CCEM-K4, EUROMET.EM-K4, APMP.EM-K4.1, SIM.EM-K4 and COOMET.EM-K4
MEASURAND : Capacitance
NOMINAL VALUE : 10 pF
FREQUENCY : ~ 1.6 kHz
Degrees of equivalence D_{i} and expanded uncertainty U_{i} (k = 2) in 10^{-6}
Click on the graph for a closer view
Red diamonds: participants in CCEM-K4
Green triangles: participants in EUROMET.EM-K4^{b}
Blue circles: participants in APMP.EM-K4.1^{b}
Purple squares: participants in SIM.EM-K4^{b}
Orange squares: participants in COOMET.EM-K4^{b}
a) Measurements made at 1000 Hz
b) Linking laboratories to CCEM-K4 not listed
CCEM-K4, EUROMET.EM-K4, APMP.EM-K4.1, SIM.EM-K4 and COOMET.EM-K4
MEASURAND : Capacitance
NOMINAL VALUE : 10 pF
FREQUENCY : ~ 1.6 kHZ
Degrees of equivalence D_{i} and expanded uncertainty U_{i} (k = 2) in 10^{-6}
*laboratories whose measurements are derived from R_{K-90}
In red: participants in CCEM-K4
In green: participants in EUROMET.EM-K4^{b}
In blue: participants in APMP.EM-K4.1^{b}
In purple: participants in SIM.EM-K4^{b}
In orange: participants in COOMET.EM-K4^{b}
a) Measurements made at 1000 Hz
b) Linking laboratories to CCEM-K4 not listed
The full matrix of equivalence of key comparisons CCEM-K4, EUROMET.EM-K4, APMP.EM-K4.1, SIM.EM-K4 and COOMET.EM-K4 is available in Summary Results (PDF file, A4 printable format).
Metrology area, Sub-field | Electricity and Magnetism, Capacitance |
Description | Comparison of capacitors |
Time of measurements | 1996 - 1998 |
Status | Approved for equivalence |
Final Reports of the comparisons | |
Measurand | Capacitance, 10 pF |
Parameters | Frequency: 1592 Hz |
Transfer device | Capacitors provided by NIST |
Comparison type | Key Comparison |
Consultative Committee | CCEM (Consultative Committee for Electricity and Magnetism) |
Conducted by | CCEM (Consultative Committee for Electricity and Magnetism) |
Comments | Results published in September 2000, then corrected for some erroneous values on 27 June 2002 EUROMET.EM-K4, APMP.EM-K4.1, SIM.EM-K4 and COOMET.EM-K4 Cresults are linked to those of CCEM-K4 Capacitance of nominal value 10 pF at frequency ~ 1.6 kHz |
Pilot institute |
NIST
National Institute of Standards and Technology United States |
Contact person | A.-M. Jeffery +1 301 975 4246 |
Pilot laboratory | |
---|---|
NIST |
National Institute of Standards and Technology, United States, SIM |
BIPM |
Bureau International des Poids et Mesures, BIPM - International Organization, N/A |
MSL |
Measurement Standards Laboratory, New Zealand, APMP |
NIM |
National Institute of Metrology, China, APMP |
NPL |
National Physical Laboratory, United Kingdom, EURAMET |
NRC |
National Research Council, Canada, SIM |
PTB |
Physikalisch-Technische Bundesanstalt, Germany, EURAMET |
VNIIM |
D.I. Mendeleyev Institute for Metrology, Rosstandart, Russian Federation, COOMET |
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CCEM-K4, EUROMET.EM-K4, APMP.EM-K4.1, SIM.EM-K4 and COOMET.EM-K4
MEASURAND : Capacitance
NOMINAL VALUE : 10 pF
FREQUENCY : ~ 1.6 kHz
The key comparison reference value of CCEM-K4 is obtained from the weighted average of the results of the CCEM-K4 participants who derive their reference standard of capacitance by means of an independent realization of the farad from a calculable capacitor. It is chosen such that: x_{R} = x_{0} x (1 + m_{R}), with x_{R} = 10 pF exactly, that is, m_{R} = 0. The standard uncertainty of m_{R} is u_{R} = 0.017x10^{-6}. |
The degree of equivalence of each laboratory with respect to the reference value is given by a pair of terms: D_{i} = (m'_{i} - m_{R}) and its expanded uncertainty (k = 2), U_{i} (see detailed calculation of U_{i} on page 17 of the CCEM-K4 Final Report), where m'_{i} is deduced from m_{i} by adding a constant factor chosen so that the reference value is a nominal 10 pF. |
The degree of equivalence between two laboratories i and j is given in the CCEM-K4 Final Report. |
The input data for establishing the link between EUROMET.EM-K4 and CCEM-K4 are taken from the two tables given in Laboratory individual measurements. Seven laboratories (BIPM, LNE, NMIA, NIST, VSL, NPL and PTB) participated in both comparisons. |
The CCEM-K4 key comparison reference value and degrees of equivalence are unaltered by the linking procedure. The linking procedure consists of evaluating the correction d to apply to the result |
The degree of equivalence of each laboratory participant in EUROMET.EM-K4 with respect to the CCEM-K4 key comparison reference value is given by a pair of terms: D_{i} = [(m_{i-EUR} - m_{iR-EUR}) + d] and its expanded uncertainty (k = 2), U_{i}, based on the quadratic combination of u_{R}, u_{d}, t_{i-EUR} and U_{i-EUR}/2 (see page 2 and Table 2 of the Linkage Report). |
The complete matrix of equivalence is built up as explained on pages 2 and 3 and in Table 3 of the Linkage Report. |
The NMIA, NIM and VNIIM participated in both ccomparisons and were used as linking laboratories. The linking procedure used to link the results of APMP.EM-K4.1 to those of CCEM-K4 is explained in paragraph 6.5 on page 17 of the APMP.EM-K4.1 Final Report, and is similar to that used to link EUROMET.EM-K4 to CCEM-K4.
