Final Report
Inter-American Metrology System (SIM)
Regional Metrology Organization (RMO)
Capacitance Comparison

SIM.EM-K4, 10 pF fused-silica standard capacitor at 1000 Hz and 1600 Hz
SIM.EM-S4, 100 pF fused-silica standard capacitor at 1000 Hz and 1600 Hz
SIM.EM-S3, 1000 pF nitrogen gas standard capacitor at 1000 Hz

Member Participants:

M. Cazabat Argentina, INTI
L. M. Ogino, G. Kyriazis, R. T. B. Vasconcellos Brazil, INMETRO
B. Wood, K. Kochav Canada, NRC
H. Sanchez, B. I. Castro Costa Rica, ICE
J. A. Moreno Mexico, CENAM
A. Koffman, N. F. Zhang, Y. Wang, S. Shields United States, NIST
D. Slomovitz, D. Izquierdo, C. Faverio Uruguay, UTE

2003 – 2006 Comparison
Pilot Laboratory: National Institute of Standards and Technology

1. Introduction …………………………………………………………………………… 1
2. Traveling Standards ….………………………………………………………………... 1
3. Organization .…………………………………………………………………………... 2
4. Pilot Laboratory Measurement Results …………………………………………. 3
5. Reported Results of Comparisons .…………………………………………………... 6
6. References ..…………………………………………………………………………. 15
Appendix A. Analysis Procedure ...………………………………………………………… 16
Appendix B. Analysis Results ...………………………………………………………… 17
Appendix C. Uncertainty Budgets for 10 pF .………………………………………….. 22
Appendix D. Uncertainty Budgets for 100 pF ...……………………………………….... 28
Appendix E. Uncertainty Budgets for 1000 pF …………………………………………... 34
Appendix F. CCEM-K4 10 pF Capacitance Linkage Analysis and Results ...……….... 38
Appendix G. Corrective Actions and Results …………………………………………... 40
Appendix H. List of Participants ...……………………………………………………….... 42
Appendix I. Photographs of included parts ...……………………………………….... 43

1

1 Introduction

In order to strengthen the Interamerican Metrology System (SIM), interaction among its National
Metrology Institutes (NMI´s) must be promoted. At the same time, in accordance with the CIPM
Mutual Recognition Agreement (MRA) objectives, NMI´s must establish the degree of
equivalence between their national measurement standards by performing regional comparisons,
among other activities.

The objective of this comparison was to compare the measurement capabilities of NMI´s within
SIM in the field of capacitance. This action was aimed at determining the degree of equivalence
of measuring capabilities in capacitance. The proposed test points were selected to evaluate the
measuring capabilities of the participants, both their measurement standards and their
measurement procedures.

SIM has undertaken three related capacitance comparisons. SIM.EM-K4 is a comparison of a
10 pF fused-silica standard at 1000 Hz and 1600 Hz. SIM.EM-S4 is a comparison of a 100 pF
fused-silica standard at 1000 Hz and 1600 Hz. SIM.EM-S3 is a comparison of a 1000 pF
nitrogen gas standard capacitor at 1000 Hz.

The participant institutes are listed in Table 1. The individual contacts are listed in Appendix I.

Table 1. Capacitance comparison participants
Country Institute Acronym
Argentina Instituto Nacional de Technologia Industrial INTI
Brazil National Institute of Metrology Standardization
and Industrial Quality
INMETRO
Canada National Research Council NRC
Costa Rica Instituto Costarricense de Electricidad ICE
Mexico Centro Nacional de Metrologia CENAM
United States National Institute of Standards and Technology NIST
Uruguay Administracion Nacional de Usinas y
Transmissiones Electricas
UTE


2 Traveling Standards

2.1 Description of the standards

The traveling standard for the SIM.EM-K4 comparison was an Andeen-Hagerling AH11A 10 pF
fused-silica standard capacitor, with serial number 01238. The traveling standard for the
SIM.EM-S4 was an Andeen-Hagerling AH11A 100 pF fused-silica standard capacitor with serial
number 01237. Both the SIM.EM-K4 and SIM.EM-S4 traveling standards were housed in the
Andeen-Hagerling AH1100 enclosure with serial number 00078. The traveling standard for the
SIM.EM-S3 comparison was a General Radio GR1404-A 1000 pF nitrogen standard capacitor
with serial number 2151.

2

The AH1100 enclosure contains a temperature controller to maintain stability of the AH11A
standards. The enclosure must be powered on to operate. The AH1100 permits operation at
voltages of 100 V, 120 V, 220 V, or 240 V. The proper fuse corresponding to the voltage of
operation must be inserted into the fuse holder on the rear of the AH1100 enclosure prior to
operation.

2.2 Transport Package Description

A wooden container was filled with polyurethane foam to hold the traveling standards and
equipment. The parts contained in the transport package consisted of
Andeen-Hagerling AH1100 enclosure SN 00078containing
o AH11A 100 pF fused-silica standard capacitor SN 01237
o AH11A 10 pF fused-silica standard capacitor SN 01238
Power cord for AH1100 (110 V, three-prong)
General Radio GR1404-A 1000 pF nitrogen standard capacitor SN 2151
one set one-meter four-terminal-pair coaxial BNC cables
one set one-meter three-terminal coaxial BNC cables
two GR874-to-BNC adapters
four female-to-female BNC connectors (barrels)
two BNC T-connectors
two BNC 90 degree (elbow) adapters
two BNC male-to-alligator connectors
one shorting cable for shorting the GR1404-A high terminal to case
one box of five 0.5 Amp fuses for the AH1100 enclosure
one bag of seven 0.25 Amp fuses for the AH1100 enclosure
one AH1100/11A Operation and Maintenance Manual

Photographs of the parts included within the shipping container are shown in Appendix I.

2.3 Quantities to be measured

Participants measured the AH11A 10 pF and 100 pF standards at 1000 Hz and 1600 Hz. The
GR1404-A 1000 pF standard was measured at 1000 Hz. All capacitance measurements with
corresponding combined standard uncertainties were reported. Enclosure temperature was
recorded with each AH11A measurement and ambient temperature was recorded with each
GR1404-A measurement. At least five measurements were reported for each frequency point.


3 Organization

The National Institute of Standards and Technology (NIST) was the pilot laboratory for
SIM.EM-K4, SIM.EM-S3, and SIM.EM-S4 comparisons. NIST used two measurement methods.
One method employed an AH2700A Capacitance Bridge with AH11A 10 pF and 100 pF
standards characterized over 50 Hz to 20 kHz as reference standards for the measurements. A
direct substitution was used for this method. Measurements were taken on a traveling standard
and a reference standard. The difference between the measured value of the reference and the

3

characterized value of the reference was added to the measured value of the traveling standard to
achieve the reported value.

The second method employed the NIST two-pair capacitance bridge for accurate 1592 Hz
measurements of the 10 pF and 100 pF AH11A traveling standards. This method was used
sparingly to check the results of the substitution method.

In order to participate in the SIM.EM-K4 10 pF fused-silica measurement at 1000 Hz and
1600 Hz, participants were to have capacitance measurement capability (including reference)
with a combined standard uncertainty of 500x10-6 at 1600 Hz. For participation in the SIM.EM-
S4 100 pF fused-silica measurement at 1000 Hz and 1600 Hz, participants were to have
capacitance measurement capability (including reference) with a combined standard uncertainty
of 500x10-6 at 1600 Hz.

For participation in the SIM.EM-S3 1000 pF gas standard measurement at 1000 Hz, participants
must have capacitance measurement capability (including reference) with a combined standard
uncertainty of 1000x10-6.

