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NIST Calibration Service for

Capacitance Standards at

Low Frequencies

NIST

Special

Publication

250^7

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00

J57

). 250-47

998

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'At Boulder, CO 80303. ^Some elements at Boulder, CO.
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

U.S. Department of Commerce

William M. Daley, Secretary

Technology Administration

Gary R. Bachula, Acting Under Secretary for Technology

April 1998

National Institute of Standards and Technology

Raymond G. Kammer, Director
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, Waslnington, DC 20402-9325
TABLE of CONTENTS

page

LIST of TABLES v

LIST of FIGURES vi

ABSTRACT 1

1. INTRODUCTION 1

2. DESCRIPTION OF SERVICE 2

2.1 Fused-Silica-Dielectric Capacitance Standards 2

2.2 Nitrogen-Dielectric Capacitance Standards 3

2.3 Three-Terminal Air-Dielectric Capacitance Standards 4

2.4 Two-Terminal Capacitance Standards with HF Coaxial Connectors 4

2.5 Two- and Three-Terminal Mica-Dielectric Capacitance Standards with

Binding Post Connectors 4

2.6 Capacitance Measurement Assurance Program (C-MAP) 5

3. DESCRIPTION OF MEASUREMENT SYSTEMS 5

3.1 Type-2 Capacitance Bridge 5

3.2 Type- 12 Capacitance Bridge 6

3.3 Impedance Meters 8

3.3.1 Capacitance Meter 8

3.3.2 Digital Impedance Meter ' 9

4. CALIBRATION PROCEDURES 9

4. 1 Type-2 Capacitance Measurement System 9

4.1.1 Fused-Silica-Dielectric Capacitors 10

4.1.2 Nitrogen-Dielectric Capacitors 10

4.1.3 Air-Dielectric Capacitors 11

4.1.4 Two-Terminal Capacitors with HF Coaxial Connectors 11

4.2 Type- 12 Capacitance Measurement System 12

4.2.1 Two-Terminal Measurements 12

4.2.2 Three-Terminal Measurements 13

5. QUALITY CONTROL IN THE IMPEDANCE CALIBRATION

LABORATORY 15

5.1. Transfer and Maintenance of the Farad 15

5.2 Type-2 System and Capacitance Meter 16

5.3 Type- 12 System, Capacitance Meter, and Digital Impedance Meter 16

iii
5.4 Customer's Standards 17

6. REPORTED VALUE AND MEASUREMENT UNCERTAINTY 17

7. CONCLUSION 18

8. REFERENCES 18

TABLES 20

FIGURES 31

APPENDIX 54

Al. General Information on Fused-Silica-Dielectric Standard Capacitors 55

A2. Typical REPORT OF CALIBRATION for Fused-Silica-Dielectric

Standard Capacitors 57

A3. General Information on Nitrogen-Dielectric Standard Capacitors 59

A4. Typical REPORT OF CALIBRATION for Nitrogen-Dielectric

Standard Capacitors 61

A5. Description of Tests used to Determine the Effect of Small Mechanical Stress on High Stability, Nitrogen-Dielectric Standard capacitors 63

A6. Typical REPORT OF CALIBRATION for Test Results of the Effect of

Small Mechanical Stress on Nitrogen-Dielectric Standard Capacitors 65

A7. General Information on Three-Terminal Standard Capacitors 67

A8. Typical REPORT OF CALIBRATION for Three-Terminal

Standard Capacitors 69

A9. General Information on Two-Terminal Standard Capacitors with

Precision Coaxial Connectors 71

AlO. Typical REPORT OF CALIBRATION for Two-Terminal

Standard Capacitors with Precision Coaxial Connectors 73

All. General Information on Mica-Dielectric Standard Capacitors with

Binding Post Connectors 75

Al 2. Typical REPORT OF CALIBRATION for Mica-Dielectric Standard Capacitors

with Binding Post Connectors 77

iv
List of Tables

Table 1 . Summary of Standard Capacitors Acceptable for Calibrations 20

Table 2. Summary of Reference and Check Standards of the Type-2 Bridge 21

Table 3. NIST Calibration Design for Fused-Silica-Dielectric Standard Capacitors ... 22

Table 4a. NIST Calibration Design for 10 pF Nitrogen-Dielectric Standard Capacitors . . 23

Table 4b. NIST Calibration Design for 100 pF Nitrogen-Dielectric Check Standards ... 23

Table 4c. NIST Calibration Design for 1000 pF Nitrogen-Dielectric Check Standards ... 23

Table 4d. NIST Calibration Design for One 1 00 pF (or 1 000 pF)

Nitrogen-Dielectric Standard Capacitors 24

Table 4e. NIST Calibration Design for Two 1 00 pF (or 1 000 pF)

Nitrogen-Dielectric Standard Capacitors 24

Table 4f NIST Calibration Design for Three 1 00 pF (or 1 000 pF)

Nitrogen-Dielectric Standard Capacitors 24

Table 5. NIST Large Uncertainty Calibration Design for Nitrogenand Air-Dielectric Standard Capacitors 25

