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10 V measurements with 1V-JVS using a resistive voltage divider
M. Real, A. Tonina, M. Bierzychudek, R. Iuzzolino Instituto Nacional de Tecnología Industrial, INTI CC157, B1650WAB Buenos Aires, ARGENTINA
Abstract
This paper describes the design, built and characterization of a resistive voltage divider to compare the 10 V solid state voltage standards output directly with a 1V-Josephson voltage standard. A recent comparison with BIPM [1] exhibits an agreement of 0.024 V/V with a combined uncertainty uc = 0.04 V/V.
Introduction
For more than 17 years INTI has a 1V Josephson voltage standard (1V-JVS) as a reference in voltage. The 1.018 V solid state voltage standard (zener) output is measured in opposition with a 1.018 V reference Josephson voltage. A high stability HP 3458 multimeter (DVM) was then used for measuring the 10 V zener output, with the 10 V multimeter range previously corrected with the 1.018 V zener output. The DVM 10 V range linearity was previously checked with Hamon boxes. With this method an expanded uncertainty of 0.5 V/V was obtained. This method has some drawbacks, as the poor accuracy of measurements, the dependence of 10 V zener output measurements with 1.018 V zener output, which is more unstable than the 10 V output, and the inaccurate method, using scaling resistors, to measure the linearity of the 10 V range of the HP3458 multimeter. To improve 10 V measurements a resistive voltage divider was designed, built and characterized. It is based on tetrahedral junctions and sealed oil-filled commercial resistors The Hamon series-parallel method is used to obtain the divider ratio [2].
temperature coefficient ≤ 0.05 ppm/ºC and a tolerance ≤ 0.005 %. Low thermal emf Cu-Te golden plated binding post connectors isolated with PTFE were used to make external connections, see figure 1. To increase specific heat and thermal stability of the surrounding medium the resistors were allocated into a cooper block and each resistor case was greased with thermal conducting grease before mounting.
Figure 1. Lateral view of the divider
The resistors are permanently connected in series by tetrahedral cooper junctions [3]. Thus, each element is a four-terminal resistor.
Resistive voltage divider
The divider has 1:10 ratio. It has 100 k as input resistance, to minimize loading errors of the 10 V zener output. A 10 k output resistance was selected to reduce the contact resistance effects. To build it a set of oil-filled and sealed Vishay resistors were selected. Their nominal values were 30 kΩ for three of them and one of 10 kΩ. All resistors have a
Figure 2. Tetrahedral cooper junctions
Divider ratio measurement
To characterize the divider the 30 k resistors are connected in parallel and compared with the 10 k resistor. Hence, it is possible to measure a 1:1 voltage ratio with a high accuracy potentiometric system, which was specially designed and built at INTI to calibrate high accuracy 10 k standard resistors. αi-j = Ri / Rj is the ratio of resistances i and j. RP and RS are the equivalent resistance values in parallel and series connections of the 30 kΩ resistors of the divider. To obtain RP terminals A-B and C-D are short-circuited by connecting cooper bars (dotted lines in Figure 3). Two extra cooper bars are used to perform four-terminal resistor ratio measurement. With R4 the resistance of the 10 k resistor, the divider ratio p-4 is determined. Junction resistances have been measured being less than 1 μΩ.
Measurement setup
The 10 V zener output was connected to the resistive voltage divider input and its output was measured in opposition with the JVS (see Figure 3). An Agilent 34420A nanovoltmeter was used as detector.
Figure 3. Diagram of connections to measure 10 V zener output with JVS using the divider. Dotted lines A,B and C,D terminals
correspond to short circuits used to perform divider ratio calibration.
The 10 V zener output VZ is
VZ
VJ
RS
R4
R4
VJ 1 S4
where current through the DVM and leakage currents
have been neglected. At first order Rs is related to Rp as S 9 P4 , then the 10 V zener output can be
determined. For each measurement the divider ratio
was measured before and after the JVS zener
measurements.
Results
A series of 10 V zener output measurements is shown in Figure 4 where the resistive divider method and the multimeter method are compared. The values of both methods are very close, but the expanded uncertainty of measurement was reduced to less than one half with the divider method.
40.0
10V divisor
38.0
10V mult
36.0
(10 - Vmed) V
34.0
32.0 30.0
28.0
26.0
24.0 10/09/2009 12/09/2009 14/09/2009 16/09/2009 18/09/2009 20/09/2009 22/09/2009 24/09/2009
Date
Figure 4. Comparison of 10 V measurements using both methods.
The type B estimated combined standard uncertainty for the divider is shown in Table 1.
Table 1. Type B uC estimated uncertainty
Source of uncertainty
Type
ui [V/V]
ci
(ciui)2
%
Ratio calibration ()
Rect
9.2E-02 0.9 6.9E-03 52.5
Loading
Rect 7.9E-02 1.0 6.9E-03 47.5
Leackage
Rect 2.0E-04 1.0 4.0E-08 0.00
uC [V/V]
0.115
100
Conclusions The use of the resistive voltage divider allowed to improve the 10 V zener output measurements using a 1V-JVS. It was possible to decrease the expanded
uncertainty to 0.1 V/V by measuring the more stable 10 V output in a direct way against JVS, avoiding the linearity deviation of the DVM 10 V range. The results of the bilateral comparison with BIPM were
very satisfactory with an agreement of 0.024 V/V.
Acknowledgments The authors would like to thank Stéphane Solve (BIPM) for the support during the bilateral comparison INTI/BIPM and R. García (INTI) for his suggestions and many helpful discussions.
References
[1] A.Tonina et al, S.Solve et al, “Bilateral comparison for 1.018 V and 10 V standards between INTI
(Argentina) and the BIPM”, to be published in the technical supplement of Metrologia, 2010.
[2] B.V. Hamon, “A 1-100 Ω build-up resistor for the calibration of standard resistors”, Journal of Scientific Instruments 31 (12), 1954.
[3] J.C. Riley, “The accuracy of series and parallel connections of four-terminal resistors”, IEEE Trans. Instrum. Meas., vol. IM-16, pp. 258-268, Sept. 1967.
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