Nonlinear Distortion and Truncation Errors in Frequency Converters and Parametric Amplifiers

Parametric amplifiers, mixers, and modulators are nonlinear devices that are used for linear processing of small signals. One question that is usually passed up in discussion of these devices is "How small must the signal be if the response is to be acceptably linear?" In this paper an expression for an upper bound on the nonlinear distortion as a function of signal amplitude is derived. If the engineer knows, or guesses, that his signals are small enough, he analyzes the linear, small signal model for the pumped nonlinear device. This linear model, which is time-variant and periodic, is still too difficult to handle. The time variation is too complicated. The usual engineering approach is to solve a simpler problem by replacing the complicated periodic time-variant element with a sinusoidally varying element. This paper also presents a bound on the error introduced by such truncation of the Fourier series of the time-variant element.