A generalization of Miller formulae for nonlinear feedback networks

The Miller theorem and its derivations are important tools to be used when analyzing feedback networks. However, they can be exploited in linear networks only. In this paper, we derive simple relationships which can be viewed as a generalization of the Miller theorem for nonlinear feedback elements. Their formulation results particularly useful when nonlinear circuits are analyzed to find, for example, harmonic distortion. Indeed, they allow to eliminate the nonlinear feedback, yielding more simple analytic relationships to be managed. The common emitter configuration is studied as an example, and comparisons between expected and simulated data confirm the validity and the accuracy of the analysis developed.

I. Introduction

The Miller theorem and its derivations provide simple and very powerful tools for the analysis of feedback networks [1]–[4]. For example, the Miller theorem is very useful to quickly find the input impedance of feedback circuits, or to evaluate the expression of the dominant pole due to “Miller” compensation. Moreover, it can be profitably employed to decouple two networks linked by a single feedback element. However, the theorem is valid only for linear circuits, in which the superposition criterion holds.