Determinantal Formulae for the Symbolic Description of Two‐Ports

ABSTRACT This paper presents an abstract framework for the general reduction of two‐ports. Working under a minimal nondegeneracy assumption, the well‐known families of admittance, impedance, hybrid, and transmission parameters can be obtained as particular cases from a unique reduction theorem in a straightforward manner, since the hypothesis supporting the existence of each one of these families amounts to the nonvanishing of one out of six parameters. In problems with independent sources, the reduction theorem captures explicitly the dependence of the equivalent sources on the internal ones, providing this way a systematic extension of the Thévenin and Norton theorems to the two‐port case. The approach combines a comprehensive use of determinantal formulae with a homogeneous formalism: the latter makes it possible to accommodate all possible descriptions of the internal immittances and sources. In uncoupled problems, the relation with the structure of spanning trees is briefly addressed. Several examples involving switches illustrate the results.