Table 6. Summary of Check Standards of the Type- 1 2 Bridge 26

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

Standard Capacitors 27

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

HF Coaxial Connector Standard Capacitors 28

Table 9. Calibration Uncertainties of Capacitance Values of Two- and

Three-Terminal Mica- Dielectric Standard Capacitors 29

Table 10. Calibration Uncertainties of Conductance Values of Two- and

Three-Terminal Mica- Dielectric Standard Capacitors 30

V
List of Figures

Figure la. Schematic Diagram of the NIST Type-2 Capacitance Bridge 31

Figure lb. Simplified Circuit Diagram of the NIST Type-2 Capacitance Bridge 32

Figure 2a. Schematic Diagram of the NIST Type- 12 Capacitance Bridge 33

Figure 2b. Simplified Circuit Diagram of the NIST Type- 12 Capacitance Bridge

(Generally Showing only the Capacitance Components) 34

Figure 3. The NIST Type- 12 Capacitance Bridge with Conductance Components 35

Figure 4. Block Diagram of Measurement Process and Standards being Used in

the Impedance Calibration Laboratory 36

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

Capacitors 37

Figure 6. Connection of Reference Adapter and HF Coaxial Connector Capacitors .... 38

Figure 7. Fixture (P2) Used with the Type- 12 Bridge for Two-Terminal

Capacitance Measurements 39

Figure 8. Components of the Type- 12 Bridge for Two-Terminal

Capacitance Measurements 40

Figure 9. Fixture (P3) Used with the Type- 12 Bridge for Three-Terminal

Capacitance Measurements 41

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

Capacitance Measurements 42

Figure 1 1 . Average Values of Four Reference Standards (1 0 pF Oil-Bath Type)

at Reference Temperature Values 43

Figure 12. Block Diagram of the Farad Transfer and Calibration Process Using

the Type-2 Bridge 44

Figure 1 3 . NIST Reference Standard # 1 02 ( 1 0 pF Air-Bath Type) 45

Figure 14. NIST Reference Standard # 1 3 1 ( 1 00 pF Air-Bath Type) 46

Figure 15. NIST Check Standard #1865 (1000 pF Nitrogen-Dielectric Capacitor) 47

Figure 16. Data of NIST Check Standard #1 865 Measured by Using

the Type-2 Bridge and C-Meter 48

Figure 17a. Measurement Differences of 1000 pF Customer's Capacitors between

using the C-Meter and the Type-2 Bridge 49

Figure 17b. Measurement Differences of 100 pF Customer's Capacitors between

using the C-Meter and the Type-2 Bridge 50

Figure 17c. Measurement Differences of 10 pF Customer's Capacitors between

using the C-Meter and the Type-2 Bridge 51

Figure 18. Three-Terminal Measurements of NIST Check Standard #27620

(0.01 |iF Mica- Dielectric Capacitor) 52

Figure 19. Data of NIST Check Standard #27620 Measured by Using

the Type- 12 Bridge, C-Meter, and DIM 53

vi
NIST Calibration Service for Capacitance Standards at Low Frequencies

Y. May Chang and Summerfield B. Tillett

ABSTRACT - This document describes the capacitance caUbration 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 jiF, 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

U.S. 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 ofnominal values in the range between 0.001 pF and 1 |liF, 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, fiised-silicadielectric 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.

1
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 cormectors 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. Twoand three-terminal mica-dielectric capacitors with exposed binding-post connectors, in the range

from 0.001 pF to 1 |iF, can be calibrated at frequencies up to 10 kHz. Two-terminal air- and micadielectric 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 persormel. 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 cormector 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-Dielectric Capacitance Standards

Due to the magnitude of their temperature coefficient, approximately 1 0 ppm/ °C, fused-silicadielectric 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.

2
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 AHl 1 A (with nominal

values of 1 pF, 1 0 pF, and 1 00 pF) is another type of commercial air-bath, fiised-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 AH1 1 A capacitor and the temperature display

reading taken at the time of measurement are reported. AHl 1 A 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 1 0 pF, 1 00 pF, and

1000 pF levels. Models GR1404 and ESI SCI 000, commercially-made capacitors with parallelplates, are the typical capacitors that are accepted for calibrations at frequencies of 1 00 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.

^ The term uncertainty as used in this document refers to the relative standard uncertainty

when the unit is expressed in ppm [5].

3
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 1 00 Hz, 400 Hz, and 1 kHz, while

GR1615-P1 capacitors are calibrated only at 1 kHz. The total uncertainty of calibration ranges

between 1 00 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 highfrequency 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 |liF to 0.1 |iF) 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-WO4, 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

GR509, which can be measured at frequencies of 66 Hz, 100 Hz, 400 Hz, 1 kHz, and 10 kHz, in twoor 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

preaiTangement.

4
2.6 Capacitance Measurement Assurance Program (C-MAP)

This is a recently re-established meaisurement 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 used 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

ofvalues 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 resistanceratio capacitance measuring system for calibration of mica-dielectric capacitors with exposed

terminals, and having nominal values from 0.001 |liF to 1 jliF, 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 la 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. la, 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

, 1 0: 1, or 1 : 1 0, according to their nominal values.

One of the internal capacitors (of nominal value of 1 pF) is constructed as a temperaturecompensated 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 ofthe unknown is determined froni the dial readings and corrections ofthe intemal

5
capacitors, and the value of the reference standard.

