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

In all experiments reported to date the measured values of the ac quantized Hall resistances R(H) varied with the frequency of the applied current, and differed significantly from the dc values of R(H), 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 R(H) to see if this is the source of the problem. Equivalent electrical circuits are utilized; they contain capacitances and leakage resistances to the sample probe shields, longitudinal resistances within the quantized Hall effect devices, and multiple connections to the devices. The algebraic solutions for the R(H) values in these circuits reveal large out-of-phase contributions to the quantized Hall voltages V(H) that would make it difficult to do accurate measurements with high precision ac bridges. These large out-of-phase contributions could introduce the linear frequency dependences observed in previous R(H) measurements. We predict, however, that quadruple-series connections to the quantum Hall devices yield only small out-of-phase contributions to V(H) which may allow accurate measurements of the quantity R(H) − R(x), where R(x) is the longitudinal resistance along the device.