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 L. M. Ogino, G. Kyriazis, R. T. B. Vasconcellos B. Wood, K. Kochav H. Sanchez, B. I. Castro J. A. Moreno A. Koffman, N. F. Zhang, Y. Wang, S. Shields D. Slomovitz, D. Izquierdo, C. Faverio
Argentina, INTI Brazil, INMETRO Canada, NRC Costa Rica, ICE Mexico, CENAM United States, NIST 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 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
Argentina
Instituto Nacional de Technologia Industrial
Brazil
National Institute of Metrology Standardization
and Industrial Quality
Canada
National Research Council
Costa Rica Instituto Costarricense de Electricidad
Mexico
Centro Nacional de Metrologia
United States National Institute of Standards and Technology
Uruguay
Administracion Nacional de Usinas y
Transmissiones Electricas
Acronym INTI INMETRO
NRC ICE CENAM NIST 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.
1
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
2
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
NIST (United States) CENAM (México) ICE (Costa Rica) NIST (United States) INTI (Argentina) UTE (Uruguay) INMETRO (Brazil) NIST (United States) NRC (Canada) NIST (United States)
Approximate measurement dates November 2003 to April 2004 July to August 2004 September to November 2004
December 2004 to February 2005 March 2005 July 2005
September 2005 December 2005 to January 2006
February to March 2006 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
3
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 4
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 5
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)
NIST USA
2003.866
1.834
NIST USA
2004.273
1.868
CENAM Mexico
2004.574
1.967
ICE Costa Rica
2004.872
-2000
NIST USA
2005.049
1.988
INTI Argentina
2005.219
2.65
UTE Uruguay
2005.521
-2.30
Combined Standard Uncertainty (μF/F)
0.123 0.123 0.17 180000 0.123
0.4 3.4
6
INMETRO Brazil NIST USA NRC Canada NIST USA
2005.726 2006.016 2006.159 2006.419
2.299 2.414 2. 689 2.510
0.2 0.123 0.079 0.123
Fig. 6. All participant results of measurement of AH11A SN 01238 10 pF at 1 kHz
7
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 8
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)
NIST USA
2003.852
1.613
NIST USA
2004.273
1.791
CENAM Mexico
2004.568
1.822
ICE Costa Rica
2004.787
-2000
NIST USA
2005.060
1.894
INTI Argentina
2005.219
1.510
UTE Uruguay
Did not participate
INMETRO Brazil 2005.729
2.207
NIST USA
2005.995
2.324
NRC Canada
2006.159
2.847
NIST USA
2006.419
2.356
Combined Standard Uncertainty (μF/F)
0.084 0.114 0.17 180000 0.096 0.35
0.2 0.093 0.069 0.114
Fig. 9. All participant results of measurement of AH11A SN 01238 10 pF at 1.6 kHz 9
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)
NIST USA
2003.907
1.386
NIST USA
2004.273
1.477
CENAM Mexico
2004.571
0.970
ICE Costa Rica
2004.787
-600
NIST USA
2005.047
1.515
INTI Argentina
2005.219
1.710
UTE Uruguay
2005.521
-1.200
INMETRO Brazil
2005.680
1.690
NIST USA
2006.003
1.750
NRC Canada
2006.159
2.190
NIST USA
2006.419
1.792
Combined Standard Uncertainty (μF/F)
0.105 0.105 0.19 19000 0.105
0.5 3.3 0.2 0.105 0.110 0.105
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Fig. 11. All participant results of measurement of AH11A SN 01237 100 pF at 1 kHz 11
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)
NIST USA
2003.896
1.362
NIST USA
2004.273
1.460
CENAM Mexico
2004.568
1.380
ICE Costa Rica
2004.787
-100
NIST USA
2005.052
1.499
INTI Argentina
2005.222
0.580
UTE Uruguay
Did not participate
INMETRO Brazil 2005.682
1.650
NIST USA
2005.997
1.732
NRC Canada
2006.159
2.452
NIST USA
2006.419
1.708
Combined Standard Uncertainty (μF/F)
0.086 0.095 0.190 19000 0.092 0.450
0.200 0.089 0.200 0.095
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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 13
5.5 SIM.EM-S3 1000 pF results at 1 kHz
Table 7. Mean 1000 Hz measurement data for all participant laboratories.
