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HIGH RESISTANCE SCALING FROM 10 k: AND QHR STANDARDS USING A CRYOGENIC CURRENT COMPARATOR
R. Elmquist, G. R. Jones, Jr., B. Pritchard†, M. Bierzychudek‡, and F. Hernandez§ National Institute of Standards and Technology
Gaithersburg, MD, USA
Abstract
We describe a cryogenic current comparator (CCC) bridge for resistance scaling that provides improved measurement uncertainty over a range of resistance values from 100 k: to 1 G:. This CCC is designed for high resistance scaling based directly on a quantized Hall resistance (QHR) standard as well as comparisons of resistance ratios of 1, 10 and 100. The QHR-to-decade-value winding ratio offset is chosen so as to approximately cancel the offset produced by resistive decade windings.
Introduction
CCC bridges are an essential tool in modern electrical metrology, but in practice their applicability is limited by difficulties in the design, ease of use, and cost. This paper will describe the results of a project to design and build high-resistance CCC systems that provide the low uncertainty of this technique with reasonable cost. The two-terminal, single-source bridge design [13] reduces noise from the feedback electronics and other non-cryogenic components of the bridge. This technique allows high-value resistors to be compared directly against the QHR standard using two-terminal connections [4, 5] with uncertainties that approach those of four-terminal CCC resistance comparisons.
ampere-turns signal necessary to maintain the bridge balance condition.
The CCC windings are coupled to the SQUID by a 4.5 cm inner-diameter superconducting shield and flux transformer, with a current sensitivity of about 1.3 PAturn/ĭ0, where ĭ0 is the flux quantum. The ratios of the 4-turn QHR winding and 31-base-turn decade windings (31, 310, and 3100 turns) create an offset of about -246 × 10-6 from the nominal resistance ratio, when decade-value resistors are compared to the QHR 12906.4035 : plateau. Canceling offsets are created by the winding resistance of the phosphorbronze wire used for the windings and cryogenic leads, which tends to reduce the uncertainty contributions of the feedback current measurement and voltage source stability for low-value resistors. Thus, in this implementation we compare the QHR to 1 M: (or 10 M:) using winding resistances of nominally 246 : (2460 :). All ratio windings except the one used with the QHR are made using various gauges of resistive wire, and this resistance is sufficient to minimize noise amplification in the SQUID detector near highfrequency resonances.
CCC design and behavior
The two-terminal CCC electronics is based on a single ramping voltage source which enables comparisons of many different values of resistance, from 10 k: up to at least 1 G:. The voltage source is designed to produce a reversing output of about 0.5 V to 1 V for use with the QHR and 5 V to 10 V for use when only standard resistors are compared. Two superconducting junctions with external leads for voltage measurements provide a well-defined bridge voltage. The CCC bridge balance equations are straightforward to solve when this voltage, the number of turns in each winding, and the bridge connection resistances are known.
This design derives its only bridge feedback current from a dc superconducting quantum interference device (dc SQUID). The feedback current is applied to a single-turn CCC winding to produce a constant dc magnetic flux, and is measured to determine the
Figure 1. Schematic diagram of the bridge, showing connections for room-temperature resistors and the voltage source (VS).
As shown in Fig. 1, three windings with 4 turns, 31 turns, and 310 turns are in opposition to a second 310 turn winding and the 3100 turn winding. All five CCC ratio windings are connected to the low side of the bridge and ground, and appropriate pairs of these windings can be used to compare resistance ratios of the QHR to 1 M: and 10 M:, as well as 1-to-1, 10-to-1, and 100-to-1 ratios. Sample measurements obtained with the bridge are shown in Fig. 2.
†Permanent address: B. Pritchard, National Measurement Institute, Bradfield Road, West Lindfield, NSW, Australia ‡Permanent address: M. Bierzychudek, Instituto Nacional de Tecnología Industrial, B1650KNA, San Martín, República Argentina §Permanent address: F. Hernandez, Centro Nacional de Metrologia, km 4.5, Carretera a Los Cués, 76241 Querétaro, México
Quantum Electrical Metrology Division, Electronics and Electrical Engineering Laboratory, U.S. Department of Commerce. Official contribution of the National Institute of Standards and Technology, not subject to copyright in the United States.
