  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.

Mesoscale and Nanoscale Physics