The traveling standards were measured at NIST at the beginning and ending of the comparison
schedule. The traveling standards travelled regionally between participant laboratories, with two
intermediate stops at NIST. The schedule of measurements is shown in Table 2.

Table 2. Schedule of measurements
Laboratory Approximate measurement dates
NIST (United States) November 2003 to April 2004
CENAM (México) July to August 2004
ICE (Costa Rica) September to November 2004
NIST (United States) December 2004 to February 2005
INTI (Argentina) March 2005
UTE (Uruguay) July 2005
INMETRO (Brazil) September 2005
NIST (United States) December 2005 to January 2006
NRC (Canada) February to March 2006
NIST (United States) May 2006 to March 2007

4 Pilot Laboratory Measurement Results

The pilot laboratory measurement results are shown in Figures 1 through 5 below. Results at
1 kHz consist only of measurements from an Andeen-Hagerling AH2700A Capacitance Bridge.
Results at 1.6 kHz consist of AH Bridge measurements as well as measurements from the NIST
2-pair Bridge.

4.1 SIM.EM-K4 10 pF results at 1 kHz

4


Fig. 1. Pilot laboratory measurements of AH11A SN 01238 10 pF standard capacitor at 1 kHz

4.2 SIM.EM-K4 10 pF results at 1.6 kHz

Fig. 2. Pilot laboratory measurements of AH11A SN 01238 10 pF standard capacitor at 1.6 kHz

5

4.3 SIM.EM-S4 100 pF results at 1 kHz

Fig. 3. Pilot laboratory measurements of AH11A SN 01237 100 pF standard capacitor at 1 kHz

4.4 SIM.EM-S4 100 pF results at 1.6 kHz

Fig. 4. Pilot laboratory measurements of AH11A SN 01237 100 pF standard capacitor at 1.6 kHz

6

4.5 SIM.EM-S3 1000 pF results at 1 kHz

Fig. 5. Pilot laboratory measurements of GR1404-A SN 2151 1000 pF standard at 1 kHz

5 Reported Results of Comparisons

Seven laboratories participated in these comparisons and provided results. Two of these
laboratories participated in follow-up bilateral comparisons with the pilot laboratory. Those two
and another laboratory submitted corrected data after the submission of the Draft A report was
circulated. Descriptions of these corrections are included in the appendix. Final analyses for
these comparisons were performed using the corrected data. Corrected data are presented in the
tables below and in accompanying figures.

5.1 SIM.EM-K4 10 pF results at 1 kHz

Table 3. Mean 1000 Hz measurement data for all participant laboratories.
Laboratory Mean Date Mean 1 kHz Capacitance Deviation
from Nominal Value (μF/F)
Combined Standard
Uncertainty (μF/F)
NIST USA 2003.866 1.834 0.123
NIST USA 2004.273 1.868 0.123
CENAM Mexico 2004.574 1.967 0.17
ICE Costa Rica 2004.872 -2000 180000
NIST USA 2005.049 1.988 0.123
INTI Argentina 2005.219 2.65 0.4
UTE Uruguay 2005.521 -2.30 3.4

7

INMETRO Brazil 2005.726 2.299 0.2
NIST USA 2006.016 2.414 0.123
NRC Canada 2006.159 2. 689 0.079
NIST USA 2006.419 2.510 0.123


Fig. 6. All participant results of measurement of AH11A SN 01238 10 pF at 1 kHz

8


Fig. 7. Most participant results of measurement of AH11A SN 01238 10 pF at 1 kHz


Fig. 8. Some participant results of measurement of AH11A SN 01238 10 pF at 1 kHz

9

5.2 SIM.EM-K4 10 pF results at 1.6 kHz

Table 4. Mean 1600 Hz measurement data for all participant laboratories.
Laboratory Mean Date Mean 1600 Hz Capacitance
Deviation from Nominal Value
(μF/F)
Combined Standard
Uncertainty (μF/F)
NIST USA 2003.852 1.613 0.084
NIST USA 2004.273 1.791 0.114
CENAM Mexico 2004.568 1.822 0.17
ICE Costa Rica 2004.787 -2000 180000
NIST USA 2005.060 1.894 0.096
INTI Argentina 2005.219 1.510 0.35
UTE Uruguay Did not participate
INMETRO Brazil 2005.729 2.207 0.2
NIST USA 2005.995 2.324 0.093
NRC Canada 2006.159 2.847 0.069
NIST USA 2006.419 2.356 0.114


Fig. 9. All participant results of measurement of AH11A SN 01238 10 pF at 1.6 kHz

10


Fig. 10. Most participant results of measurement of AH11A SN 01238 10 pF at 1.6 kHz


5.3 SIM.EM-S4 100 pF results at 1 kHz

Table 5. Mean 1000 Hz measurement data for all participant laboratories.
Laboratory Mean Date Mean 1 kHz Capacitance Deviation
from Nominal Value (μF/F)
Combined Standard
Uncertainty (μF/F)
NIST USA 2003.907 1.386 0.105
NIST USA 2004.273 1.477 0.105
CENAM Mexico 2004.571 0.970 0.19
ICE Costa Rica 2004.787 -600 19000
NIST USA 2005.047 1.515 0.105
INTI Argentina 2005.219 1.710 0.5
UTE Uruguay 2005.521 -1.200 3.3
INMETRO Brazil 2005.680 1.690 0.2
NIST USA 2006.003 1.750 0.105
NRC Canada 2006.159 2.190 0.110
NIST USA 2006.419 1.792 0.105

11

Fig. 11. All participant results of measurement of AH11A SN 01237 100 pF at 1 kHz

12


Fig. 12. Most participant results of measurement of AH11A SN 01237 100 pF at 1 kHz

5.4 SIM.EM-S4 100 pF results at 1.6 kHz

Table 6. Mean 1600 Hz measurement data for all participant laboratories.
Laboratory Mean Date Mean 1600 Hz Capacitance
Deviation from Nominal Value
(μF/F)
Combined Standard
Uncertainty (μF/F)
NIST USA 2003.896 1.362 0.086
NIST USA 2004.273 1.460 0.095
CENAM Mexico 2004.568 1.380 0.190
ICE Costa Rica 2004.787 -100 19000
NIST USA 2005.052 1.499 0.092
INTI Argentina 2005.222 0.580 0.450
UTE Uruguay Did not participate
INMETRO Brazil 2005.682 1.650 0.200
NIST USA 2005.997 1.732 0.089
NRC Canada 2006.159 2.452 0.200
NIST USA 2006.419 1.708 0.095

13


Fig. 13. All participant results of measurement of AH11A SN 01237 100 pF at 1.6 kHz


Fig. 14. Most participant results of measurement of AH11A SN 01237 100 pF at 1.6 kHz

14


5.5 SIM.EM-S3 1000 pF results at 1 kHz

Table 7. Mean 1000 Hz measurement data for all participant laboratories.
Laboratory Mean
Date
Mean 1 kHz Capacitance
Deviation from Nominal
Value (μF/F)
Combined
Standard
Uncertainty
(μF/F)
Mean
Measurement
Temperature
(degrees C)
NIST USA 2003.893 26.14 0.789 22.88
NIST USA 2004.292 26.10 0.789 22.84
CENAM Mexico 2004.571 25.67 0.250 23.02
ICE Costa Rica 2004.787 -220 1800 23.30
NIST USA 2005.047 28.31 0.789 23.01
INTI Argentina 2005.227 26.00 0.900 22.95
UTE Uruguay 2005.518 24.46 6.3 23.03
INMETRO Brazil 2005.688 25.41 0.200 22.10
NIST USA 2006.003 27.40 0.789 22.85
NRC Canada 2006.159 22.84 0.250 21.28
NIST USA 2006.449 27.54 0.789 22.80


Fig. 15. All participant results of measurement of GR 1404-A SN 2151 1000 pF at 1 kHz

15


Fig. 16. Most participant results of measurement of GR 1404-A SN 2151 1000 pF at 1 kHz

6 References

[1] N.F. Zhang, H.-K. Liu, N. Sedransk, and W.E. Strawderman, Statistical analysis of key
comparisons with linear trends, Metrologia, 41, pp. 231-237, 2004.

