An algorithm for generating real describing functions

A classical method of dealing with the non-linear elements in a transfer function is to assume that they can be separated from the linear section and can then be represented by describing functions. The standard method of calculating these describing functions has been to use a graphical method which breaks the non-linear characteristic into a series of linear sections and super-imposes their effects onto a sinusoidal input. The output is assumed to be a Fourier series and the Fourier transform for the first coefficient of this series is calculated in a piecemeal fashion. The process is not difficult but there is a considerable amount of calculation involved. In this paper an algorithm is presented which enables the describing functions of real non-linearities, with any number of linearized sections, to be simply written down without the usual onerous calculations. Additionally, a method of quickly sketching the general shape of describing functions is outlined.