A harmonic balance method and its implementation for the steady-state analysis of nonlinear networks

Abstract

A method for finding the petiodic solution of nonlinear networks which avoids the time domain solution of the dynamic equations has been investigated. In the method, the network under consideration is decomposed into one linear and several nonlinear subnetworks. Only frequency domain solution of the linear subnetwork is required. Various forms of the Mixed Nodal Tableau equations which are used in formulating the linear subnetwork in the frequency domain are explained through the introduction of a technique for obtaining voltage and current graphs of a network. A new expression for the gradient of the error function in the case that the period T of the oscillations is unknown has been developed and compared to the one derived by Nakhla and Vlach. The method has been, tested on several examples. It is shown. that considerable reduction in the size of the computational problem is achreved by taking advantage of the linearities present in the network.