In addition, the Type-2 bridge has a conductance balEince 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"^ \xS to 1 |iS. 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 lb is a simplified circuit diagram showing the Type-2 bridge, where Cg is the reference

capacitor, C^^ is the unknown capacitor to be calibrated, C^j is the sum of internal dial capacitors,

is the conductance of the internal capacitors, Gj. 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 \iF and conductance up to 1000 |iS. 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, directreading 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 Gs). Each standard is adjustable with ten steps to be interpreted as dial readings. The

dials of cover from (0.1 to 1) |iF and from (0.01 to 0.1) |xF. The dials of cover from (0.001

to 0.01) |iF, (0.0001 to 0.001) ^F, and (0.00001 to 0.0001) |iF, plus a continuously adjustable

capacitor providing a capacitance range of (1 1 ± 0.5) pF. A mica capacitor of 0.005 |iF (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 |aF steps of (the lowest step of mica dials) and of (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 |iF

steps to be used as reference, in terms of dial corrections. The dials of Gs, from (10 to 100) [iS and

from (100 to 1000) ^iS, plus a continuously adjustable dial with range of (-1 to 1 1) |iS, 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
is connected to arm AD and/or arm CD, according to the measurement configurations. Rj and R2

are resistors with a ratio of 1 : 1, is the value of C^, and and are the effective capacitance

from the differential air capacitors, , on arms AD and CD, respectively, such that:

C^ + C^^C (a constant). (1)

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-(q-Q) + C, (2)

where is the value of C^ corresponding to the dial reading, r.

By substituting Eq. (1) into Eq. (2), it becomes:

Cr-2C,. (3)

Let Ca„ Ca2, and C^a represent the three dials of C^ for 0.001 |aF/step, 0.0001 |iF/step, and 0.00001

laF/step, respectively. Using C^a 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, 1 0 pF, 1 5 pF, and 20 pF. When the dial readings

of Ca3, r^, are increased from 0 to 1, 1 to 2, , 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 = 0, all four capacitors are on arm CD, then ^

^a3 ^ ^' therefore, C^^ ^ ^•

At dial reading /-j = 1 , the 5 pF capacitor is on arm AD, the other three are on arm CD, then ^ 45 pF and C^^ = 5 pF; therefore, Cj.3 = 10 pF,

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

At dial reading r^= 10, all four capacitors are on arm AD, and then

Q3 = 0 and Ca3 = 50 pF; therefore, " 1^0 pF.

The final value of Cj. is the sum of the values of all three air dial capacitors, Cj.j, Cj.2, and C^^-

Similar to the internal air capacitors, the conductance standard ofthe Type- 12 bridge is a differential7
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, R^, (see Fig. 2a), which serves as a

range shifter. Kg, so that the reading of the conductance standard is divided by 1, 10, 100, 1000, or 10 000. Gj^ is the conductance component of the unknown capacitor, C^^. Specifications and

operating procedures of conductance standard of the Type- 12 bridge were described in detail by

Wimheim [10]. As shown in Fig. 2b, {G^l K^) and ( G^, / A^g ) are effective conductances on arm

AD and arm CD, respectively, and the quantity ( + G^, ) 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 a constant.

The Type- 12 system is used mainly to measure two- and three-terminal mica capacitors with

binding-post connectors from 0.001 |iF to 1 |iF. 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, fiised-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).

8
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 fi-om the NIST Type12 bridge. During the calibration of customer's standards, both the customer's standard and the

NIST check standard ofthe 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 ofcapacitance 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.

9
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. lb), 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. lb. 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, fiised-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.

10
For capacitors having nominal values of 100 pF and 1000 pF, a two-step process is performed. First,

the secondary reference #1 3 1 is used to measure the NIST check standards #493 and #5 1 7 (or # 1 7 1

7

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 cahbrate 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 fiveminute 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 ofthis 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

11
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°, 1 80°, 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 connectors in two- or three-terminal configurations from 0.001 |iF up to 1 |iF. 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 cormecting 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 (see

Fig. 7). The HIGH terminal of P2 is connected to the bridge comer "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

undemeath 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,

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:

(Cm* - Cmo) + (Q' - Qo) ' (4)

where is the reading of mica dials when C,^ is connected to the bridge,

C^Q is the reading of mica dials when Cj, is disconnected from the bridge.

12
is the reading of air dials when is connected to the bridge, and

CfQ is the reading of air dials when is disconnected from the bridge.

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

During measurements when is not connected to the bridge, the mica dials are always set to zero,

i.e. Cj^o ^ ^- Then Eq. (4) becomes:

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

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

larger than 0.005 fiF.

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 comer "D", the LOW terminal is connected to a switch (S^c in Fig. 2a), which can be selected

to connect the LOW terminal to either bridge comer "C" or "A", and the GROUND is connected to the plate. For support, a piece of rectangular brass is constmcted 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 Cj^ to the arm CD and then to the arm AD, as shovm 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 |iF,

additional capacitance on the arm CD is required. This is achieved by connecting a capacitance

decade box, C^,, to the arm, CD, also shown in Fig. 10. Therefore, C^, 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 fiF, Cj, is set to a fixed value

during both balances, using it as a dummy capacitor.

For capacitors of nominal values up to 0.005 ^iF, 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, , can be expressed as:

Q ~ ^m' + (^r ^rO) • (5)

(6)

4.2.2 Three-Terminal Measurements

13
C^ = (l/2) (Q2-Cri), (7)

where C^2 the reading of air dials when is connected to the arm CD of the bridge, and

is the reading of air dials when is connected to the arm AD of the bridge.

For capacitors of nominal values from higher than 0.005 |liF to 0.5 |aF, a certain setting of the decade

box, Cj,, 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, Cy^ , can be expressed as:

Cx = (l/2)C^ + (l/4)(Cr2-Qi), (8)

where 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 |iF, a different measurement procedure is used.