[2] A.-M. Jeffery, Final Report CCEM-K4 Comparison of 10 pF Capacitance Standards,
March 2001.

[3] N. F. Zhang, W. E. Strawderman, H. K. Liu, and N. Sedransk, Statistical analysis for
multiple artifact problem in key comparisons with linear trends, Metrologia, 43, pp. 21-
26, 2006.

[4] W. Zhang, N. F. Zhang, and H. K. Liu, A generalized method for the multiple artifacts
problem in interlaboratory comparisons with linear trends, Metrologia, 46, pp. 345-350,
2009.

[5] N. F. Zhang, Linking the results of CIPM and RMO key comparisons with linear trends,
Journal of Research of the National Institute of Standards and Technology, 115, pp. 179-
194, 2010.

16

Appendix A. Analysis Procedure

It is well known that for a standard of capacitance, the measurements typically show a trend in
time, which under our assumption can be modeled as a linear trend with time. As in [1] and [3],
we assume that the measurements of any particular laboratory have a linear trend in time and the
slopes of the linear trends for the laboratories are the same, while we allow different intercepts
for different laboratories. In each of the SIM comparisons, only one traveling standard was used.
In each comparison, the traveling standard was measured at the pilot laboratory – NIST – for five
periods, while for each of the non-pilot laboratories it was measured for only one time period.

For each non-pilot laboratory, an uncertainty budget was reported and the combined standard
uncertainty was calculated. For NIST, in each of the three 1000 Hz comparison points, i.e., for
SIM.EM-K4 10 pF at 1000 Hz, SIM.EM.-S4 100 pF at 1000Hz, and SIM.EM-S3, the Type A
uncertainties as well as the Type B uncertainties for each period are the same. However, for the
two 1600 Hz comparison points, i.e., SIM.EM-K4 10 pF at 1600 Hz and SIM.EM-S4 100 pF at
1600 Hz, the Type A uncertainties as well as the Type B uncertainties for each period of NIST
measurements are different. Thus, a general statistical analysis procedure proposed in [4] was
used.

It should be noted that the time periods for measurement at each laboratory varied from one day
to four or five weeks and the time periods for measurement at the pilot laboratory were
sometimes much longer, from weeks to months.

Additionally, the laboratories performed measurements at varying ambient temperatures, with
differences of greater than 1.5 ºC between pilot and some other laboratories. For the SIM.EM-S3
traveling standard (GR 1404-A), the temperature coefficient of capacitance is 2 ± 2 µF/F/ºC.
Unfortunately, no temperature corrections were requested within the comparison protocol. Future
comparisons should provide for either temperature enclosure for all standards or temperature
correction of the results obtained under significantly differing environmental conditions.

17

Appendix B. Analysis Results

The results were calculated based on the statistical analysis in Appendix A and are listed below.

1. SIM.EM-K4 10 pF

a. 1 kHz results

The 1000 Hz capacitance drift of the traveling standard was determined from pilot laboratory
measurements using a linear fit, cap = beta*(t-tinit) + alpha, where beta = 0.282, alpha = 1.767,
and tinit = 2003.866. The key comparison reference value (KCRV) as a deviation from the
nominal value of 10 pF, is 2.429 μF/F, with a standard uncertainty of 0.058 μF/F. The optimal
time, t, for the CRV, is t = 2005.356. Statistics are computed according to reference [1].

The degree of equivalence of all laboratories with respect to the CRV for 1000 Hz is shown in
Table 1 and the pair-wise degree of equivalence and their uncertainties are given in Table 2.
Note that for Tables 1 and 2, the degree of equivalence and their uncertainties are given in F/F.

Table B1. 1000 Hz degree of equivalence of all laboratories with respect to the CRV.
Laboratory Degree of Equivalence Uncertainty of Degree of
Equivalence
NIST -0.155 0.100
CENAM -0.155 0.162
ICE -2002 1800000
INTI 0.346 0.396
UTE -4.689 3.400
INMETRO -0.148 0.192
NRC 0.120 0.056

Table B2. Pair-wise 1000 Hz degree of equivalence with uncertainties in parentheses.
NIST CENAM ICE INTI UTE INMETRO NRC
NIST 0.000214
(0.205)
2002
(180000)
-0.501
(0.416)
4.535
(3.40)
-0.00643
(0.231)
-0.274
(0.141)
CENAM -0.000214
(0.205)
2002
(180000)
-0.5008
(0.435)
4.534
(3.40)
-0.00664
(0.264)
-0.274
(0.191)
ICE -2002
(180000)
-2002
(180000)
-2003
(180000)
-1998
(180000)
-2002
(180000)
-2002
(180000)
INTI 0.501
(0.416)
0.501
(0.435)
2003
(180000)
5.035
(3.42)
0.494
(0.447)
0.226
(0.408)
UTE -4.535
(3.40)
-4.534
(3.40)
1998
(180000)
-5.035
(3.42)
-4.541
(3.41)
-4.809
(3.40)
INMETRO 0.00643
(0.231)
0.00664
(0.264)
2002
(180000)
-0.494
(0.447)
4.541
(3.41)
-0.268
(0.215)
NRC 0.274
(0.141)
0.274
(0.191)
2002
(180000)
-0.226
(0.408)
4.809
(3.40)
0.268
(0.215)


b. 1.6 kHz results

18

The 1600 Hz capacitance drift of the traveling standard was determined from pilot laboratory
measurements using a linear fit, cap = beta*(t-tinit) + alpha, where beta = 0.303, alpha = 1.612,
and tinit = 2003.852. The comparison reference value (CRV) as a deviation from the nominal
value of 10 pF, is 2.194 μF/F, with an uncertainty of 0.035 μF/F. The optimal t = 2005.210.

The degree of equivalence of all laboratories with respect to the CRV for 1600 Hz is shown in
Table 3 and the pair-wise degree of equivalence and their uncertainties are given in Table 4.
Note that for Tables 3 and 4, the degree of equivalence is given in units of pF while the
uncertainties are given in F/F.

