Reflection angles of in-phase and split counter-rotating eigenvalues of the three-port circulator

The reflection angle of the in-phase eigenvalue and that of the reflection coefficient at port 1 of a terminated circulator are equal at a unique frequency at which the gyrotropy produces a return loss of 9.5 dB. The frequency response of the terminated circulator, beyond that value of gyrotropy, displays four such frequencies. The angles of the reflection coefficients at the inner two frequencies also coincide with the in-phase reflection angle. The two outside frequencies at which the return loss at port 1 are 9.5 dB coincide with the counter-rotating reflection angles. Below this value of gyrotropy, the angles of the reflection coefficient are equal to those of the split counter-rotating eigenvalues under these same conditions. A knowledge of the three reflection angles is both necessary and sufficient for the characterization of this class of circuit at both its midband and split frequencies. © 2006 IEEE.