Due to the limitation of internal mica capacitors of the Type- 12 bridge, four balances, instead oftwo,

are needed and the decade box Cj, is set to either zero or the nominal value of the unknown. Using

Cj^ = 1 |iF as an example, the four steps of connections and settings are :

1) Connect C,^ to arm AD, set mica dials to zero, and Cj, to 1 |iF. Use air dials to obtain

balance, and record the reading as C^^.

2) Disconnect C^, and leave C]^ at 1 |liF. Use both air and mica dials to obtain balance, and

record the readings as and C^^t), respectively.

3) Connect C^ to arm CD, and set Cj^ to zero. Use both air and mica dials to obtain balance,

and record the readings as C^^ and C^^,, respectively.

4) Disconnect C^^, set both mica dials and Cj, to zero. Use air dials to obtain balance, and

record the reading as C^^.

After the above four measurements and data recordings are completed, the value of the unknown,

Cy^ , can be calculated from:

= (1/2) (C^b + C^c) + (1/2) [(C,b - Cra) + (C.^ - Qj)] • (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- 1 2 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, Cj^, 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 Cy^ and capacitance dial readings with Gy^ and conductance dial

readings, respectively.

14
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 ex£imining 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-silicadielectric 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 1 1 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 temperaturecontrolled 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 oftwo 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
confidence level) and enclosure temperatures, dating from 1990. These secondary references are

utilized to calibrate the check standards which are used as woridng standards to calibrate customer's

capacitance standards with dielectrics other than flised-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 fi^om 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 1 7a, 1 7b, and

1 7c are plots of the measurement differences of customer's capacitors between using the C-Meter

and the Type-2 bridge in the 1 000 pF, 1 00 pF, and 1 0 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 \x¥ to 1 |iF, 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
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 1 9 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=ku^, (10)

where is the combined standard uncertainty and k 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" (rootsum-of-squares) of both types as :

u,= [u^'+u^'r, (11)

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

17
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[ nsi? + nsjf , (12)

where and Sj 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 intemal 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. Highquality commercial instruments, such as detectors and function generators, are now used in the Type2 system to improve its resolution. The use 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
4. "NIST Calibration Services Users Guide," Natl. Inst. Stand. Tech. Special Publication 250,

1991 edition, U. S. Government Printing Office, Washington, DC 20402.

5. 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.

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

7. C. R. Levy, "Testing to Quantify the Effects of Handling of Gas Dielectric Standard

Capacitors," NBS Technical Note 1161, October 1982.

8. 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 1-7, nos. 3 & 4, pp. 253-261, December 1958.

9. W. D. Voelker, "An Improved Capacitance Bridge for Precision Measurements," Bell Labs

Record, vol. 20, pp. 133-137, January 1942.

10. H. T. Wilhelm, "The Type-12 Capacitance Bridge," Bell Labs Memorandum,

MM 70-4735-9, Case 70052-213, File 37954-15, May 1970.

11. Y. M. Chang, "NIST Capacitance Measurement Assurance Program (MAP),"

Measurement Science Conference, Anaheim, CA, January 1993.

12. Y. M. Chang and S. B. Tillett, "Calibration Procedures for Inductance Standards Using

a Commercial Impedance Meter as a Comparator," NISTIR 4466, November 1990.

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

September 1974.

14. 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.

15. International Bureau of Weights and Measures (BIPM) Working Group on the Statement

of Uncertainties, Metrologia, vol. 17, pp. 73-74, 1981.

19
Table 1 . Summary of Standard Capacitors Acceptable for Calibrations

Manufacturer ana iviouei

Norminal Values Terminal Configuration Frequency (Hz)

General Radio Co.*

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

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

GR1405 1 pF to 20 pF 2-T Coaxial 1000

GR1406 50 pF to 1000 pF 2-T Coaxial 1000

GR1407 0.001 |iiF to 0.1 ^iF 2-T Coaxial 1000

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

GR1409 0.001 jaF to 1 fiF 2-T & 3-T Binding Post 66 100 400 1000 & 10 000

GR509 0.001 |uF to 1 ^F 2-T Binding Post 66 100 400 1000 & 10 000

GR1615-P1 10 000 pF 3-T Coaxial 1000

GR900-WO 0.172 pF

(open-circuit termination)

2-T HF Coaxial 1000

GR900-WO4 2.67 pF

(open-circuit termination)

2-T HF Coaxial 1000

Electro-Scientific

Industries Inc.

ESI SCI 000 1000 pF 3-T Coaxial 100 400 & 1000

Andeen-Hagerling Inc.

AHllA 1 pF to 100 pF 3-T BNC 100 400 & 1000

* or one of its successor companies.

20
Table 2. Summary of Reference and Check Standards of the Type-2 Bridge

Serial No. Values (pF) Dielectric Control Temperature (°C)

Pnmary #121 10 Fused-Silica Oil-Bath 25

Reference #181 10

#183 10

#184 10

Secondary #102 10 Fused-Silica Air-Bath 30

Reierence #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
Table 3. NIST Calibration Design for Fused-Silica-Dielectric Standard Capacitors

Standards

Used

Primary

Reference

Secondary Reference Customer's Capacitors

(GR-1408 and AHllA)

Serial No. #121 #102 #131 Cxoi Cxii Cx21

Nominal

Value lU pr 10 pF 100 pF 1 pF 10 pF 100 pF

Group A +0.1 -0.1

+0.1 -1

+0.1 -1

-0.1 +0.1

-0.1 +1

-0.1 +1

Group B +1 -1

+1 -1

+1 -1

-1 +1

-1 +1

-1 +1

Group C +1 -0.1

+1 -0.1

+0.1 -0.1

-1 +0.1

-1 +0.1

-0.1 +0.1

22
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 )

