The dual-input describing function and its use in the analysis of non-linear feedback systems

Abstract
A new method is presented for the frequency-response analysis of non-linear elements. This involves evaluating the gain of one of the frequency components in passing through the non-linear element when the input to the element consists of two sinusoidal waves of differing amplitudes, phases and frequencies. A cubic characteristic is analysed fully as an example.The paper describes the use of this method for analysing four different types of problem arising in feedback systems containing one simple-type amplitude non-linearity. The method can be considered as an extension of the describing-function technique with a correspondingly wider field of application.