Laboratory
Mean Mean 1 kHz Capacitance Combined
Date
Deviation from Nominal Standard
Value (μF/F)
Uncertainty
(μF/F)
NIST USA
2003.893
26.14
0.789
NIST USA
2004.292
26.10
0.789
CENAM Mexico 2004.571
25.67
0.250
ICE Costa Rica
2004.787
-220
1800
NIST USA
2005.047
28.31
0.789
INTI Argentina
2005.227
26.00
0.900
UTE Uruguay
2005.518
24.46
6.3
INMETRO Brazil 2005.688
25.41
0.200
NIST USA
2006.003
27.40
0.789
NRC Canada
2006.159
22.84
0.250
NIST USA
2006.449
27.54
0.789
Mean Measurement Temperature (degrees C)
22.88 22.84 23.02 23.30 23.01 22.95 23.03 22.10 22.85 21.28 22.80
Fig. 15. All participant results of measurement of GR 1404-A SN 2151 1000 pF at 1 kHz 14
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. 2126, 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. 179194, 2010.
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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.
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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 CENAM ICE INTI UTE INMETRO NRC
-0.000214 (0.205) -2002 (180000) 0.501 (0.416) -4.535 (3.40) 0.00643 (0.231) 0.274 (0.141)
0.000214 (0.205)
-2002 (180000)
0.501 (0.435) -4.534 (3.40) 0.00664 (0.264) 0.274 (0.191)
2002 (180000)
2002 (180000)
2003 (180000)
1998 (180000)
2002 (180000)
2002 (180000)
-0.501 (0.416) -0.5008 (0.435) -2003 (180000)
-5.035 (3.42) -0.494 (0.447) -0.226 (0.408)
4.535 (3.40) 4.534 (3.40) -1998 (180000) 5.035 (3.42)
4.541 (3.41) 4.809 (3.40)
-0.00643 (0.231) -0.00664 (0.264) -2002 (180000) 0.494 (0.447) -4.541 (3.41)
0.268 (0.215)
-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
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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
CENAM ICE INTI INMETRO NRC
-0.00635 (0.177) -2002 (180000) -0.515 (0.353) 0.0273 (0.207) 0.537 (0.096)
0.00635 (0.177)
-2002 (180000)
-0.509 (0.390) 0.0337 (0.268) 0.543 (0.197)
2002 (180000)
2002 (180000)
2001 (180000)
2002 (180000)
2002 (180000)
0.515 (0.353) 0.509 (0.390) -2001 (180000)
0.543 (0.404) 1.053 (0.359)
-0.0273 (0.207) -0.0337 (0.268) -2002 (180000) -0.543 (0.404)
0.510 (0.212)
-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.
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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 CENAM ICE INTI UTE INMETRO NRC
-0.524 (0.216) -601.5 (19000) 0.112 (0.510) -2.847 (3.30) 0.0172 (0.225) 0.440 (0.225)
0.524 (0.216)
-601.0 (19000) 0.635 (0.535) -2.323 (3.305) 0.541 (0.276) 0.964 (0.277)
601.5 (19000) 601.0 (19000)
601.6 (19000) 598.7 (19000) 601.5 (19000) 602.0 (19000)
-0.112 (0.510) -0.635 (0.535) -601.6 (19000)
-2.959 (3.34) -0.0943 (0.539) 0.328 (0.539)
2.847 (3.30) 2.323 (3.31) -598.7 (19000) 2.959 (3.34)
2.864 (3.31) 3.287 (3.31)
-0.0172 (0.225) -0.541 (0.276) -601.5 (19000) 0.0943 (0.539) -2.864 (3.31)
0.423 (0.283)
-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.
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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 CENAM ICE INTI INMETRO NRC
-0.0907 (0.196) -101.5 (19000) -0.987 (0.452) 0.0160 (0.206) 0.748 (0.126)
0.0907 (0.196)
-101.4 (19000) -0.896 (0.489) 0.107 (0.280) 0.839 (0.230)
101.5 (19000) 101.4 (19000)
100.5 (19000) 101.5 (19000) 102.3 (19000)
0.987 (0.452) 0.896 (0.489) -100.5 (19000)
1.003 (0.493) 1.735 (0.465)
-0.0160 (0.206) -0.107 (0.280) -101.5 (19000) -1.003 (0.493)
0.732 (0.229)
-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.
