Modulation in Nonlinear Filters with Parametric Feedback

A class of nonlinear second-order filters is considered which may be described and analysed by the theory of quasi-linear differential equations. It is shown that the effect of nonlinearity in these equations is equivalent to that obtained by parametric feedback where the system parameters are functions of the output amplitude. This leads to an extension of the filter class by admitting phase parametric feedback. Filters of this class exhibit startling characteristics in comparison with the behavior of LLFPB circuits. The methods of Mandelstam and Papalexi, and Andronow and Witt in complex notation underlie the derivations. After examining the solution under sinusoidal inputs, the more interesting problem of modulation response is considered. Under small signal conditions a second-order linear differential equation with complex coefficients is derived to describe the modulation response. One example is offered of a filter with phase feedback that discriminates between amplitude and phase modulation by passing the former and rejecting the latter.