NIST Special Publication 250-76 

NIST MEASUREMENT SERVICES 

Three-Terminal Precision Standard 

Capacitor Calibrations at NIST 

____________________________________________________________ 

Andrew Koffman 

Yicheng Wang 

Scott Shields 

Quantum Electrical Metrology Division 

Electronics and Electrical Engineering Laboratory 

National Institute of Standards and Technology 

Gaithersburg, Maryland 20899-8170 

September 2007 

____________________________________________________________ 

U.S. Department of Commerce 

Carlos M. Gutierrez, Secretary 

National Institute of Standards and Technology 

William A. Jeffrey, Director 
Table of Contents 

List of Figures ................................................................................................. ii 

List of Tables ................................................................................................. iii 

1. INTRODUCTION ........................................................................................ 1 

2. REFERENCE CHARACTERIZATION ............................................................. 2 

3. REFERENCE AND CUSTOMER CAPACITANCE MEASUREMENTS ................ 3 

4. DATA PROCESSING ............................................................................... 5 

5. UNCERTAINTY BUDGETS ........................................................................... 5 

6. CALIBRATION SERVICES ...................................................................... 7 

7. REPORT OF CALIBRATION ...................................................................... 8 

8. DATA STORAGE ........................................................................................ 8 

9. REFERENCES ........................................................................................ 8 

APPENDICES ....................................................................................... 10 

APPENDIX A Report of Calibration for NIST Service ID 52130C/52131C 

APPENDIX B Report of Calibration for NIST Service ID 52140C/52141C 

APPENDIX C Report of Calibration for NIST Service ID 52160C/52161C 

APPENDIX D AH2700A Capacitance Bridge Accuracy for 1 pF, 10 pF, 100 pF, and 

1000 pF Standards 

APPENDIX E Calibration procedure for three-terminal fused-silica standard capacitors 

APPENDIX F Calibration procedure for high-accuracy three-terminal nitrogen gas 

standard capacitors 

APPENDIX G Calibration procedure for low-accuracy three-terminal nitrogen gas 

standard capacitors 

List of Figures 

Figure 1. Four-rod cross capacitor. 

Figure 2. NIST nitrogen gas and fused-silica standard capacitor traceability chain. 

Figure 3. Frequency dependence of 100 pF, 10 pF, and 10 pF calibration reference standards. 

Figure 4. Low-frequency plot of frequency dependence curves in Fig. 3. 

Figure 5. Measurement of three-terminal standard capacitor using automatic capacitance 

bridge. 

Figure 6. Bridge loading effects for 100 pF fused-silica reference standard measurements at 20 

kHz. 

Figure 7. Bridge loading effects for 10 pF fused-silica reference standard measurements at 20 

kHz. 

Figure 8. Bridge loading effects for 1 pF fused-silica reference standard measurements at 20 

kHz. 

Figure 9. Photograph of the capacitance bridge, controlling laptop, and reference and customer 

fused-silica standard capacitors. 

ii
Figure 10. Photograph of fused-silica standard capacitor enclosures without temperature 

readouts. Right enclosure contains SPRT. 

Figure 11. Photograph of fused-silica standard capacitor enclosures with temperature readouts. 

Figure 12. Photograph of nitrogen gas standard capacitors. 

Figure 13. Short-term stability of 100 pF reference standard (6 bridge measurements taken 

within 24 hours). 

Figure 14. Low-frequency portion of short-term stability of 100 pF reference standard (Fig. 13). 

Figure 15. Long-term stability of 100 pF reference (bridge measurements taken over more than 

three years). 

Figure 16. Normalized long-term stability of 100 pF reference (Figure 15 with average 

subtracted out). 

Figure 17. Short-term stability of 10 pF reference standard (6 bridge measurements taken within 

24 hours). 

Figure 18. Low-frequency portion of short-term stability of 10 pF reference standard (Fig. 16). 

Figure 19. Long-term stability of 10 pF reference (bridge measurements taken over more than 

three years). 

Figure 20. Normalized long-term stability of 10 pF reference (Figure 19 with average subtracted 

out). 

Figure 21. Short-term stability of 1 pF reference standard (6 bridge measurements taken within 

24 hours). 

Figure 22. Low-frequency portion of short-term stability of 10 pF reference standard (Fig. 19). 

Figure 23. Long-term stability of 1 pF reference (bridge measurements taken over more than two 

years). 

Figure 24. Normalized long-term stability of 1 pF reference (Figure 23 with average subtracted 

out). 

Figure 25. Expanded uncertainty (k=2) for 100 pF 3T fused-silica standard capacitor calibration. 

Figure 26. Expanded uncertainty (k=2) for 10 pF 3T fused-silica standard capacitor calibration. 

Figure 27. Expanded uncertainty (k=2) for 1 pF 3T fused-silica standard capacitor calibration. 

Figure 28. Expanded uncertainty (k=2) for 1000 pF 3T nitrogen gas standard capacitor 

calibration. 

Figure 29. Expanded uncertainty (k=2) for 100 pF 3T nitrogen gas standard capacitor 

calibration. 

Figure 30. Expanded uncertainty (k=2) for 10 pF 3T nitrogen gas standard capacitor calibration. 

List of Tables 

Table 1. Frequency dependence for NIST 100 pF, 10 pF, and 1 pF reference fused-silica 

standard capacitors. 

Table 2. Uncertainty budget for NIST 100 pF fused-silica standard capacitors. 

Table 3. Uncertainty budget for NIST 10 pF fused-silica standard capacitors. 

Table 4. Uncertainty budget for NIST 1 pF fused-silica standard capacitors. 

Table 5. Uncertainty budget for NIST 1000 pF nitrogen gas standard capacitors. 

Table 6. Uncertainty budget for NIST 100 pF nitrogen gas standard capacitors. 

Table 7. Uncertainty budget for NIST 10 pF nitrogen gas standard capacitors. 

iii
1. INTRODUCTION 

We have recently made improvements in capacitance measurements by expanding the frequency 

range of and lowering the uncertainty assigned to three-terminal (3T) fused-silica and nitrogen 

gas dielectric standard capacitor calibrations. These improvements are based on the recent 

frequency response characterization of the NIST primary capacitance maintenance standard from 

50 Hz to 20 kHz [1, 2]. The traceability chain from the NIST calculable capacitor to the 

customer standard capacitor is also shortened and the calibration service automated through the 

use of a commercial capacitance bridge as a transfer standard between the reference standard and 

the capacitor under test. This publication describes the revised procedure for 3T capacitance 

calibrations covered under test services 52130C/52131C, 52140C/52141C, and 52160C/52161C. 

The NIST farad representation for capacitance calibrations consists of a bank of four 10 pF 

fused-silica standards (referred to as the Farad Bank) which are maintained in an oil bath at 

25 °C. The Farad Bank is very stable, drifting only about 0.02 μF/F per year. The standards are 

calibrated at least once a year indirectly against the calculable capacitor [2] at NIST at a 

frequency of ≈1592 Hz (ω = 104

 rad/s), using a 10 pF transportable fused-silica capacitor, C112. 

This frequency was chosen for a convenient link between the farad and the ohm. 

The NIST calculable capacitor is based on the Thompson-Lampard theorem [3]. It is comprised 

of four parallel, uniform electrodes with very small gaps between them as shown in Fig. 1. The 

capacitances per unit length, Ca and Cb, between the opposing pairs of electrodes obey the 

relationship: 

=−+− 1)/exp()/exp( C oa C ob π ε π ε , 

where εo is the permittivity of vacuum. When Ca = Cb = C, this reduces to 

π

ε 2ln o C = , 

which is a constant that directly links to the defined speed of light. The calculable capacitor 

provides an absolute determination of capacitance in terms of length only and is the ultimate 

reference for all impedance measurements in the U.S. 

The reference fused-silica standard capacitors of value 100 pF, 10 pF, and 1 pF are calibrated 

directly against the Farad Bank at 1592 Hz at least once per year to determine the drift of the 

standards. The frequency dependencies of these capacitance standards have been measured [1, 2] 

from 50 Hz to 20 kHz using a combination of a 1 pF cross capacitor that has negligible 

frequency dependence due to electrode surface films and a 10 pF nitrogen gas dielectric 

capacitor with a very small residual inductance as references. The frequency response curve of a 

fused-silica standard capacitor is very stable and needs to be re-characterized only infrequently. 

The calibrated reference standards are then used in a substitution scheme and measured each 

time a customer standard is sent to NIST for calibration. The difference between the calibrated 

1 
value and measured value of the reference at each required frequency is used to correct the 

measured value of the customer standard. Fig. 2 shows the traceability chain for NIST 3T 

nitrogen gas and fused-silica standard capacitor calibrations. The calibration procedure will be 

described in detail below in terms of the reference characterization, reference and customer 

capacitance measurements, data processing, uncertainty budgets, and report generation. 

The 1592 Hz reference point is derived from NIST Calculable Capacitor measurements that are 

transferred to the Primary 10 pF Bank of standards. The reference standard 1 pF, 10 pF, and 

100 pF capacitors are compared directly with the Primary 10 pF Bank at 1592 Hz on a periodic 

basis at least once per year. The frequency response curve for each reference standard is 

traceable to a series of measurements on a 1 pF, 9-bar, nitrogen gas cross capacitor, as well as a 

10 pF nitrogen gas cylindrical capacitor. References [1] and [2] describe fully the work to 

characterize fused-silica reference standards across frequencies from 50 Hz to 20 kHz. 

2. REFERENCE CHARACTERIZATION 

NIST standard reference capacitors of nominal values 100 pF, 10 pF, and 1 pF have been 

characterized for frequency dependence of the capacitance [1, 2]. Table 1 gives the frequency 

dependence for the 100 pF, 10 pF, and 1 pF AH11A reference standards used to provide 

customer calibrations. Figures 3 and 4 show plots of the frequency dependences. These curves 

show the change in capacitance with respect to the capacitance value at 1592 Hz, as measured 

against two reference standard capacitors on the NIST four-terminal-pair capacitance bridge. The 

reference standard capacitors used were a 1 pF cross capacitor, chosen for its negligible 

frequency dependence at low frequencies, and a 10 pF nitrogen gas capacitor chosen because it 

has good reference characteristics at higher frequencies [2]. The frequency dependence curves 

for the fused-silica reference standards have been shown to have stability on the order of one or 

two parts in 108

 over a period of many years [3, 4] and so updates are not required frequently. 

However, normal drift of the reference standards requires periodic calibration at 1592 Hz against 

the NIST Primary Bank of 10 pF standards. The Primary Bank of standards is calibrated against 

the NIST Calculable Capacitor approximately once per year. The calibration of all reference 

standards against the Primary Bank at 1592 Hz is performed no less than once per year. A spot 

check of the frequency dependence will be performed every ten years to verify the values. 

