A general method for deriving the describing functions for a certain class of nonlinearities

Since Goldfarb's original work on describing functions, a considerable number of papers have been published in which the describing functions of particular nonlinearities have been derived. It appears however that little effort has been made to classify the nonlinearities. Since the describing function method is one of the more powerful methods available at present to analyze nonlinear feedback systems, it appears desirable to collect the expressions for the describing functions of a few different types of nonlinearities in one paper. It is the purpose of this paper to derive the describing functions of two general types of nonlinearities and show how the describing functions of many other practical types of nonlinearities for which the describing function analysis is valid naturally follow.