Table B3. 1600 Hz degree of equivalence of all laboratories with respect to the CRV.
Laboratory Degree of Equivalence Uncertainty of Degree of
Equivalence
NIST -0.136 0.029
CENAM -0.143 0.170
ICE -2002 180000
INTI -0.652 0.348
INMETRO -0.109 0.198
NRC 0.401 0.070

Table B4. Pair-wise 1600 Hz degree of equivalence with uncertainties in parentheses.
NIST CENAM ICE INTI INMETRO NRC
NIST 0.00635
(0.177)
2002
(180000)
0.515
(0.353)
-0.0273
(0.207)
-0.537
(0.096)
CENAM -0.00635
(0.177)
2002
(180000)
0.509
(0.390)
-0.0337
(0.268)
-0.543
(0.197)
ICE -2002
(180000)
-2002
(180000)
-2001
(180000)
-2002
(180000)
-2002
(180000)
INTI -0.515
(0.353)
-0.509
(0.390)
2001
(180000)
-0.543
(0.404)
-1.053
(0.359)
INMETRO 0.0273
(0.207)
0.0337
(0.268)
2002
(180000)
0.543
(0.404)
-0.510
(0.212)
NRC 0.537
(0.096)
0.543
(0.197)
2002
(180000)
1.053
(0.359)
0.510
(0.212)



2. SIM.EM-S4 100 pF

a. 1 kHz results

The 1000 Hz capacitance drift of the traveling standard was determined from pilot laboratory
measurements using a linear fit, cap = beta*(t-tinit) + alpha, where beta = 0.162, alpha = 1.387,
and tinit = 2003.866. The comparison reference value (CRV) as a deviation from the nominal
value of 100 pF, is 1.590 μF/F, with a standard uncertainty of 0.075 μF/F. The optimal time, t,
for the CRV, is t = 2005.267. Statistics are computed according to reference [1].

The degree of equivalence of all laboratories with respect to the CRV for 1000 Hz is shown in
Table 5 and the pair-wise degree of equivalence and their uncertainties are given in Table 6.
Note that for Tables 5 and 6, the degree of equivalence and their uncertainties are given in F/F.

19


Table B5. 1000 Hz degree of equivalence of all laboratories with respect to the CRV.
Laboratory Degree of Equivalence Uncertainty of Degree of
Equivalence
NIST 0.016 0.069
CENAM -0.508 0.175
ICE -601.5 19000
INTI 0.128 0.494
UTE -2.831 3.299
INMETRO 0.034 0.186
NRC 0.456 0.186

Table B6. Pair-wise 1000 Hz degree of equivalence with uncertainties in parentheses.
NIST CENAM ICE INTI UTE INMETRO NRC
NIST 0.524
(0.216)
601.5
(19000)
-0.112
(0.510)
2.847
(3.30)
-0.0172
(0.225)
-0.440
(0.225)
CENAM -0.524
(0.216)
601.0
(19000)
-0.635
(0.535)
2.323
(3.31)
-0.541
(0.276)
-0.964
(0.277)
ICE -601.5
(19000)
-601.0
(19000)
-601.6
(19000)
-598.7
(19000)
-601.5
(19000)
-602.0
(19000)
INTI 0.112
(0.510)
0.635
(0.535)
601.6
(19000)
2.959
(3.34)
0.0943
(0.539)
-0.328
(0.539)
UTE -2.847
(3.30)
-2.323
(3.305)
598.7
(19000)
-2.959
(3.34)
-2.864
(3.31)
-3.287
(3.31)
INMETRO 0.0172
(0.225)
0.541
(0.276)
601.5
(19000)
-0.0943
(0.539)
2.864
(3.31)
-0.423
(0.283)
NRC 0.440
(0.225)
0.964
(0.277)
602.0
(19000)
0.328
(0.539)
3.287
(3.31)
0.423
(0.283)



b. 1.6 kHz results

The 1600 Hz capacitance drift of the traveling standard was determined from pilot laboratory
measurements using a linear fit, cap = beta*(t-tinit) + alpha, where beta = 0.147, alpha = 1.372,
and tinit = 2003.852. The comparison reference value (CRV) as a deviation from the nominal
value of 100 pF, is 1.639 μF/F, with an uncertainty of 0.037 μF/F. The optimal t = 2005.135.

The degree of equivalence of all laboratories with respect to the CRV for 1000 Hz is shown in
Table 7 and the pair-wise degree of equivalence and their uncertainties are given in Table 8.
Note that for Tables 7 and 8 the degree of equivalence is given in units of pF while the
uncertainties are given in F/F.

20

Table B7. 1600 Hz degree of equivalence of all laboratories with respect to the CRV.
Laboratory Degree of Equivalence Uncertainty of Degree of
Equivalence
NIST -0.074 0.018
CENAM -0.165 0.019
ICE -101.6 19000
INTI -1.060 0.449
INMETRO -0.058 0.198
NRC 0.674 0.111

Table B8. Pair-wise 1600 Hz degree of equivalence with uncertainties in parentheses.
NIST CENAM ICE INTI INMETRO NRC
NIST 0.0907
(0.196)
101.5
(19000)
0.987
(0.452)
-0.0160
(0.206)
-0.748
(0.126)
CENAM -0.0907
(0.196)
101.4
(19000)
0.896
(0.489)
-0.107
(0.280)
-0.839
(0.230)
ICE -101.5
(19000)
-101.4
(19000)
-100.5
(19000)
-101.5
(19000)
-102.3
(19000)
INTI -0.987
(0.452)
-0.896
(0.489)
100.5
(19000)
-1.003
(0.493)
-1.735
(0.465)
INMETRO 0.0160
(0.206)
0.107
(0.280)
101.5
(19000)
1.003
(0.493)
-0.732
(0.229)
NRC 0.748
(0.126)
0.839
(0.230)
102.3
(19000)
1.735
(0.465)
0.732
(0.229)


3. SIM.EM-S3 1000 pF

a. 1 kHz results

The 1000 Hz capacitance drift of the traveling standard was determined from pilot laboratory
measurements using a linear fit, cap = beta*(t-tinit) + alpha, where beta = 0.584, alpha = 26.369,
and tinit = 2003.866. The comparison reference value (CRV) as a deviation from the nominal
value of 1000 pF, is 24.997 μF/F, with an uncertainty of 0.125 μF/F. The optimal time, t, for the
CRV, is t = 2005.467. Statistics are computed according to reference [1].

The degree of equivalence of all laboratories with respect to the CRV for 1000 Hz is shown in
Table 9 and the pair-wise degree of equivalence and their uncertainties are given in Table 10.
Note that for Tables 9 and 10, the degree of equivalence and their uncertainties are given in
F/F.

21


Table B9. 1000 Hz degree of equivalence of all laboratories with respect to the CRV.
Laboratory Degree of Equivalence Uncertainty of Degree of
Equivalence
NIST 2.292 0.412
CENAM 1.197 0.377
ICE -244.6 1800
INTI 1.148 0.895
UTE -0.570 6.299
INMETRO 0.285 0.174
NRC -2.562 0.322

Table B10. Pair-wise 1000 Hz degree of equivalence with uncertainties in parentheses.
NIST CENAM ICE INTI UTE INMETRO NRC
NIST 1.095
(0.522)
246.9
(1800)
1.148
(0.992)
2.862
(6.32)
2.007
(0.498)
4.854
(0.599)
CENAM -1.095
(0.522)
245.8
(1800)
0.0532
(0.961)
1.767
(6.31)
0.9120
(0.501)
3.759
(0.651)
ICE -246.9
(1800)
-245.8
(1800)
-245.7
(1800)
-244.0
(1800)
-244.9
(1800)
-242.0
(1800)
INTI -1.148
(0.992)
-0.0532
(0.961)
245.7
(1800)
1.714
(6.36)
0.8587
(0.936)
3.706
(0.988)
UTE -2.862
(6.32)
-1.767
(6.31)
244.0
(1800)
-1.714
(6.36)
-0.8548
(6.30)
1.992
(6.31)
INMETRO -2.007
(0.498)
-0.912
(0.501)
244.9
(1800)
-0.8587
(0.936)
0.8548
(6.30)
2.847
(0.359)
NRC -4.854
(0.598)
-3.759
(0.651)
242.0
(1800)
-3.706
(0.988)
-1.992
(6.31)
-2.847
(0.359)

