF and 1 pF, at frequencies of (66, 100, 400,
1000, and 10 000) Hz, as shown in Table 1. The primary reference of the NIST Impedance
Calibration Laboratory (ICL) is a group of NIST-made 10 pF oil-bath type, fused-silica-dielectric
capacitors, whose values are traceable to the NIST calculable capacitor. which is used as the U.S.
realization of the farad [1]. ICL staff also maintain a pair of commercial air-bath type, fused-silica-
dielectric capacitors used as secondary reference standards having one 10 pF and one 100 pF
capacitor in each temperature-controlled air bath, and a group of check standards of nominal values
of (1, 10, 100, 1000, and 10 000) pF. The secondary references are calibrated against the primary
reference periodically by using a transformer ratio capacitance measuring system [2], known as the
"Type-2" bridge, at 1:1 and 1:10 ratios. The Type-2 bridge is also utilized to measure the NIST
check standards and customer’s standards with coaxial connectors.

‘There is another system in the ICL, a resistance-ratio-type capacitance measuring system, known as
the "Type-12" bridge. It is mainly used to measure mica-dielectric capacitors with binding post
connectors. The references of the Type-12 bridge are internal dial! capacitors, which have
corrections that are traceable to the reference used with the Type-2 bridge. Commercial impedance
meters also have been utilized to support capacitance calibrations in the ICL after being
characterized in terms of NIST standards.

' The term dial as used in this document refers to the settings or values of adjustable
components used to balance bridges.


Figure la.
Figure 1b.
Figure 2a.
Figure 2b.

Figure 3.
Figure 4.

Figure 5.

Figure 6.
Figure 7.

Figure 8.
Figure 9.
Figure 10.
Figure 11.
Figure 12.
Figure 13.
Figure 14.
Figure 15.
Figure 16.
Figure 17a.
Figure 17b.
Figure 17c.

Figure 18.

Figure 19.

List of Figures

Schematic Diagram of the NIST Type-2 Capacitance Bridge .............. 31
Simplified Circuit Diagram of the NIST Type-2 Capacitance Bridge 32
Schematic Diagram of the NIST Type-12 Capacitance Bridge ............. 33
Simplified Circuit Diagram of the NIST Type-12 Capacitance Bridge

(Generally Showing only the Capacitance Components) ................+ 34
The NIST Type-12 Capacitance Bridge with Conductance Components ..... 35
Block Diagram of Measurement Process and Standards being Used in

the Impedance Calibration Laboratory ........... 000s cece eee cece eee e ee 36
NIST Reference Adapter for Two-Terminal HF Coaxial Connector

CapacitOrs 2. cece eee eee eee ete eect eee n ee nnee 37
Connection of Reference Adapter and HF Coaxial Connector Capacitors ....38
Fixture (P2) Used with the Type-12 Bridge for Two-Terminal

Capacitance Measurements ............ 0 eee e cece eee ence e eens 39
Components of the Type-12 Bridge for Two-Terminal

Capacitance Measurements ........... 00s c eee e cece eee teen eee ee 40
Fixture (P3) Used with the Type-12 Bridge for Three-Terminal

Capacitance Measurements ........... 00 0c cece cece cece e eee e nee e nee 4l
Components of the Type-12 Bridge for Three-Terminal

Capacitance Measurements .......... 00.00 cece cece e nent ence eee 42
Average Values of Four Reference Standards (10 pF Oil-Bath Type)

at Reference Temperature Valucs ......... 00sec cece cece cece eee eens 43
Block Diagram of the Farad Transfer and Calibration Process Using

the Type-2 Bridge 2.00.0... e cece ence eee eee e nee
NIST Reference Standard #102 (10 pF Air-Bath Type)
NIST Reference Standard #131 (100 pF Air-Bath Type)

NIST Check Standard #1865 (1000 pF Nitrogen-Dielectric Capacitor) ...... 47
Data of NIST Check Standard #1865 Measured by Using

the Type-2 Bridge and C-Meter ............. Pee e cece cece eee eceneens 48
Measurement Differences of 1000 pF Customer’s Capacitors between

using the C-Meter and the Type-2 Bridge ................ cee ceeeeeeees 49
Measurement Differences of 100 pF Customer’s Capacitors between

using the C-Meter and the Type-2 Bridge ........... 0... e cece cece eee 50
Measurement Differences of 10 pF Customer’s Capacitors between

using the C-Meter and the Type-2 Bridge ........... 0... cece cece eee e ee 51
Threc-Terminal Measurements of NIST Check Standard #27620

(0.01 uF Mica- Dielectric Capacitor) ....... 0... c eee eee eee eee 52
Data of NIST Check Standard #27620 Measured by Using

the Type-12 Bridge, C-Meter, and DIM ...........0eccceeceeeneeeeees 53

vi


C;' is the reading of air dials when C, is connected to the bridge, and
Co is the reading of air dials when C, is disconnected from the bridge.

The relationship of air dials reading, C, and values of the differential air capacitors C, was given in
Section 3.2, and, according to Eq. (3), C.=2C,.

During measurements when C, is not connected to the bridge, the mica dials are always set to zero,
i.e. Cyyg = 0. Then Eq. (4) becomes:

Cy= Cm + (Cy Cy) (5)

For measurements of two-terminal capacitors of nominal values up to 0.005 pF, only air dials are
needed to balance the bridge without using the mica dials, i.e. C,,' = 0; then Eq. (5) becomes:

Cx= (Gi - Cro) - (0)

Therefore, Eq. (5) is used to calculate the value of two-terminal capacitors with nominal values
larger than 0.005 pF.

4.2.2 Three-Terminal Measurements

The three-terminal configuration for mica dielectric capacitors is to connect the HIGH, LOW, and
GROUND terminal-plugs separately to the Type-12 bridge, via the HIGH, LOW, and GROUND
binding posts of a brass plate - fixture P3 (see Fig. 9). The HIGH terminal of P3 is connected to the
bridge corner "D", the LOW terminal is connected to a switch (Sqc in Fig. 2a), which can be selected
to connect the LOW terminal to either bridge corner "C" or "A", and the GROUND is connected to
the plate. For support, a piece of rectangular brass is constructed underneath the plate. The plate
also has internal leads to make the proper connections between the capacitor binding posts and the
terminals to be plugged onto the bridge, while a brass bushing is used to mount the fixture to the
bridge, also shown in Fig, 9. The procedure for three-terminal measurements is to balance the bridge
twice, first by connecting the unknown C, to the arm CD and then to the arm AD, as shown in
Fig. 10. Since this can be accomplished by changing the positions of the bridge switch, S,c, the
capacitor being calibrated remains connected to P3 during the measurements.

In order to obtain a balance for unknown capacitors of nominal values higher then 0.005 pF,
additional capacitance on the arm CD is required. This is achieved by connecting a capacitance
decade box, Cy, to the arm, CD, also shown in Fig. 10. Therefore, Cy, is always connected to the
bridge in performing three-terminal measurements, and it is set to zero when lower valued capacitors
are being measured. For capacitors with nominal values up to 0.5 pF, Cy is set to a fixed value
during both balances, using it as a dummy capacitor.