Additionally, errors in the automatic bridge measurements due to bridge loading from the stray 

capacitances of the measured capacitors must be corrected each calibration for fused-silica 

standard capacitors. Nitrogen gas standard capacitors are not corrected for bridge loading errors. 

Fig. 5 shows a schematic diagram of the automatic capacitance bridge measuring a threeterminal standard capacitor. The low-to-high capacitance of the standard capacitor is labeled 

as CLH and the stray capacitances from the low side of the standard, point B, to ground and from 

the high side, point A, to ground, are labeled as CLG and CHG, respectively. The effects on bridge 

measurements at 20 kHz from varying the stray capacitances at points A and B of the reference 

standards have been measured and are shown for 100 pF calibration reference standard (C272) in 

Fig. 6. The loading effect curves produced for the automatic capacitance bridge at points A and 

B using a 10 pF calibration reference standard (C172) are shown in Fig. 7, and those produced 

using a 1 pF calibration reference standard (C016) are shown in Fig. 8. The increase in 

capacitance bridge measurement value with increase in stray capacitance is a linear curve for 

2 
both the high and low sides of the bridge. This effect will change with frequency according to the 

square of the frequency [1, 2] and so the effect on measured capacitance due to bridge loading 

will decrease dramatically at lower frequencies. This effect becomes negligible (as can be seen in 

Tables 2-7 below) at frequencies below a few kilohertz. It is important to note that the bridge is 

loaded differently for each standard measured. The differences between the stray capacitances of 

the reference standard and the customer standard at the high and low terminals are the critical 

quantities for a customer calibration. Customer standards that have stray capacitance values close 

to the stray capacitance values of the reference standard will have no significant loading 

corrections. 

An example computation of loading correction follows using the 20 kHz bridge loading curve in 

Fig. 6 for the 100 pF calibration reference standard. The value of reference capacitor C272 with a 

stray capacitance at the high terminal, point A, adjusted to 3 nF above its normal value of 

approximately 205 pF, gives a measurement across the high-to-low terminals of 100.01896 pF. 

Adjusting the stray capacitance to the normal value of 205 pF (zero added stray capacitance) 

gives a high-to-low capacitance of 100.00269 pF. Normalizing to μF/F of the 100 pF nominal 

value gives a slope on the loading curve for the high terminal of (189.6 – 26.9 = ) 162.7 μF/F per 

3 nF, which reduces to 0.0542 μF/F per 1 pF. If the customer standard has a stray capacitance at 

point A that measures 195 pF, the difference in loading at point A between calibration reference 

standard C272 and the customer standard is (205 – 195 =) 10 pF, which gives a 20 kHz loading 

correction at the high terminal (point A) of 0.542 μF/F, compared to the expanded uncertainty of 

the customer 100 pF at 20 kHz of 2.35 μF/F. Scaling this correction from 20 kHz to 1 kHz, 

according to a frequency-squared relationship, gives a 1 kHz loading correction at point A of 

approximately 0.001 μF/F, compared to an expanded uncertainty at 1 kHz of 0.21 μF/F. The 

bridge loading curve for point B, in Fig. 4, has a smaller slope, producing smaller corrections 

than for point A. Of course, corrections for both the high terminal (point A) and the low terminal 

(point B) must be computed to properly correct for the loading effects of the bridge. 

The stray capacitances of the reference standards vary little from month to month and therefore, 

measurements are required only twice per year in order to provide bridge loading corrections for 

customer fused-silica standard capacitors. For convenience, the stray capacitance measurements 

on the NIST reference standard as well as the customer standard capacitor are performed at 

1 kHz and the correction is computed at the required frequencies from 50 Hz to 20 kHz 

according to the frequency squared. 

3. REFERENCE AND CUSTOMER CAPACITANCE MEASUREMENTS 

Capacitance measurements on the reference and customer standard capacitors are performed 

using the Andeen-Hagerling AH2700A 50 Hz – 20 kHz Ultra-Precision Capacitance Bridge†. 

The bridge is controlled using a personal computer with a software driver and a GPIB interface. 

Figure 9 shows a photograph of the bridge, controlling laptop, and reference and customer fusedsilica standard capacitors. 

 

†

 The identification of a specific commercial product does not imply endorsement by NIST, nor does it imply that 

the product identified is the best available for a particular purpose. 

3 
Since the frequency dependences of the reference standard capacitors have been determined and 

straightforward measurements can provide corrections for the loading effects of capacitors on the 

automatic capacitance bridge, the bridge can be used as an effective transfer instrument. 

Measurements on the reference and customer standards, along with the calibrated values for the 

reference standards, are used in a substitution procedure. For each customer calibration, five sets 

of data are taken on different days for all required frequencies over a period of approximately 

two weeks. At the time of each measurement run, data are taken closely in time on the standard 

under test and the NIST calibration reference standard of the same nominal value. The only 

exception to using the same nominal value reference and customer standards is that the 100 pF 

fused-silica reference standard is used to calibrate 1000 pF nitrogen gas standards, with a 

corresponding uncertainty component for the 10:1 ratio comparison. 

The difference between the measured value of the reference standard and the calibrated value of 

the reference standard at each frequency is used, along with the loading correction, to determine 

the calibrated value of the standard under test. So the equation used to produce a calibrated 

capacitance value for a device under test (DUT) for a single measurement at a single frequency, 

would be 

( ) )1( DUTcal CC DUTmeas REFcal CC REFmeas Loading = + − + ε

where is the calibrated capacitance of the DUT, CDUTcal

 is the measured value of the DUT, CDUTmeas

 is the value of the reference standard calibrated against the NIST Primary Bank, CREFcal

 is the measured value of the reference standard, and CREFmeas

Loading ε is the total loading correction for the capacitance bridge with respect to the DUT. 

Five such capacitance measurements are performed to produce a reported value for the high 

accuracy calibrations of fused-silica or nitrogen gas dielectric standard capacitors (NIST test IDs 

52130C/52131C and 52140C/52141C). The mean of the five measurements along with the 

Type A uncertainty and expanded uncertainty are reported in the Report of Calibration for high 

accuracy tests. Three such measurements are performed to produce a reported value for low 

accuracy tests on nitrogen gas dielectric standard capacitors (NIST test ID 52160C/52161C). The 

mean of the three corrected measurements along with the expanded uncertainty are reported in 

the Report of Calibration for low accuracy tests. Control software is used to automatically 

perform the measurements and store the results. See reference [7] for definitions of Type A and 

expanded uncertainties. 

The laboratory ambient temperature is maintained at 23.0 oC. The relative humidity of the 

laboratory varies seasonally but is held below 50 %. Laboratory ambient temperature and relative 

humidity are recorded at the time of each customer measurement and the mean value over all 

measurement sets is given on the Report of Calibration. Customer standards are energized and/or 

allowed to stabilize within the lab for at least 72 hours prior to measurement. Measurements are 

4 
not performed if the temperature has varied from the laboratory set point of 23.0 oC by more than 

0.5 oC or if relative humidity has increased above 50 % within the last 72 hours. 

Typical commercial fused-silica standard capacitors provide enclosure temperature control to 

maintain stability of the standard capacitor. Some older types of standards, however, do not 

provide a temperature display. Calibration of fused-silica standards without a temperature 

display requires a standard platinum resistance thermometer (SPRT) to be placed inside the 

standard capacitor enclosure in order to record the temperature within the standard capacitor at 

the time of measurement. A resistance thermometry bridge is used to provide such 

measurements. Enclosure temperature is recorded at the time of each measurement. Mean 

enclosure temperature and enclosure temperature variation are reported on the Report of 

Calibration. Figure 10 shows two fused-silica standard capacitor enclosures without enclosure 

temperature readouts. An SPRT is placed within the right enclosure to record the temperature 

during measurement. Two standard capacitors are potentially housed within each enclosure. 

Figure 11 shows a photograph of two fused-silica standard capacitor enclosures that have 

temperature readouts. Four standard capacitors are potentially housed within each of these 

enclosures. 

Figure 12 shows three 3T nitrogen gas standard capacitors. The upper standard has been placed 

inside of a foam container in order to reduce handling of the standard and to facilitate 

temperature stability of the unit. The bridge cable leads are connected to the upper standard and a 

shorting clip is used to short the outer shields of the high and low terminals of the standard, as 

some commercial nitrogen gas standards are constructed with the high- and low-terminal shields 

electrically connected, and some are not connected. 

4. DATA PROCESSING 

Once all of the measurement data sets have been obtained, they are stored in a spreadsheet file. 

The corrected values of all capacitance measurements are computed as shown in Eq. (1). The 

mean values over the five corrected measurements at each frequency are computed. The Type A 

uncertainty for each frequency is computed as the standard deviation of each group of five 

corrected measurements. The ambient temperature, relative humidity, and enclosure temperature 

for the customer standard are averaged over the five measurement runs and are reported, along 

with the variation in the enclosure temperature. Also, the expanded uncertainty of each 

capacitance calibration value is computed using a coverage factor of k=2, with the Type A 

component for a given calibration being the only contributor to the expanded uncertainty that 

varies from calibration to calibration. The expanded uncertainties reported in this publication are 

computed such that the Type A uncertainty of a customer standard must increase beyond a 

specific threshold before the expanded uncertainty must be increased above the normal reported 

value for that nominal capacitance and frequency. 

5. UNCERTAINTY BUDGETS 

The uncertainty components contributing to the combined standard uncertainty of a customer 

calibration for a 3T fused-silica or nitrogen gas standard capacitor are the reference standard 

uncertainty, the reference standard drift, the Type A uncertainty of the DUT, the drift of the 

5 
DUT, the capacitance bridge thermal, mechanical, and linearity components, and the bridge 

loading component (see Tables 2, 3, 4, 5, 6, and 7). The 1000 pF nitrogen gas standard capacitor 

calibration uncertainty budget also contains a component for the 10:1 ratio due to using a 100 pF 

reference standard (see Table 5). Reviewing Eq. (1), there are four terms on the right side of the 

equation. 

( ) )1( DUTcal CC DUTmeas REFcal CC REFmeas Loading = + − + ε

The component uncertainties are statistically independent and correspond to the terms of Eq. (1) 

according to: 

Term 1: Type A Uncertainty, DUT Drift, and 10:1 Ratio Uncertainty (1000 pF only) 

Term 2: Reference Uncertainty and Reference Drift 

Term 3: Bridge Thermal, Mechanical, and Linearity 

Term 4: Bridge Loading 

Since the terms are statistically independent, they can be combined in a root-sum-squared 

fashion to produce the combined standard uncertainties (not shown in tables). The combined 

standard uncertainties are used with a coverage factor of k=2 to produce the expanded 

uncertainties shown in the tables. 