20
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 CENAM ICE INTI UTE INMETRO NRC
-1.095 (0.522) -246.9 (1800) -1.148 (0.992) -2.862 (6.32) -2.007 (0.498) -4.854 (0.598)
1.095 (0.522)
-245.8 (1800) -0.0532 (0.961) -1.767 (6.31) -0.912 (0.501) -3.759 (0.651)
246.9 (1800) 245.8 (1800)
245.7 (1800) 244.0 (1800) 244.9 (1800) 242.0 (1800)
1.148 (0.992) 0.0532 (0.961) -245.7 (1800)
-1.714 (6.36) -0.8587 (0.936) -3.706 (0.988)
2.862 (6.32) 1.767 (6.31) -244.0 (1800) 1.714 (6.36)
0.8548 (6.30) -1.992 (6.31)
2.007 (0.498) 0.9120 (0.501) -244.9 (1800) 0.8587 (0.936) -0.8548 (6.30)
-2.847 (0.359)
4.854 (0.599) 3.759 (0.651) -242.0 (1800) 3.706 (0.988) 1.992 (6.31) 2.847 (0.359)
21
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
CN (1)
C
C
R
CX CN (2) Error (3) CX (4) RK-90 (5) Biannual
(6)
Drift
Standard uncertainty
5.0E-07 pF 3.72E-06 4.90E-07 5E-08 pF 0.0018 pF 0.1 1E-08 pF 8E-08 pF 1.0E-07 pF 5.2E-07 pF 1.00E-06 pF 1.00E-06 pF
Sensitivity coefficient
1 1.00E-02 pF 1.80E-05 pF 6.63E-05 2.60E-07 6.63E-07 pF 1 1 1 1 1 1
Type
Type B Type A Type A Type B Type B Type B Type B Combined Type B Combined Type B Type A
CX (7)
0.0000020 pF
Combined
22
Table C4. INMETRO 10 pF 1600 Hz Uncertainty Budget
Quantity CN (1)
C
C
Standard uncertainty
4.0E-07 pF 3.16E-06 7.48E-07 4E-08 pF 0.0008 pF
Sensitivity coefficient
1 1.00E-02 pF 8.00E-06 pF 6.56E-05 8.00E-07
Type
Type B Type A Type A Type B Type B
R
CX CN (2) Error (3) CX (4) RK-90 (5)
Biannual
(6)
Drift
0.1 1E-08 pF 7E-08 pF 1.50E-07 pF 4.3E-07 pF 1.00E-06 pF 1.00E-06 pF
6.56E-07 pF 1 1 1 1 1 1
Type B Type B Combined Type B Combined Type B Type A
CX (7)
0.0000020 pF
Combined
3. NRC
Quantity
Reference Standard Test Standard Voltage Dependence Frequency Dependence
10:1 Ratio Meter Nonlinearity Other Combined
Table C5. NRC 10 pF 1000 Hz Uncertainty Budget
Type
Uncertainty Sensitivity
(µF/F)
coefficient
Sensitivity factor
Standard uncertainty (µF/F)
Combined 0.078
1
1
0.078
Type A 0.005
1
1
0.005
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.004
1
1
0.004
Type B 0.005
0
1
0.000
0.079
Degrees of freedom
15.0 9.0 4.9 4.9 4.9
4.9 4.9 15.2
23
Quantity
Reference Standard Test Standard Voltage Dependence Frequency Dependence
10:1 Ratio Meter Nonlinearity Other Combined
Table C6. NRC 10 pF 1600 Hz Uncertainty Budget
Type
Uncertainty Sensitivity
(µF/F)
coefficient
Sensitivity factor
Standard uncertainty (µF/F)
Combined 0.068
1
1
0.068
Type A 0.005
1
1
0.005
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.004
1
1
0.004
Type B 0.005
0
1
0.000
0.069
Degrees of freedom
10.5 9.0 4.9 4.9 4.9
4.9 4.9 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
24
Uncertainty Component
Reference Standard Value Reference Standard Long Term Stability Test Standard Voltage Dependence Frequency Dependence Capacitance Bridge Cables Correction
CX
Table C9. CENAM 10 pF 1000 Hz Uncertainty Budget
Estimate xi
Relative Standard Uncertainty u(xi) ( F/F)
Probability Distribution /
Method of Evaluation (A,B)
Sensitivity Coefficient
ci
Uncertainty Degrees of Contribution Freedom
ui (cX) ( F/F)
i
10 pF + 23,0 aF
0.115
Normal
1
0,115
60
---
0.085
Normal
1.5
0,128
60
