Comparison Display

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

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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

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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

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).

Comparison

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EUROMET.EM-K4

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Information & contact
Participants

Metrology area, Sub-field	Electricity and Magnetism, Capacitance
Description	Comparison of capacitors
Time of measurements	1995 - 1998
Status	Approved for equivalence

Final Reports of the comparisons	Metrologia, 2002, 39, Tech. Suppl., 01004 Metrologia, 2002, 39, Tech. Suppl., 01005 Metrologia, 2000, 37, 313-316
Measurand	Capacitance: 10 pF
Parameters	Frequency: 1592 Hz, 1 kHz
Transfer device	Dielectric capacitors in thermostatic enclosure

Comparison type	Key Comparison
Consultative Committee	CCEM (Consultative Committee for Electricity and Magnetism)
Conducted by	EURAMET (European Association of National Metrology Institutes)
RMO Internal Identifier	EUROMET Project No 345
Comments	Results published on 06 September 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	NPL National Physical Laboratory United Kingdom
Contact person	J.H. Belliss +44 (0) 20 8943 6294

Pilot laboratory
NPL	National Physical Laboratory, United Kingdom, EURAMET

BEV	Bundesamt für Eich- und Vermessungswesen, Austria, EURAMET

BIPM	Bureau International des Poids et Mesures, BIPM - International Organization, N/A

CEM	Centro Español de Metrologia, Spain, EURAMET

CMI	Czech Metrology Institute, Czechia, EURAMET

GUM	Glowny Urzad Miar, Central Office of Measures, Poland, EURAMET

METAS

Federal Institute of Metrology, Switzerland, EURAMET

NIST	National Institute of Standards and Technology, United States, SIM

PTB	Physikalisch-Technische Bundesanstalt, Germany, EURAMET

UME	TÜBITAK Ulusal Metroloji Enstitüsü, Türkiye, EURAMET

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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

Key comparison CCEM-K4

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 = x₀ 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.

Linking EUROMET.EM-K4 to CCEM-K4

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.
In three cases, two EUROMET values are reported; the mean of the two values is used as the final result.

Seven laboratories (BIPM, LNE, NMIA, NIST, VSL, NPL and PTB) participated in both comparisons.
Each was asked if its results should be used for the link and, if so, to provide a one-sigma estimate of the uncertainty, r_i, corresponding to the imperfect reproductibility of its measurements during the time ellapsed between its measurements for the two comparisons. One of the common participants (LNE) asked that its results not be used for the link.

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
(m_i_-EUR- m_i_R-EUR) of a laboratory participating in EUROMET.EM-K4 only, so that the corrected result represents the best estimate of what would have been the result of this laboratory had it actually participated in CCEM-K4.
The correction d is obtained as the weighted average of the differences of the results
[(m'_i - m_R) - (m_i_-EUR- m_i_R-EUR)] obtained by the 6 linking laboratories in both comparisons.
The weights are inversely proportional to the quantities s_i² = t_i² + t_i-EUR² + 2 r_i², where t_iand t_i-EURare the standard transfer uncertainties in the CCEM-K4 and EUROMET.EM-K4 key comparisons.
The result is: d = 0.007x10^-6with a standard uncertainty u_d = 0.0202x10^-6.

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.

Linking APMP.EM-K4.1 to CCEM-K4

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.

Linking SIM.EM-K4 to CCEM-K4

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.

Linking COOMET.EM-K4 to CCEM-K4

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.

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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

Key comparison CCEM-K4, Pilot laboratory : NIST

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 = x₀ x (1 + m_i), with x₀ = 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

Key comparison EUROMET.EM-K4, Pilot laboratory : NPL

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= x₀ x (1 + m_i_-EUR), with x₀ = 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

Key comparison APMP.EM-K4.1, Pilot laboratory : NMIA

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.

Key comparison SIM.EM-K4, Pilot laboratory : NIST

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.

Key comparison COOMET.EM-K4, Pilot laboratory : SE "Ukrmetrteststandard"

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.

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Key and supplementary comparisons - Print out