For capacitors of nominal values up to 0.005 pF, only air dials are needed to balance the bridge, as

in the two-terminal case. With both the mica dials and the decade box set to zero, the value of the
unknown, C, , can be expressed as:

13


Model GR1408 is a typical commercial air-bath type, fused-silica-dielectric capacitance standard
with nominal values of 10 pF and 100 pF, that is accepted for calibrations at frequencies of 100 Hz,
400 Hz, and 1 kHz. Since the exact temperature coefficients of individual capacitors are unknown,
no correction for temperature is made, however, both the capacitance values of GR1408 capacitors
and the air-bath temperature at the time of measurement are reported. Model AH11A (with nominal
values of 1 pF, 10 pF, and 100 pF) is another type of commercial air-bath, fused-silica capacitor that
is accepted for calibrations at the above three frequencies. However, this model of capacitor is
completely sealed within a temperature-controlled oven, without any possibility to measure the
oven’s internal temperature. Since the actual temperature of the capacitor cannot be measured, it is
not reported. Both the capacitance value of the AH11A capacitor and the temperature display
reading taken at the time of measurement are reported. AH11A capacitors with nominal values other
than (1, 10, and 100) pF are acceptable for calibration as "Special Test".

All oil-bath type, fused-silica capacitors are also acceptable for calibration as "Special Test". These
are measured in the oil bath in the ICL at a temperature of 25 °C + 0.01 °C.

2.2 Nitrogen-Dielectric Capacitance Standards

Nitrogen-dielectric capacitors are the most common standard capacitors at the 10 pF, 100 pF, and
1000 pF levels. Models GR1404 and ESI SC1000, commercially-made capacitors with parallel-
plates, are the typical capacitors that are accepted for calibrations at frequencies of 100 Hz, 400 Hz,
and 1 kHz.

There are two different types of measurements performed on these capacitors according to the
desired uncertainty level of the calibration. The "large-uncertainty" calibration is performed at
laboratory conditions with an uncertainty of 25 ppm*. The "small-uncertainty" calibration process
monitors the capacitor for a longer period of time under a physically stable condition with an
uncertainty as low as 4 ppm [6].

Also, a supplementary test should be considered for new standards whose properties with regard to
transportation and mechanical shocks are not known. This series of physical tests determines the
relative effect on the capacitance resulting from various impacts and changes in orientation [7].
These tests which simulate the conditions during shipping of the capacitor, normally are performed
prior to the small- uncertainty measurement to estimate the variation of the capacitance values during
shipment. The maximum variations in capacitance values for each type of physical test are reported.
Requests for calibrations at the small-uncertainty level without performing the physical tests are also
accepted. NIST issues separate calibration reports for each of the above measurements.

3 The term uncertainty as used in this document refers to the relative standard uncertainty
when the unit is expressed in ppm [5].


10.

11.

12.

13.

14.

15.

"NIST Calibration Services Users Guide," Natl. Inst. Stand. Tech. Special Publication 250,
1991 edition, U. S. Government Printing Office, Washington, DC 20402.

B.N. Taylor and C. E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty
of NIST Measurement Results," NIST Technical Note 1297, 1994 Ed., September 1994.

Y. M. Chang, "Error Analysis and Calibration Uncertainty of Capacitance Standards at
NIST," NIST Technical Note (to be published)

C. R. Levy, "Testing to Quantify the Effects of Handling of Gas Dielectric Standard
Capacitors," NBS Technical Note 1161, October 1982.

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.
Instrum. vol I-7, nos. 3 & 4, pp. 253-261, December 1958.

W. D. Voelker, "An Improved Capacitance Bridge for Precision Measurements," Bell Labs
Record, vol. 20, pp. 133-137, January 1942.

H. T. Wilhelm, "The Type-12 Capacitance Bridge," Bell Labs Memorandum,
MM 70-4735-9, Case 70052-213, File 37954-15, May 1970.

Y. M. Chang, "NIST Capacitance Measurement Assurance Program (MAP),"
Measurement Science Conference, Anaheim, CA, January 1993.

Y. M. Chang and S. B. Tillett, "Calibration Procedures for Inductance Standards Using
a Commercial Impedance Meter as a Comparator," NISTIR 4466, November 1990.

J. M. Cameron, "The Use of the Method of Least Squares in Calibration," NBSIR 74-587,
September 1974.

W. G. Eicke and J. M. Cameron, "Designs for Surveillance of the Volt Maintained by a
Small Group of Saturated Standard Cells," NBS Technical Note 430, October 1967.

International Bureau of Weights and Measures (BIPM) Working Group on the Statement
of Uncertainties, Metrologia, vol. 17, pp. 73-74, 1981.

19


NIST Special Publication 250-47

NIST MEASUREMENT SERVICES:

NIST Calibration Service for Capacitance
Standards at Low Frequencies

Y. May Chang and Summerfield B. Tillett

Electricity Division

Electronics and Electrical Engineering Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899-0001

April 1998

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U.S. Department of Commerce
William M. Daley, Secretary

Technology Administration
Gary R. Bachula, Acting Under Secretary for Technology

National Institute of Standards and Technology
Raymond G. Kammer, Director


Figure 10. Components of the Type-12 Bridge for Three-Terminal Capacitance Measurements.

42


capacitors, and the value of the reference standard.

In addition, the Type-2 bridge has a conductance balance circuit, also described in [8], to measure
the conductance component of the unknown capacitor. As shown in Fig. la, the conductance
balance is controlled by a set of four dials and a multiplier switch to provide a total conductance
from 10° pS to 1 pS. There is another switch which reverses the sign of the conductance component
to allow the measured components to have greater or less conductance than the internal capacitors.
Figure 1b is a simplified circuit diagram showing the Type-2 bridge, where C, is the reference
capacitor, C,, is the unknown capacitor to be calibrated, Cy is the sum of internal dial capacitors,
G, is the conductance of the internal capacitors, G, is the settings of the conductance dials, and M
is ‘the multiplier switch for the conductance readings. The conductance balance control provides an
in-phase balance to compensate for the difference in the loss components of the reference, internal,

and unknown capacitors in order to obtain a precise comparison of the unknown capacitor and the
reference capacitor. The uncertainty of the conductance dial readings, which depends on the ac
characteristics of a fixed metal film resistor, is very large, about 1%, but the conductance
measurement of unknown capacitors using the Type-2 bridge is not reported for NIST calibrations.

