Eigenvalues of strictly regular Hall-plates

Abstract

This work is about uniform, plane, singly connected, strictly regular Hall-plates with an arbitrary number of peripheral contacts exposed to a uniform magnetic field of arbitrary strength. The strictly regular symmetry is the highest possible degree of symmetry, and it is found in commercial Hall-plates for magnetic field sensors or circulators. It means that all contacts and contact spacings are equally large, if the Hall-plate is mapped conformally to the unit disk. The indefinite conductance matrices of such Hall-plates are circulant matrices, whose complex eigenvalues can be computed in closed form. It is shown how to express the conductance and resistance matrices of these Hall-plates, how to compute their equivalent resistor circuit, their Hall-output voltages or currents, their signal-to-thermal noise ratio, and their power as functions of the eigenvalues. It is also proven that the noise efficiency of strictly regular Hall-plates with many contacts can be up to 112% better than for conventional Hall-plates with four contacts, and it is explained why their optimal biasing uses patterns of supply voltages or currents, which vary sinusoidally along their boundary.