Figure 13 shows a short-term stability plot for the 100 pF calibration reference standard. Six 

measurements across all frequencies from 50 Hz to 20 kHz were performed within 24 hours and 

are presented. Figure 14 shows the same data from 50 Hz to 1 kHz only. Figure 15 shows a longterm stability plot of the 100 pF calibration reference measurements. The plot contains all bridge 

measurements of the 100 pF reference standard taken over more than three years. Figure 16 

shows the data from Fig. 15 with the average of all capacitance measurement data subrtracted 

out. 

Figures 17, 18, 19, and 20 show the corresponding short-term and long-term stability plots for 

the 10 pF calibration reference standard as shown in Figs. 13, 14, 15, and 16 for the 100 pF 

reference. Figures 21, 22, 23, and 24 show the corresponding plots for the 1 pF calibration 

reference standard. These figures demonstrate stability and repeatability of the capacitance 

bridge measurements. 

Tables 2, 3, and 4 show the uncertainty budgets for the 100 pF, 10 pF, and 1 pF fused-silica 

standard capacitor calibration services at NIST, provided under test IDs 52130C and 52131C. 

Tables 5, 6, and 7 show the uncertainty budgets for the 1000 pF, 100 pF, and 10 pF nitrogen gas 

standard capacitor calibration services at NIST, provided under test IDs 52140C and 52141C. 

Test IDs 52160C and 52161C are used to provide low accuracy/high uncertainty calibrations for 

fixed 3T standard capacitors with coaxial connectors. One of the standard types covered under 

test IDs 52160C and 52161C is the fixed 3T nitrogen gas dielectric standard capacitor that is also 

calibrated with high accuracy/low uncertainty under test IDs 52140C and 52141C. When test IDs 

52160C and 52161C are used to calibrate fixed 3T nitrogen gas dielectric standard capacitors, 

the expanded uncertainty is always 25 μF/F, for frequencies from 50 Hz to 20 kHz. The only 

exception is that 35 μF/F is used for the 10 pF standard at a frequency of 20 kHz. A table of the 

6 
capacitance bridge accuracy for 1 pF, 10 pF, 100 pF, and 1000 pF measurements is included in 

the Appendix. The expanded uncertainty for all calibrations is the combined standard uncertainty 

of the calibrated value multiplied by a coverage factor of k=2, consistent with practice 

recommended by the International Bureau of Weights and Measures (BIPM) [7]. In equation 

form, this is U = k uc, where uc is the relative combined standard uncertainty for all known 

sources of error and k is a coverage factor. Consistent with international practice, NIST uses a 

coverage factor of k = 2. The expanded uncertainty is thus given by 

U = 2 uc = 2 ∑ 2

ui , 

where ui is the estimated relative standard uncertainty associated with the i

th source of error and 

expressed as an equivalent standard deviation. It is assumed that the probability distribution 

characterized by the capacitance calibration measurement is approximately normal or Gaussian. 

A probability interval around the true measurand, Y, within which lies the measurement result, y, 

is defined such that y - uc(y) ≤ Y ≤ y + uc(y), commonly expressed as Y = y ± uc(y), where 

uc(y) is the combined standard uncertainty of y. The normal distribution assumption establishes a 

level of confidence of approximately 68 % that the true measurand is within the uncertainty 

interval. Applying the coverage factor of k = 2 raises the level of confidence to approximately 95

%, that Y = y ± U(y), where U(y) is the expanded uncertainty of y, using a coverage factor of 

 = 2 [7]. 

rmed 

ally 

ed in 

 pF, and 

f 3T nitrogen gas standard capacitors of values 

1000 pF, 100 pF, and 10 pF, respectively.

. CALIBRATION SERVICES 

k

Summarizing the components listed in Tables 2-7, the reference uncertainties are the combined 

standard uncertainties produced from calibration of the reference standards with traceability to 

the NIST Calculable Capacitor. Calibrations of the reference standard capacitors are perfo

at a minimum of once per year at 1592 Hz with spot checks of the frequency curve being 

performed once per ten years. The Reference Drift is the short-term drift in the calibrated values 

of the reference standard. The Type A Uncertainty is a conservative limit determining a typic

behaving standard. Any customer standard not performing to within this limit will require a 

larger uncertainty to be assigned. The DUT drift allows for the drift of the device under test, and 

is identical in value to the Reference Drift. The Bridge Thermal, Bridge Mechanical, and Bridge

Linearity components are taken from the manual of the commercial capacitance bridge us

performing the calibrations [5]. The Bridge Loading component is the uncertainty on the 

correction for the difference between the bridge loading during measurements of the reference 

and test standards. Measurement of the stray capacitances of the reference standard capacitors 

used in computing the bridge loading corrections are performed at least twice yearly. Details of 

the NIST method of expressing uncertainties can be found in reference [7]. Figures 25, 26, and 

27 present plots of the expanded uncertainties (k=2) for NIST calibrations of 100 pF, 10

1 pF 3T fused-silica standard capacitors, respectively. Figures 28, 29, and 30 show the 

corresponding plots for NIST calibrations o

6

For many years NIST has offered calibrations for 3T fused-silica and nitrogen gas dielectric 

standard capacitors of values 1 pF, 10 pF, 100 pF, and 1000 pF only at 100 Hz, 400 Hz, and 

1000 Hz [7, 8]. Because of the tedious manual bridge measurements required for calibration, 

multiple measurement points were charged at a rate similar to the fee of the initial calibration 

7 
point. The fee for having a standard capacitor calibrated at all three frequencies mentioned ab

was approximately three times the fee for only one frequency. The work done to expand and 

automate the standard capacitor calibration service has allowed NIST to reduce the fee for t

initial point by a factor of more than one third from the previous fee. Moreover, the fee for 

additional calibration frequencies has been reduced by more than a factor of 15 over the previ

fee. The service has expanded from the three frequencies mentioned above to 20 frequencies 

ranging from 50 Hz to 20 kHz, as shown in the Uncertainty Budget section. Calibration turnaround time is typically estimated at eight weeks for fused-silica standard capacitor calibrations 

(NIST test IDs 52130C and 52131C). For the nitrogen gas dielectric standard capacitors, NIST 

also offers a calibration that assesses the effects of physical handling of the standard, under NIS

test ID 52150C, recommended only for standards that are used outside of a laboratory setting. 

When a physical handling test is required in addition to the normal capacitance calibration of

nitrogen gas dielectric standard capacitor, the calibration turn-around time is typically eight 

weeks (NIST test IDs 52140C, 52141C and 52150C). When no such physical handling test is 

required, the turn-around time is typically six weeks (NIST test IDs 52140C and 52141C). The 

turn-around time for the low accuracy calibration of nitrogen gas dielectric standard capacitors is 

six weeks (NIST test IDs 52160C and 52161C). For more information, visit the NIST C

website at 

ove 

he 

ous 

T 

 a 

alibration 

http://ts.nist.gov/MeasurementServices/Calibrations and follow the links to 

lectromagnetic and then to Impedance Measurements. 

. REPORT OF CALIBRATION 

s 

acitor, and low accuracy nitrogen gas standard capacitor) is included in the 

ppendix. 

ntum 

y Manuals 

r information on calibration procedures and equipment maintenance information. 

. REFERENCES 

[1] tors,” 2003 NCSL 

International Workshop and Symposium, Tampa, FL, Aug. 18-21, 2003. 

[2] ce standards,” Review of Scientific 

Instruments, Vol. 74, No. 9, September 2003. 

[3] d its Application 

to Calculable Standards of Capacitance,” Nature, 177, 888 (1956).

E

7

The REPORT OF CALIBRATION returned to each standard capacitor calibration customer 

contains a brief introductory description, a table of test results, a table of test conditions, a 

signatory line, and a fact sheet describing the measurement service. A sample REPORT OF

CALIBRATION for each calibration service (fused-silica standard capacitor, nitrogen ga

standard cap

A

All customer standard capacitor calibration information and reports are stored in the Qua

Electrical Metrology Division ISSC. Additionally, all calibration measurement data and 

spreadsheet data are stored on division computers. Please refer to the division Qualit

fo

8

Y. Wang, “Measurements of frequency dependence of fused-silica capaci

Y. Wang, “Frequency dependence of capacitan

A.M. Thompson and D.G. Lampard, “A New Theorem in Electrostatics an

8 
[4] Cutkosky, R. D. and Lee, L. H., “Improved ten-picofarad fused silica dielectric capacitor,” 

] A.-M. Jeffery and A.D. Koffman, "Improved 1 kHz capacitance calibration uncertainty," 

] Andeen-Hagerling, Inc., “AH2700A 50 Hz – 20 kHz Ultra-Precision Capacitance Bridge, 

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

] Y.M. Chang and S.B. Tillett, “NIST Calibration Service for Capacitance Standards at Low 

[9] Y.M. Chang, “Error Analysis and Calibration Uncertainty of Capacitance Standards at 

NIST,” NIST Special Publication 250-52, January 2000. 

Journal of Research of the National Bureau of Standards, 69C (3) 173-179, 1965. 

[5

Proc. of the 2002 Inst. Meas. Tech. Conf. (Anchorage Alaska, May 21-23), 73 (2002). 

[6

Operation and Maintenance Manual,” Cleveland, OH, 2003. 

[7

of NIST Measurement Results,” NIST Tech. Note No. 1297, September 1994. 

[8

Frequency,” NIST Special Publication 250-47, April 1998. 

9 
APPENDICES 

A. REPORT OF CALIBRATION for a 100 pF fused-silica standard capacitor under NIST 

test ID 52130C/52131C 

B. REPORT OF CALIBRATION for a 1000 pF nitrogen gas standard capacitor under NIST 

test ID 52140C/52141C 

C. REPORT OF CALIBRATION for a 100 pF nitrogen gas standard capacitor (low 

accuracy) under NIST test ID 52160C/52161C 

D. AH2700A Capacitance Bridge Accuracy for 1 pF, 10 pF, 100 pF, and 1000 pF standards 

E. Calibration procedure for three-terminal fused-silica standard capacitors 

F. Calibration procedure for high-accuracy three-terminal nitrogen gas standard capacitors 

G. Calibration procedure for low-accuracy three-terminal nitrogen gas standard capacitors 

10 
Test Report No.: 817/275555-06 1of 3 

Reference: 7654321 

Date: July 31, 2006 

Telephone Contact: 301-975-4221 

APPENDIX A 

REPORT OF CALIBRATION 

Standard Capacitor 

Andeen-Hagerling, Inc., Model AH11A 

Serial Number 01234 

AH1100 Enclosure Serial Number 00068 

Submitted by: 

XYZ Laboratory 

Gaithersburg, MD 20899-8172 

This standard capacitor was calibrated between January 31 and March 3, 2006. The measurement conditions are 

given in Table 1. The results are reported in Table 2. These values are based on at least five independent 

comparisons of this standard with NIST capacitance standards that are traceable to the SI, as described on the 

attached fact sheet. 