Sena! No. #102 #871 Cxi2

Nominal

Value 10 pF 10 pF 10 pF

Group D +1 -1 +1 -1 +1 -1

-1 +1

-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
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) Cx22 (or Cx3l)

Nominal

Value 100 (or 1000) pF 100 (or 1000) pF 100 (or 1000) pF

Group of +1 -1 3 Standards -1 +1

-1 +1

-1 +1

+1 -1 +1 -1

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

Standards

Used

Working Standards

( GR-1404 without trimmers )

Two Customer's Capacitors

( GR-1404 & ESI SC-1000 ) Serial No. #493 (or #1717) #517 (or #1865) Cx22(0r Cx3l) Cx23(0r Cx32)

Nominal

Value 100 (or 1000) pF 100 (or 1000) pF 100 (or 1000) pF 100 (or 1000) pF

Group of

4 Standards

+1 -1 +1 -1

-1 +1

+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) Cx22(or Cx3l) Cx23 (or Cx32) Cx24 (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 -1 +1 -1

-1 +1

-1 +1

+1 -1 +1 -1

-1 +1

-1 +1

-1 +1

24
Table 5. NIST Large Uncertainty Calibration Design for Nitrogen- and Air-Dielectric

Standard Capacitors

Standards

Used

Working

Standards

Customer's

Capacitors

Working

Standard

Customer's

Capacitor

Nominal Value 1 pF to 10 000 pF 1 pFto 10 000 pF 1 pF 0.1 pF

Ratio 1 : 1 1 : 10

+1 -1 +0.1 -1

-1 +1 -0.1 +1

25
Table 6. Summary of Check Standards of the Type- 12 Bridge

Serial No. Nominal Model

Value GR1409

Primary Secondary

Set Set Tvne

W 1 O 1 o 0.001 F

ffj4/ -W1 1 nA 1 ff 1 1 /41 0.002 G

#4VO ffl 1 /Do 0.005 K

ft2 1 ozU 0.01 L

ff 1 juy ff 1 1 loU 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
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 Uncertamty

100 400 1000 100 400 1000 100, 400, & 1000

Nominal Value (pF)

1 8.5 4.5 3.8

10 4 2.5 1.7 6 5 4 25

100 4 2.5 1.7 6 5 4 25

1000 6 5 4 25

27
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 1 r\f\ 100 5 200

1 +/-. 1 r\f\r\

1 to 1 UUU 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
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 (|j,F)

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
Table 10. Calibration Uncertainties of Conductance Values of Two- and

Three-Terminal Mica-Dielectric Standard Capacitors

Expanded Uncertainties of Conductance (jj,S)

Frequency (Hz) 66 & 100 400 & 1000 10 000

Nominal Value (\iF)

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

yj.yj/. 0U.UUU 000^J u.uz

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
31
gure lb. Simplified Circuit Diagram of the NIST Type-2 Capacitance Bridge.

32
^GROOND SHIELD

NOTE-. SOME SWITCHES AND ANCILLARY eLEMfrMTS HAVE: BEEIjX

OMITTED TO S/MPLlr"y THIS SCHEMATIC DIAGRAM.

Ca: air capacitor (0>^ (IOOO, ioo, |o} PF + |0 PF DIFFERENTIAL CONT/KiUOUSCk- DIVIOE-BV-T^N CAPACITOR:' 600 PF OR 100 PF {SeR- NOs. f\soVB noo,ooo)

Cm- MICA CAPACITANCE STD lo?^ ( o.i, o.oi) UF

G.S • COKJDUCTAWCIT 5TA^JDARi> '. /<9x(/00^/o) UMHO+ |-|| UMHO

Rk: conductance D/V1D£R RFSI^TT-R-S : O, /8oo, /9<S00-a; 0J9?es Z MCG^.

(DIVIDE; Gs BY \, lO ^ \0 tO^ lO'^)

RijR2- 1 000 - Of r/\TIO ARiVi^ ' Sac • DIRECT CAPACITANCE A-QR-C 5WITC.H

Sg-k: CONDDCTANCer. pIVlDEK J^^WITCH icK^ CAPACITANCE DlViDEf^ SWITCH

56G-- BALANCE OR GP-O'UJO SWITCT|,TZ: D- 179^32 2oHz-200 kHz DOUBLc- SHIELDED TRAIV-: FORM C/rS

(D-I5S4';0 20t^M;/- 200kl-|£ 'N 3/^)C>6£S e£FOKL vV-/o;nS-o)

D TEST TERM InJaLS,

•J3 JD ' DIRL'CT CAPACITANCE T£ST JACi\^. ,5^.^ 1/23/69 ^r^V

ISSUE

1 g/zs////,

2. '0/26/67 /V TO.. 3 2./ 20/^'-^

J 4- 3/r//.< -."aV-.c'

CNSR ^'^'^.NO. IZ-TYPE CAPACITAKJCE BRIDGE

SIMPLIFIED SCHEMATIC

BELL TELEPHONE LABORATORIES

INCORPORATED DRAWN B-I4D 495 NO. or f HCCTS rc« tlT _

SHEET

Figure 2a. Schematic Diagram of the NIST Type- 12 Capacitance Bridge.

33
ure 2b. Simplified Circuit Diagram of the NIST Type- 12 Capacitance Bridge.

