Synthesis of multiport gyrators

An analytical circuit theory approach to synthesis of multiport gyrators, with the structure of the gyrators simplified, is worked out. An annular arrangement consisting of passive elements, nullators, and norators is employed. Input and output poles are selected and a matrix transform of the admittance functional parameters is derived. Multiport gyrators can be synthesized with a smaller number of active elements, an arbitrary number of input and output poles, and with resistive and capacitive mutual conductances. Groups of inductive or frequency-dependent elements can be replaced in a complex substitution rather than one at a time.