---
0.010
---
0.005
Normal Normal
1
0,010
16
1
0,005
60
---
---
---
---
---
---
-3,06 aF
0.011
Normal
1
0,011
60
---
10 pF + 19.9 aF
0.001
Normal
1
0,001
60
0.17
120
Uncertainty Component
Reference Standard Value Reference Standard Long Term Stability Test Standard Voltage Dependence Frequency Dependence Capacitance Bridge Cables Correction
CX
Table C10. CENAM 10 pF 1600 Hz Uncertainty Budget
Estimate xi
Relative Standard Uncertainty u(xi) ( F/F)
Probability Distribution /
Method of Evaluation (A,B)
Sensitivity Coefficient
ci
Uncertainty Degrees of Contribution Freedom
ui (cX) ( F/F)
i
10 pF + 22,5 aF
0.115
Normal
1
0.115
60
---
0.085
Normal
1.5
0.128
60
---
0.010
---
0.005
Normal Normal
1
0.010
16
1
0.005
60
---
---
---
---
---
---
-3,06 aF
0.011
Normal
1
0.011
60
---
10 pF + 19.9 aF
0.001
Normal
1
0.001
60
0.17
120
6. NIST
25
Table C11. NIST AH Bridge 10 pF 1000 Hz Uncertainty Budget
Quantity
Type
Standard uncertainty (µF/F)
Reference Standard Reference Drift Test Drift Bridge Thermal Bridge Mechanical Bridge Linearity Bridge Loading Test Variation
Type B Type B Type B Type B Type B Type B Type B Type A
0.050 0.030 0.030 0.050 0.050 0.050 0.000 0.030
Combined
0.123
Table C12. NIST AH Bridge 10 pF 1600 Hz Uncertainty Budget
Quantity
Type
Standard uncertainty (µF/F)
Reference Standard Reference Drift Test Drift Bridge Thermal Bridge Mechanical Bridge Linearity Bridge Loading Test Variation
Type B Type B Type B Type B Type B Type B Type B Type A
0.020 0.030 0.030 0.050 0.050 0.050 0.010 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 Transformer Bridge 10 pF Correction Calculation Test Variation
Type B Type B Type B Type A
0.019 0.005 0.002 0.002
Combined
0.020
7. UTE
26
Table C14. UTE 10 pF 1000 Hz Uncertainty Budget
Uncertainty Component
Standard
Probability Sensitivity
Uncertainty u(xi) Distribution 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) Detector current angle
3.32E-4 pF
Normal
1,00E-1 F/F 3.3E-5 pF
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
27
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 CN (1)
Standard uncertainty 5.0E-06 pF 2.24E-05
Sensitivity coefficient 1 1.00E-02 pF
Type
Type B 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
CX CN (2) Error (3)
1E-08 pF
1
7E-07 pF
1
1.0E-06 pF
1
CX (4) RK-90 (5)
5.1E-06 pF
1
1.00E-05 pF
1
Biannual Drift 1.00E-05 pF
1
(6)
Type B Combined Type B Combined Type B Type A
0.000020 pF
Combined
28
Table D4. INMETRO 100 pF 1600 Hz Uncertainty Budget
Quantity
Standard
Sensitivity
Type
CN (1)
uncertainty 4.0E-06 pF 2.24E-05
coefficient 1 1.00E-02 pF
Type B 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
CX CN (2) Error (3)
1E-08 pF
1
7E-07 pF
1
1.50E-06 pF
1
CX (4) RK-90 (5)
4.3E-06 pF
1
1.00E-05 pF
1
Biannual Drift 1.00E-05 pF
1
(6)
Type B Combined Type B Combined Type B Type A
CX (7)
0.000020 pF
Combined
3. NRC
Quantity
Reference Standard Test Standard Voltage Dependence Frequency Dependence
10:1 Ratio Meter Nonlinearity Other Combined
Table D5. NRC 100 pF 1000 Hz Uncertainty Budget
Type
Uncertainty Sensitivity
(µF/F)
coefficient
Sensitivity factor
Standard uncertainty (µF/F)
Combined 0.100
