Double-valued relays with random inputs

TLDR: It is shown, by comparing experimentally measured equivalent gains with theoretical gain expressions, that the f(x,x?) model is a poor approximation to an actual double-valued relay.

Abstract: The paper considers some theoretical methods which have been proposed for linearising double-valued relay nonlinearities with Gaussian inputs. Most methods depend on the description of the relay as a function of the input and its derivative, which will be referred to as the f(x,x?) model. It is shown, by comparing experimentally measured equivalent gains with theoretical gain expressions, that the f(x,x?) model is a poor approximation to an actual double-valued relay. Some qualitative and approximate theoretical results are derived for double-valued relays without resorting to the f(x,x?) model. These predict the following two effects, which are clearly seen in the experimental measurements, and which are not given by existing methods: (a) the equivalent gains depend on the input signal spectrum and (b) the imaginary part of the equivalent gain is very small. It almost always makes a negligible contribution to the overall equivalent gain.