The calculated linking correction d = -0.004 µF/F, with a standard uncertainty u_{d }= 0.017 µF/F.
The degree of equivalence of each laboratory participant in APMP.EM-K4.1 with respect to the CCEM-K4 key comparison reference value is given by a pair of terms D_{i} and its expanded uncertainty (k = 2), U_{i}. The computation of D_{i} and U_{i} can be found in paragraph 6.5.4 on page 19 of the APMP.EM-K4.1 Final Report. |
The complete matrix of equivalence is built up as explained in paragraph 6.5.5 on page 20 of the APMP.EM-K4.1 Final Report. |
The NIST and NRC participated in both comparisons and were used as linking laboratories. The linking procedure used to link the results of SIM.EM-K4 to those of CCEM-K4 is explained in Appendix F on page 40 of the SIM.EM-K4 Final Report.
The degree of equivalence of each laboratory participant in SIM.EM-K4 with respect to the CCEM-K4 key comparison reference value is given by a pair of terms D_{i} and its expanded uncertainty (k = 2), U_{i}. |
The pair-wise degrees of equivalence involving the SIM.EM-K4 participants are not computed. |
The PTB and VNIIM participated in both comparisons and were used as linking laboratories. The linking procedure used to link the results of COOMET.EM-K4 to those of CCEM-K4 is explained in Section 7.4 of the COOMET.EM-K4 Final Report.
The degree of equivalence of each laboratory participant in COOMET.EM-K4 with respect to the CCEM-K4 key comparison reference value is given by a pair of terms D_{i} and its expanded uncertainty (k = 2), U_{i}. |
The pair-wise degrees of equivalencebetween participants in COOMET.EM-K4 are given on p. 12 of the COOMET.EM-K4 Final Report. |
CCEM-K4, EUROMET.EM-K4, APMP.EM-K4.1, SIM.EM-K4 and COOMET.EM-K4
MEASURAND : Capacitance
NOMINAL VALUE : 10 pF
FREQUENCY : ~ 1.6 kHz
x_{i} : result of measurements of capacitors S/N 108 and S/N 185, or S/N 190 and S/N 193, carried out by laboratory i, related to the fractional difference from the nominal value 10 pF, m_{i}, by: x_{i} = x_{0} x (1 + m_{i}), with x_{0} = 10 pF
The values assigned by NIST to each capacitor are obtained by interpolation of the NIST measurement results to the measurement dates of other laboratories.
u_{i} : combined standard uncertainty of m_{i}, reported by laboratory i
measurements derived from R_{K-90} | |||||||||||
measurements derived from calculable capacitors | |||||||||||
BIPM-1, -2 | two BIPM measurements of the same capacitor on two different dates | ||||||||||
Note: bold numbers refer to the capacitors whose serial numbers are in bold |
x_{i}_{-EUR }: result of measurements of capacitor S/N 01031 carried out by laboratory i, related to the fractional difference from the nominal value 10 pF, m_{i}_{-EUR}, by:
x_{i}_{-EUR}= x_{0} x (1 + m_{i}_{-EUR}), with x_{0} = 10 pF
U_{i}_{-EUR }: expanded uncertainty (k = 2) of m_{i}_{-EUR}, reported by laboratory i
m_{i}_{R-EUR }: value of reference referred to the date of measurement at laboratory i (see section 5.13.2 and subsequent graphs in the EUROMET.EM-K4 Final Report), based on a weighted mean of EUROMET.EM-K4 participants' measurements.
Its expanded uncertainty (k = 2) is U_{i}_{R-EUR }= 0.037x10^{-6} at all dates.
measurements derived from R_{K-90} | ||||||
measurements derived from calculable capacitors |
The measurement results and associated standard uncertainties of the laboratories having participated in key comparison APMP.EM-K4.1 are given in paragraph 6.2 on page 14 of the APMP.EM-K4.1 Final Report.
Measurements were carried out between May 2004 and August 2006.
The measurement results and associated standard uncertainties of the laboratories having participated in key comparison SIM.EM-K4 are given in paragraph 5.2 on page 8 of the SIM.EM-K4 Final Report.
Measurements were carried out between 2003 and 2006.
The measurement results and associated standard uncertainties of the laboratories having participated in key comparison COOMET.EM-K4 are given in Table 5, p.8, of the COOMET.EM-K4 Final Report.
Measurements were carried out between 2006 and 2009.