22

Appendix C. Uncertainty Budgets for 10 pF

1. INTI

Table C1. INTI 10 pF 1000 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Reference capacitor uncertainty 0.4
Short-term stability 0.01
1:1 comparison uncertainty 0.03
Combined standard uncertainty 0.4

Table C2. INTI 10 pF 1600 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Reference capacitor uncertainty 0.35
Short-term stability 0.0082
1:1 comparison uncertainty 0.03
Combined standard uncertainty 0.35

2. INMETRO

Table C3. INMETRO 10 pF 1000 Hz Uncertainty Budget
Quantity Standard
uncertainty
Sensitivity
coefficient
Type
CN
(1) 5.0E-07 pF 1 Type B
3.72E-06 1.00E-02 pF Type A
4.90E-07 1.80E-05 pF Type A
C 5E-08 pF 6.63E-05 Type B
C 0.0018 pF 2.60E-07 Type B
0.1 6.63E-07 pF Type B
R 1E-08 pF 1 Type B
CX CN
(2) 8E-08 pF 1 Combined
Error (3) 1.0E-07 pF 1 Type B
CX
(4) 5.2E-07 pF 1 Combined
RK-90
(5) 1.00E-06 pF 1 Type B
Biannual Drift
(6)
1.00E-06 pF 1 Type A
CX
(7) 0.0000020 pF Combined

23

Table C4. INMETRO 10 pF 1600 Hz Uncertainty Budget
Quantity Standard
uncertainty
Sensitivity
coefficient
Type
CN
(1) 4.0E-07 pF 1 Type B
3.16E-06 1.00E-02 pF Type A
7.48E-07 8.00E-06 pF Type A
C 4E-08 pF 6.56E-05 Type B
C 0.0008 pF 8.00E-07 Type B
0.1 6.56E-07 pF Type B
R 1E-08 pF 1 Type B
CX CN
(2) 7E-08 pF 1 Combined
Error (3) 1.50E-07 pF 1 Type B
CX
(4) 4.3E-07 pF 1 Combined
RK-90
(5) 1.00E-06 pF 1 Type B
Biannual Drift
(6)
1.00E-06 pF 1 Type A
CX
(7) 0.0000020 pF Combined


3. NRC

Table C5. NRC 10 pF 1000 Hz Uncertainty Budget
Quantity Type Uncertainty
(µF/F)
Sensitivity
coefficient
Sensitivity
factor
Standard
uncertainty
(µF/F)
Degrees of
freedom
Reference
Standard
Combined 0.078 1 1 0.078 15.0
Test Standard Type A 0.005 1 1 0.005 9.0
Voltage
Dependence
Type B 0.000 1 1 0.000 4.9
Frequency
Dependence
Type B 0.000 1 1 0.000 4.9
10:1 Ratio
Type B 0.000 1 1 0.000 4.9
Meter
Nonlinearity
Type B 0.004 1 1 0.004 4.9
Other Type B 0.005 0 1 0.000 4.9
Combined 0.079 15.2

24

Table C6. NRC 10 pF 1600 Hz Uncertainty Budget
Quantity Type Uncertainty
(µF/F)
Sensitivity
coefficient
Sensitivity
factor
Standard
uncertainty
(µF/F)
Degrees of
freedom
Reference
Standard
Combined 0.068 1 1 0.068 10.5
Test Standard Type A 0.005 1 1 0.005 9.0
Voltage
Dependence
Type B 0.000 1 1 0.000 4.9
Frequency
Dependence
Type B 0.000 1 1 0.000 4.9
10:1 Ratio
Type B 0.000 1 1 0.000 4.9
Meter
Nonlinearity
Type B 0.004 1 1 0.004 4.9
Other Type B 0.005 0 1 0.000 4.9
Combined 0.069 10.6


4. ICE

Table C7. ICE 10 pF 1000 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Type B 90900
Type A 155000
Combined standard uncertainty 180000

Table C8. ICE 10 pF 1600 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Type B 90900
Type A 155000
Combined standard uncertainty 180000


5. CENAM

25

Table C9. CENAM 10 pF 1000 Hz Uncertainty Budget
Uncertainty
Component
Estimate
xi
Relative Standard
Uncertainty
u(xi) ( F/F)
Probability
Distribution /
Method of
Evaluation (A,B)
Sensitivity
Coefficient
ci
Uncertainty
Contribution
ui (cX) ( F/F)
Degrees of
Freedom
i
Reference
Standard Value
10 pF +
23,0 aF
0.115 Normal 1 0,115 60
Reference
Standard Long
Term Stability
--- 0.085 Normal 1.5 0,128 60
Test Standard --- 0.010 Normal 1 0,010 16
Voltage
Dependence
--- 0.005 Normal 1 0,005 60
Frequency
Dependence
--- --- --- --- --- ---
Capacitance
Bridge
-3,06 aF 0.011 Normal 1 0,011 60
Cables
Correction
--- 0.001 Normal 1 0,001 60
CX
10 pF +
19.9 aF
0.17 120

Table C10. CENAM 10 pF 1600 Hz Uncertainty Budget
Uncertainty
Component
Estimate
xi
Relative Standard
Uncertainty
u(xi) ( F/F)
Probability
Distribution /
Method of
Evaluation (A,B)
Sensitivity
Coefficient
ci
Uncertainty
Contribution
ui (cX) ( F/F)
Degrees of
Freedom
i
Reference
Standard Value
10 pF +
22,5 aF
0.115 Normal 1 0.115 60
Reference
Standard Long
Term Stability
--- 0.085 Normal 1.5 0.128 60
Test Standard --- 0.010 Normal 1 0.010 16
Voltage
Dependence
--- 0.005 Normal 1 0.005 60
Frequency
Dependence
--- --- --- --- --- ---
Capacitance
Bridge
-3,06 aF 0.011 Normal 1 0.011 60
Cables
Correction
--- 0.001 Normal 1 0.001 60
CX
10 pF +
19.9 aF
0.17 120

6. NIST

26


Table C11. NIST AH Bridge 10 pF 1000 Hz Uncertainty Budget
Quantity Type Standard uncertainty (µF/F)
Reference Standard Type B 0.050
Reference Drift Type B 0.030
Test Drift Type B 0.030
Bridge Thermal Type B 0.050
Bridge Mechanical Type B 0.050
Bridge Linearity Type B 0.050
Bridge Loading Type B 0.000
Test Variation Type A 0.030
Combined 0.123

Table C12. NIST AH Bridge 10 pF 1600 Hz Uncertainty Budget
Quantity Type Standard uncertainty (µF/F)
Reference Standard Type B 0.020
Reference Drift Type B 0.030
Test Drift Type B 0.030
Bridge Thermal Type B 0.050
Bridge Mechanical Type B 0.050
Bridge Linearity Type B 0.050
Bridge Loading Type B 0.010
Test Variation Type A 0.030
Combined 0.114

Table C13. NIST 2-Pair Bridge 10 pF 1592 Hz Uncertainty Budget
Quantity Type Standard uncertainty (µF/F)
Calculable Capacitor Type B 0.019
Transformer Bridge Type B 0.005
10 pF Correction Calculation Type B 0.002
Test Variation Type A 0.002
Combined 0.020



7. UTE

27

Table C14. UTE 10 pF 1000 Hz Uncertainty Budget
Uncertainty Component Standard
Uncertainty u(xi)
Probability
Distribution
Sensitivity
coefficient ci
Uncertainty
contribution ui(y)
k=1

