Performance of lossy H-plane Y circulators

The properties of lossless 3-port junctions with threefold rotation symmetry, as they can be derived from the scattering matrix, are briefly reviewed. An extension is given for junctions which contain lossy materials. It is shown that to have a circulator, i.e., a 3-port where zero reflection and infinitely large isolation coincide, one must satisfy two pairs of equations simultaneously. When the losses of the three eigenvectors are not equal, the pairs of equations are in conflict. A circulator cannot be obtained then. Formulas for the relative deviations of the eigenvalues from their ideal values are derived from a perturbation theory. These formulas are applied to the simple example of a thin ferrite post located on the axis of a junction. It is shown that in this case dielectric and magnetic ferrite losses must be equal to make a circulator possible. If they are not, zero reflection and infinitely large isolation occur at different values of frequency and bias field. This has been confirmed by experiment. The perturbation formulas can also be used to evaluate such circulator properties as bandwidth, tuning range, and temperature dependence.