Circulation solutions of three-port circulators using first order split impedance zeros

The conventional operation of the three-port circulator relies on a pair of split, counter-rotating, impedance poles and one in-phase impedance zero. It is, however, also possible to realize circulation solutions about the dual problem of a pair of split, counter-rotating impedance zeros and an in-phase impedance pole. One such case involving a classic stripline circulator using a disk gyromagnetic resonator has been identified in the literature but its origin has not been fully spelled out. The purpose of this letter is to do so in terms of split counter-rotating impedance zeros instead of the more usual poles.