1
1
0.100
Type A 0.002
1
1
0.002
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.040
1
1
0.040
Type B 0.004
0
1
0.000
0.11
Degrees of freedom
14.2
9.0 4.9
4.9
4.9
4.9
4.9 17.8
29
Quantity
Reference Standard Test Standard Voltage Dependence Frequency Dependence
10:1 Ratio Meter Nonlinearity Other Combined
Table D6. NRC 100 pF 1600 Hz Uncertainty Budget
Type
Uncertainty Sensitivity
(µF/F)
coefficient
Sensitivity factor
Standard uncertainty (µF/F)
Combined 0.100
1
1
0.100
Type A 0.002
1
1
0.002
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.040
1
1
0.040
Type B 0.018
0
1
0.000
0.11
Degrees of freedom
14.2
9.0 4.9
4.9
4.9
4.9
4.9 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
30
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 Degrees of Contribution Freedom
ui (cX) ( F/F)
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 Degrees of Contribution Freedom
ui (cX) ( F/F)
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
31
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
32
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
Test current I) Reference standard C2) Detector current angle
Detector current amplitude Id)
IVD deviation
1.68E-6 pF
6
3.05E-11 A Rectangular
3.32E-4 pF
Normal
5.03E-2 rad Rectangular
4.62E-14 A Rectangular
5.00E-07 V/V
Normal
1 -5,71E-11 F/A 1,00E-1 F/F -1,13E-16 F 4,88E-06 F/A
1,10E-11 F
1.7E-6 pF -1.7E-9 pF 3.3E-5 pF -5.7E-6 pF 2.3E-7 pF
5.5E-6 pF
Combined
3.4E-5 pF
33
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 CN (1)
Standard uncertainty 5.0E-06 pF 2.24E-05
Sensitivity coefficient 1 1.00E-02 pF
Type
Type B 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
CX CN (2) Error (3)
1E-08 pF
1
7E-07 pF
1
1.0E-06 pF
1
CX (4) RK-90 (5)
5.1E-06 pF
1
1.00E-05 pF
1
Biannual Drift 1.00E-05 pF
1
(6)
Type B Combined Type B Combined Type B Type A
0.000020 pF
Combined
34
3. NRC
Quantity
Reference Standard Test Standard Voltage Dependence Frequency Dependence
10:1 Ratio Meter Nonlinearity Loading & cable corrections Combined
Table E3. NRC 100 pF 1000 Hz Uncertainty Budget
Type
Uncertainty Sensitivity Sensitivity Standard
(µF/F)
coefficient factor
uncertainty
(µF/F)
Combined 0.100
1
1
0.130
Type A 0.002
1
1
0.003
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.000
1
1
0.000
Type B 0.040
1
1
0.010
Type B 0.004
0
1
0.000
0.13
Degrees of freedom 22.5 9.0 4.9 4.9 4.9
4.9 4.9 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
35
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 Degrees of Contribution Freedom
ui (cX) ( F/F)
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
36
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
Test current I) Reference standard C2) Detector current angle
Detector current amplitude Id)
IVD deviation
1.68E-6 pF
6
3.05E-11 A Rectangular
3.32E-4 pF
Normal
5.03E-2 rad Rectangular
4.62E-14 A Rectangular
5.00E-07 V/V
Normal
1 -5,71E-11 F/A 1,00E-1 F/F -1,13E-16 F 4,88E-06 F/A
1,10E-11 F
1.7E-6 pF -1.7E-9 pF 3.3E-5 pF -5.7E-6 pF 2.3E-7 pF
5.5E-6 pF
Combined
3.4E-5 pF
37
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 CCEMK4 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.
