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Bilateral Comparison of 10 pF Capacitance Standards
(ongoing BIPM key comparison BIPM.EM-K14.a)
between the BIM, Bulgaria, and the BIPM, April-September 2012
I. Sapunova**, N. Fletcher*, R. Goebel* and M. Stock*
*Bureau International des Poids et Mesures (BIPM), F-92312 Sèvres Cedex, France
**Bulgarian Institute of Metrology (BIM), 52 B, G.M. Dimitrov Blvd, 1040 Sofia, Bulgaria
Final Report March 2014
Introduction
This bilateral comparison between the BIM, Bulgaria and the BIPM was carried out from
April to September 2012. Two 10 pF travelling standards belonging to the BIPM were used.
The comparison was carried out with an ‘A-B-A’ pattern of measurements; the standard was
measured first at the BIPM for a period of about one month, then for a similar period at the
BIM, and finally again at the BIPM. The measurand was the two terminal-pair capacitance at
a frequency of 1000 Hz and for a measuring voltage of 15 V. The BIPM was the pilot
laboratory, and the comparison forms part of the ongoing BIPM key comparison
BIPM.EM-K14.a.
Travelling standard
The two BIPM travelling standards are Andeen-Hagerling model AH11A capacitance
modules having nominal values of 10 pF (S/N 01228 and S/N 01229) mounted in a frame
model AH1100 (S/N 00105). The effect of ambient temperature on the standards mounted in
the frame has been tested in the range 20 °C to 25 °C. No changes in the capacitance values
greater than 1 part in 108 were detected over this range. Both laboratories measured the
travelling standards at ambient temperatures between 22.5 °C and 23.5 °C. Under these
conditions, the temperature corrections are negligible. The ‘drift’ and temperature indications
of the AH1100 frame were recorded for completeness during all measurement periods, but
these are not reported here. The effects of normal variations in atmospheric pressure and
humidity are also negligible, and therefore no corrections have been applied for changes in
ambient conditions. The AH1100 frame was shipped between the two laboratories by
standard air freight.
The standard conditions for 10 pF measurements at the BIPM are 100 V and 1592 Hz, and the
repeated BIPM measurements are made at these values. The travelling standards have been
separately characterized for frequency and voltage dependence against known BIPM
references. The ultimate reference for these measurements is the BIPM multi-frequency
quadrature bridge and calculable coaxial resistors [1]. The uncertainties for these corrections
are included in the BIPM uncertainty budget. Whilst the uncertainty on the frequency
correction of the measurements is the largest component in the BIPM uncertainty budget it
does not limit the overall uncertainty of the comparison.
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Measurement principle
BIM capacitance standard and measurement method
The travelling standards were compared to the BIM reference standard of the same type and
nominal value of 100 pF in the ratio 1:10. An ultra-precision capacitance bridge type
AH2550A was used. The ratio between travelling and reference standards was evaluated from
the bridge readings. The value of capacitance of the unknown (travelling standard) was
calculated by means of the ratio and predicted value of the reference standard. The cable
correction was set in the bridge. The measurements were carried out at nominal frequency
1000 Hz and nominal voltage 15 V. The ambient temperature was 23.0±0.5 °C.
The BIM reference standard is one of the set of four capacitance standards (type AH11A,
serial numbers 01622, 01623, 01624 and 01625, all nominal value 100 pF) mounted in a
frame type AH1100. This set is used to maintain the capacitance value at the BIM. The
standards are frequently checked by internal comparisons in the periods between external
calibrations. The differences between the capacitance values are analyzed to detect the drift or
other anomalies.
Traceability to the SI is obtained by calibration of capacitance standards at the BIPM or an
NMI. The four standards were calibrated by the CMI, Czech Republic, in July 2008, and three
of the standards with serial numbers 01622, 01623 and 01624 at the BIPM in October 2010.
BIPM capacitance standard and measurement method
The BIPM maintains a reference group of four fused silica 10 pF capacitors (one NBS type
and three GR 1408-A type). Since 1999, the mean value of the group has been measured
twice a year using a measurement chain linking the 10 pF capacitances to the recommended
value of the von Klitzing constant, RK-90 = 25 812.807 . The chain includes a capacitance
bridge with a ratio of 10:1, a multi-frequency quadrature bridge, an ac-dc coaxial resistor with
calculable frequency dependence of resistance, and a quantum Hall device operated at 1 Hz.
The relative drift rate of the mean value of the reference group is about –3.5 parts in 108 per
year.
The travelling standards were measured in terms of the BIPM 10 pF reference group by
substitution on a coaxial bridge for two terminal-pair capacitances with a 10:1 ratio and an
intermediate 100 pF tare standard. The measurements were made using the standard BIPM
conditions for 10 pF: nominal frequency of 1592 Hz and nominal voltage of 100 V (rms). The
frequency and voltage coefficients of the travelling standards were measured separately
against the known properties of a 100 pF reference. These coefficients were used to correct
the BIPM results to match the conditions of 1000 Hz and 15 V, and this transfer is covered in
the BIPM uncertainty.
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Results
Figures 1 and 2 show all the individual measurements of both the BIPM and the BIM. The
mean values of the BIM measurements are shown, along with their uncertainty bars (1σ). A fit
to the BIPM before and after measurements is also shown, along with the predicted value at
the mean time of the BIM measurements (11 July 2012). For standard 01228 (figure 1), a
linear model is a good fit to the standard’s behaviour over time, and is used for the prediction.
