Losses in multiport stripline/microstrip circulators

We have included losses in the analysis of a 3N-port stripline/microstrip circulator and have reformulated the circulation conditions previously postulated for the lossless case. Our calculations have been compared to published data on circulator designs biased above ferromagnetic resonance (FMR). Scattering parameters at each port have been calculated as a function of assumed material losses and coupling capacitance of a multiport circulator.