The reported expanded uncertainties are consistent with international practice and are given by U = 2 uc, where uc is 

the relative combined standard uncertainty for all known sources of error and 2 is the coverage factor. The 

expanded uncertainty contains allowances for short-term drift of the reference and test standards, thermal and 

mechanical errors of the test standard, and linearity errors and loading errors of the bridge. The expanded 

uncertainties contain no allowance for long-term drift of the standard under calibration or for the possible effects of 

transporting the standard between laboratories. 

Additional information is given in the attached fact sheet. 

Table 1. Test conditions 

Date the standard arrived at NIST January 25, 2006 

Condition of the standard upon arrival No visible damage 

NIST SP250 Test Number(s) 52130C, 52131C 

Mean Enclosure Temperature 32.2 oC 

Enclosure Temperature Variation 0.4 oC 

Mean ambient temperature during measurements 22.94 oC ± 0.1 oC 

Mean relative humidity during measurements 33 % ± 5 % 

Measurements performed by: For the Director, 

Andrew D. Koffman, Electronics Engineer Gerald J. FitzPatrick, Group Leader 

Quantum Electrical Metrology Division Quantum Electrical Metrology Division 
Andeen-Hagerling, Inc. 

Model AH11A, Serial No. 01234 

Model AH1100, Serial No. 00068 

Table 2. Test results 

Frequency 

(kHz ± 0.01 %) 

Capacitance (pF) Type A 

Uncertainty 

(μF/F) 

Expanded 

Uncertainty 

(μF/F) (k=2) 

0.05 100.00032 0.32 1.64 

0.08 100.00032 0.20 0.99 

0.1 100.00032 0.15 0.77 

0.16 100.00033 0.10 0.57 

0.2 100.00033 0.08 0.51 

0.32 100.000327 0.06 0.41 

0.4 100.000326 0.05 0.35 

0.6 100.000329 0.04 0.28 

0.8 100.000329 0.03 0.24 

1.0 100.000330 0.03 0.21 

1.6 100.000332 0.03 0.19 

2.0 100.000332 0.03 0.20 

3.0 100.000332 0.03 0.24 

4.0 100.000332 0.04 0.29 

6.0 100.000335 0.05 0.40 

8.0 100.00035 0.07 0.54 

10.0 100.00036 0.10 0.72 

12.0 100.00039 0.16 1.08 

16.0 100.00042 0.22 1.54 

20.0 100.00048 0.34 2.35 

Fact Sheet: NIST Measurement of Fused-Silica Dielectric Capacitors 

Representation of the Unit of Capacitance 

As a result of the 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]. Since that time, the reported 

values of capacitance 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 less than or equal to ± 0.1 part in 106

. 

Fused-Silica Dielectric Standard Capacitors 

Three-terminal standard capacitors of fused-silica dielectric are calibrated using an automatic capacitance bridge as 

a transfer standard. Fused-silica reference standard capacitors that are periodically characterized against NIST 10 pF 

fused-silica primary standards [3] are measured at all test frequencies immediately prior to measuring the standard 

under test using the same automatic capacitance bridge. The frequency dependence of the reference standards are 

determined using the method described in reference [4]. The difference between the measured and characterized 

values of the reference standard is added to the measured value of the standard under test to produce the calibration 

value of the standard under test. 

The reported value is the mean of the result of five or more measurements with the standard under test connected to 

the capacitance bridge as a two-terminal-pair admittance [5]. All standard capacitors must be in the calibration 

laboratory for at least 72 hours prior to measurement. The average ambient temperature of the laboratory is 

23.0 ± 1.0 oC with hourly variations of about 0.1 oC. The relative humidity in the laboratory varies but does not 

exceed 50 %. 

Test Report No.: 817/275554-06 

Reference: 1234567 2 of 3 

Date: March 15, 2006 

Telephone Contact: 301-975-4221 
Andeen-Hagerling, Inc. 

Model AH11A, Serial No. 01234 

Model AH1100, Serial No. 00068 

For standards with an air bath temperature well, the temperature at measurement is taken using 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 oC. For best accuracy of measurement for standards with an air bath temperature well, corrections for the 

capacitance value are required if the temperature of the air bath is changed significantly. If it is not possible to apply 

corrections for the temperature differences, the magnitude of the errors usually can be estimated from information 

supplied by the manufacturer, and the uncertainty of the measurement increased accordingly. 

Uncertainties 

The reported value of capacitance is in terms of the NIST unit of capacitance maintained with a group of stable 

standards [3]. The reported uncertainty, consistent with practice recommended by the International Bureau of 

Weights and Measures (BIPM), is the expanded uncertainty, U = k uc, where uc is the relative combined standard 

uncertainty for all known sources of error and k is a coverage factor. Consistent with international practice, NIST 

uses a coverage factor of k = 2. The expanded uncertainty is thus given by 

U = 2 uc = 2 ∑ 2

ui

where ui is the estimated relative standard uncertainty associated with the i

th source of error and expressed as an 

equivalent standard deviation. One component is an estimated Type A standard uncertainty based on the standard 

deviation of the mean of five or more individual measurements. The uncertainty contains no allowances for the 

long-term drift of the standard under calibration or for the possible effects of transporting the standard between 

laboratories. Details of the NIST method of expressing uncertainties can be found in reference [6]. 

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. on Instrumentation and Measurements, Vol. IM 38, No. 2, pp. 249-251, Apr. 1989. 

[3] R.D. Cutkosky and L.H. Lee, “Improved Ten-picofarad Fused Silica Dielectric Capacitor,” Journal of Research 

NBS, Vol. 69C, No. 3, July & Sept. 1965. 

[4] Y. Wang, “Frequency dependence of capacitance standards,” Review of Scientific Instruments, Vol. 74, No. 9, 

September 2003. 

[5] A.M. Thompson, “The Precise Measurement of Small Capacitances,” IRE Trans. on Instr., Vol. I-7, No. 3 & 4, 

pp. 245-255, Dec. 1958. 

[6] B.N. Taylor and C.E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement 

Results,” NIST Tech. Note No. 1297, September 1994. 

Test Report No.: 817/275554-06 

Reference: 1234567 3 of 3 

Date: March 15, 2006 

Telephone Contact: 301-975-4221 
Test Report No.: 817/275555-06 1of 2 

Reference: 7654321 

Date: July 31, 2006 

Telephone Contact: 301-975-4221 

APPENDIX B

REPORT OF CALIBRATION 

Standard Capacitor 

General Radio Company, Model 1404-A 

Serial Number 2316 

Submitted by: 

NIST 

Gaithersburg, MD 20899 

This standard capacitor was calibrated between June 29 and July 19, 2006. The measurement conditions are reported 

in Table 1. The results are given in Table 2. The values are based on at least five independent comparisons of this 

standard with NIST capacitance standards that are traceable to the SI unit of capacitance, as described on the 

attached fact sheet. 

The reported expanded uncertainties are consistent with international practice and are given by U = 2 uc, where uc is 

the relative combined standard uncertainty for all known sources of error and 2 is the coverage factor. The 

expanded uncertainty contains allowances for short-term drift of the reference and test standards, thermal and 

mechanical errors of the test standard, and linearity errors of the bridge. The expanded uncertainties contain no 

allowance for long-term drift of the standard under calibration, for loading effects of the automatic capacitance 

bridge, or for the possible effects of transporting the standard between laboratories. 

Additional information is given in the attached fact sheet. 

Table 1. Test conditions 

Date the standards arrived at NIST June 22, 2006 

Condition of the standards upon arrival No visible damage 

NIST SP250 Test Number(s) 52140C, 52141C 

Mean ambient temperature during measurements 22.85 ± 0.1 oC 

Mean relative humidity during measurements 32 ± 5 % 

Table 2. Test results 

Frequency 

(kHz ± 0.01 %) 

Capacitance (pF) Expanded 

Uncertainty 

(μF/F) (k=2) 

0.05 1000. 1301 4.5 

0.1 1000.1253 3.6 

0.4 1000.1162 2.6 

1.0 1000.1147 2.2 

1.6 1000.1180 2.2 

Measurements performed by: For the Director, 

Andrew D. Koffman, Electronics Engineer Gerald J. FitzPatrick, Group Leader 

Quantum Electrical Metrology Division Quantum Electrical Metrology Division 
General Radio Company 

Model 1404-B, Serial No. 517 

Fact Sheet: NIST Measurement of Nitrogen Dielectric Standard Capacitors 

Representation of the Unit of Capacitance 

As a result of the 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]. Since that time, the reported 

values of capacitance 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 less than or equal to ± 0.1 part in 106

. 

Nitrogen Dielectric Standard Capacitors 

Three-terminal standard capacitors of nitrogen dielectric are calibrated using an automatic capacitance bridge as a 

transfer standard. Fused-silica reference standard capacitors with known frequency dependence [3] that are 

periodically characterized against NIST 10 pF fused-silica primary standards [4] are measured at all test frequencies 

immediately prior to measuring the standard under test using the automatic capacitance bridge. The difference 

between the measured and characterized values of the reference standard is added to the measured value of the 

standard under test to produce the calibration value of the standard under test. 

The reported value is the mean of the result of five or more measurements. If the terminals of the standard under test 

are not two-terminal-pair, connections with negligible impedance are made to make them so [5]. All standard 

capacitors must be in the calibration laboratory for at least 72 hours prior to measurement. The average ambient 

temperature of the laboratory is 23.0 ± 1.0 oC with hourly variations of about 0.1 oC. The relative humidity in the 

laboratory varies but calibrations are not performed if the value is above 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 measurements, and are assigned to the capacitance values using a coverage factor k = 2 [6]. The expanded 

uncertainty is thus given by 

U = 2 uc = 2 ∑ 2

ui

where ui is the estimated relative standard uncertainty associated with the i

th source of error and expressed as an 

equivalent standard deviation. The uncertainty values do not include any uncertainty components that may be 

associated with long-term instability, temperature hysteresis, changes due to stresses incurred during shipment, or 

loading effects of the capacitance bridge. 

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. on Instrumentation and Measurements, Vol. IM 38, No. 2, pp. 249-251, Apr. 1989. 

[3] Y. Wang, “Frequency dependence of capacitance standards,” Review of Scientific Instruments, Vol. 74, No. 9, 

September 2003. 

[4] R.D. Cutkosky and L.H. Lee, “Improved Ten-picofarad Fused Silica Dielectric Capacitor,” Journal of Research 

NBS, Vol. 69C, No. 3, July & Sept. 1965. 

[5] A.M. Thompson, “The Precise Measurement of Small Capacitances,” IRE Trans. on Instr., Vol. I-7, No. 3 & 4, 

pp. 245-255, Dec. 1958. 

[6] B.N. Taylor and C.E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement 

Results,” NIST Tech. Note No. 1297, September 1994.

