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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).