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 de values of R-H, making it difficult to u se the ac quantum Hall effect as an absolute impedance standard. We analyze the effects due to the large capacitances-to-shields existing in the sampl e probes on measurements of R-H to see if this is the source of the problem . Equivalent electrical circuits are utilized; they contain capacitances an d 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 revea l 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, ho wever, that quadruple-series connections to the quantum Hall devices yield only small out-of-phase contributions to V-H which may allow accurate measu rements of the quantity R-H - R-x, where R-x is the longitudinal resistance along the device.