Multi-gain representation for a single-valued non-linearity with several inputs, and the evaluation of their equivalent gains by a cursor method

A general method is described for calculating the equivalent gain through a non-linear element for a signal of known amplitude probability distribution, in the presence of other, uncorrelated, signals or disturbances, also of known amplitude-probability distributions. A cursor method for calculating the equivalent gains is developed, and cursor results are verified by theoretical and experimental points, for the equivalent gains of Gaussian and sinusoidal signals applied together to certain non-linearities. An example is given, showing how the behaviour of a non-linear feedback system may be analysed when two signals of different amplitude probabilities are applied to it. It is shown also that the equivalent gain to a Gaussian noise signal in the presence of other signals applied to a single-valued non-linearity has the same value as the incremental d.c. gain through the non-linearity (with the input signals present). Experimental results are given using this as a method of obtaining the value of equivalent gain.