BNM- CSIRO-
BIPM LCIE 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- 0.13 0.00 -0.25 -0.19 -0.18 -0.21 0.56 -0.41 -0.25 -0.21 0.10
LCIE
CSIRO- 0.13 0.12 0.00
0.06 0.08 0.04 0.81 -0.16 0.00 0.04 0.35
NML
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 CCEMK4 10 pF Comparison were calculated based on the statistical analysis in reference [5] and are listed below.
38
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
BIPM
0.112
180000
0.323
BNM-LCIE
0.109
180000
0.322
CSIRO-NML
0.108
180000
0.322
MSL
0.119
180000
0.326
NIM
0.166
180000
0.345
NMi
0.608
180000
0.680
NPL
0.115
180000
0.324
PTB
0.112
180000
0.323
VNIIM
0.225
180000
0.377
INMETRO 0.147 0.145 0.144 0.153 0.191 0.616 0.150 0.147 0.244
39
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.
Date
2004.571 2004.571
Table G1. CENAM Corrective Results
Nominal Frequency Capacitance
Value (pF) (Hz)
(pF)
100
1000
100.000140
1000
1000
1000.02655
Uncertainty (µF/F) 0.38 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.
Date
2004.787 2004.787 2004.787 2004.787 2004.787
Table G1. ICE Corrective Results
Nominal Frequency Capacitance
Value (pF) (Hz)
(pF)
10
1000
9.9958
10
1600
9.9957
100
1000
99.9832
100
1600
99.9890
1000
1000
999.954
Uncertainty (µF/F) 44.2 75.3 6.3 57.8 4.3
40
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.
Date
2005.219 2005.219 2005.222 2005.222 2005.227
Table G2. INTI Corrective Results
Nominal Frequency Capacitance
Value (pF) (Hz)
(pF)
10
1000
10.0000223
10
1600
10.0000207
100
1000
100.000143
100
1600
100.000136
1000
1000
1000.0257
Uncertainty (µF/F) 0.40 0.35 0.50 0.45 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.
Date
2005.219 2005.219 2006.159 2006.159 2006.159
Table G3. NRC Corrective Results
Nominal Frequency Capacitance
Value (pF) (Hz)
(pF)
10
1000 10.00002766
10
1600 10.00002376
100
1000
100.000231
100
1600 100.0001922
1000
1000
1000.02262
Uncertainty (µF/F) 0.15 0.14 0.2 0.2 0.25
41
Appendix H. List of Participants
Organization NIST NRC
CENAM ICE
INTI
UTE INMETRO
Country United States
Canada Mexico Costa Rica
Argentina
Uruguay Brazil
Table H1. List of Participants
Contact Person
E-mail
Andrew Koffman andrew.koffman@nist.gov
Dave Inglis
Dave.Inglis@nrccnrc.gc.ca
Jose A Moreno
jmoreno@cenam.mx
Harold Sanchez
hsanchez@ice.co.cr cazamar@inti.gov.ar
Marcelo Cazabat
Sergio Teliz
STeliz@ute.com.uy lmogino@inmetro.gov.br
Luiz Macoto Ogino
Shipping Address
NIST, 100 Bureau Drive, MS 8171,
Gaithersburg, Maryland, 20899-
8171 USA National Research Council of Canada M-36, 1200 Montreal
Road, Ottawa, Ontario K1A 0R6,
Canada CENAM, Queretaro,
Mexico Laboratorio Metrologico, ICE San Pedro, San Jose, Costa Rica 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, Montevideo,
Uruguay Laboratorio de Capactancia e
Indutancia – Diele/Dimci/Incetro, Av. Nossa Senhora
das Gracas 50, Xerem, Duque de Caxias, RJ, Brazil, CEP:25 250-02
42
Appendix I. Photographs of included parts
Figure I1. Front view of AH1100 Enclosure
Figure I2. Rear view of AH1100 Enclosure with fuse removed
43
Figure I3. AH1100/11A Operation and Maintenance Manual
Figure I4. GR1404-A Capacitance Standard in foam carton
44
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
45
Ver+/-