3.2 Type-12 Capacitance Bridge

The NIST Type-12 bridge is a resistance-ratio capacitance measurement system using internal
standards as the reference and is used to calibrate customer’s mica capacitors. This type of bridge
was originally designed by Bell Laboratories in 1942 [9] to provide precision measurements of
capacitance up to 1.11 WF and conductance up to 1000 pS. Later on, an improved unity-ratio
admittance bridge, known as the Type-12 capacitance bridge was developed, also by Bell
Laboratories, with a capacitance divider to measure low capacitance values and multi-range, direct-
reading conductance standards. Figure 2a is the schematic of the Type-12 bridge. Specifications of
bridge components and internal standards, and operation procedures of the Type-12 bridge were
described in detail by Wimhelm [10]. As illustrated in Fig. 2a, the internal standards consist of two
mica capacitance standards (represented schematically as one standard, C,,), three air differential
capacitance standards (represented as C,), and two differential conductance (resistance) standards
(represented as Gg). Each standard is adjustable with ten steps to be interpreted as dial readings. The
dials of C,, cover from (0.1 to 1) pF and from (0.01 to 0.1) uF. The dials of C, cover from (0.001

to 0.01) pF, (0.0001 to 0.001) pF, and (0.00001 to 0.0001) pF, plus a continuously adjustable
capacitor providing a capacitance range of (11 + 0.5) pF. A mica capacitor of 0.005 yF (not shown
in Fig. 2a) is used as a transfer standard and is measured using the Type-2 bridge, and then used to
calibrate the 0.01 uF steps of Cy, (the lowest step of mica dials) and of C, (the highest step of air
dials) of the Type-12 bridge. All other steps of mica and air dials are calibrated from the 0.01 uF
steps to be used as reference, in terms of dial corrections. The dials of Gg, from (10 to 100) pS and
from (100 to 1000) pS, plus a continuously adjustable dial with range of (-1 to 11) uS, are calibrated
by resistance standards. During calibration measurements, both capacitance and conductance dials
are used simultaneously to obtain a balance, and both capacitance and conductance values of the
customer’s capacitor are reported.

Figure 2b is a simplified diagram of the Type-12 bridge showing only the components which need
to be considered for capacitance measurements. C, is the unknown capacitor to be measured, which

6


2.6 Capacitance Measurement Assurance Program (C-MAP)

This is a recently re-established measurement service implemented using a commercial meter (based
on fused-silica reference capacitors) as a transport standard to measure capacitance standards with
nominal values of 100 pF and 1000 pF, at a frequency of 1 kHz. Besides determining the values of
customer’s capacitance standards, the C-MAP is uscd to evaluate the customer’s capacitance
measurement system. The C-MAP has the advantage that the customer’s standards remain in their
laboratory to reduce the down-time due to the absence of the standards, and to avoid any changes
of values due to transportation. The Type-A uncertainties of the C-MAP are usually lower than those
of the regular calibration because the changes of values in the customer’s capacitors due to shipping
and hysteresis effects from variation of environmental conditions do not enter into the experiment.
The NIST C-MAP service is described in detail by Chang [3].

3. DESCRIPTION OF MEASUREMENT SYSTEMS

The NIST capacitance calibration facility consists of two major measurement systems. One is the
Type-2 bridge, which is mainly used to calibrate high-quality standards (such as nitrogen-, air-, and
fused-silica-dielectric capacitors) with shielded terminals, and of nominal values up to 10 000 pF
at frequencies of 100 Hz, 400 Hz, and 1 kHz. The other is the Type-12 bridge, which is a resistance-
ratio capacitance measuring system for calibration of mica-dielectric capacitors with exposed
terminals, and having nominal values from 0.001 pF to 1 pF, at frequencies of (66, 100, 400, 1000,
and 10 000) Hz. Recently, two commercial impedance meters that have been carefully characterized
using NIST standards are also used to support capacitance calibrations.

3.1 Type-2 Capacitance Bridge

The NIST Type-2 bridge is a transformer-ratio capacitance bridge using both external capacitors and
internal capacitors to perform measurements of unknown capacitors. Figure 1a is the schematic
diagram of the Type-2 bridge. Construction of the bridge components and bridge operation
procedures were described in detail by Cutkosky [2]. As illustrated in Fig. 1a, the internal capacitors
are a set of eight fixed-cylindrical air capacitors with values ranging from 10° pF to 100 pF to
provide a total capacitance up to 111 pF. These capacitors are connected to the voltage taps of the
transformer via linear switches to form the equivalent of a decade capacitance of each capacitor by
using dial (or switch) settings. During calibrations, an unknown capacitor is compared to a reference
capacitance standard whose value is well defined, and the dial settings of the internal capacitors are
adjusted to obtain a balance of the bridge. The reference capacitor and the unknown capacitor are
connected to the bridge terminals at ratios of 1:1, 10:1, or 1:10, according to their nominal values.
One of the internal capacitors (of nominal value of 1 pF) is constructed as a temperature-
compensated capacitor, as described in detail in [8]. Other internal capacitors can be calibrated
against the 1 pF unit immediately after it is compared to a reference capacitance standard. The
capacitance value of the unknown is determined from the dial readings and corrections of the internal


é *s | UNITED STATES DEPARTMENT OF COMMERCE
t + | National institute of Standards and Technology
*, & | Gaithersburg, Maryland 20899-0001

GENERAL INFORMATION ON FUSED-SILICA-DIELECTRIC CAPACITORS

1. Representation of the Unit of Capacitance

Asa result of new absolute measurements of the farad in terms of the units of length and time, the
legal unit of capacitance was established at NIST/NBS in 1975 [1], and re-established in 1989 [2].
The reported values of capacitance since that time reflect the values assigned to NIST standards used
for the maintenance of the legal unit. Since 1989, the difference between the NIST unit, which
includes an allowance for possible drift, and the farad is believed to be no greater than +0.1 ppm.

2. Fused-Silica Dielectric Standard Capacitors

Three-terminal standard capacitors of fused-silica dielectric are calibrated with a NIST transformer
bridge [3] using NIST fused-silica 10-pF capacitors [4] as reference standards. Capacitance is
measured by intercomparison with the reference standards in a least squares design.

The measured capacitances are the mean of the results of several measurements of direct capacitance
with the capacitor connected to the NIST transformer bridge as a two-terminal-pair admittance [5].
If the terminals of the capacitor are not two-terminal-pair, connections with negligible impedance
are made to make them so. All capacitors must be in the calibration laboratory for 72 hours or more
before measurements are performed.

The temperature of an air-bath type fused-silica capacitor is obtained by means of a platinum
resistance thermometer placed in the well of the bath. The Type B uncertainty of the measured
temperatures is estimated to be 0.002 °C.. The bridge used in measuring the resistance of the
thermometer has a limiting resolution of 0.0001 °C.

The average ambient temperature of the laboratory is 23 °C + 1 °C with hourly variations of about
0.1°C. The variation of the ambient temperature may affect the temperature of the air-bath, which
determines the value of a capacitor. Therefore, for best accuracy in the use of this type of
capacitors, corrections for the capacitance value are required if the temperature of the air-bath is
changed significantly. If it is not possible to apply corrections for the temperature differences, the
magnitude of the errors usually can be estimated from information supplied by the manufacturer, and
the uncertainty in the measurement increased accordingly.

