Nonlinear circuit theory: Resistive networks

The impact of computers on circuit analysis and design and the advent of new electronic devices and integrated circuits have generated much interest in nonlinear circuit theory. Recent successes in the analysis of large-scale systems using network models have further enhanced the importance of the subject. A key to the understanding and analysis of nonlinear circuits is the study of nonlinear resistive networks both in theory and in computation. In the study of nonlinear resistive networks it is necessary to know the global properties of nonlinear functions. Thus Palais' global inverse function theorem is of paramount importance. In addition, a global implicit function theorem is often needed. The latter is given in this paper. We apply the global theorems to derive results on nonlinear networks with unique solutions and with multiple solutions. The theory obtained for networks with multiple solutions can be used to analyze and design bistable circuits. In computation, we extend Katzenelson's piecewise-linear analysis to general nonlinear resistive networks. For networks which have a unique solution under all possible inputs, the method converges in a finite number of steps. In addition, we present an efficient method of computing input-output characteristics of networks with single or multiple solutions.