A theory of nonenergic N‐ports

A circuit element is nonenergic if the instantaneous power flow into it is always zero. Well‐known examples include the ideal diode, transformer, gyrator and circulator. Most of the interesting nonenergic elements are nonlinear N ‐ports with N ⩾ 2, and many of their properties are quite counterintuitive. For example, there exists a surprisingly large class of nonenergic multiport capacitors and inductors, all of which, it turns out, are nonlinear and reciprocal. Nonenergic linear N ‐ports, on the other hand, are necessarily resistive and antireciprocal. In this paper, we present a rigorous fundamental theory of nonenergic N ‐ports that results in a general canonical representation. Special canonical forms are developed for nonenergic resistors, capacitors and inductors, and numerous examples are given.