Capacitance dispersion 1.68E-6 pF 6 1 1.7E-6 pF
Test current I) 3.05E-11 A Rectangular -5,71E-11 F/A -1.7E-9 pF
Reference standard C2) 3.32E-4 pF Normal 1,00E-1 F/F 3.3E-5 pF
Detector current angle 5.03E-2 rad Rectangular -1,13E-16 F -5.7E-6 pF
Detector current amplitude Id) 4.62E-14 A Rectangular 4,88E-06 F/A 2.3E-7 pF
IVD deviation 5.00E-07 V/V Normal 1,10E-11 F 5.5E-6 pF

Combined 3.4E-5 pF

28

Appendix D. Uncertainty Budgets for 100 pF

1. INTI

Table D1. INTI 100 pF 1000 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Reference capacitor uncertainty 0.5
Short-term stability 0.012
1:1 comparison uncertainty 0.03
Combined standard uncertainty 0.5

Table D2. INTI 100 pF 1600 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Reference capacitor uncertainty 0.45
Short-term stability 0.015
1:1 comparison uncertainty 0.03
Combined standard uncertainty 0.45

2. INMETRO

Table D3. INMETRO 100 pF 1000 Hz Uncertainty Budget
Quantity Standard
uncertainty
Sensitivity
coefficient
Type
CN
(1) 5.0E-06 pF 1 Type B
2.24E-05 1.00E-02 pF Type A
2.56E-06 1.80E-05 pF Type A
C 5E-08 pF 6.15E-04 Type B
C 0.0018 pF 5.80E-06 Type B
0.1 6.15E-06 pF Type B
R 1E-08 pF 1 Type B
CX CN
(2) 7E-07 pF 1 Combined
Error (3) 1.0E-06 pF 1 Type B
CX
(4) 5.1E-06 pF 1 Combined
RK-90
(5) 1.00E-05 pF 1 Type B
Biannual Drift
(6)
1.00E-05 pF 1 Type A
0.000020 pF Combined

29

Table D4. INMETRO 100 pF 1600 Hz Uncertainty Budget
Quantity Standard
uncertainty
Sensitivity
coefficient
Type
CN
(1) 4.0E-06 pF 1 Type B
2.24E-05 1.00E-02 pF Type A
4.54E-06 8.00E-06 pF Type A
C 4E-08 pF 6.14E-04 Type B
C 0.0008 pF 8.94E-06 Type B
0.1 6.14E-06 pF Type B
R 1E-08 pF 1 Type B
CX CN
(2) 7E-07 pF 1 Combined
Error (3) 1.50E-06 pF 1 Type B
CX
(4) 4.3E-06 pF 1 Combined
RK-90
(5) 1.00E-05 pF 1 Type B
Biannual Drift
(6)
1.00E-05 pF 1 Type A
CX
(7) 0.000020 pF Combined


3. NRC

Table D5. NRC 100 pF 1000 Hz Uncertainty Budget
Quantity Type Uncertainty
(µF/F)
Sensitivity
coefficient
Sensitivity
factor
Standard
uncertainty
(µF/F)
Degrees of
freedom
Reference
Standard
Combined 0.100 1 1 0.100 14.2
Test Standard Type A 0.002 1 1 0.002 9.0
Voltage
Dependence
Type B 0.000 1 1 0.000 4.9
Frequency
Dependence
Type B 0.000 1 1 0.000 4.9
10:1 Ratio
Type B 0.000 1 1 0.000 4.9
Meter
Nonlinearity
Type B 0.040 1 1 0.040 4.9
Other Type B 0.004 0 1 0.000 4.9
Combined 0.11 17.8

30

Table D6. NRC 100 pF 1600 Hz Uncertainty Budget
Quantity Type Uncertainty
(µF/F)
Sensitivity
coefficient
Sensitivity
factor
Standard
uncertainty
(µF/F)
Degrees of
freedom
Reference
Standard
Combined 0.100 1 1 0.100 14.2
Test Standard Type A 0.002 1 1 0.002 9.0
Voltage
Dependence
Type B 0.000 1 1 0.000 4.9
Frequency
Dependence
Type B 0.000 1 1 0.000 4.9
10:1 Ratio
Type B 0.000 1 1 0.000 4.9
Meter
Nonlinearity
Type B 0.040 1 1 0.040 4.9
Other Type B 0.018 0 1 0.000 4.9
Combined 0.11 17.8


4. ICE

Table D7. ICE 100 pF 1000 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Type B 9090
Type A 16600
Combined standard uncertainty 19000

Table D8. ICE 100 pF 1600 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Type B 9090
Type A 16600
Combined standard uncertainty 19000

31

5. CENAM

Table D9. CENAM 100 pF 1000 Hz Uncertainty Budget
Uncertainty
Component
Relative Standard
Uncertainty
u(xi) ( F/F)
Probability
Distribution /
Method of
Evaluation (A,B)
Sensitivity
Coefficient
ci
Uncertainty
Contribution
ui (cX) ( F/F)
Degrees of
Freedom
i
Reference
Standard Value
0,115 Normal 10 0,115 60
Reference
Standard Long
Term Stability
0,0085 Normal 15 0,128 60
Test Standard 0,007 Normal 1 0,007 16
Voltage
Dependence
0,0005 Normal 10 0,005 60
Frequency
Dependence
--- --- --- --- ---
Capacitance
Bridge
0,079 Normal 1 0,079 60
Cables
Correction
0,001 Normal 1 0,001 60
0.19 160

Table D10. CENAM 100 pF 1600 Hz Uncertainty Budget
Uncertainty
Component
Relative Standard
Uncertainty
u(xi) ( F/F)
Probability
Distribution /
Method of
Evaluation (A,B)
Sensitivity
Coefficient
ci
Uncertainty
Contribution
ui (cX) ( F/F)
Degrees of
Freedom
i
Reference
Standard Value
0,0115 Normal 10 0,115 60
Reference
Standard Long
Term Stability
0,0085 Normal 15 0,128 60
Test Standard 0,005 Normal 1 0,005 16
Voltage
Dependence
0,0005 Normal 10 0,005 60
Frequency
Dependence
0.0001 Normal 10 0.001 60
Capacitance
Bridge
0,073 Normal 1 0,073 60
Cables
Correction
0,001 Normal 1 0,001 60
0.19 156

32

6. NIST

Table D11. NIST AH Bridge 100 pF 1000 Hz Uncertainty Budget
Quantity Type Standard uncertainty (µF/F)
Reference Standard Type B 0.050
Reference Drift Type B 0.030
Test Drift Type B 0.030
Bridge Thermal Type B 0.050
Bridge Mechanical Type B 0.050
Bridge Linearity Type B 0.030
Bridge Loading Type B 0.004
Test Variation Type A 0.030
Combined 0.105

Table D12. NIST AH Bridge 100 pF 1600 Hz Uncertainty Budget
Quantity Type Standard uncertainty (µF/F)
Reference Standard Type B 0.020
Reference Drift Type B 0.030
Test Drift Type B 0.030
Bridge Thermal Type B 0.050
Bridge Mechanical Type B 0.050
Bridge Linearity Type B 0.030
Bridge Loading Type B 0.010
Test Variation Type A 0.030
Combined 0.095

Table D13. NIST 2-Pair Bridge 100 pF 1592 Hz Uncertainty Budget
Quantity Type Standard uncertainty (µF/F)
Calculable Capacitor Type B 0.019
Transformer Bridge Type B 0.005
10 pF Correction Calculation Type B 0.002
10:1 Ratio Type B 0.005
Test Variation Type A 0.002
Combined 0.020

