Geometric properties of nonlinear networks containing capacitor-only cutsets and/or inductor-only loops. Part II: Symmetries

This paper is the last in a two-part sequence which studies nonlinear networks, containing capacitor-only cutsets and/or inductor-only loops, from the geometric coordinate-free point of view of the theory of differentiable manifolds. For such circuits, it is shown that (subject to certain assumptions) there is a naturally defined Lie group action of on the state space ofN, where₀ is the sum of the number of independent capacitor-only cutsets and the number of independent inductor-only loops. Circuit theoretic sufficient conditions on the reactive constitutive relations are derived for the circuit dynamics to be invariant under this Lie group action.This work was supported by the Natural Sciences and Engineering Research Council of Canada, under Grant Number A7113, and by scholarships from the Natural Sciences and Engineering Research Council of Canada and the Ontario Provincial Government.