Nonlinear RLC Networks

This article considers the questions of existence and uniqueness of the response of nonlinear time-varying RLC networks. It is proved that under conditions imposed on the network elements and the network topology the response exists, is unique, and is defined by a set of ordinary differential equations satisfying some Lipschitz conditions. Thus, from the conditions imposed on the network it follows that the response of a network of this class is continuous whenever the sources applied to the network are continuous functions of time. In other words, for the class of networks under consideration, jump phenomena (of the type that occur in relaxation oscillators) are excluded.1 One motivation for studying this problem is the construction of nonlinear network models for physical devices and processes. The behavior of these models is often investigated by simulation studies performed on digital computers. It is clear that in order to get meaningful answers the existence and uniqueness of the model's response have to be assured. The simulation study requires the setting up of an appropriate set of differential equations and their integration. As networks of the class * On leave of absence from the Department of Electrical Engineering, University of California, Berkeley, California.