33

7. UTE

Table D14. UTE 10 pF 1000 Hz Uncertainty Budget
Uncertainty Component Standard
Uncertainty u(xi)
Probability
Distribution
Sensitivity
coefficient ci
Uncertainty
contribution ui(y)
k=1

Capacitance dispersion 1.68E-6 pF 6 1 1.7E-6 pF
Test current I) 3.05E-11 A Rectangular -5,71E-11 F/A -1.7E-9 pF
Reference standard C2) 3.32E-4 pF Normal 1,00E-1 F/F 3.3E-5 pF
Detector current angle 5.03E-2 rad Rectangular -1,13E-16 F -5.7E-6 pF
Detector current
amplitude Id)
4.62E-14 A Rectangular 4,88E-06 F/A 2.3E-7 pF
IVD deviation 5.00E-07 V/V Normal 1,10E-11 F 5.5E-6 pF

Combined 3.4E-5 pF

34

Appendix E. Uncertainty Budgets for 1000 pF

1. INTI

Table E1. INTI 100 pF 1000 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Reference capacitor uncertainty 0.5
Short-term stability 0.06
10:1 comparison uncertainty 0.7
Combined standard uncertainty 0.9


2. INMETRO

Table E2. INMETRO 100 pF 1000 Hz Uncertainty Budget
Quantity Standard
uncertainty
Sensitivity
coefficient
Type
CN
(1) 5.0E-06 pF 1 Type B
2.24E-05 1.00E-02 pF Type A
2.56E-06 1.80E-05 pF Type A
C 5E-08 pF 6.15E-04 Type B
C 0.0018 pF 5.80E-06 Type B
0.1 6.15E-06 pF Type B
R 1E-08 pF 1 Type B
CX CN
(2) 7E-07 pF 1 Combined
Error (3) 1.0E-06 pF 1 Type B
CX
(4) 5.1E-06 pF 1 Combined
RK-90
(5) 1.00E-05 pF 1 Type B
Biannual Drift
(6)
1.00E-05 pF 1 Type A
0.000020 pF Combined

35

3. NRC

Table E3. NRC 100 pF 1000 Hz Uncertainty Budget
Quantity Type Uncertainty
(µF/F)
Sensitivity
coefficient
Sensitivity
factor
Standard
uncertainty
(µF/F)
Degrees of
freedom
Reference
Standard
Combined 0.100 1 1 0.130 22.5
Test Standard Type A 0.002 1 1 0.003 9.0
Voltage
Dependence
Type B 0.000 1 1 0.000 4.9
Frequency
Dependence
Type B 0.000 1 1 0.000 4.9
10:1 Ratio
Type B 0.000 1 1 0.000 4.9
Meter
Nonlinearity
Type B 0.040 1 1 0.010 4.9
Loading & cable
corrections
Type B 0.004 0 1 0.000 4.9
Combined 0.13 22.8


4. ICE

Table E4. ICE 100 pF 1000 Hz Uncertainty Budget
Component Uncertainty (µF/F)
Type B 909
Type A 1550
Combined standard uncertainty 1800

36

5. CENAM

Table E5. CENAM 100 pF 1000 Hz Uncertainty Budget
Uncertainty
Component
Relative Standard
Uncertainty
u(xi) ( F/F)
Probability
Distribution /
Method of
Evaluation (A,B)
Sensitivity
Coefficient
ci
Uncertainty
Contribution
ui (cX) ( F/F)
Degrees of
Freedom
i
Reference
Standard Value
0,115 Normal 10 0,115 60
Reference
Standard Long
Term Stability
0,0085 Normal 15 0,128 60
Test Standard 0,007 Normal 1 0,007 16
Voltage
Dependence
0,0005 Normal 10 0,005 60
Frequency
Dependence
--- --- --- --- ---
Capacitance
Bridge
0,079 Normal 1 0,079 60
Cables
Correction
0,001 Normal 1 0,001 60
0.19 160


6. NIST

Table E6. NIST AH Bridge 100 pF 1000 Hz Uncertainty Budget
Quantity Type Standard uncertainty (µF/F)
Reference Standard Type B 0.050
Reference Drift Type B 0.030
Test Drift Type B 0.030
Bridge Thermal Type B 0.050
Bridge Mechanical Type B 0.050
Bridge Linearity Type B 0.030
Bridge Loading Type B 0.004
Test Variation Type A 0.030
Combined 0.105

37

7. UTE

Table E7. UTE 10 pF 1000 Hz Uncertainty Budget
Uncertainty Component Standard
Uncertainty u(xi)
Probability
Distribution
Sensitivity
coefficient ci
Uncertainty
contribution ui(y)
k=1

Capacitance dispersion 1.68E-6 pF 6 1 1.7E-6 pF
Test current I) 3.05E-11 A Rectangular -5,71E-11 F/A -1.7E-9 pF
Reference standard C2) 3.32E-4 pF Normal 1,00E-1 F/F 3.3E-5 pF
Detector current angle 5.03E-2 rad Rectangular -1,13E-16 F -5.7E-6 pF
Detector current
amplitude Id)
4.62E-14 A Rectangular 4,88E-06 F/A 2.3E-7 pF
IVD deviation 5.00E-07 V/V Normal 1,10E-11 F 5.5E-6 pF

Combined 3.4E-5 pF

38


Appendix F. CCEM-K4 10 pF Capacitance Linkage Analysis and Results

Data for Tables F1, and F2 are taken from [2], the CCEM-K4 Final Report of March 2001,
Tables 5 and 6, respectively. The CCEM-K4 comparison evaluated a 10 pF capacitance standard
at 1.592 kHz. Herein we presume equivalence between 1.592 kHz and 1.6 kHz. For the CCEM-
K4 and SIM.EM-K4 Comparisons, there are two linking laboratories: NIST and NRC.

Table F1. 10 pF 1600 Hz degree of equivalence relative to the CCEM-K4 KCRV, with
corresponding standard uncertainties (µF/F).
Laboratory Degree of Equivalence Uncertainty of Degree of
Equivalence
BIPM -0.018 0.050
BNM-LCIE -0.216 0.043
CSIRO-NML 0.035 0.039
MSL -0.026 0.064
NIM -0.04 0.132
NIST (pilot) -0.003 0.022
NMi -0.772 0.600
NPL 0.198 0.056
NRC 0.037 0.161
PTB -0.004 0.049
VNIIM -0.318 0.201

Table F2. 10 pF 1600 Hz pairwise degrees of equivalence for CCEM-K4 (above diagonal) and
corresponding uncertainties (below diagonal), all in µF/F.
BIPM
BNM-
LCIE
CSIRO-
NML MSL NIM NIST NMi NPL NRC PTB VNIIM
BIPM 0.00 0.20 -0.05 0.01 0.02 -0.02 0.75 -0.22 -0.06 -0.01 0.30
BNM-
LCIE
0.13 0.00 -0.25 -0.19 -0.18 -0.21 0.56 -0.41 -0.25 -0.21 0.10
CSIRO-
NML
0.13 0.12 0.00 0.06 0.08 0.04 0.81 -0.16 0.00 0.04 0.35
MSL 0.16 0.15 0.15 0.00 0.01 -0.02 0.74 -0.22 -0.06 -0.02 0.29
NIM 0.28 0.28 0.27 0.29 0.00 -0.04 0.73 -0.24 -0.08 -0.04 0.28
NIST 0.11 0.10 0.09 0.13 0.27 0.00 0.77 -0.20 -0.04 0.00 0.32
NMi 1.20 1.20 1.20 1.21 1.23 1.20 0.00 -0.97 -0.81 -0.77 -0.45
NPL 0.15 0.14 0.14 0.17 0.29 0.12 1.21 0.00 0.16 0.20 0.52
NRC 0.34 0.33 0.33 0.35 0.42 0.33 1.24 0.34 0.00 0.04 0.36
PTB 0.15 0.14 0.13 0.17 0.28 0.12 1.20 0.16 0.34 0.00 0.31
VNIIM 0.41 0.41 0.41 0.42 0.48 0.40 1.27 0.42 0.52 0.42 0.00


Linkage Analysis Results

The results of statistically linking the SIM.EM-K4 10 pF Comparison at 1600 Hz to the CCEM-
K4 10 pF Comparison were calculated based on the statistical analysis in reference [5] and are
listed below.