Test Report No.: 817/275556-06 2 of 2 

Reference: ABC123 

Date: July 31, 2006 

Telephone Contact: 301-975-4221 
Test Report No.: 817/275556-06 1 of 2 

Reference: ABC123 

Date: July 31, 2006 

Telephone Contact: 301-975-4221 

APPENDIX C 

REPORT OF CALIBRATION 

Standard Capacitor 

General Radio Company, Model 1404-B 

Serial Number 517 

Submitted by: 

XYZ Laboratory 

Gaithersburg, MD 20899-8172 

This standard capacitor was calibrated between March 1 and July 9, 2006. The results are reported in Table 1. The 

measurement conditions are given in Table 2. The values are based on at least three independent comparisons of 

this standard with NIST capacitance standards that are traceable to the SI unit of capacitance, as described on the 

attached Fact Sheet. 

The test conditions are summarized in Table 2 and additional information is given in the attached Fact Sheet. 

Table 1. Test results 

Frequency 

(kHz ± 0.01 %) 

Capacitance (pF) Expanded 

Uncertainty 

(μF/F) (k=2) 

0.1 99.9998 25 

0.4 99.9995 25 

1.0 99.9994 25 

Table 2. Test conditions 

Date the standard arrived at NIST February 25, 2006 

Condition of the standard upon arrival No visible damage 

NIST SP250 Test Number(s) 52160C, 52161C 

Mean ambient temperature during measurements 23.0 ± 1.0 oC 

Mean relative humidity during measurements 33 ± 10 % 

Measurements performed by: For the Director, 

Andrew D. Koffman, Electronics Engineer Gerald J. FitzPatrick, Group Leader, AEM 

Quantum Electrical Metrology Division Quantum Electrical Metrology Division 
Fact Sheet: NIST Measurement of Nitrogen Dielectric Standard Capacitors 

Representation of the Unit of Capacitance 

As a result of the 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]. Since that time, the reported 

values of capacitance 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 less than or equal to ± 0.1 part in 106

. 

Nitrogen Dielectric Standard Capacitors 

Three-terminal standard capacitors of nitrogen dielectric are calibrated using an automatic capacitance bridge as a 

transfer standard. Fused-silica reference standard capacitors that are periodically characterized against NIST 10 pF 

fused-silica primary standards [3] are measured at all test frequencies immediately prior to measuring the standard 

under test using the automatic capacitance bridge. The difference between the measured and characterized values of 

the reference standard is added to the measured value of the standard under test to produce the calibration value of 

the standard under test. 

The reported value is the mean of the result of three or more measurements. If the terminals of the standard under 

test are not two-terminal-pair, connections with negligible impedance are made to make them so [4]. All standard 

capacitors must be in the calibration laboratory for at least 72 hours prior to measurement. The average ambient 

temperature of the laboratory is 23.0 ± 1.0 oC with hourly variations of about 0.1 oC. The relative humidity in the 

laboratory varies but does not exceed 60 %. 

The reported value of capacitance is in terms of the NIST unit of capacitance maintained with a group of stable 

standards [3]. The expanded uncertainties include allowance for both Type A and Type B uncertainties in the chain 

of measurements. The reported expanded uncertainties are consistent with international practice and are given by 

U = 2 uc, where uc is the relative combined standard uncertainty for all known sources of error and 2 is the coverage 

factor [5]. The expanded uncertainty contains allowances for short-term drift of the reference and test standards, 

thermal and mechanical errors of the test standard, and linearity errors of the bridge. The expanded uncertainties 

contain no allowance for long-term drift of the standard under calibration, for temperature hysteresis, for loading 

effects of the automatic capacitance bridge, or for changes due to stresses incurred during shipment. 

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. on Instrumentation and Measurements, Vol. IM 38, No. 2, pp. 249-251, Apr. 1989. 

[3] R.D. Cutkosky and L.H. Lee, “Improved Ten-picofarad Fused Silica Dielectric Capacitor,” Journal of Research 

NBS, Vol. 69C, No. 3, July & Sept. 1965. 

[4] A.M. Thompson, “The Precise Measurement of Small Capacitances,” IRE Trans. on Instr., Vol. I-7, No. 3 & 4, 

pp. 245-255, Dec. 1958. 

[5] B.N. Taylor and C.E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement 

Results,” NIST Tech. Note No. 1297, September 1994. 
APPENDIX D

AH2700A Capacitance Bridge Accuracy for 1 pF, 10 pF, 100 pF, and 1000 pF Standards‡

Frequency 1 pF 10 pF 100 pF 1000 pF 

(Hz) Bridge Accuracy Bridge Accuracy Bridge Accuracy Bridge Accuracy 

(μF/F) (μF/F) (μF/F) (μF/F) 

50 62.0 18.8 14.5 14.5 

80 30.9 12.4 10.5 10.5 

100 23.1 10.5 9.2 9.2 

160 13.6 7.9 7.3 7.3 

200 11.1 7.1 6.7 6.7 

320 8.0 6.0 5.8 5.8 

400 7.1 5.6 5.5 5.5 

600 6.2 5.3 5.2 5.2 

800 5.9 5.2 5.1 5.1 

1000 5.8 5.1 5.0 5.0 

1600 6.4 5.4 5.2 5.2 

2000 7.1 5.6 5.4 5.4 

3000 9.2 6.5 5.9 5.9 

4000 12.0 7.5 6.5 6.6 

6000 19.7 10.1 7.9 8.1 

8000 30.2 13.5 9.6 9.9 

10000 43.4 17.5 11.4 12.0 

12000 59.3 22.1 13.4 14.5 

16000 99.2 33.5 18.1 20.3 

20000 150.1 47.6 23.6 27.5 

 

‡

 AH2700A specifications obtained from ah2700aSpecCalculator.xls spreadsheet downloaded from AndeenHagerling web site www.andeen-hagerling.com. 
APPENDIX E 

Calibration procedure for three-terminal fused-silica standard capacitors 

Arrival of Standards 

Standards arrive at the division shipping room. The division shipping specialist documents any 

issues involving unusual shipping circumstances and transports the standards to the Impedance 

Calibration Laboratory (ICL). Calibration personnel should coordinate with shipping staff to 

assure that improper handling during customer packing or shipping is documented and 

communicated to the customer prior to performing the calibration. 

Calibration staff logs standard artifacts into the customer log book in the ICL. Customer name, 

address, contact name and telephone number, standard model number, standard serial number, 

NIST test ID number (52130C/52131C), frequencies required for calibration, the date of arrival 

at NIST, and the date of power-up of the standard, are documented in the customer log book. 

During the calibration period, the dates of measurement, and the date of report submission are 

recorded in the customer log book. Any comments pertaining to the calibration, such as whether 

connectors arrived with the standard or whether any irregularities were noticed upon arrival, 

requiring customer contact, are also noted in the customer log book. Date of return shipment is 

documented by the Calibration Coordinator. 

Standards are placed at the capacitance calibration workstation in the ICL and powered up for at 

least 72 hours prior to calibration to allow for temperature stabilization. Standards are not moved 

during the period of calibration. Laboratory temperature is maintained at 22.9 °C. Stabilization 

requires that laboratory temperature not vary more than 0.3 °C during the previous 72 hours. 

Laboratory relative humidity must remain below 50 % in order to perform calibration 

measurements. Customer standards without BNC connectors require BNC adapters to be fixed 

on the terminals of the standard. 

General Information 

Commercial three-terminal (3T) fused-silica standard capacitors are typically housed in a 

temperature-controlled enclosure to maintain stability of the capacitance. There are two 

predominant types of fused-silica standard capacitors that are calibrated in the Impedance 

Calibration Laboratory at NIST. They are an older type of standard without a temperature 

readout, having values of 10 pF or 100 pF, and a newer type with a built-in temperature readout, 

having values of 1 pF, 10 pF, or 100 pF. The temperature of the enclosure must be recorded at 

the time of measurement, regardless of the model. Therefore, the older type of standard requires 

calibration staff to place a standard platinum resistance thermometer (SPRT) inside the well of 

the enclosure in order to record the temperature. An automatic resistance thermometry bridge is 

used to measure the SPRT resistance at the time of measurement on all days when calibration 

measurements are performed. The resistance value taken from the thermometry bridge is 

converted into a temperature. The mean and variation of the enclosure temperature, along with 

the laboratory mean ambient temperature and mean relative humidity are recorded on the Report 

of Calibration. 
Fused-silica standard capacitors can be calibrated at the following frequencies (listed in Hertz): 

50, 80, 100, 160, 200, 300, 400, 600, 800, 1000, 1600, 2000, 3000, 4000, 6000, 8000, 10000, 

12000, 16000, and 20000. 

Reference three-terminal fused-silica standard capacitors with nominal values 100 pF, 10 pF, and 

1 pF are calibrated against the NIST primary bank of 10 pF fused-silica standard capacitors at 

1592 Hz at least once per year. 

Technical Procedures

Calibration of three-terminal fused-silica standard capacitors is performed using an AH2700A 

automatic capacitance bridge. A calibration consists of the mean of at least five separate 

capacitance measurements taken on different days over approximately two weeks. Stray 

capacitance, that is, capacitance across the low-to-ground terminals and high-to-ground terminals 

of the standard capacitor under test, is also measured one time during the calibration period, to 

allow for correction of the calibrated value of capacitance. 

For each of the five measurements, the standard under test is measured and the NIST reference 

standard capacitor of the same nominal value is measured on the same work day. The difference 

between the measured value of the reference standard and the calibrated value of the reference 

standard is used as a substitutionary correction to the measured value of the standard under test. 

To perform a measurement on a standard capacitor, connect the coaxial BNC cables from the 

AH2700A capacitance bridge controlled by the computer at the capacitance calibration 

workstation, to the standard capacitor to be measured. Check to be sure the red connector on 

either end of the cables is fixed to the high terminal of the bridge and of the standard, and the 

blue connector at either end is fixed to the low terminal of the bridge and of the standard. Open 

the LabVIEW program library entitled C:\LabVIEW_VIs\ah2700a.llb. Select the VI (virtual 

instrument) named AH2700A_Cap_Calibration.vi. 

This program performs capacitance and loss measurements at the 20 frequencies listed above. 

Ten measurements are averaged for each frequency. The mean and standard deviation of the 

measurements at each frequency are shown on the front panel of the VI and are saved in a text 

file under C:\calibrations\FreqDep\’mmmyy’\cModel_SerialNumber_MMDDYY_Time.txt. 

On the front panel of the VI, select the nominal value of the standard to be measured, select the 

model of the standard to be measured, enter the serial number of the standard to be measured, 

and run the VI. The VI will prompt the user to verify that the name of the file to be saved is 

satisfactory. Click on the ‘OK’ button and the program will run over approximately the next 20 

minutes. When the customer standard has been measured, repeat the measurement procedure for 

the NIST reference standard of the same nominal value as the customer standard. Multiple 

customer values of the same nominal value require only one corresponding measurement of the 

NIST reference standard. 
Enter the data into a spreadsheet file following the templates in the directory 

C:\calibrations\AHData and store the spreadsheet in the directory 

C:\calibrations\AHData\FusedSilicaResults\cModel_Customer_SerialNumber_MMYY.xls 

Once the measurements are completed, the Report of Calibration must be generated. The ISSC is 

used to generate the reports for all normal calibrations. The ISSC requires a text file containing 

the exact data for the Test results table of the Report of Calibration (see Appendix A, Table 2). 

