A transformation method for the study of nonlinear components

A simple transformation is advanced for correlating the characteristic of a nonlinear element with the harmonic content in its frequency response to sinusoidal inputs. By a process of curve fitting the characteristic is represented by a polynomial. The frequency response to sinusoidal inputs is represented as a Fourier series. The polynomial and the Fourier series are related by means of the simple transformation x = sin θ. The method is applied to some of the common nonlinearities encountered in control system components. Its use in the determination of the describing function, as well as the harmonic response function, is discussed. Details in the case of an experimental verification are included.