Random noise with bias signals in nonlinear devices

A number of investigations have been made in recent years about the transmission of Gaussian noise through nonlinear devices. In many cases, simplification or approximations were needed to make analytical solutions possible, and only zero-average Gaussian input signals were used when the results were applied to feedback control systems. This paper presents a different approach to the problem of noise transmission through non-linear single-valued elements. Basically, amplitudes removed by nonlinear saturation or deadzones are replaced by impulses in the amplitude distribution functions of the output signals, and the resulting first and second moments of the output distribution are computed to yield the average and rms value of the output signal. The solution may be found by graphical or mathematical integration, a visual representation of the phenomenon is obtained, and input signals with any distributions having non-zero average values may be considered. It is shown that there is an equivalent transmission function or describing function for the average value of the noise, another for the rms value, and that one is a function of the other. Examples of the functions are given and the simpler functions with zero-average values are compared to the results obtained by other methods. Finally, the application of the noise describing functions to feedback control systems is discussed. Theoretical results are compared with those obtained from analog simulations.