The text files that are input into the ISSC are stored in the directory 

C:\calibrations\Reports\Fused-silica\ISSCTextFiles\Model_Customer_SerialNumber_MMYY.txt. 

All calibration files are backed up in the group directory G:\adk\calibrations following the same 

directory and filename patterns as above. This directory is located on a network server and is 

regularly backed up. 
APPENDIX F 

Calibration procedure for high-accuracy three-terminal nitrogen gas standard capacitors 

Arrival of Standards 

Standards arrive at the division shipping room. The division shipping specialist documents any 

issues involving unusual shipping circumstances and transports the standards to the Impedance 

Calibration Laboratory (ICL). Calibration personnel should coordinate with shipping staff to 

assure that improper handling during customer packing or shipping is documented and 

communicated to the customer prior to performing the calibration. 

Calibration staff logs standard artifacts into the customer log book in the ICL. Customer name, 

address, contact name and telephone number, standard model number, standard serial number, 

NIST test ID number (52140C/52141C), frequencies required for calibration, the date of arrival 

at NIST, and the date of arrival at the ICL, are documented in the customer log book. During the 

calibration period, the dates of measurement, and the date of report submission are recorded in 

the customer log book. Any comments pertaining to the calibration, such as whether connectors 

arrived with the standard or whether any irregularities were noticed upon arrival, requiring 

customer contact, are also noted in the customer log book. Date of return shipment is 

documented by the Calibration Coordinator. 

Standards are placed in a foam insulating container at the capacitance calibration workstation in 

the ICL for at least 72 hours prior to calibration to allow for temperature stabilization. Standards 

are not moved during the period of calibration. Laboratory temperature is maintained at 22.9 °C. 

Stabilization requires that laboratory temperature not vary more than 0.3 °C during the previous 

72 hours. Laboratory relative humidity must remain below 50 % in order to perform calibration 

measurements. Customer standards without BNC connectors require BNC adapters to be fixed 

on the terminals of the standard. 

General Information 

Commercial three-terminal (3T) nitrogen gas standard capacitors have a temperature coefficient 

of capacitance of several parts in 106

 and are typically not housed in a temperature-controlled 

enclosure. Therefore, temperature stability of the laboratory is critical to the calibration. There 

are two predominant types of commercial nitrogen gas standard capacitors that are calibrated in 

the Impedance Calibration Laboratory at NIST. One type of standard comes with nominal values 

of 10 pF, 100 pF, or 1000 pF, and the other type has only the nominal value of 1000 pF. 

Nitrogen gas standard capacitors can be calibrated at the following frequencies (listed in Hertz): 

50, 80, 100, 160, 200, 300, 400, 600, 800, 1000, 1600, 2000, 3000, 4000, 6000, 8000, 10000, 

12000, 16000, and 20000. 

Reference three-terminal fused-silica standard capacitors with nominal values 100 pF, 10 pF, and 

1 pF are calibrated against the NIST primary bank of 10 pF fused-silica standard capacitors at 

1592 Hz at least once per year. 
Technical Procedures

Calibration of three-terminal nitrogen gas standard capacitors is performed using an AH2700A 

automatic capacitance bridge. A calibration consists of the mean of at least five separate 

capacitance measurements taken on different days over approximately two weeks. For each of 

the five measurements, the standard under test is measured and the NIST reference standard 

capacitor of the same nominal value (the 100 pF reference is also used for a 1000 pF calibration) 

is measured on the same work day. The difference between the measured value of the reference 

standard and the calibrated value of the reference standard is used as a substitutionary correction 

to the measured value of the standard under test. 

To perform a measurement on a standard capacitor, connect the coaxial BNC cables from the 

AH2700A capacitance bridge controlled by the computer at the capacitance calibration 

workstation, to the standard capacitor to be measured. Check to be sure the red connector on 

either end of the cables is fixed to the high terminal of the bridge and of the standard, and the 

blue connector at either end is fixed to the low terminal of the bridge and of the standard. Open 

the LabVIEW program library entitled C:\LabVIEW_VIs\ah2700a.llb. Select the VI (virtual 

instrument) named AH2700A_Cap_Calibration.vi. 

This program performs capacitance and loss measurements at the 20 frequencies listed above. 

Ten measurements are averaged for each frequency. The mean and standard deviation of the 

measurements at each frequency are shown on the front panel of the VI and are saved in a text 

file under C:\calibrations\FreqDep\’mmmyy’\cModel_SerialNumber_MMDDYY_Time.txt. 

On the front panel of the VI, select the nominal value of the standard to be measured, select the 

model of the standard to be measured, enter the serial number of the standard to be measured, 

and run the VI. The VI will prompt the user to verify that the name of the file to be saved is 

satisfactory. Click on the ‘OK’ button and the program will run over approximately the next 20 

minutes. When the customer standard has been measured, repeat the measurement procedure for 

the NIST reference standard of the same nominal value as the customer standard. Multiple 

customer values of the same nominal value require only one corresponding measurement of the 

NIST reference standard. 

Enter the data into a spreadsheet file following the templates in the directory 

C:\calibrations\AHData and store the spreadsheet in the directory 

C:\calibrations\AHData\GasResults\cModel_Customer_SerialNumber_MMYY.xls 

Once the measurements are completed, the Report of Calibration must be generated. The ISSC is 

used to generate the reports for all normal calibrations. The ISSC requires a text file containing 

the exact data for the Test results table of the Report of Calibration (see Appendix B, Table 2). 

The text files that are input into the ISSC are stored in the directory 

C:\calibrations\Reports\Gas\ISSCTextFiles\Model_Customer_SerialNumber_MMYY.txt. The 

laboratory mean ambient temperature and mean relative humidity are recorded on the Report of 

Calibration. 
All calibration files are backed up in the group directory G:\adk\calibrations following the same 

directory and filename patterns as above. This directory is located on a network server and is 

regularly backed up. 
APPENDIX G 

Calibration procedure for low-accuracy three-terminal nitrogen gas standard capacitors 

Arrival of Standards 

Standards arrive at the division shipping room. The division shipping specialist documents any 

issues involving unusual shipping circumstances and transports the standards to the Impedance 

Calibration Laboratory (ICL). Calibration personnel should coordinate with shipping staff to 

assure that improper handling during customer packing or shipping is documented and 

communicated to the customer prior to performing the calibration. 

Calibration staff logs standard artifacts into the customer log book in the ICL. Customer name, 

address, contact name and telephone number, standard model number, standard serial number, 

NIST test ID number (52160C/52161C), frequencies required for calibration, the date of arrival 

at NIST, and the date of arrival at the ICL, are documented in the customer log book. During the 

calibration period, the dates of measurement, and the date of report submission are recorded in 

the customer log book. Any comments pertaining to the calibration, such as whether connectors 

arrived with the standard or whether any irregularities were noticed upon arrival, requiring 

customer contact, are also noted in the customer log book. Date of return shipment is 

documented by the Calibration Coordinator. 

Standards are placed in a foam insulating container at the capacitance calibration workstation in 

the ICL for at least 72 hours prior to calibration to allow for temperature stabilization. Standards 

are not moved during the period of calibration. Laboratory temperature is maintained at 22.9 °C. 

Stabilization requires that laboratory temperature not vary more than 0.3 °C during the previous 

72 hours. Laboratory relative humidity must remain below 50 % in order to perform calibration 

measurements. Customer standards without BNC connectors require BNC adapters to be fixed 

on the terminals of the standard. 

General Information 

Commercial three-terminal (3T) nitrogen gas standard capacitors have a temperature coefficient 

of capacitance of several parts in 106

 and are typically not housed in a temperature-controlled 

enclosure. Therefore, temperature stability of the laboratory is critical to the calibration. There 

are two predominant types of commercial nitrogen gas standard capacitors that are calibrated in 

the Impedance Calibration Laboratory at NIST. One type of standard comes with nominal values 

of 10 pF, 100 pF, or 1000 pF, and the other type has only the nominal value of 1000 pF. 

Nitrogen gas standard capacitors can be calibrated at the following frequencies (listed in Hertz): 

50, 80, 100, 160, 200, 300, 400, 600, 800, 1000, 1600, 2000, 3000, 4000, 6000, 8000, 10000, 

12000, 16000, and 20000. 

Reference three-terminal fused-silica standard capacitors with nominal values 100 pF, 10 pF, and 

1 pF are calibrated against the NIST primary bank of 10 pF fused-silica standard capacitors at 

1592 Hz at least once per year. 
Technical Procedures

Low-accuracy calibration of three-terminal nitrogen gas standard capacitors is performed using 

an AH2700A automatic capacitance bridge. A calibration consists of the mean of at least two 

separate capacitance measurements taken on different days. For both of the measurements, the 

standard under test is measured and the NIST reference standard capacitor of the same nominal 

value (the 100 pF reference is also used for a 1000 pF calibration) is measured on the same work 

day. The difference between the measured value of the reference standard and the calibrated 

value of the reference standard is used as a substitutionary correction to the measured value of 

the standard under test. 

To perform a measurement on a standard capacitor, connect the coaxial BNC cables from the 

AH2700A capacitance bridge controlled by the computer at the capacitance calibration 

workstation, to the standard capacitor to be measured. Check to be sure the red connector on 

either end of the cables is fixed to the high terminal of the bridge and of the standard, and the 

blue connector at either end is fixed to the low terminal of the bridge and of the standard. Open 

the LabVIEW program library entitled C:\LabVIEW_VIs\ah2700a.llb. Select the VI (virtual 

instrument) named AH2700A_Cap_Calibration.vi. 

This program performs capacitance and loss measurements at the 20 frequencies listed above. 

Ten measurements are averaged for each frequency. The mean and standard deviation of the 

measurements at each frequency are shown on the front panel of the VI and are saved in a text 

file under C:\calibrations\FreqDep\’mmmyy’\cModel_SerialNumber_MMDDYY_Time.txt. 

On the front panel of the VI, select the nominal value of the standard to be measured, select the 

model of the standard to be measured, enter the serial number of the standard to be measured, 

and run the VI. The VI will prompt the user to verify that the name of the file to be saved is 

satisfactory. Click on the ‘OK’ button and the program will run over approximately the next 20 

minutes. When the customer standard has been measured, repeat the measurement procedure for 

the NIST reference standard of the same nominal value as the customer standard. Multiple 

customer values of the same nominal value require only one corresponding measurement of the 

NIST reference standard. 

