Modified Equivalent Gain Analysis of Non-linear Systems with Gaussian Noise

Abstract

In this paper a modified equivalent gain expression is determined for a class of non-linear transfer characteristics subjected to Gaussian random disturbances. The non-linearites considered are of the non-memory saturating piecewise-linear type, which are important both in their own right and because they can be used to approximate, to any desired degree of accuracy, many other non-linear transfer characteristics. This equivalent gain expression is then used in a frequency domain analysis to predict the amplitude and frequency of self-sustained oscillations in systems containing these non-linearities. In an example, a system containing a quantizer subjected to Gaussian noise is analysed by this technique. The results are found to agree closely with those of a digital computer simulation of the system.