An approximation to the harmonic response of saturating devices

The paper derives an analytical expression for the describing function and for the Fourier coefficients corresponding to saturating systems which are excited by sinusoidal signals. The saturation characteristics are assumed to be symmetrical and single valued. The method involves an approximation of the actual system characteristic by means of an exponential curve. The results are given in the form of graphs of the fundamental and third-harmonic components of the system output and a graph of the system describing function. The latter will be of use in the analysis of non-linear feedback systems. A comparison is shown between the present method and the technique of approximating saturation characteristics by means of straight lines. Formulae are given by means of which the higher-order harmonic components of the system output may be computed. Secondary results of this paper are Tables of the modified Struve functions L1(z) and L2(z) which are not available elsewhere in the literature.