The limiting resolution at 1000 Hz of the NIST transformer bridge and detector is 0.02 ppm. This
is larger than the change of capacitance corresponding to the limiting resolution of the temperature
measurement, which is equivalent in capacitance to 0.0012 ppm. Therefore, if the standard deviation
of the average temperature is expressed as a change in capacitance, then it may be smaller than the

5s NisT


UNKNOWN CAPACITOR

CONNECTOR - UNKNOWN

CONNECTOR - REFERENCE ADAPTER

Figure 6. Connection of Reference Adapter and HF Coaxial Connector Capacitors

38


Table 6. Summary of Check Standards of the Type-12 Bridge

Serial No. Nominal Model
Value GR1409
Primary Secondary
Set Set (uF) Type

#3068 #1812 0.001 F
#547 #11741 0.002 G
#496 #11758 0.005 K
#27620 #10541 0.01 L
#1509 #11180 0.02 M
#3687 #11525 0.05 R
#5149 #12223 0.1 T
#7632 #5248 0.2 U
#3938 #3858 0.5 x
#4214 #3390 1 Y

26



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Table 5. NIST Large Uncertainty Calibration Design for Nitrogen- and Air-Dielectric

Standard Capacitors

Standards Working Customer's Working Customer's
Used Standards Capacitors Standard Capacitor
(Nominal Value | 1 pF to 10000 pF | 1 pF to 10 000 pF 1 pF 0.1 pF
Ratio 1: : 10
+1 -1 +0.1 -1
-1 +1 -0.1 +1

25



of these differences is given as the result of this test.

KNOCK SOFT TEST - In this test the capacitor is struck by a rubber tipped pendulum. ‘he torce
generated by the pendulum is roughly equivalent to that generated by a mild wrist motion blow of
the human hand. The capacitor is placed in the usual upright position and its capacitance measured.
Then the pendulum is rotated 45 degrees and allowed to strike the capacitor's top edge once, after
which its capacitance is measured. This is repeated for the remaining sides and the four corners.
The successive differences between the measured capacitances are calculated. The range of these
differences is given as the result of this test.

KNOCK HARD TEST - This test is identical to the Knock Soft Test except that a plastic tipped
pendulum rotated 15 degrees is used.

DROP TEST - The capacitor is placed in the upright position and its capacitance measured. Then
the bottom of a side is raised 3.8 centimeters and allowed to drop freely. The capacitance is re-
measured after this drop. This is repeated for the remaining sides. The successive differences are
calculated and the range of these differences is given as the result of this test.

64


2. DESCRIPTION OF SERVICE

NIST offers a calibration service for capacitance standards in a wide range of capacitance values and
geometrical configurations in the audio-frequency range. Three-terminal fused-silica-, nitrogen-, and
air-dielectric standard capacitors with GR874’ coaxial connectors and with nominal values of (1,
10, 100, 1000, and 10 000) pF can be calibrated at frequencies of 100 Hz, 400 Hz, and 1 kHz. Two-
and three-terminal mica-dielectric capacitors with exposed binding-post connectors, in the range
from 0.001 pF to 1 pF, can be calibrated at frequencies up to 10 kHz. Two-terminal air- and mica-
dielectric capacitors with high-frequency (HF) GR900 coaxial connectors, including the GR900
terminations, are calibrated only at 1 kHz. Table 1 contains a summary of the commonly known
capacitance standards that are accepted for calibration with the stated configurations at the specified
frequencies. Requests for capacitance types other than those described in Table 1 are handled under
the category of "Special Test", which requires prearrangement with NIST personnel. Additionally,
NIST provides a MAP transfer service, known as the Capacitance Measurement Assurance Program
(C-MAP) for capacitance standards at the 100 pF and 1000 pF levels and at a frequency of 1 kHz
[3]. In the ICL, all capacitors except fused-silica-dielectric capacitors, are measured at an ambient
temperature of 23°C + 1 °C and relative humidity levels of less than 50 percent.

It is the customer’s responsibility to ensure that the capacitance standard received by NIST is in good
working condition, i.e. having tight connectors and good solder joints. The capacitor will be
returned to the customer without calibration if it is found to be defective, or its connector has been
modified, unless prior arrangements are made.

When a Report of Calibration is issued to the customer, general information on each type of standard
capacitor is also enclosed. Examples of the report and the information of various types of capacitors
submitted for calibration are included in the Appendix.

Detailed information on calibration services at NIST is described in the NIST Special Publication
250 (SP250) [4]. The cost of services is listed in the Fee Schedule which is the Appendix of SP250
and is updated periodically.

2.1 Fused-Silica-Diclectric Capacitance Standards

Due to the magnitude of their temperature coefficient, approximately 10 ppm/°C, fused-silica-
dielectric standard capacitors are designed for use in temperature controlled ovens, either air baths
or oil baths. Unless the air-bath type capacitors are submitted in temperature-controlled ovens with
temperature sensors having a resolution of 0.001 °C, the ICL staff will provide, where possible,
temperature measurements using standard platinum resistance thermometers taken at the time of the
measured capacitance value.

? Commercial connectors or standards are identified in this technical note only to specify
that these are being used to perform measurements. It is not to be taken as a recommendation or
endorsement by NIST, nor does it imply that these are necessarily the best available connectors
and standards for the purpose.


confidence level) and enclosure temperatures, dating from 1990. These secondary references are
utilized to calibrate the check standards which are used as working standards to calibrate customer’s
capacitance standards with dielectrics other than fused-silica, such as nitrogen, air, and mica, also
shown in Fig. 12.

5.2 Type-2 System and Capacitance Meter

The ICL staff also maintain control charts for each check standard given in Table 2 to assure that
both the Type-2 system and the check standards are in statistical control. After the check standards
have been measured against the secondary reference, the data are examined to ensure that they are
within control limits. Then the check standards are used as the working standards to calibrate
customer’s capacitors, as indicated in Fig. 12. Figure 15 is an example illustrating the data history
and control limits of one of the check standards of the Type-2 bridge.

The C-Meter is characterized by using the check standards of the Type-2 system to observe its
stability and to determine measurement differences from the Type-2 bridge. Results from several
years of collecting data depict that the differences in measurements between using the Type-2 bridge
and the C-Meter to measure all reference and check standards are within +0.4 ppm at the 100 pF and
1000 pF levels and +0.7 ppm at the 10 pF level. Figure 16 is an example showing the data from
measurements performed by both systems on the same check standard (#1865, shown in Fig. 15).
Since 1993, the C-Meter is also used to measure customer’s nitrogen-dielectric capacitors on the
same date when the capacitors are being calibrated using the Type-2 bridge. Figures 17a, 17b, and
17c are plots of the measurement differences of customer’s capacitors between using the C-Meter
and the Type-2 bridge in the 1000 pF, 100 pF, and 10 pF levels, respectively. Therefore, the C-Meter
has been utilized to perform calibrations on capacitors with an uncertainty higher than 25 ppm at a
frequency of 1 kHz. Together with the Type-2 bridge, it is also used for lower uncertainty
calibrations to monitor the customer’s nitrogen-dielectric capacitors at 1 kHz for a period of several
days to ensure that the measured variations of the capacitors are within the assigned limits. If the
difference of measurements between using the C- Meter and the Type-2 bridge on the same day is
within +0.4 ppm for the 100 pF and 1000 pF levels and within +0.7 ppm for the 10 pF level, the
average of all measurements are reported. The measurement differences are taken into account for
the calibration uncertainties assigned.

5.3 Type-12 System, Capacitance Meter, and Digital Impedance Meter

The Type-12 bridge uses its internal capacitors as the reference in performing measurements. Thus,
the ICL staff maintain a database with control charts of two sets of check standards, which are mica
capacitors of nominal values from 0.001 1F to 1 y:F, to assure that the Type-12 system is in a state
of statistical control. Table 6 is a list of NIST check standards of the Type-12 system. Figure 18 is
an example illustrating the data and control limits of one of the check standards (#27620).