Enter the data into a spreadsheet file following the templates in the directory 

C:\calibrations\AHData and store the spreadsheet in the directory 

C:\calibrations\AHData\25ppmResults\cModel_Customer_SerialNumber_MMYY.xls 

Once the measurements are completed, the Report of Calibration must be generated. The ISSC is 

used to generate the reports for all normal calibrations. The ISSC requires a text file containing 

the exact data for the Test results table of the Report of Calibration (see Appendix B, Table 2). 

The text files that are input into the ISSC are stored in the directory 

C:\calibrations\Reports\Gas\ISSCTextFiles\Model_Customer_SerialNumber_MMYY.txt. The 

laboratory ambient temperature is reported as 23.0 °C ± 1.0 °C. The mean relative humidity is 

also recorded on the Report of Calibration. 
All calibration files are backed up in the group directory G:\adk\calibrations following the same 

directory and filename patterns as above. This directory is located on a network server and is 

regularly backed up. 
1 2

C Cb

a

3 4

Fi

g. 1. Four-rod cross capacitor. Dashed line represents a ground shield. 

Calculable Capacitor 

0.5 pF, 1592 Hz 

Uncertainty 0.019 μF/F 

Fig. 2. NIST nitrogen gas and fused-silica standard capacitor traceability chain with 1600 Hz uncertainties.

10 pF Transfer Std 

Primary 10 pF Bank 

100 pF, 10 pF, 1 pF 

Reference Standards 

Unc: 0.02, 0.02, 0.13 μF/F

1 pF 9 Bar Cross Capacitor/ 

10 pF nitrogen gas 

Cylindrical Capacitor 

50 Hz to 20 kHz 

100 pF, 10 pF, 1 pF 

Customer Fused-silica Standards

Unc.: 0.19, 0.23, 1.26 μF/F (k=2)

1000 pF, 100 pF, 10 pF 

Customer N Gas Standards 

Unc.: 1.57, 1.85, 2.10 μF/F (k=2)
-0.6

-0.4-0.2

0

0.20.40.60.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 1800

Frequency (Hz)

Frequency Dependence (uF/F)

100 pF10 pF1 pF

Fig. 3. Frequency dependence of 100 pF, 10 pF, and 1 pF calibration reference standards. 
-0.2

0

0.20.40.60.8

1

0 200 400 600 800 1000 1200 1400 1600 180

Frequency (Hz)

Frequency Dependence (uF/F)

100 pF10 pF1 pF

Fig. 4. Low-frequency plot of frequency dependence curves in Fig. 3.
High 

Low

Fig. 5. Measurement of three-terminal standard capacitor using automatic capacitance bridge. 

B A

Automatic Capacitance Bridge 

CLG

Standard Capacitor 

CLH

CHG
99.998

100.000100.002100.004100.006100.008100.010100.012100.014100.016100.018

0.0 0.5 1.0 1.5 2.0 2.5 

Loading Capacitance (nF)

C272 Low-High Capacitance (pF)

Loading at Point A (High)Loading at Point B (Low)

Fig. 6. Bridge loading effects for 100 pF fused-silica reference standard measurements at 20 kHz. 
9.9995

10.000010.000510.001010.001510.002010.0025

0 0.511.522.5 

Loading Capacitance (nF)

C172 High-Low Capacitance (pF)

Loading at Point A (High)Loading at Point B (Low)

Fig. 7. Bridge loading effects for 10 pF fused-silica reference standard measurements at 20 kHz. 
1.0000

1.00011.00021.00031.00041.00051.00061.00071.00081.0009

0.0 0.5 1.0 1.5 2.0 2.5 

Loading Capacitance (nF)

C016 Low-High Capacitance (pF)

Loading at Point A (High)Loading at Point B (Low)

Fig. 8. Bridge loading effects for 1 pF fused-silica reference standard measurements at 20 kHz. 
Fig. 9. Photograph of the capacitance bridge, controlling laptop, and reference and customer fused-silica standard cap
Fig. 10. Photograph of fused-silica standard capacitor enclosures without temperature readouts. Right enclosure contai
Fig. 11. Photograph of fused-silica standard capacitor enclosures with temperature readouts. 
Fig. 12. Photograph of nitrogen gas standard capacitors. 
99.99935

99.9994099.9994599.9995099.9995599.9996099.9996599.9997099.9997599.9998099.9998599.9999099.99995

100.00000100.00005100.00010100.00015100.00020100.00025100.00030100.00035100.00040

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency

Capacitance (pF)

Fig. 13. Short-term stability of 100 pF reference standard (6 bridge measurements taken within 24 hours). 
99.999390

99.99939599.99940099.99940599.99941099.99941599.99942099.99942599.99943099.99943599.99944099.99944599.99945099.99945599.999460

0 200 400 600 800 

Frequency (Hz)

Capacitance (pF)

Fig. 14. Low-frequency portion of short-term stability of 100 pF reference standard (Fig. 13). 
99.9993

99.999499.999599.999699.999799.999899.9999

100.0000100.0001100.0002100.0003100.0004100.0005100.0006

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

Capacitance (pF)

Fig. 15. Long-term stability of 100 pF reference (bridge measurements taken over more than three years). 
-0.000150

-0.000125-0.000100-0.000075-0.000050-0.000025

0.0000000.0000250.0000500.0000750.0001000.0001250.0001500.0001750.0002000.0002250.000250

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

C - Cavg (pF)

Fig. 16. Normalized long-term stability of 100 pF reference (Figure 15 with average subtracted out). 
9.99995

9.999969.999979.999989.99999

10.0000010.0000110.0000210.0000310.0000410.0000510.0000610.0000710.00008

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 

Frequency (Hz)

Capacitance (pF)

Fig. 17. Short-term stability of 10 pF reference standard (6 bridge measurements taken within 24 hours). 
9.999951

9.9999529.9999539.9999549.9999559.9999569.9999579.9999589.9999599.9999609.9999619.9999629.999963

0 200 400 600 800 

Frequency (Hz)

Capacitance (pF)

Fig. 18. Low-frequency portion of short-term stability of 10 pF reference standard (Fig. 16).
9.99994

9.999959.999969.999979.999989.99999

10.0000010.0000110.0000210.0000310.0000410.0000510.0000610.0000710.0000810.0000910.0001010.0001110.00012

0 2000 4000 6000 8000 10000 12000 14000 16000 1800

Frequency (Hz)

Capacitance (pF)

Fig. 19. Long-term stability of 10 pF reference (bridge measurements taken over more than three years). 
-0.000040

-0.000035-0.000030-0.000025-0.000020-0.000015-0.000010-0.000005

0.0000000.0000050.0000100.0000150.0000200.0000250.0000300.0000350.0000400.0000450.0000500.0000550.0000600.000065

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

C - Cavg (pF)

Fig. 20. Normalized long-term stability of 10 pF reference (Figure 19 with average subtracted out).
0.999975

0.9999800.9999850.9999900.9999951.0000001.0000051.0000101.0000151.0000201.0000251.0000301.0000351.0000401.0000451.0000501.0000551.0000601.0000651.0000701.0000751.0000801.000085

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

Capacitance (pF)

Fig. 21. Short-term stability of 1 pF reference standard (6 bridge measurements taken within 24 hours). 
0.999978

0.9999800.9999820.9999840.9999860.9999880.9999900.9999920.9999940.9999960.9999981.0000001.0000021.0000041.0000061.0000081.0000101.000012

0 200 400 600 800 

Frequency (Hz)

Capacitance (pF)

Fig. 22. Low-frequency portion of short-term stability of 1 pF reference standard (Fig. 13).
0.99998

0.999991.000001.000011.000021.000031.000041.000051.000061.000071.000081.00009

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

Capacitance (pF)

Fig. 23. Long-term stability of 1 pF reference (bridge measurements taken over more than two years). 
-0.000020

-0.000015-0.000010-0.000005

0.0000000.0000050.0000100.0000150.0000200.000025

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

C - Cavg (pF)

Fig. 24. Normalized long-term stability of 1 pF reference (Figure 23 with average subtracted out). 
0.0

0.20.40.60.81.01.21.41.61.82.02.22.4

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

Expanded Uncertainty (k=2) (uF/F)

Fig. 25. Expanded uncertainty (k=2) for 100 pF 3T fused-silica standard capacitor calibration. 
0.00

0.501.001.502.002.503.003.50

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

Expanded Uncertainty (k=2) (uF/F)

Fig. 26. Expanded uncertainty (k=2) for 10 pF 3T fused-silica standard capacitor calibration.
0

2468

10121416182022242628303234

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

Expanded Uncertainty (k=2) (uF/F)

Fig. 27. Expanded uncertainty (k=2) for 1 pF 3T fused-silica standard capacitor calibration.
0.0

1.02.03.04.05.06.07.08.09.0

10.011.012.013.014.0

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

Expanded Uncertainty (k=2) (uF/F)

Fig. 28. Expanded uncertainty (k=2) for 1000 pF 3T nitrogen gas standard capacitor calibration.
1

23456789

10

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

Expanded Uncertainty (k=2) (uF/F)

Fig. 29. Expanded uncertainty (k=2) for 100 pF 3T nitrogen gas standard capacitor calibration.
2

3456789

10111213141516171819202122232425

0 2000 4000 6000 8000 10000 12000 14000 16000 

Frequency (Hz)

Expanded Uncertainty (k=2) (uF/F)

Fig. 30. Expanded uncertainty (k=2) for 10 pF 3T nitrogen gas standard capacitor calibration.
Frequency 100 pF Reference 10 pF Reference 1 pF Reference 

(Hz) (272) Frequency (172) Frequency (016) Frequency 

Dependence (μF/F) Dependence (μF/F) Dependence (μF/F) 

50 0.08 0.95 0.73 80 0.07 0.85 0.33 

100 0.05 0.73 0.18 160 0.09 0.67 0.01 200 0.06 0.57 0.00 300 0.04 0.47 0.00 400 0.04 0.39 0.00 600 0.02 0.26 0.00 800 0.01 0.18 0.00 

1000 0.03 0.14 0.00 1600 0.00 0.00 0.00 2000 -0.03 -0.08 0.00 3000 -0.07 -0.23 0.01 4000 -0.11 -0.34 0.02 6000 -0.12 -0.46 0.05 8000 -0.08 -0.54 0.10 

10000 0.07 -0.51 0.15 12000 0.27 -0.44 0.26 16000 0.56 -0.29 0.40 20000 1.01 -0.04 0.63 

Table 1. Frequency dependence for NIST 100 pF, 10 pF, and 1 pF reference fused-silica standard capacitors
Frequency Reference Reference Type A DUT Bridge Bridge Bridge B

