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

Abstract

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\(\mathbb{R}^{\delta _0 }\) on the state space ∑ ofN, whereδ0 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.