Since 1993, both the C-Meter and the DIM have been characterized at 1 kHz using the check
standards of the Type-12 bridge to observe their stabilities and measurement differences from the

16


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‘Stares of

REPORT OF CALIBRATION
Standard Capacitor

General Radio Company
Type 1404-A, Serial No. ####

Submitted by:
Expanded
Frequency Temperature Capacitance Uncertainty
(Bz) cc) (PF) (pm)
1000 22.34 999.9998 4

The expanded uncertainty stated above is valid only if the results of the tests used to determine the effects
of small mechanical stresses are of the order of a few tenths of a ppm. These test results are given in the
accompanying report.

For additional information regarding the calibration of capacitors of this type at NIST, the user should
consult the information sheet(s) enclosed with this report.

Date of Calibration: April 3, 1997

Measurements performed by: For the Director,
Sumerfield B. Tillett Barry A. Bell, Group Leader
Electricity Division Electricity Division

Test No. 811/

Reference:

Date: January 6, 1998

Telephone Contact: 301-975-4221

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33


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Figure 2b. Simplified Circuit Diagram of the NIST Type-12 Capacitance Bridge.
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Table 3. NIST Calibration Design for Fused-Silica-Dielectric Standard Capacitors

Standards Primary Secondary Reference Customer's Capacitors
Used Reference (GR-1408 and AH11A)
Serial No. #121 #102 #131 Cxor Cx Cyr

Nominal
Value 10 pF 10 pF 100 pF 1 pF 10 pF 100 pF
Group A +0.1 _ -0.1
] +0.1 -1
P +01 | -l
-0.1 +0.1
-0.1 +1
-0.1 +1
Group B 41
+1 -1
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-1 +1
Group C 4H _ 0.1 _
+1 -0.1
+0.1 -0.1
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DESCRIPTION OF TESTS USED TO DETERMINE THE EFFECT OF SMALL
MECHANICAL STRESSES ON HIGH STABILITY, NITROGEN-DIELECTRIC
STANDARD CAPACITORS

The high stability, nitrogen-dielectric standard capacitors with coaxial connectors and having
nominal values of (10, 100 and 1000) pF are not susceptible to changes due to the stresses of normal
handling and proper shipping. However, experience has shown that there are a significant number
that exhibit unusual changes in value when mechanical stresses are applied. These changes are not
usually detected during calibration measurements because most operators will handle the capacitors
very carefully. Careful handling during measurement, while appropriate for the actual determination
of capacitance value, will not result in the detection of changes in capacitance which may occur
when the capacitor is handled roughly or during shipment. Six tests have been devised to determine
a capacitor's response to some small stresses which any capacitor may be subjected to.

These tests are named the Orientation Test, Small Angle Test, Tilt Test, Knock Soft Test, Knock
Hard Test, and Drop Test. These names are nomenclatures rather than accurate descriptors of the
tests. They are performed in the order given since some of the stresses in the first tests do affect the
later tests.

The following is a brief description of each test's procedure and data reduction. Except for the
orientation and small angle tests, data reduction is the same for all tests.

ORJENTATION TEST - The capacitance is measured with the capacitor in its usual upright position,
lying on each of its four sides, and back to the original upright position. The five differences
between the capacitances of the six orientations are calculated. Then the maximum difference is
given as the result for this test. The original purpose of this test was to determine whether it could
be used to predict the results of the other tests or not. It has becn shown that it is not correlated with
the other tests except for the Small Angle Test.

SMALL ANGLE TEST - The capacitor is placed on a horizontal surface and its capacitance
measured. Then a side is elevated three degrees above horizontal and the capacitance measured.
This is repeated for the remaining three sides. The changes in capacitance resulting from the
elevation of each side from the horizontal are calculated. The range of these changes is given as the
result of this test.

TILT TEST - The capacitor is placed in the usual upright position and its capacitance measured.
Then one side of the capacitor is rotated to the horizontal position and returned to the upright
position and its capacitance re-measured. This is repeated for the remaining sides and for the top.
The five successive differences between the six measured capacitances are calculated. The range

ae NisT


5.4 Customer’s Standards ....... 6... eee e cece eee eee e ence een eee eens 17

6. REPORTED VALUE AND MEASUREMENT UNCERTAINTY .........--55 7
7.
8.
TABLES
FIGURES
APPENDIX
Al. — General Information on Fused-Silica-Dielectric Standard Capacitors ........... 55
A2. Typical REPORT OF CALIBRATION for Fused-Silica-Dielectric

Standard Capacitors 0.00... c ccc cece een ence eee nen n eee
A3. — General Information on Nitrogen-Dielectric Standard Capacitors
A4. Typical REPORT OF CALIBRATION for Nitrogen-Dielectric

Standard Capacitors 0.6.6... e eee nccne eer eee n teen e ene 61
A5. _ Description of Tests used to Determine the Effect of Small Mechanical Stress

on High Stability, Nitrogen-Dielectric Standard capacitors...............2+055 63
A6. Typical REPORT OF CALIBRATION for Test Results of the Effect of

Small Mechanical Stress on Nitrogen-Dielectric Standard Capacitors an
A7. — General Information on Three-Terminal Standard Capacitors ...............5.
A8. Typical REPORT OF CALIBRATION for Three-Terminal

Standard Capacitors
A9. — General Information on Two-Terminal Standard Capacitors with

Precision Coaxial Connectors .... 2... 22.22.20 0 71
Al0. Typical REPORT OF CALIBRATION for Two-Terminal

Standard Capacitors with Precision Coaxial Connectors ..............-000e0- B
All. Gencral Information on Mica-Diclectric Standard Capacitors with

Binding Post Connectors ......... 0.20 c eee e cece eee eee eee e eee ees 75
Al2. Typical REPORT OF CALIBRATION for Mica-Dielectric Standard Capacitors

with Binding Post Connectors... 6... cece cee eect teen ees 77

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GENERAL INFORMATION ON THREE-TERMINAL STANDARD CAPACITORS

1. Representation of the Unit of Capacitance

As aresult of new absolute measurements of the farad in terms of the units of length and time, the
legal unit of capacitance was established at NIST/NBS in 1975 [1], and re-established in 1989 [2].
The reported values of capacitance since that time reflect the values assigned to NIST standards used
for the maintenance of the legal unit. Since 1989, the difference between the NIST unit, which
includes an allowance for possible drift, and the farad is believed to be no greater than +0.1 ppm.

2. Three-Terminal Standard Capacitors

Three-terminal standard capacitors of nitrogen and air dielectric are calibrated with a NIST
transformer bridge [3] using NIST fused-silica 10-pF capacitors [4] as reference standards.
Capacitance is measured by direct comparison with stable working standards, which are calibrated
in terms of the reference standards. This is done each time they are used.

The measured capacitances are the results of two or more measurements of direct capacitance with
the capacitor connected to the NIST transformer bridge as a two-terminal-pair admittance [5). If the
terminals of the capacitor are not two-terminal-pair, connections with negligible impedance are made
to make them so. All capacitors must be in the calibration laboratory for 72 hours or more before
measurements are performed.

