Self impedance matched Hall-effect gyrators and circulators

TL;DR

This paper models a Hall-effect microwave gyrator with impedance matching capabilities, demonstrating ideal gyration at specific frequencies, low impedance operation without auxiliary matching, and potential for high bandwidth and circulator implementation.

Contribution

It introduces a three-electrode Hall-effect gyrator model with impedance matching, analyzes parasitic effects, and proposes an interferometric circulator design for non-reciprocal microwave components.

Findings

Ideal gyration achievable at specific frequencies

Impedance can be made arbitrarily small without auxiliary matching

Bandwidth up to 150 MHz at 50Ω with reduced magnetic field

Abstract

We present a model study of an alternative implementation of a two-port Hall-effect microwave gyrator. Our set-up involves three electrodes, one of which acts as a common ground for the others. Based on the capacitive-coupling model of Viola and DiVincenzo, we analyze the performance of the device and we predict that ideal gyration can be achieved at specific frequencies. Interestingly, the impedance of the three-terminal gyrator can be made arbitrarily small for certain coupling strengths, so that no auxiliary impedance matching is required. Although the bandwidth of the device shrinks as the impedance decreases, it can be improved by reducing the magnetic field; it can be realistically increased up to $ 150 \mathrm{MHz}$ at $50\mathrm{\Omega}$ by working at filling factor $\nu=10$. We examine also the effects of the parasitic capacitive coupling between electrodes and we find that, although in general they strongly influence the response of device, their effect is negligible at low impedance. Finally, we analyze an interferometric implementation of a circulator, which incorporates the gyrator in a Mach-Zender-like construction. Perfect circulation in both directions can be achieved, depending on frequency and on the details of the interferometer.