Interconnection, Reciprocity and a Hierarchical Classification of Generalized Multiports

Interconnection of (linear, time-invariant, resistive) n-ports is a fundamental concept of circuit theory. We discuss their full and terminal interconnectability, analogously to full and terminal solvability of networks and provide a necessary condition for the full interconnectability (also sufficient under some genericity assumption), which can be checked in polynomial time using matroid algorithms. Reciprocity is another fundamental concept for ordinary n-ports, where the number r of linearly independent equations equals to n, There is a well-known concept of generalized or g-reciprocity if r > n. For r <; n we introduce the concept of potential or p-reciprocity if further equations can be added to the equation system of the n-port to obtain an ordinary reciprocal n-port. We prove that an n-port is p-reciprocal if and only if its dual is g-reciprocal and study the relations of these concepts to the spectrum of the n-port, leading to a hierarchical classification of n-ports. We also prove that the interconnection of p- or g-reciprocal n-ports preserves these properties, give polynomial algorithms to recognize p- or g-reciprocity and, in case of p-reciprocity, to extend the equation system to that of a reciprocal n-port.