The average ambient temperature of the laboratory is 23 °C + 1°C, with hourly variations of about
0.1 °C, which is the temperature values given in the Report of Calibration. Measurements are not
made if the ambient laboratory temperature differed from the set-point by more than 1°C during the
last 24 hours. The standard deviation of the capacitance measurements is also calculated to assure
it is within limits of the estimated population standard deviation. The relative humidity in the
laboratory varies but does not exceed 50%.

The reported value of capacitance is in terms of the NIST unit of capacitance maintained with a
group of stable standards [4]. The expanded uncertainties include allowance for both Type A and
Type B uncertainties in the chain of calibration measurements, and are assigned to the capacitance
values using the coverage factor k = 2 [6]. These do not include any uncertainties that may be
associated with long term instability, temperature hysteresis, changes due to stresses incurred during
shipment. In addition, no allowance is made for the variations in the capacitance of unsealed air
dielectric capacitors due to changes in humidity since the magnitude of these variations is dependent
upon the surface conditions of the plates.

° NUsT


3.3.2 Digital Impedance Meter

This type of Digital Impedance Meter employed in the ICL (hereafter referred to as DIM) uses
standard ac resistors as internal references and measures standard capacitors, inductors, and ac
resistors, over a frequency range from 12 Hz to 1 MHz. The DIM does not have the precision
achievable with the C-Meter, but operates at multiple frequencies. It is also characterized by using
it to monitor the NIST mica-dielectric check standard capacitors at various frequencies. The DIM
is used to calibrate customer’s mica-dielectric capacitors at 1 kHz, and will be used at other
frequencies after the database of check standards is established at other frequencies.

The process of characterization of a meter is to use the meter to monitor the NIST check standards
for a period of three years or more, and to compare the data with those obtained from the NIST Type-
12 bridge. During the calibration of customer’s standards, both the customer’s standard and the
NIST check standard of the identical nominal value are measured using the meter. A predicted value
of the NIST check standard is obtained by using the linear regression analysis performed on its
database of the Type-12 measurements . The measured value of the customer’s standard is adjusted
by using the difference of the predicted value and the measured value of the NIST check standard.
Detailed description of such process is given in [12], as the "substitution method".

The DIM is also utilized to perform "Special Test" measurements, especially in responding to
requests for capacitance measurements at frequencies not specified in SP250.

4. CALIBRATION PROCEDURES

4.1 Type-2 Capacitance Measurement System

As mentioned previously, the Type-2 system, with its internal capacitors, is used to compare
customer’s standards with shielded terminals to external NIST reference standards. Due to the
unknown temperature coefficients of the internal bridge capacitors, it is necessary to calibrate them
immediately prior to performing the measurements in order to obtain the uncertainty required. The
procedure used to calibrate the internal dial capacitors of the Type-2 bridge and the equations used
to calculate the dial corrections are discussed in detail by Chang [6]. The Type-2 bridge is also
employed to transfer the unit of capacitance from the Primary Standards Laboratory (PSL) to achieve
traceability of the unit of the farad.

The process of using the Type-2 bridge to measure customer’s standards is based on use of
redundant measurement designs in calibration, as described by Cameron [13]. The procedure is to
perform a sequence of measurements in accordance with the calibration design to redundantly
intercompare a number of reference standards and unknowns. The solution to the design provides
true values for each of the unknowns based on the known value of the reference standard, and the
design also provides an estimate of the Type-A measurement uncertainty. Table 2 is a list of NIST
reference standards and the check standards of the Type-2 system.


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REPORT OF CALIBRATION

Standard Capacitor
General Radio Company
Type 1408-A, Serial No. ####
Enclosure Serial No. ####

Submitted by:

Average Range of Type-A Expanded
Frequency Temperature Temperature Capacitance Uncertainty Uncertainty
(Hz) coe co (F) (opm) (mpm)
1000 23.1234 0.1234 10.0012346 0.02 25

The reported temperatures are based upon ten or more measurements. The capacitance is based upon five
or more intercomparisons with similar capacitors. The Type-A uncertainty given above is calculated from
measured values, indicating the capacitor's behavior. The expanded uncertainty given above is the
combined standard uncertainty expanded by a coverage factor of k = 2.

For additional information regarding the calibration of capacitors of this type at NIST, the user should
consult the information sheet(s) enclosed with this report.

Period of Calibration: December 1, 1997 to December 15, 1997

Measurements performed by: For the Director,
Summerfield B. Tillett Barry A. Bell, Group Leader
Engineering Technician Electricity Division

Test Report No.: 811/

Reference:

Date: January 6, 1998

Telephone Contact: 301-975-4221

1 NIST


For capacitors having nominal values of 100 pF and 1000 pF, a two-step process is performed. First,
the secondary reference #131 is used to measure the NIST check standards #493 and #517 (or #1717
and #1865) of nominal values of 100 pF (or 1000 pF) at a ratio of 1:1 (or 10:1), as shown in Tables
4b and 4c. Then, the check standards are used as working standards to calibrate simultaneously one,
two, or three customer’s standards of the identical nominal values at a ratio of 1:1, as shown in
Tables 4d, 4e, and 4f, respectively. Likewise, capacitors of nominal values of 1 pF and 10 000 pF
can be calibrated by using the 10 pF working standard at 1:10 ratio and the 1000 pF working
standard at 10:1 ratio, respectively. Since 1994, the C-Meter has been used to perform additional
measurements of customer’s nitrogen dielectric capacitors at 1 kHz for a period of several days to
observe their stabilities. The average value of the Type-2 bridge and all of the C-Meter
measurements is reported.

In the case of large uncertainty (> 25 ppm) calibrations, a simpler measurement procedure is used.
After the check standards have been measured, the unknown is compared to a check standard of the
same nominal value twice by interchanging their positions in the bridge at the 1:1 ratio, as shown
in Table 5. Since 1993, the C-Meter has also been included as part of the large uncertainty
calibration at 1 kHz by monitoring the capacitance standards for a period of 30 minutes at five-
minute intervals. The average value of these measurements is the reported value and the standard
deviation is used to determine the variability of the capacitor.

The C-Meter is also utilized to perform measurements of capacitors subjected to physical tests, if
requested. Such tests are performed at 1 kHz and only the changes of capacitance values during the
tests are reported.

4.1.3 Air-Dielectric Capacitors

Since the total calibration uncertainties of this type of capacitor are between 100 ppm and 2000 ppm,
the measurement procedure given in Table 5 is used for those capacitors of nominal values equal to
and greater than 0.1 pF, either at a 1:1 ratio or a 1:10 ratio. For air-dielectric capacitors of lower
values (0.01 pF and 0.001 pF), these are calibrated directly against the internal capacitors of the
Type-2 bridge by connecting them to the +1 and -1 output taps of the transformer and the detector.
The C-Meter is also utilized to measure all air-dielectric capacitors at 1 kHz, in the same manner as
in the large uncertainty calibration above.

