State-Variable Analysis of RLC Networks Containing Nonlinear Coupling Elements

This paper deals with the state-variable analysis of the most general class of lumped time-invariant networks. The hybrid descriptions of coupled elements are discussed in connection with the mixed analysis of networks. Sufficient conditions for the uniqueness of solutions of coupled resistor networks and networks are given in terms of hybrid descriptions. The set of state variables are taken so that the order of state equations coincides with the number of finite natural frequencies in the linear case. A simple method for determining such a set of state variables by means of two particular trees, -normal tree and - normal tree, is also presented. The standard form of state equations are represented by means of a signal flow graph.