(Generally Showing only the Capacitance Components)

34
35
#121 (or other Primary Refeence)

(10 pF)

#102 (or #254)

(10 pF)

Customer's

Nitrogen (or Air)

Cap Stds

Cxi2(10pF)

Customer's

Air Cap Stds

Cxo2(> PF)

Customer's

Fused Silica

Cap Stds

Cxoi (1 Cxii(lOpF)

#871

(10 pF)

#89790

(1 pF)

Customer's

Air Cap Stds

Cx, (0.1 pF)

Customer's

Air Cap Stds

CX2 (0.01 pF)

Customer's

Air Cap Stds

Cx3 (0.001 pF)

#131 (or #230)

(100 pF)

#493 & #5 17 (100 pF)

Customer's

Nitrogen (or Air)

Cap Stds

Cx22(100 pF)

Cx23 (100 pF)

Cx24 (100 pF)

Customer's

Fused Silica Cap Stds

Cx2,(100 pF)

#1717݉

(1000 pF)

NBS#1615

(10000 pF)

Customer's

Nitrogen (or Air)

Cap Stds

Cx3,(1000 pF)

Cx32 (1000 pF)

Cx33 (1000 pF)

Customer's

Air Cap Stds

Cx4, (10000 pF)

Figure 4. Block Diagram of Measurement Process and Standards being Used

In the Impedance Calibration Laboratory.

36
NIST REFERENCE ADAPTER
UNKNOWN CAPAOTOR

OR

TERMINATION

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

38
39

ASS

SHING

CC 3

m CD

nil

MM

41
42
%

t

I—

<

(Uo

-C.

-oc

oU

-OnON

oo

ON

ON

OS

ON

in

ON

ON

in

ON

ON H- ^

(N

>n oo On •n CM m

in in in in

in in in »n in in »n in in in

m m m m m 1 m m m

(U >

;-< <U&

S

H

(Uo

C

•

CI,

I—

>

P3O

Cu o

COa

c

*->

<L) O

c

<L)

o

IX,o

>

DO

cd>

0)

ix

3n|By\ i^uiuiojvj uiojj mdd

43
Primary Standards Lab

Reference Bank

4x lOpF Oil Bath

Fused Silica Cap Stds

Impedance Calibration Lab

Transfer Standard

10 pF Air Bath

Fused Silica Cap Stds

Primary Reference

4x lOpFOil Bath

Fused Silica Cap Stds

Customer's

Fused Silica

Cap Stds

Secondary References

2 X 10 pF & 2 X 100 pF Air Bath

Fused Silica Cap Stds

Check Standards

IpF, lOpF,

2x 100 pF&2x 1000 pF

Nitrogen Dielectric

Cap Stds

Customer's

Nitrogen Dielectric,

Air Dielectric, and

HF Coaxial Cap Stds

Figure 12. Block Diagram of the Farad Transfer and Calibration Process

Using the Type-2 Bridge.

44
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0\ 0^ ON CTv CJN On On On On On qo

(N CNl (N <N (N <N (N <N r^l <Non

OT^OOONONOOOOr~;r-;NO W-1 O m O W-» O O >noo

3n\T3\ 90ireji0BdB3 |BUTmojs[ uioij uidd

45
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0\ On OS ON 0\ On Os On On On qo

CN< <N <N (N (N <N CM <N PnI

46
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47
ooON

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3n|By\ |euiuio]\[ uiojj uidd

48
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'

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On

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49
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On

-.- o

On

ON

ON + ?^

CD

ON

ON

ON

CM

On

ON

I

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'

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I I I I I I I O (N CO o o o o

B

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a,

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CNl 0)

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50
J I

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Os

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so

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so

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OS

SO

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51
(Srl) snp/^ 9oirepnpuo3

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52
(SrI) anjB/^ aoirepnpuo^

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ooosooonooonooonoo ^ On 0\ OS On
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.

A5. 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.

A1 0. 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
UNITED STATES DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

Gaithersburg. Man/land 20899-CXXD1

GENERAL rNFORMATION ON FUSED-SILICA-DIELECTRIC 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 cqjacitance was established at NIST/NBS in 1975 [1], and re-estabUshed in 1989 [2].

The reported values ofcapacitance 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 rbO.l ppm.

2. Fused-Silica Dielectric Standard Capacitors

Three-terminal standard capacitors of fiised-silica dielectric are calibrated with a NIST transformer

bridge [3] using NIST fused-silica lO-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 ofthe results of several measurements of direct capacitance

with the capacitor coimected 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 fiised-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 eire 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 ofthe 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

55 Nisr
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] 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.

[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. 1-7, 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. 1-7, 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] R.N. Jones, "A Technique for Extrapolating the 1 kC Values of Secondary Capacitance

Standards to Higher Frequencies," NBS Tech. Note No. 201, Nov. 1963.

56
UNITED STATES DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

Gaithersburg, Maryland 2D899-0001

REPORT OF CALIBRATION

Standard Capacitor

General Radio Company

Type 1408-A, Serial No. UM#

Enclosure Serial No. MM

Submitted by:

Frequency

(Hz)

Average

Temperature

CQ

TypeA

Uncertainty

(ppm)

Expanded

Uncertainty

(ppm)

1000 23.1234 0.1234 10.0012346 0.02 2.5

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 ^ = 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

57 Nisr

UNITED STATES DEPARTf/IErVIT OF COMMERCE

National Institute of Standards and Technology

Gaithersburg. Maryland 20899-OO01

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 ofcapacitance 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 fiised-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 coimecled 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

in a 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 ofthe capacitance measurements is also calculated to assure it is within limits based on the estimated population standard deviation.