(Hz) Uncertainty Drift (C272) Uncertainty Drift Thermal Mechanical Linearity Lo

C272 (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μ

50 0.68 0.03 0.32 0.03 0.05 0.05 0.32 080 0.39 0.03 0.20 0.03 0.05 0.05 0.20 0

100 0.31 0.03 0.15 0.03 0.05 0.05 0.15 0160 0.24 0.03 0.1 0.03 0.05 0.05 0.10 0200 0.21 0.03 0.08 0.03 0.05 0.05 0.08 0300 0.17 0.03 0.06 0.03 0.05 0.05 0.06 0400 0.14 0.03 0.05 0.03 0.05 0.05 0.05 0600 0.10 0.03 0.04 0.03 0.05 0.05 0.04 0800 0.07 0.03 0.03 0.03 0.05 0.05 0.03 0

1000 0.05 0.03 0.03 0.03 0.05 0.05 0.03 01600 0.02 0.03 0.03 0.03 0.05 0.05 0.03 02000 0.03 0.03 0.03 0.03 0.05 0.05 0.03 03000 0.07 0.03 0.03 0.03 0.05 0.05 0.03 04000 0.10 0.03 0.04 0.03 0.05 0.05 0.04 06000 0.14 0.03 0.05 0.03 0.05 0.05 0.05 08000 0.17 0.03 0.07 0.03 0.05 0.05 0.07 0

10000 0.20 0.03 0.10 0.03 0.05 0.05 0.10 012000 0.24 0.03 0.16 0.03 0.05 0.05 0.16 016000 0.29 0.03 0.22 0.03 0.05 0.05 0.22 020000 0.37 0.03 0.34 0.03 0.05 0.05 0.34 1

Table 2. Uncertainty budget for NIST 100 pF fused-silica standard capacitors. 
Frequency Reference Reference Type A DUT Bridge Bridge Bridge Br

(Hz) Uncertainty Drift (C172) Uncertainty Drift Thermal Mechanical Linearity Lo

C172 (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μ

50 0.61 0.03 1.08 0.03 0.05 0.05 1.08 080 0.38 0.03 0.68 0.03 0.05 0.05 0.68 0

100 0.30 0.03 0.45 0.03 0.05 0.05 0.45 0160 0.23 0.03 0.24 0.03 0.05 0.05 0.24 0200 0.21 0.03 0.18 0.03 0.05 0.05 0.18 0300 0.17 0.03 0.12 0.03 0.05 0.05 0.12 0400 0.14 0.03 0.09 0.03 0.05 0.05 0.09 0600 0.10 0.03 0.06 0.03 0.05 0.05 0.06 0800 0.07 0.03 0.05 0.03 0.05 0.05 0.05 0

1000 0.05 0.03 0.05 0.03 0.05 0.05 0.05 01600 0.02 0.03 0.05 0.03 0.05 0.05 0.05 02000 0.03 0.03 0.05 0.03 0.05 0.05 0.05 03000 0.07 0.03 0.06 0.03 0.05 0.05 0.06 04000 0.09 0.03 0.07 0.03 0.05 0.05 0.07 06000 0.14 0.03 0.12 0.03 0.05 0.05 0.12 08000 0.17 0.03 0.18 0.03 0.05 0.05 0.18 0

10000 0.20 0.03 0.27 0.03 0.05 0.05 0.27 012000 0.24 0.03 0.43 0.03 0.05 0.05 0.43 016000 0.29 0.03 0.63 0.03 0.05 0.05 0.63 020000 0.37 0.03 0.97 0.03 0.05 0.05 0.97 1

Table 3. Uncertainty budget for NIST 10 pF fused-silica standard capacitors. 
Frequency Reference Reference Type A DUT Bridge Bridge Bridge B

(Hz) Uncertainty Drift (C016) Uncertainty Drift Thermal Mechanical Linearity Lo

C016 (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μ

50 3.02 0.13 3.31 0.13 0.05 0.05 4.01 080 1.36 0.13 1.74 0.13 0.05 0.05 1.85 0

100 0.78 0.13 1.17 0.13 0.05 0.05 1.62 0160 0.34 0.13 0.74 0.13 0.05 0.05 0.90 0200 0.25 0.13 0.58 0.13 0.05 0.05 0.66 0300 0.17 0.13 0.42 0.13 0.05 0.05 0.55 0400 0.15 0.13 0.30 0.13 0.05 0.05 0.50 0600 0.14 0.13 0.33 0.13 0.05 0.05 0.51 0800 0.13 0.13 0.32 0.13 0.05 0.05 0.48 0

1000 0.13 0.13 0.30 0.13 0.05 0.05 0.47 01600 0.13 0.13 0.30 0.13 0.05 0.05 0.50 02000 0.13 0.13 0.30 0.13 0.05 0.05 0.49 03000 0.13 0.13 0.39 0.13 0.05 0.05 0.65 04000 0.13 0.13 0.51 0.13 0.05 0.05 0.83 06000 0.14 0.13 0.90 0.13 0.05 0.05 1.47 08000 0.17 0.13 1.57 0.13 0.05 0.05 2.50 0

10000 0.21 0.13 2.57 0.13 0.05 0.05 3.98 012000 0.30 0.13 3.49 0.13 0.05 0.05 5.69 016000 0.42 0.13 6.34 0.13 0.05 0.05 9.39 120000 0.65 0.13 9.36 0.13 0.05 0.05 13.57 2

Table 4. Uncertainty budget for NIST 1 pF fused-silica standard capacitors. 
Frequency Reference Reference 10:1 Ratio Type A DUT Bridge Bridge Bridge B

(Hz) Uncertainty Drift (C272) Uncertainty Uncertainty Drift Thermal Mechanical Linearity L

C272 (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (

50 0.68 0.03 0.10 1.50 0.03 0.05 0.05 1.60 80 0.39 0.03 0.10 1.35 0.03 0.05 0.05 0.90 

100 0.31 0.03 0.10 1.25 0.03 0.05 0.05 0.70 160 0.24 0.03 0.10 1.15 0.03 0.05 0.05 0.50 200 0.21 0.03 0.10 1.05 0.03 0.05 0.05 0.40 300 0.17 0.03 0.10 0.95 0.03 0.05 0.05 0.30 400 0.14 0.03 0.10 0.90 0.03 0.05 0.05 0.20 600 0.1 0.03 0.10 0.85 0.03 0.05 0.05 0.20 800 0.07 0.03 0.10 0.80 0.03 0.05 0.05 0.20 

1000 0.05 0.03 0.10 0.75 0.03 0.05 0.05 0.20 1600 0.02 0.03 0.10 0.75 0.03 0.05 0.05 0.20 2000 0.03 0.03 0.10 0.75 0.03 0.05 0.05 0.20 3000 0.07 0.03 0.10 0.75 0.03 0.05 0.05 0.20 4000 0.1 0.03 0.10 0.75 0.03 0.05 0.05 0.30 6000 0.14 0.03 0.10 0.80 0.03 0.05 0.05 0.60 8000 0.17 0.03 0.10 0.85 0.03 0.05 0.05 1.00 

10000 0.2 0.03 0.10 0.90 0.03 0.05 0.05 1.60 12000 0.24 0.03 0.10 0.95 0.03 0.05 0.05 2.30 16000 0.29 0.03 0.10 1.00 0.03 0.05 0.05 4.20 20000 0.37 0.03 0.10 1.10 0.03 0.05 0.05 6.80 

Table 5. Uncertainty budget for NIST 1000 pF nitrogen gas standard capacitors. 
Frequency Reference Reference Type A DUT Bridge Bridge Bridge B

(Hz) Uncertainty Drift (C272) Uncertainty Drift Thermal Mechanical Linearity Lo

C272 (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (

50 0.68 0.03 1.75 0.03 0.05 0.05 1.60 80 0.39 0.03 1.60 0.03 0.05 0.05 0.90 

100 0.31 0.03 1.50 0.03 0.05 0.05 0.70 160 0.24 0.03 1.40 0.03 0.05 0.05 0.50 200 0.21 0.03 1.30 0.03 0.05 0.05 0.40 300 0.17 0.03 1.20 0.03 0.05 0.05 0.30 400 0.14 0.03 1.10 0.03 0.05 0.05 0.20 600 0.1 0.03 1.05 0.03 0.05 0.05 0.20 800 0.07 0.03 1.00 0.03 0.05 0.05 0.20 

1000 0.05 0.03 0.90 0.03 0.05 0.05 0.20 1600 0.02 0.03 0.90 0.03 0.05 0.05 0.20 2000 0.03 0.03 0.90 0.03 0.05 0.05 0.20 3000 0.07 0.03 0.90 0.03 0.05 0.05 0.20 4000 0.1 0.03 0.95 0.03 0.05 0.05 0.30 6000 0.14 0.03 1.00 0.03 0.05 0.05 0.50 8000 0.17 0.03 1.05 0.03 0.05 0.05 0.80 

10000 0.2 0.03 1.10 0.03 0.05 0.05 1.20 12000 0.24 0.03 1.20 0.03 0.05 0.05 1.60 16000 0.29 0.03 1.40 0.03 0.05 0.05 2.80 20000 0.37 0.03 1.60 0.03 0.05 0.05 4.40 

Table 6. Uncertainty budget for NIST 100 pF nitrogen gas standard capacitors. 
Frequency Reference Reference Type A DUT Bridge Bridge Bridge B

(Hz) Uncertainty Drift (C172) Uncertainty Drift Thermal Mechanical Linearity L

C172 (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) (μF/F) 

50 0.61 0.03 2.00 0.03 0.05 0.05 5.90 80 0.38 0.03 1.75 0.03 0.05 0.05 2.80 

100 0.3 0.03 1.60 0.03 0.05 0.05 2.00 160 0.23 0.03 1.50 0.03 0.05 0.05 1.10 200 0.21 0.03 1.40 0.03 0.05 0.05 0.80 300 0.17 0.03 1.30 0.03 0.05 0.05 0.50 400 0.14 0.03 1.20 0.03 0.05 0.05 0.40 600 0.1 0.03 1.13 0.03 0.05 0.05 0.30 800 0.07 0.03 1.06 0.03 0.05 0.05 0.20 

1000 0.05 0.03 1.00 0.03 0.05 0.05 0.20 1600 0.02 0.03 1.00 0.03 0.05 0.05 0.30 2000 0.03 0.03 1.00 0.03 0.05 0.05 0.30 3000 0.07 0.03 1.00 0.03 0.05 0.05 0.40 4000 0.09 0.03 1.05 0.03 0.05 0.05 0.60 6000 0.14 0.03 1.10 0.03 0.05 0.05 1.20 8000 0.17 0.03 1.15 0.03 0.05 0.05 2.00 

10000 0.2 0.03 1.20 0.03 0.05 0.05 3.10 12000 0.24 0.03 1.30 0.03 0.05 0.05 4.40 16000 0.29 0.03 1.50 0.03 0.05 0.05 7.70 20000 0.37 0.03 1.70 0.03 0.05 0.05 11.90 

Table 7. Uncertainty budget for NIST 10 pF nitrogen gas standard capacitors.