CCEMK4, EUROMET.EMK4, APMP.EMK4.1, SIM.EMK4 and COOMET.EMK4
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 CCEMK4
Green triangles: participants in EUROMET.EMK4^{b}
Blue circles: participants in APMP.EMK4.1^{b}
Purple squares: participants in SIM.EMK4^{b}
Orange squares: participants in COOMET.EMK4^{b}
a) Measurements made at 1000 Hz
b) Linking laboratories to CCEMK4 not listed
CCEMK4, EUROMET.EMK4, APMP.EMK4.1, SIM.EMK4 and COOMET.EMK4
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_{K90}
In red: participants in CCEMK4
In green: participants in EUROMET.EMK4^{b}
In blue: participants in APMP.EMK4.1^{b}
In purple: participants in SIM.EMK4^{b}
In orange: participants in COOMET.EMK4^{b}
a) Measurements made at 1000 Hz
b) Linking laboratories to CCEMK4 not listed
The full matrix of equivalence of key comparisons CCEMK4, EUROMET.EMK4, APMP.EMK4.1, SIM.EMK4 and COOMET.EMK4 is available in Summary Results (PDF file, A4 printable format).
Metrology area, Subfield  Electricity and Magnetism, Capacitance 
Description  Comparison of capacitors 
Time of measurements  2004  2006 
Status  Approved for equivalence 
Final Reports of the comparisons  
Measurand  Capacitance: 10 pF 
Parameters  Frequency: 1592 Hz 
Transfer device  Fused silica capacitance standards 
Comparison type  Key Comparison 
Consultative Committee  CCEM (Consultative Committee for Electricity and Magnetism) 
Conducted by  APMP (Asia Pacific Metrology Programme) 
RMO Internal Identifier  APMP Project No P2APMP.EMK4.1 
Comments 
Results published on 03 March 2009 EUROMET.EMK4, APMP.EMK4.1, SIM.EMK4 and COOMET.EMK4 results are linked to those of CCEMK4 Capacitance of nominal value 10 pF at frequency ~ 1.6 kHz

Pilot institute 
NMIA
National Measurement Institute, Australia Australia 
Contact person  H.L. Johnson +61 2 8467 3529 
Pilot laboratory  

NMIA 
National Measurement Institute, Australia, Australia, APMP 
CMS/ITRI 
Industrial Technology Research Institute/Center for Measurement Standards, Chinese Taipei, APMP 
KRISS 
Korea Research Institute of Standards and Science, Korea, Republic of, APMP 
NIM 
National Institute of Metrology, China, APMP 
NIMT 
National Institute of Metrology (Thailand), Thailand, APMP 
NMC, A*STAR 
National Metrology Centre, Agency for Science, Technology and Research, Singapore, APMP 
NMIJ AIST 
National Metrology Institute of Japan, Japan, APMP 
NMISA 
National Metrology Institute of South Africa, South Africa, AFRIMETS 
NMLSIRIM 
National Metrology Laboratory, SIRIM Berhad (became NMIM), Malaysia, APMP 
NPLI 
CSIR National Physical Laboratory of India, India, APMP 
Puslit KIMLIPI 
Research Center for Calibration, Instrumentation and Metrology – Indonesian Institute of Sciences, Indonesia, APMP 
SCL 
Standards and Calibration Laboratory, Hong Kong, China, APMP 
VNIIM 
D.I. Mendeleyev Institute for Metrology, Rosstandart, Russian Federation, COOMET 
This page proposes printout on A4 paper (portrait) of the comparison details (best printed out using a black and white printer).
Please, select items to be printed out, then click on "OK" :
CCEMK4, EUROMET.EMK4, APMP.EMK4.1, SIM.EMK4 and COOMET.EMK4
MEASURAND : Capacitance
NOMINAL VALUE : 10 pF
FREQUENCY : ~ 1.6 kHz
The key comparison reference value of CCEMK4 is obtained from the weighted average of the results of the CCEMK4 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 CCEMK4 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 CCEMK4 Final Report. 
The input data for establishing the link between EUROMET.EMK4 and CCEMK4 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 CCEMK4 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.EMK4 with respect to the CCEMK4 key comparison reference value is given by a pair of terms: D_{i} = [(m_{iEUR}  m_{iREUR}) + d] and its expanded uncertainty (k = 2), U_{i}, based on the quadratic combination of u_{R}, u_{d}, t_{iEUR} and U_{iEUR}/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.EMK4.1 to those of CCEMK4 is explained in paragraph 6.5 on page 17 of the APMP.EMK4.1 Final Report, and is similar to that used to link EUROMET.EMK4 to CCEMK4.
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.EMK4.1 with respect to the CCEMK4 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.EMK4.1 Final Report. 
The complete matrix of equivalence is built up as explained in paragraph 6.5.5 on page 20 of the APMP.EMK4.1 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.EMK4 to those of CCEMK4 is explained in Appendix F on page 40 of the SIM.EMK4 Final Report.
The degree of equivalence of each laboratory participant in SIM.EMK4 with respect to the CCEMK4 key comparison reference value is given by a pair of terms D_{i} and its expanded uncertainty (k = 2), U_{i}. 
The pairwise degrees of equivalence involving the SIM.EMK4 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.EMK4 to those of CCEMK4 is explained in Section 7.4 of the COOMET.EMK4 Final Report.
The degree of equivalence of each laboratory participant in COOMET.EMK4 with respect to the CCEMK4 key comparison reference value is given by a pair of terms D_{i} and its expanded uncertainty (k = 2), U_{i}. 
The pairwise degrees of equivalencebetween participants in COOMET.EMK4 are given on p. 12 of the COOMET.EMK4 Final Report. 
CCEMK4, EUROMET.EMK4, APMP.EMK4.1, SIM.EMK4 and COOMET.EMK4
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_{K90}  
measurements derived from calculable capacitors  
BIPM1, 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}_{REUR }: value of reference referred to the date of measurement at laboratory i (see section 5.13.2 and subsequent graphs in the EUROMET.EMK4 Final Report), based on a weighted mean of EUROMET.EMK4 participants' measurements.
Its expanded uncertainty (k = 2) is U_{i}_{REUR }= 0.037x10^{6} at all dates.
measurements derived from R_{K90}  
measurements derived from calculable capacitors 
The measurement results and associated standard uncertainties of the laboratories having participated in key comparison APMP.EMK4.1 are given in paragraph 6.2 on page 14 of the APMP.EMK4.1 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.EMK4 are given in paragraph 5.2 on page 8 of the SIM.EMK4 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.EMK4 are given in Table 5, p.8, of the COOMET.EMK4 Final Report.
Measurements were carried out between 2006 and 2009.