If it 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

59 Nisr
Type B uncertainties in the chain of measurements, and are assigned to the capacitance values using

the coverage factor /: = 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 ] 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.

[2] J. Q. Shields, R. F. Dziuba, and H. P. Layer, 'TSFew 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. 1-7, 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 Insfr.,

Vol. 1-7, 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] R.N. Jones, "A Technique for Extrapolating the 1 kC Values of Secondary Capacitance

Standards to Higher Frequencies," NBS Tech. Note No. 201, Nov. 1963.

60
UNITED STATES DEPARTMENT OF COMMERCE

National institute of Standards and Technology

Gaithersburg, Marvland 20899-O001

REPORT OF CALIBRATION

Standard Capacitor

General Radio Company

Type 1404-A, Serial No. MM

Submitted by:

Temperatune

CO

Capacitance

(pF)

Expanded

Uncertainty

(ppm)

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 Electricity Division

Barry A. Bell, Group Leader

Electricity Division

Test No. 811/

Reference:

Date: January 6, 1998

Telephone Contact: 301-975-4221

61 Nisr

UNITED STATES DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

Gaidiersburg. Mar/land 20899-OO01

DESCRIPTION OF TESTS USED TO DETEEIMFNE 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.

ORIENTATION 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 ofthe other tests or not. It has been 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 firom 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

63 Nisr
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. The force

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 comers. 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 1 5 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 fi-eely. 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
UNITED STATES DEPARTMENT OF COMMERCE

National institute of Standards and Technology

Gaithersburg, MarYland 20a99-CXXi1

REPORT OF CALIBRATION

Standard Capacitor

General Radio Company

Type 1404-A

Serial No. UMU

Submitted by:

Orientation

(Maximum)

0.74

Small

Angle

(Range)

0.13

Tilt (Range)

0.11

Knock

Soft

(Range)

0.13

Knock

Hani

(Range)

0.21

Drop

(Range)

0.06

The results of the six tests are used to determine the effects of small mechanical stresses on high-stabilit\',

nitrogen dielectric standard capacitors are given above, in units of parts per million (ppm). They are not included in the expanded uncertainty given in the accompanying report of calibration (NIST SP250

Service ID No. 52 HOC). 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 Engineering TechnicianBarry A. Bell, Group Leader

Electricity Division

Test Report No.: 811/

Reference:

Date: January 5, 1998

Telephone Contact: 301-975-4221

65 Nisr
i
UNITED STATES DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

Gaithersburg. Maryland 20899-OCXD1

GENERAL INFORMATION ON THREE-TERMINAL 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 ofcapacitance 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, £ind the farad is believed to be no greater than ±0. 1 ppm.

Three-terminal standard capacitors of nitrogen and air dielectric are calibrated with a NIST

transformer bridge [3] using NIST fiised-silica 10-pF capacitors [4] as reference standards.

Capacitance is measured by direct comparison with stable working standzirds, 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 ofthe 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 c£ilibration 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 mstability, 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.

2. Three-Terminal Standard Capacitors

67 NIST
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," IEEE Trans, on

Instrumentation and Measurements, Vol. IM 23, No. 4, Dec. 1974.

[2] J. Q. Shields, R. F. Dziuba, and H. P. Layer, 'Tvlew 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. 1-7, 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. 1-7, 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] R.N. Jones, "A Technique for Extrapolating the I kC Values of Secondary Capacitance

Standards to Higher Frequencies," NBS Tech. Note No. 201, Nov. 1963.

68
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:

Frequency

(Hz)

1000

Capacitance

(pF)

100.013

Expanded

Uncertainty

(%)

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 ± 1

" C

Date of Calibration: December I, 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 6, 1998

Telephone Contact: 301-975-4221

69 Nisr

UNITED STATES DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

Gaithersburg. Man/land 20899-aX)1

GENERAL INFORMATION ON TWO-TERMINAL STANDARD CAPACITORS

WITH PRECISION COAXIAL CONNECTORS

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. Two-Terminal 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 discormected, rotated 90

degrees around the vertical axis ofthe 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 ofthe 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 ofthe end ofthe inner conductors

or damage to the leaf contacts can easily change the capacitance values by 0.0 1 pF or more. The use of any non-precision or different connector with these capacitors virtually will destroy any useflihiess

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.

71 Nisr
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%.

3. References

[1] 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.

[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] "IEEE Standard for Precision Coaxial Connectors," IEEE Trans, on Instr. Meas., Vol. IM- 1 7,

No. 3, pp. 204-218, Sept. 1968.

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

Apparatus at the National Bureau of Standards for Absolute Capacitance Measurement," IRE

Trans, on Instr., Vol. 1-7, No. 3 & 4, pp. 253-261, Dec. 1958.

[5] 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.

[6] R. D. Cutkosky, "Capacitance Bridge — NBS Type 2," National Bureau of Standards Report

7103, March 1961.

[7] J. F. Hersh, "A Close Look at Connection Errors in Capacitance Measurements," General

Radio Experimenter, Vol. 33, No. 7, July 1959.

[8] R. W. Orr, "Capacitance Standards with Precision Connectors," General Radio Experimenter,

Vol. 41, No. 9, Sept. 1967.

[9] B. N. Taylor and C. E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty

of NIST Measurement Results," NIST Tech. Note No. 1297, Jan. 1 993.

