Anne-Marie Jeffery

Determination of the von Klitzing constant and the fine-structure constant through a comparison of the quantized Hall resistance and the ohm derived from the NIST calculable capacitor

This paper describes a recent determination of the von Klitzing constant and the fine-structure constant by comparisons of values of the ohm as defined in the International System of Units (SI), derived from the National Institute of Standards and Technology (NIST) calculable cross-capacitor, and values of the international practical unit of resistance derived from the integral quantum Hall effect. In this determination, the comparisons were made in a series of measurements lasting three years. A small difference is observed between this determination and an earlier comparison carried out in this laboratory and reported in 1988. The most recent value of the fine-structure constant based on the experimental value and theoretical expression for the magnetic moment anomaly of the electron, which has the smallest uncertainty of any value currently available, is consistent with both of these results. The new value exceeds the 1990 conventional value of the von Klitzing constant RK-90 by slightly more than twice the relative standard uncertainty of the present measurement, which is 2.4 × 10-8.

NIST comparison of the quantized Hall resistance and the realization of the SI ohm through the calculable capacitor

The latest NIST result from the comparison of the quantized Hall resistance (QHR) with the realization of the SI ohm obtained from the NIST calculable capacitor is reported. A small difference between the 1988 result and the present result has led to a re-evaluation of the sources and magnitudes of possible systematic errors.

Precision Tests of a Quantum Hall Effect Device DC Equivalent Circuit Using Double-Series and Triple-Series Connections

Precision tests verify the dc equivalent circuit used by Ricketts and Kemeny to describe a quantum Hall effect device in terms of electrical circuit elements. The tests employ the use of cryogenic current comparators and the double-series and triple-series connection techniques of Delahaye. Verification of the dc equivalent circuit in double-series and triple-series connections is a necessary step in developing the ac quantum Hall effect as an intrinsic standard of resistance.

Model tests to investigate the effects of geometrical imperfections on the NIST calculable capacitor

The calculable capacitor at National Institute of Standards and Technology (NIST) links the U.S. capacitance unit to the SI unit and has a relative standard uncertainty of 2/spl times/10/sup -8/. Geometrical imperfections are one of the largest sources of this uncertainty. Tests with a model calculable capacitor have been done to better evaluate and reduce this uncertainty. These included evaluations of the effect of eccentricity of the blocking electrodes used to define the capacitors length and of uniform taper on all the calculable capacitor bars. In addition, the effect of tilt of the blocking electrode and taper in three or fewer bars was investigated. A new cone-shape for the tip of the blocking electrode was also studied.

Intrinsic Capacitances and Inductances of Quantum Hall Effect Devices

Analytic solutions are obtained for the internal capacitances, kinetic inductances, and magnetic inductances of quantum Hall effect devices to investigate whether or not the quantized Hall resistance is the only intrinsic impedance of importance in measurements of the ac quantum Hall effect. The internal capacitances and inductances are obtained by using the results of Cage and Lavine, who determined the current and potential distributions across the widths of quantum Hall effect devices. These intrinsic capacitances and inductances produce small out-of-phase impedance corrections to the in-phase quantized Hall resistance and to the in-phase longitudinal resistance.

The Ampere and Electrical Standards.

This paper describes some of the major contributions to metrology and physics made by the NIST Electricity Division, which has existed since 1901. It was one of the six original divisions of the National Bureau of Standards. The Electricity Division provides dc and low-frequency calibrations for industrial, scientific, and research organizations, and conducts research on topics related to electrical metrology and fundamental constants. The early work of the Electricity Division staff included the development of precision standards, such as Rosa and Thomas standard resistors and the ac-dc thermal converter. Research contributions helped define the early international system of measurement units and bring about the transition to absolute units based on fundamental principles and physical and dimensional measurements. NIST research has helped to develop and refine electrical standards using the quantum Hall effect and the Josephson effect, which are both based on quantum physics. Four projects covering a number of voltage and impedance measurements are described in detail. Several other areas of current research at NIST are described, including the use of the Internet for international compatibility in metrology, determination of the fine-structure and Planck constants, and construction of the electronic kilogram.

Characterization of four-terminal-pair resistance standards: a comparison of measurements and theory

Coaxial straight-wire resistance standards with calculable frequency dependence have been used to tie alternating-current (AC) measurements to direct-current (DC) measurements of resistance. Coaxial standards of values 100 /spl Omega/ and 1000 /spl Omega/ are compared with each other and with other resistance standards at several frequencies up to 15920 Hz using AC bridges.

Calculating the Effects of Longitudinal Resistance in Multi-Series-Connected Quantum Hall Effect Devices

Many ac quantized Hall resistance experiments have measured significant values of ac longitudinal resistances under temperature and magnetic field conditions in which the dc longitudinal resistance values were negligible. We investigate the effect of non-vanishing ac longitudinal resistances on measurements of the quantized Hall resistances by analyzing equivalent circuits of quantized Hall effect resistors. These circuits are based on ones reported previously for dc quantized Hall resistors, but use additional resistors to represent longitudinal resistances. For simplification, no capacitances or inductances are included in the circuits. The analysis is performed for many combinations of multi-series connections to quantum Hall effect devices. The exact algebraic solutions for the quantized Hall resistances under these conditions of finite ac longitudinal resistances provide corrections to the measured quantized Hall resistances, but these corrections do not account for the frequency dependences of the ac quantized Hall resistances reported in the literature.

An Easy-To-Use Combination Four-Terminal-Pair/Two-Terminal-Pair AC Transformer Bridge

A new four-terminal-pair bridge, capable of achieving a relative standard uncertainty of 1×10−9, was constructed at the National Institute of Standards and Technology by converting a two-terminal-pair bridge. The conversion requires only the addition of components which are easily removed if two-terminal-pair measurements are to be made. The design and testing of this bridge is described. The new four-terminal-pair bridge requires fewer auxiliary balances than the present four-terminal-pair bridge employed at NIST, which makes it much easier to use. This new design can be used to compare capacitance, resistance, and inductance standards.

Equivalent Electrical Circuit Representations of AC Quantized Hall Resistance Standards

We use equivalent electrical circuits to analyze the effects of large parasitic impedances existing in all sample probes on four-terminal-pair measurements of the ac quantized Hall resistance RH. The circuit components include the externally measurable parasitic capacitances, inductances, lead resistances, and leakage resistances of ac quantized Hall resistance standards, as well as components that represent the electrical characteristics of the quantum Hall effect device (QHE). Two kinds of electrical circuit connections to the QHE are described and considered: single-series “offset” and quadruple-series. (We eliminated other connections in earlier analyses because they did not provide the desired accuracy with all sample probe leads attached at the device.) Exact, but complicated, algebraic equations are derived for the currents and measured quantized Hall voltages for these two circuits. Only the quadruple-series connection circuit meets our desired goal of measuring RH for both ac and dc currents with a one-standard-deviation uncertainty of 10−8 RH or less during the same cool-down with all leads attached at the device. The single-series “offset” connection circuit meets our other desired goal of also measuring the longitudinal resistance Rx for both ac and dc currents during that same cool-down. We will use these predictions to apply small measurable corrections, and uncertainties of the corrections, to ac measurements of RH in order to realize an intrinsic ac quantized Hall resistance standard of 10−8 RH uncertainty or less.