For standard 01229 (figure 2), there seems to be a step change with a transient effect after
transport. The first two points of the return measurements are eliminated, and mean values for
the before and after periods are calculated. The predicted value is simply the mid-point
between these two values.
A transport uncertainty is estimated for each standard. For standard 01228, it is calculated
from the residuals to the linear fit in the usual way. For standard 01229, we assume a
rectangular distribution spanning the before and after values to cover the value of the standard
during the BIM measurements, and we use this to estimate a standard uncertainty. These
transport uncertainties are included in the uncertainty bars for the BIPM values shown on the
graphs. The BIPM results, BIM results and the transport uncertainties for both standards are
given in table 1.
Standard 01228 Standard 01229
CBIPM 10.000 019 40 pF 10.000 022 68 pF
uBIPM (1σ, rel) 0.071×10–6
0.071×10–6
CBIM 10.000 018 6 pF 10.000 025 0 pF
uBIM (1σ, rel) 0.52×10–6
0.53×10–6
uTransport (1σ, rel) 0.013×10–6
0.19×10–6
Δ=(CBIM-CBIPM)/10 pF −0.080×10–6
+0.232×10–6
Table 1: Results and transport uncertainties for standards 01228 and 01229.
We calculate the weighted mean of the two differences, Δ01228 and Δ01229, using the transport
uncertainties as the weights, in the standard way:
�̅�𝑤 =∑ 𝑤𝑖𝑥𝑖
∑ 𝑤𝑖; 𝑤𝑖 =
1
𝑢𝑖2
𝑢�̅�𝑤= (∑ 𝑤𝑖)
−1 2⁄
This gives: Δ = −0.079×10–6
utransfer = 0.013×10–6
The combined relative standard uncertainty on the difference is given by
(uBIPM2+ uBIM
2+ utransfer
2)½: u = 0.53×10
–6
The result can be summarized in the form of a degree of equivalence, DBIM, between the BIM
and the BIPM for measurements of 10 pF standards at 1000 Hz and 15 V, with its associated
expanded uncertainty, UBIM (k = 2, 95 % confidence):
DBIM = (CBIM − CBIPM) / 10 pF = − 0.1 × 10−6
UBIM = 1.1 × 10−6
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Figure 1: all results for standard 01228, showing BIPM measurements and linear fit, plus
BIM measurements with means and 1σ uncertainty bars.
Figure 2: all results for standard 01229, showing BIPM measurements with before and after
values, plus BIM measurements with means and 1σ uncertainty bars.
04/04/2012 04/05/2012 04/06/2012 04/07/2012 04/08/2012 04/09/20121.2
1.4
1.6
1.8
2.0
2.2
2.4 10 pF 01228
BIPM
BIM
10
6
(C
/10
pF
- 1
)
Date
04/04/2012 04/05/2012 04/06/2012 04/07/2012 04/08/2012 04/09/2012
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2 10 pF 01229
BIPM
BIM
10
6
(C
/10
pF
- 1
)
Date
5/6
Comments
One of the travelling standards in this comparison behaved well, the other less so. However,
the transport uncertainty is not the limiting factor in the final uncertainty of the comparison.
The BIM has taken its capacitance traceability from the BIPM via calibration of its reference
standards, and also from the CMI, Czech Republic, which in turn takes its traceability from
the BIPM. The purpose and interpretation of this bilateral comparison may therefore not be
clear, as there is no independent realization of the farad at the BIM which is being tested.
What is being tested, however, is the ability of the BIM to use the previous external
calibrations to provide a continuous calibration service to its clients. The last calibration
provided by the BIPM was in October 2010, so this comparison is a good test of the ability of
the BIM to extrapolate the value of the reference, and of the uncertainty budgets that cover
this and the use of the equipment required for capacitance scaling from the 100 pF reference
to 10 pF.
An identical comparison of 100 pF standards was carried out at the same time, and is being
published simultaneously. It shows very similar results to those presented here.
Reference
[1] F. Delahaye and R. Goebel, ‘Evaluation of the frequency dependence of the resistance
and capacitance standards in the BIPM quadrature bridge’, IEEE. Trans. Instrum. Meas., 54,
no 2, pp 533-537 (2005)
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Annex: Uncertainty budgets
BIPM Uncertainty Budget
Component Relative
uncertainty/10-9
Values at 1 Hz of 51.6 kΩ resistors used in quadrature bridge, with
respect to RK-90
14
1 Hz – 1541 Hz difference of 51.6 kΩ resistors 22
Operation of quadrature bridge at 1541 Hz 13
Scaling from 2000 pF capacitors of quadrature bridge to 10 pF reference 15
Extrapolation of the value of the 10 pF reference group 14
Link between unknown and 10 pF reference group 15
Uncertainty on voltage correction (change from 100 V to 15 V) 20
Uncertainty on frequency correction (change from 1592 Hz to 1000 Hz) 58
Total 71
All values are standard uncertainties (1σ estimates).
BIM Uncertainty Budget
Source of Uncertainty Relative
uncertainty /10-6
Distribution
/ Type
Mean value of ratio between unknown and reference 0.32 Normal / A
Prediction of reference standard 0.05 Normal / A
Drift of the reference standard 0.058 Rectangular / B
Temperature stability of the reference standard 0.003 Rectangular / B
Temperature stability of the unknown standard 0.003 Rectangular / B
Uncertainty due to bridge: non-linearity, resolution,
noise, temperature stability, power-line fluctuation
0.41 Trapezoidal / B
Total 0.53
All values are standard uncertainties (1σ estimates).