72

ll
UNITED STATES DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

Gaithersburg, Maryland 20899-0(X)1

REPORT OF CALIBRATION

Standard Capacitor

General Radio Company

Type 1406-A, Serial No. MM

Submitted by:

Expanded

Frequency Capacitance Uncertainty

(Hz) (pF) (%)

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: For the Director,

Summerfield B. Tillett Barry A. Bell, Group Leader

Electricity Division Electricity Division

Test No. 811/

Reference:

Date: January 6, 1998

Telephone Contact: 301-975-4221

73 Nisr

UNITED STATES DEPARTIVIEIMT OF COIVir/JERCE

National Institute of Standards and Technology

Gaithersburg, Maryland 20899-CO01 c

GENERAL INFORMATION ON MICA-DIELECTRIC STANDARD CAPACITORS

WITH BINDING POST CONNECTORS

1. Representation of the Unit of Capacitance

As a result of new absolute measurements of the f£irad 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 ofcapacitance 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.

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 ftised 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.

2. Mica-Dielectric Capacitors with Binding Post Connectors

75 Nisr
The reported values of capacitance are in terms of the NIST representation of the farad. The

capacitance cahbration 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 h=2 [7]. The standard deviation is estimated to be less than 40 ppm for zdl nominal values and frequencies except for 1 000 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

[1] 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.

[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] 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
UNITED STATES DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

Gaithersburg. Maryland 20899-0001

REPORT OF CALIBRATION

Standard Capacitor

General Radio Company

Type 1409-Y, Serial No. MM

Submitted by:

Type of Capacitance Conductance

Measurement Frequency Capacitance Uncertainty Conductance Uncertainty

(Hz) (,iF) (%) (mS) (mS)

2-TenTiinal 1000 0.99878 0.018 0.5 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 Electricity DivisionBarry A. Bell, Group Leader

Electricity Division

Test No. 811/

Reference:

Date: January 5, 1998

Telephone Contact: 301-975-4221

77
I r
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SP 250-1 Spectral Radiance Calibrations PB871 79883

SP 250-2 Far Ultraviolet Detector Standards PB87227609

SP 250-3 Radiometric Standards in the Vacuum

Ultraviolet PB87227625

SP 250-4 Fricke Dosimetry in High-Energy Electron Beams

PB881 10374

SP 250-5 Alpha-Particle Calibrations PB881 68620

SP 250-6 Regular Spectral Transmittance PB881 08550

SP 250-7 Radiance Temperature Calibrations PB881 23674

SP 250-8 Spectral Reflectance PB881 09905

SP 250-9 Calibration of Beta-Particle-Emitting

Ophthalmic Applicators

PB881 08535

SP 250-10 Radioactivity Calibrations with the "4ir" Gamma Ionization Chamber and Other

Radioactivity Calibration Capabilities

PB881 23708

SP 250-1 1 Dosimetry for High Dose Applications

PB88201587

SP 250-12 Neutron Personnel Dosimetry

PB87227617

SP 250-13 Activation Foil Irradiation with Californium

Fission Sources PB88217443

SP 250-14 Activation Foil Irradiation by Reactor Cavity

Fission Sources PB88217435

SP 250-15 Photometric Calibrations PB881 53747

SP 250-16 Calibration of X-Ray and Gamma-Ray

Measuring Instruments PB88211826

SP 250-17 The NBS Photodetector Spectral Response

Calibration Transfer Program

PB88201595

SP 250-18 Neutron Source Strength Calibrations PB88211818

SP 250-19 Calibration of Gamma-Ray-Emitting

Brachytherapy Sources PB891 93858

SP 250-20 Spectral Irradiance Calibrations PB881 23781 SP 250-21 Calibration of Beta-Particle Radiation Instrumentation PB88201579

SP 250-22 Platinum Resistance Thermometer

Calibrations PB88 138367 SP 250-23 Liquid-in-Glass Thermometer

Calibration Service PB891 28888

SP 250-24 Standard Cell Calibrations PB88 123690 SP 250-25 Calibration Service for Inductive Voltage Dividers SP 250-26 NBS Phase Angle Calibration Services PB88225636

SP 250-27 AC-DC Difference Calibrations PB892222616

SP 250-28 Solid-State DC Voltage Standard Calibrations PB88 168703 SP 250-29 Traceable Frequency Calibrations PB881 68364

SP 250-30 GOES Satellite Time Code Dissemination:

Description and Operation

PB881 68760

SP 250-31 Mass Calibrations PB891 53894

SP 250-32 A Calibration Service for 30 MHz

Attenuation and Phase Shift PB88238324

SP 250-33 A Calibration Service for Voltage Transformers and High-Voltage Capacitors

PB882252903

SP 250-34 High Vacuum Standard and Its Use

PB891 93841 SP 250-35 The Calibration of Thermocouples

and Thermocouple Materials PB89209340

SP 250-36 A Calibration Service for Current Transformers SP 250-38 NIST Leak Calibration Service SP 250-40 Absorbed-Dose Calibration of Ionization Chambers in a ^Co Gamma-Ray Beam

SN003-003-03034-1 $2.00

* Entries Entries containing a stock number (SN003-003-) and price can be purchased from the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402. GPO will accept checks, money orders, VISA, and MasterCard. For more infomation,

or to place an order, call (202) 783-3238. Be sure to cite the stock number on all orders.

Entries containing PB numbers can be purchased from the National Technical Information Service, Springfield, VA 22161. NTIS will accept American Express in addition to the payment methods listed for GPO. For more information call (703) 487-4650; to place an order

call (800) 336-4700. Be sure to cite the PB number on all orders.

Entries without stock or PB numbers are in preparation.
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