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Equivalent Electrical Circuit Representations of AC Quantized Hall Resistance Standards



Marvin E. Cage, Anne-Marie Jeffery, J. Matthews


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 Rη. 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 Rη for both ac and dc currents with a one-standard-deviation uncertainty of 10-8 Rη 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 Rχ 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 Rη in order to realize an intrinsic ac quantized Hall resistance standard of 10-8 Rη uncertainty or less.
Journal of Research (NIST JRES) -


ac quantum Hall effect, equivalent electrical circuits, intrinsic impedance standard, multi-series connections, quantized Hall resistance, parasitic impedances


Cage, M. , Jeffery, A. and Matthews, J. (1999), Equivalent Electrical Circuit Representations of AC Quantized Hall Resistance Standards, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed June 13, 2024)


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Created October 31, 1999, Updated October 12, 2021