39


Of the six NMIs which participated in the SIM.EM-K4 10 pF 1600 Hz Comparison, two
participated in the CCEM-K4 Comparison (NIST and NRC) and four did not participate
(CENAM, ICE, INTI, and INMETRO).

Table F3 lists the degree of equivalence of the four non-participating laboratories with respect to
the CCEM-K4 key comparison reference value (KCRV) for CCEM-K4. Tables F4 and F5
provide the pair-wise degree of equivalence and uncertainty, respectively. The degrees of
equivalence and their uncertainties are given in F/F.

Table F3. 1600 Hz degree of equivalence relative to the CCEM-K4 KCRV.
Laboratory Degree of Equivalence Uncertainty of Degree of
Equivalence
CENAM -0.030 0.101
ICE -2002 180000
INTI -0.539 0.319
INMETRO 0.004 0.139

Table F4. Pair-wise 10 pF 1600 Hz degree of equivalence.
CENAM ICE INTI INMETRO
BIPM 0.012 2002 0.521 -0.022
BNM-LCIE -0.186 2002 0.323 -0.219
CSIRO-NML 0.065 2002 0.574 0.031
MSL 0.004 2002 0.513 -0.030
NIM -0.010 2002 0.499 -0.044
NMi -0.742 2001 -0.233 -0.776
NPL 0.228 2002 0.737 0.194
PTB 0.026 2002 0.535 -0.008
VNIIM -0.288 2002 0.221 -0.322

Table F5. Pair-wise 10 pF 1600 Hz uncertainties.
CENAM ICE INTI INMETRO
BIPM 0.112 180000 0.323 0.147
BNM-LCIE 0.109 180000 0.322 0.145
CSIRO-NML 0.108 180000 0.322 0.144
MSL 0.119 180000 0.326 0.153
NIM 0.166 180000 0.345 0.191
NMi 0.608 180000 0.680 0.616
NPL 0.115 180000 0.324 0.150
PTB 0.112 180000 0.323 0.147
VNIIM 0.225 180000 0.377 0.244

40

Appendix G. Corrective Actions and Results

Several participant laboratories provided post-comparison corrections to their comparison
results. The corrections could not be included in the comparison results but are shown below.

CENAM

CENAM reported after the submission of their results that they had made a slight error in the
computation of the 1 kHz results for the 100 pF and 1000 pF standards. These measurements
required a 10:1 ratio factor with which an incorrect sign was used. The corrected results are
given in Table G1.

Table G1. CENAM Corrective Results
Date
Nominal
Value (pF)
Frequency
(Hz)
Capacitance
(pF)
Uncertainty
(µF/F)
2004.571 100 1000 100.000140 0.38
2004.571 1000 1000 1000.02655 0.5

ICE

The ICE results were corrected based upon an improved calibration, performed by INMETRO in
2006, of the reference standards used by ICE in the comparison. The corrected results are shown
in Table G1.

Table G1. ICE Corrective Results
Date
Nominal
Value (pF)
Frequency
(Hz)
Capacitance
(pF)
Uncertainty
(µF/F)
2004.787 10 1000 9.9958 44.2
2004.787 10 1600 9.9957 75.3
2004.787 100 1000 99.9832 6.3
2004.787 100 1600 99.9890 57.8
2004.787 1000 1000 999.954 4.3

41

INTI

The INTI results were corrected using an improved calibration from BIPM in 2008 of the
reference standards used in the comparison. The corrected INTI results are shown in Table G2.

Table G2. INTI Corrective Results
Date
Nominal
Value (pF)
Frequency
(Hz)
Capacitance
(pF)
Uncertainty
(µF/F)
2005.219 10 1000 10.0000223 0.40
2005.219 10 1600 10.0000207 0.35
2005.222 100 1000 100.000143 0.50
2005.222 100 1600 100.000136 0.45
2005.227 1000 1000 1000.0257 0.9

NRC

The NRC results were corrected based upon an improved analysis using data from previous
calibrations from other NMIs as well as from the CCEM-K4 report. The corrected data are
shown in Table G3.


Table G3. NRC Corrective Results
Date
Nominal
Value (pF)
Frequency
(Hz)
Capacitance
(pF)
Uncertainty
(µF/F)
2005.219 10 1000 10.00002766 0.15
2005.219 10 1600 10.00002376 0.14
2006.159 100 1000 100.000231 0.2
2006.159 100 1600 100.0001922 0.2
2006.159 1000 1000 1000.02262 0.25

42

Appendix H. List of Participants


Table H1. List of Participants
Organization Country Contact Person E-mail Shipping Address
NIST United States Andrew Koffman andrew.koffman@nist.gov
NIST, 100 Bureau
Drive, MS 8171,
Gaithersburg,
Maryland, 20899-
8171 USA
NRC Canada Dave Inglis
Dave.Inglis@nrc-
cnrc.gc.ca
National Research
Council of Canada
M-36, 1200 Montreal
Road, Ottawa,
Ontario K1A 0R6,
Canada
CENAM Mexico Jose A Moreno jmoreno@cenam.mx
CENAM, Queretaro,
Mexico
ICE Costa Rica Harold Sanchez hsanchez@ice.co.cr
Laboratorio
Metrologico, ICE -
San Pedro, San
Jose, Costa Rica
INTI Argentina Marcelo Cazabat
cazamar@inti.gov.ar Instituto Nacional de
Tecnología Industrial
(INTI), Centro de
Investigación y
Desarrollo en Física
(CEFIS), Div.
Electricidad, Av.
Gral. Paz y
Albarellos CP 1650.
San Martín. Pcia. Bs.
As. Argentina
UTE Uruguay Sergio Teliz
STeliz@ute.com.uy UTE, Montevideo,
Uruguay
INMETRO Brazil
Luiz Macoto
Ogino
lmogino@inmetro.gov.br Laboratorio de
Capactancia e
Indutancia –
Diele/Dimci/Incetro,
Av. Nossa Senhora
das Gracas 50,
Xerem, Duque de
Caxias, RJ, Brazil,
CEP:25 250-02

43

Appendix I. Photographs of included parts






















Figure I1. Front view of AH1100 Enclosure





















Figure I2. Rear view of AH1100 Enclosure with fuse removed

44
























Figure I3. AH1100/11A Operation and Maintenance Manual



















Figure I4. GR1404-A Capacitance Standard in foam carton

45












Figure I5. 0.25 A fuses and 0.5 A fuses Figure I6. Shorting cable












Figure I7. BNC elbow and T-connectors Figure I8. BNC-to-GR874 connectors












Figure I9. BNC barrel adapters Figure I10. BNC-to-alligator clips











Figure I11. Two-terminal-pair twisted BNC cable Figure I12. Four-terminal-pair BNC cable