4.1.4 Two-Terminal Capacitors with HF Coaxial Connectors
Since NIST only provides calibration services on this type of capacitor at a frequency of 1 kHz, the
C-Meter is used to perform measurements on all capacitors with HF coaxial connectors, including
the terminations.
In order to perform three-terminal measurements on the two-terminal HF coaxial capacitors, a

precision adapter was constructed by mounting a GR900 connector to a fixture such that the
capacitance value can be defined and measured. Figure 5 illustrates the construction of the NIST

ll


TABLE of CONTENTS

DESCRIPTION OF SERVICE ......... 000 cee cece eee eee e eee een eneee

2.1 Fused-Silica-Dielectric Capacitance Standards .

2.2 Nitrogen-Dielectric Capacitance Standards. .......

2.3 Three-Terminal Air-Dielectric Capacitance Standards ......

2.4 Two-Terminal Capacitance Standards with HF Coaxial Connectors ....

2.5 Two- and Three-Terminal Mica-Dielectric Capacitance Standards with
Binding Post Connectors

2.6 Capacitance Measurement Assurance Program (C-MAP) ....

DESCRIPTION OF MEASUREMENT SYSTEMS .............0. 00 e ee eee 5
3.1 Type-2 Capacitance Bridge ..
3.2 Type-12 Capacitance Bridge .
3.3 Impedance Meters .......
3.3.1 Capacitance Meter ....
3.3.2 Digital Impedance Meter

CoO nN

CALIBRATION PROCEDURES .
4.1 Type-2 Capacitance Measurement System 9
4.1.1 Fused-Silica-Dielectric Capacitors . .10

4.1.2 Nitrogen-Dielectric Capacitors ..
4.1.3 Air-Dielectric Capacitors

4.1.4 Two-Terminal Capacitors with HF Coaxial Connectors ............. ll
4.2 Type-12 Capacitance Measurement System ............. 00sec cece eee ee 12
4.2.1 Two-Terminal Measurements .............- 12
4.2.2 Three-Terminal Measurements 13

QUALITY CONTROL IN THE IMPEDANCE CALIBRATION
LABORATORY 2.0.0.2... cece ccc eee ec nee eee ete e teen eens
5.1. Transfer and Maintenance of the Farad
5.2 Type-2 System and Capacitance Meter ..
5.3 Type-12 System, Capacitance Meter, and Digital Impedance Meter

iii


Ex

Figure 1b. Simplified Circuit Diagram of the NIST Type-2 Capacitance Bridge.

32


Table 1. Summary of Standard Capacitors Acceptable for Calibrations

Manufacturer Norminal Values Terminal Configuration Frequency (Hz)
and Model

General Radio Co.*

GR1403 0.001 pF to 1000 pF 3-T Coaxial 100 400 & 1000

GR1404 10pF to 1000pF 3-T Coaxial 100 400 & 1000

GR1405 1lpF to 20 pF 2-T Coaxial 1000

GR1406 50 pF to 1000 pF 2-T Coaxial 1000

GR1407 0.001pF to 0.1 pF 2-T Coaxial 1000

GR1408 10 pF and 100 pF 3-T Coaxial 100 400 & 1000

GR1409 0.001 pF to 1 uF 2-T & 3-T Binding Post | 66 100 400 1000 & 10000

GRS509 0.001 pF to 1 pF 2-T Binding Post 66 100 400 1000 & 10000
GRI615-P1 10 000 pF 3-T Coaxial 1000
GR900-WO 0.172 pF 2-T HF Coaxial 1000

(open-circuit termination)

GR900-WO4 2.67 pF 2-T HF Coaxial 1000
(open-circuit termination)

Electro-Scientific
Industries Inc.

ESI SC1000 1000 pF 3-T Coaxial 100 400 & 1000

Andeen-Hagerling Inc.

AHIIA lpF to 100pF 3-T BNC 100 400 & 1000

* or one of its successor companies.

20



National Institute of Standards and Technology Special Publication 250-47
Natl. Inst. Stand. Technol. Spec. Publ. 250-47, 79 pages (Apr. 1998)
CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON: 1998

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325


Primary Standards Lab

Impedance Calibration Lab

Reference Bank
4x 10 pF Oil Bath
Fused Silica Cap Stds

Transfer Standard

- 10pFAirBah |-----~-------
Fused Silica Cap Stds
Primary Reference Customer's
4x 10 pF Oil Bath Fused Silica
Fused Silica Cap Stds Cap Stds
Secondary References
2x 10 pF & 2x 100 pF Air Bath
Fused Silica Cap Stds
Check Standards Cust '
2x 100 pF & 2 x 1000 pF roger econ
. . Air Dielectric, and
Nitrogen Dielectric HF Coaxial Cap Stds
Cap Stds

Figure 12. Block Diagram of the Farad Transfer and Calibration Process
Using the Type-2 Bridge.



Table 8. Calibration Uncertainties of Air-Dielectric and Two-Terminal HF Coaxial Connector

Standard Capacitors
Expanded Uncertainties (ppm)

Configuration Three-Terminal Coaxial Two-Terminal HF Coaxial

Dielectric Type Air Air and Mica
Frequency (Hz) 100 400 & 1000 Frequency (Hz) 1000

Nominal Value (pF) Nominal Value (pF)
0.001 2000 1 840
0.01 1500 200 2 420
0.1 230 100 5 200
1 to 1000 100 100 10 100
10 000 150 20 75
50 to 1000 60
5000 to 10 000 65
(Open-Circuit Terminations)

0.172 1000
2.67 450

28


NIST REFERENCE ADAPTER

TO HIGH TERMINAL

TO DETECTOR

Figure 5. NIST Reference Adapter for Two-Terminal HF Coaxial Connector Capacitors.

37


Table 4a. NIST Calibration Design for 10 pF Nitrogen-Dielectric Standard Capacitors

Standards Secondary Check Standard Customer's Capacitor
Used Reference (GR-1404 without trimmers) (GR-1404 )
Serial No. #102 #871 Cx
Nominal
Value 10 pF 10 pF 10 pF
Group D +1 -l
+1 ee -1
+1 -1
-1 ns!
-1 +1
-1 +1
Table 4b. NIST Calibration Design for 100 pF Nitrogen-Dielectric Check Standards
Standards Secondary Check Standard Check Standard
Used Reference (GR-1404 without trimmers) | (GR-1404 without trimmers)
Serial No. #131 #493 #517
Nominal
Value 100 pF 100 pF 100 pF
Group E +1 -1
+1 _ -1
+1 -1
-1 +1
‘1 - +1
-1 +1
Table 4c. NIST Calibration Design for 1000 pF Nitrogen-Dielectric Check Standards
Standards Secondary Check Standard Check Standard
Used Reference (GR-1404 without trimmers) | (GR-1404 without trimmers)
Serial No. #131 #1717 #1865
Nominal
Value 100 pF 1000 pF 1000 pF
Group F +1 -0.1
+1 -0.1
+0.1 -0.1 |
-1 +0.1
“1 +0.1
-0.1 +0.1

23


is connected to arm AD and/or arm CD, according to the measurement configurations. Rj and Ry
are resistors with a ratio of 1:1, C,, is the value of C,,, and C, and C, are the effective capacitance
from the differential air capacitors, C, , on arms AD and CD, respectively, such that:

C,+C,=C (aconstant) . qd)