268
10000920
10000910
Resistance (: )
10000900
10000890
10000880 0
500
1000
1500
2000
Measurement Time (s)
2500
Figure 2. Comparison of a 10 M: Hamon-network resistance against the QHR i = 2 plateau, measured at ± 0.9 V, with 10 s integration time for each point in each current direction. The relative standard deviation of the mean is 0.05 P:/:.
The fundamental noise current for a resistance R at temperature T is In = (4kBT/R)1/2, where kB is the Boltzman constant, and this In is 1.25 × 10-10 A/Hz1/2 for a 10 M: resistor at 293 C. When in series with the 3100 turn winding, this current noise level is equivalent to a flux noise of 9.6 × 10-5 ĭ0/Hz1/2, which is significantly larger than the typical dc SQUID input flux noise and thus is likely to be one limiting factor in such a measurement. At a bridge voltage of 1 V, this 10 M: noise current is equivalent to 0.4 (P:/:)/Hz1/2, in terms of the relative uncertainty contribution.
Decade Resistance Comparisons
The many components of uncertainty that influence
our CCC comparisons for decade resistor values of 10
k: to 1 G: are described in a separate paper [6].
Below 1 M: the winding-resistance and lead
resistance corrections are the largest predicted
component of the total combined uncertainty. At
higher resistance values, current noise in the resistors
and the measurement of the feedback current become
dominant, and leakage effects can be more critical.
Many different types of film and wire-wound
resistance elements exist in commercial standards for
values above 1 M:, and we have investigated
dielectric settling-time effects [7] using source reversal
delays of 4 s to 64 s. At present, using a ± 10 V bridge
voltage, standard deviations of CCC bridge
measurements with 20 s total integration time are
approximately as shown in Table 1.
Table 1.
Secondar Primary Standard Deviation
y
(:)
(P:/:)
(:)
100 k: 1 M:
0.002
100 k: 10 M:
0.040
1 M:
10 M:
0.040
1 M: 100 M:
0.40
10 M: 100 M:
0.40
10 M:
1 G:
4.0
Conclusion
We describe two-terminal CCC bridges that provide low combined uncertainties for high-resistance scaling. Measurements of guarded Hamon devices [8] show good agreement in scaling, especially where compact film-type resistor elements make up the resistance networks. Differences in scaling due to settling time constants can be characterized using certain other standards. Comparisons between the new systems and other CCC bridges designed for high-resistance scaling from the QHR will be presented at the conference. Comparisons with scaling based on 10 k: fourterminal CCC measurements will also be described.
References
[1] D.B. Sullivan and R.F. Dziuba, “A lowtemperature direct-current comparator bridge,” IEEE Trans. Instrum. Meas., vol. 23, pp. 256-260, (1974).
[2] R. E. Elmquist, N. M. Zimmerman, and W. H. Huber, “Using a high-value resistor in triangle comparisons of electrical standards,” IEEE Trans. Instrum. Meas., vol. 52, pp. 590-593, (2003).
[3] R. E. Elmquist, E. Hourdakis, D. G. Jarrett and N. M. Zimmerman, “Direct resistance comparisons from the QHR to 100 Mȍ using a cryogenic current comparator,” IEEE Trans. Instrum. Meas., vol. 54, 525-528, Apr. 2005.
[4] F. Delahaye, “Series and parallel connection of multiterminal quantum Hall effect devices,” J. Appl. Phys. 73, 7915-7920, 1993.
[5] A. Jeffery, R. E. Elmquist, and M. E. Cage, “Precision tests of a quantum Hall effect device DC equivalent circuit using double-series and tripleseries connections,” J. Res. Natl. Inst. Stand. Technol. 100, 677 (1995).
[6] M. E. Bierzychudek and R. E. Elmquist, “Uncertainty evaluation in a two-terminal cryogenic current comparator,” submitted to this conference.
[7] D. G. Jarrett and R. E. Elmquist, “Settling times of high value standard resistors,” CPEM 2004 Digest, p. 522, London, England, 27 June - 2 July, 2004.
[8] D. G. Jarrett, “Evaluation of guarded highresistance Hamon transfer standards,” IEEE Trans. Instrum. Meas., vol. 48, pp 324-328, (1999).
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