The quantum Hall effect (QHE) provides an invariant reference for resistance linked to natural constants It is used worldwide to maintain and compare the unit of resistance The reproducibility reached today is almost two orders of magnitude better than the uncertainty of the determination of the ohm in the international system of units SI In this article, mainly the aspects of the QHE relevant for its metrological application are reviewed After a short introduction of the theoretical models describing the integer QHE, the properties of the devices used in metrology and the measurement techniques are described A detailed summary is given on the measurements carried out to demonstrate the universality of the quantized Hall resistance and to assess all the effects leading to deviations of the Hall resistance from the quantized value In addition, the present and future role of the QHE in the SI and the field of natural constants is discussed

https://iopscience.iop.org/article/10.1088/0034-4885/64/12/201/pdf

The quantum Hall effect as an electrical resistance standard

A ratio bridge has been built which compares four-terminal resistances by measuring the current ratio corresponding to voltage drop equality. A current ratio, corresponding to turns ratio, is automatically maintained by a self-balancing direct current comparator and is adjustable in part-per-million steps. The two current sources are isolated so that, at balance, there is no current in the potential circuit. The bridge can be direct reading in either resistance or conductance ratio. The bridge makes use of the ability of a self-balancing direct current comparator to measure and compare accurately the ratio of two isolated direct currents. A detailed description of the bridge is presented with an analysis of its accuracy limitations. In its optimum operating range accuracies of better than one part per million can be achieved. The bridge is particularly suited to the scaling of resistance standards from one hundred ohms to a fraction of a milliohm. It can be used at any ratio up to one thousand to one. It permits the calibration of low value shunts at full operating current with an accuracy limited only by their noise level and stability.

A Direct-Current-Comparator Ratio Bridge for Four-Terminal Resistance Measurements

The direct current comparator is a current ratio device which uses a two-core magnetic modulator as an ampere-turn balance detector. The applications of this comparator to precision measurements are very limited, unless it is made self-balancing by feedback. A transistorized self-balancing direct current comparator for 20 000 amperes which employs two stages to obtain a maximum ratio of 20 000/1 is described. The self-balancing circuit has a range of ±10 percent and an open loop gain of over 10 000. An analysis is made of the errors of the comparator including the effects of large external magnetic fields, magnetic memory, and alternating currents in the ratio windings. The total error increases with the amount of self-balancing required, but does not exceed 10 parts per million, provided the comparator is operated near its rated ampere-turn level. Applications of the comparator to the calibration of transductors (tic current transformers) and dc shunts at full rated current are discussed.

A self-balancing direct current comparator for 20 000 amperes

An impedance bridge for high-voltage capacitance and related measurements to an accuracy of 1 ppm is described and the background research and development which made it possible is documented. The bridge is of the transformer-ratioarm type, the principal components of which are a comparator and several two-stage transformers. The bridge can be used to measure capacitance ratios over a range from 1/1 to 107/1 with a resolution between 0.1 and 0.25 ppm. The highest accuracies are obtained at the principal power frequencies of 50-60 Hz, but the bridge is usable up to 400 Hz. The factors which limited the accuracy of previously developed bridges of this type were reexamined and their influence reduced. Two independent methods were developed for the calibration of the bridge.

A Wide-Range High-Voltage Capacitance Bridge with One PPM Accuracy

The quantum Hall effect (QHE) provides an invariant reference for resistance linked to natural constants. It is used worldwide to maintain and compare the unit of resistance. The reproducibility reached today is almost two orders of magnitude better than the uncertainty of the determination of the ohm in the International System of Units. This article is a summary of a recently published review article which focuses mainly on the aspects of the QHE relevant for its metrological application.

https://iopscience.iop.org/article/10.1088/0957-0233/14/8/306/pdf

A high-voltage capacitance ratio bridge based on the current comparator principle is described. The inherent advantages of this bridge are high sensitivity and high accuracy without the necessity of a secondary balance. By suitable design the bridge is made direct reading in capacitance ratio and dissipation factor. It has a resolution of 1 ppm (part per million) and an accuracy of approximately 10 ppm. The highest capacitance ratio internally available with full resolution is 1,000/1. Design considerations and construction details are given. Possible applications are discussed.

A transformer-ratio-arm bridge for high-voltage capacitance measurements

A method is presented for the measurement of the variation of capacitance with voltage in gas-dielectric capacitors. It consists of applying to the capacitor a direct voltage and using a small alternating voltage to measure the capacitance variation. The direct voltage coefficient obtained in this manner differs from that obtained with alternating voltage, and this relationship is studied theoretically and verified experimentally. High-voltage compressed gas capacitors can have appreciable voltage coefficients because of eccentricity in their electrode structure. A method is presented for detecting and correcting such eccentricity without opening the capacitor. The voltage coefficients of a few solid dielectric capacitors were measured by comparison with a known air-dielectric capacitor and the results reported.

The voltage coefficients of precision capacitors

A magnetic d-c ratio device has been developed that is capable of attaining accuracies approaching 1 part per million The operating characteristics and some of the design problems are discussed, and construction details of an experimental model, rated at 4,000 ampere-turns and capable of handling ratios up to 400 to 1, are given The use of this device for the scaling of fundamental resistance standards is proposed

A current comparator for the precision measurement of D-C ratios

A magnetic d-c ratio device has been developed that is capable of attaining accuracies approaching 1 part per million. The operating characteristics and some of the design problems are discussed, and construction details of an experimental model, rated at 4,000 ampere-turns and capable of handling ratios up to 400 to 1, are given. The use of this device for the scaling of fundamental resistance standards is proposed

IN JUNE 1960, the Hydro-Electric Power Commission of Ontario inquired whether the United States National Bureau of Standards (NBS) in Washington could measure for them the ratio and phase-angle errors of a 350-kv voltage transformer then being built to their order. This request was also made at about the same time of the National Research Council of Canada (NRC) in Ottawa. Neither laboratory had, at that time, made calibration measurements on instrument transformers at this voltage level, but both had given the problem considerable thought; and it appeared that the request by Ontario Hydro afforded a unique opportunity not only to examine some of the problems involved in voltage-ratio measurements at 350 kv, but also to compare measurement results between the two national laboratories.

N. L. Kusters

Papers

A transformer-ratio-arm bridge for high-voltage capacitance measurements

The voltage coefficients of precision capacitors

A current comparator for the precision measurement of D-C ratios

A current comparator for the precision measurement of D-C ratios

An International comparison of voltage-transformer calibrations to 350 kv