In addition, each dial of C, is arranged so that the dial reading indicates the difference of the
effective capacitance between arms AD and CD, plus the constant capacitance C, such that:

Cr= (Cy-Cg) +C, (2)
where C, is the value of C, corresponding to the dial reading, r.
By substituting Eq. (1) into Eq. (2), it becomes:

C,=2C,. (3)
Let Cy), Cy, and C,; represent the three dials of C, for 0.001 yF/step, 0.0001 yF/step, and 0.00001
pF/step, respectively. Using C,; as an example, the total capacitance of this dial is equal to 50 pF
(C), and contains a set of four capacitors of 5 pF, 10 pF, 15 pF, and 20 pF. When the dial readings
of Cy3, 73, are increased from 0 to 1, 1 to 2, .......soe , and 9 to 10, these capacitors are switched back
and forth individually between arms CD and AD to achieve the relationship in Eq. (1). The
capacitance values corresponding to the dial readings are obtained in accordance with Eq. (3) and

to the following procedure to switch these capacitors:

At dial reading r; = 0, all four capacitors are on arm CD, then
C3 = 50 pF and C,3 = 0; therefore, C,; = 0.

At dial reading r; = 1, the 5 pF capacitor is on arm AD, the other three are on arm CD, then
C3 = 45 pF and C,3 = 5 pF; therefore, C,3 = 10 pF.

At dial reading r = 2, the 10 pF capacitor is on arm AD, the other three are on arm CD, then
C3 = 40 pF and C,3 = 10 pF; therefore, C,, = 20 pF.

At dial reading r, = 10, all four capacitors are on arm AD, and then
C3 = 0 and C,3 = 50 pF; therefore, C,, = 100 pF.

The final value of C, is the sum of the values of all three air dial capacitors, C,1, Cy, and C,3.
Similar to the internal air capacitors, the conductance standard of the Type-12 bridge is a differential-

7


Type B uncertainties in the chain of measurements, and are assigned to the capacitance values using
the coverage factor k = 2 [6]. These do not include any uncertainties that may be associated with
long term instability, temperature hysteresis, and changes due to stresses incurred during shipment.

Measurements of three-terminal coaxial standard capacitors are not made at frequencies exceeding
1 kHz because of limitations in the present NIST measurement apparatus. Depending upon the
construction and presence of films, the frequency dependence of the capacitors considered here
ranges from 1 ppm to about 10 ppm for a frequency change from 100 Hz to 1 kHz. The principal
factor causing such changes is usually the variation in dielectric constant with frequency of insulating
material located so that it changes the electrostatic field associated with the direct capacitance.
Frequency dependence due to series inductance and resistance can be estimated from manufacturer's
data or by resonance methods [7].

For best accuracy in the use of this type of capacitors, corrections for the capacitance values may
be required if the temperature is changed significantly. If it is not possible to apply corrections for
the temperature differences, the magnitude of the errors usually can be estimated from information
supplied by the manufacturer, and the uncertainty in the measurement increased accordingly.

1.5 References

{1] | RD. Cutkosky, "New NBS Measurements of the Absolute Farad and Ohm," IEEE Trans. on
Instrumentation and Measurements, Vol. IM 23, No. 4, Dec. 1974.

(2] J. Q. Shields, R. F. Dziuba, and H. P. Layer, “New Realization of the Ohm and Farad Using
the NBS Calculable Capacitor,” IEEE Trans. Instrum. Meas. Vol. 38, No. 2, pp. 249-251,
April 1989.

[3] 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 Instr., Vol. I-7, No. 3 & 4, pp. 253-261, Dec. 1958.

[4] R. D. Cutkosky and L. H. Lee, "Improved Ten-picofarad Fused Silica Dielectric Capacitor,"
Jour. of Res. NBS, Vol. 69C, No. 3, July & Sept. 1965.

[5] | A.M. Thompson, "The Precise Measurement of Small Capacitances," IRE Trans. on Instr.,
Vol. I-7, No. 3 & 4, pp. 245-255, Dec. 1958.

{6]  B.N. Taylor and C. E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty
of NIST Measurement Results," NIST Tech. Note No. 1297, Jan. 1993.

(7) RN. Jones, “A Technique for Extrapolating the 1 kC Values of Secondary Capacitance
Standards to Higher Frequencies," NBS Tech. Note No. 201, Nov. 1963.

60


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The calibration design used in the ICL is similar to the experimental designs for groups of 3, 4, and
5 standards, described by Eicke and Cameron [14]. For example, the design for a group of 3
standards is to perform intercomparison of these standards six times by connecting them to the
positive (+) and negative (—) output terminals of the Type-2 bridge (see Fig. 1b), thus performing
a left-right balance in order to eliminate certain systematic errors. Table 3 illustrates the experimental
design for three different groups (A, B, and C) of 3 standards, which are used in the ICL as the three
measurement sets for the calibration of fused-silica standard capacitors of nominals of 1 pF, 10 pF,
and 100 pF, respectively. In Table 3, each row represents one measurement, and the symbols of +1,
-1, +0.1, and -0.1 under each capacitor refer to the connections of one end of the capacitor to the
respective output terminals of the Type-2 bridge, to obtain ratios of 1:1 and 10:1, as shown in
Fig. 1b. In each group, there are six measurements to be performed by using the primary reference
to compare and determine the values of the secondary reference and one customer’s standard, or two
customer’s standards if it is requested. Figure 4 is a block diagram to illustrate the measurement
process and the standards being used in the ICL to transfer the capacitance value from the primary
reference (in the oil bath) to the customer’s standards of various nominal values and dielectrics.

4.1.1 Fused-Silica-Dielectric Capacitors

Customer’s fused-silica capacitors, as well as ICL secondary reference standards (nominal values
of 10 pF and 100 pF), are calibrated, at ratios of 1:1 and 10:1, respectively, directly against the ICL
primary reference, maintained in the oil bath. The procedure also requires recording the values of
the resistive temperature sensors of oil-bath type capacitors and the temperatures of air-bath type
capacitors. The value used for the primary reference is corrected from the predicted value at
reference temperature (in terms of resistance value), using the known temperature coefficient and
the resistive sensor value at the time of measurement. Calibration results of air-bath capacitors are
not temperature corrected and, hence, reflect both capacitance and temperature variations.

Since the temperature coefficients of customer’s air-bath type, fused-silica capacitors are unknown,
it is necessary to perform multiple measurements over a two- to three-week period to compare the
variations in capacitance to measurements of similar capacitors to determine if the capacitor is
behaving normally. Both the average capacitance value and the average temperature are reported.

The calibration design for fused-silica capacitors in the ICL is that used for groups of 3 standards
(see Table 3), which requires three standards to perform one set of measurements. Therefore, the
secondary reference is used if only one unknown fused-silica capacitor is being calibrated.

4.1.2 Nitrogen-Dielectric Capacitors

Measurement process and standards used for the calibration of nitrogen-dielectric capacitors are
illustrated in Fig. 4, Tables 4a to 4f, and discussed in the following.

Customer’s nitrogen-dielectric capacitors of nominal value of 10 pF are calibrated directly with the
secondary reference #102 and the NIST check standard #871 at 1:1 ratio, as shown in Table 4a.

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