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A Problem in AC Quantized Hall Resistance Measurements and a Proposed Solution



Marvin E. Cage, Anne-Marie Jeffery


In all experiments reported to date the measurement values of the ac quantized Hall resistances RH varied with the applied current frequency, and differed significantly from the dc values of RH, making it difficult to use the ac quantum Hall effect as an absolute impedance standard. We analyze the effects due to the large capacitances-to-shields existing in the sample probes on measurements of RH to see if this is the source of the problem. Equivalent electrical circuits are utilized; the contain capacitances and leakage resistance to the sample probe shields, longitudinal resistances within the quantized Hall effect devices, and multiple connections to the devices. The algebraic solutions for the RH values in these circuits reveal large out-of-phase contributions to the quantized Hall voltages VH that would prevent accurate measurements with the ac bridges used at NIST. These large out-of-phase contributions could introduce the linear frequency dependencies observed in previous RH measurements. We predict, however, that quadruple-series connections to the quantum Hall devices yield only small out-of-phase contributions to VH which should allow accurate measurements of the quantity [RH - Rx], where Rx is the longitudinal resistance along the device.
Journal of Research (NIST JRES) -


ac quantum Hall effect, capacitance-to-shield, equivalent electrical circuit, longitudinal resistance, multi-series connections, quantized Hall resistance


Cage, M. and Jeffery, A. (1998), A Problem in AC Quantized Hall Resistance Measurements and a Proposed Solution, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed April 14, 2024)
Created October 31, 1998, Updated October 12, 2021