Derivation of an electronic equivalent of QHE devices

A network with only resistors and unity gain amplifiers has been proven to be equivalent to the Ricketts and Kemeny (1988) electrical model of multiterminal QHE devices. This new circuit allows to simulate QHE behavior both by means of usual electronic circuit analysis software or even by direct measurement on a physical model, but its applicability is limited to devices in perfect quantization state. There are instances, e.g. in the analysis of AC QHE, where a model with nonzero longitudinal resistance is needed. In the following we present an enhanced electronic equivalent, suited to model QHE devices with any value of longitudinal resistance, and discuss its properties. The circuit is shown to belong to a class of nonreciprocal electrical elements (gyrators), that can be regarded as generalized equivalents of Hall effect devices, thus setting a general framework for the derivation of electrical models of QHE.