1-port topology of the degree-1 and 2 terminated circulator

The equivalent circuit in the impedance plane at port-1 of a 3-port circulator with ports 2 and 3 terminated in ideal resistive loads is a classic result. The purpose of the paper is to synthesise 1-port topology in the admittance plane in the case for which ports 2 and 3 are terminated in real resistive loads and in that for which the ports are loaded by broadband matching networks. This is done in terms of the eigenvalues of the problem region under the assumption that the in-phase eigen-network may be idealised by a short-circuited boundary condition and an ideal 2-port gyrator circuit. The real part circuit and those at the split frequencies of the counter-rotating eigenvalues are also deduced as a preamble to realising the general circuit. The properties displayed by these circuits are compatible with existing experimental procedures for this class of device.