Perturbation-Based Fourier Series Analysis of Transistor Amplifier

Abstract

A perturbation-based Fourier series model is proposed to approximate the nonlinear distortion in weakly nonlinear circuits. This general model is applicable to any set of multi-variable state equations that completely describe a nonlinear circuit. This model is applied to a common emitter amplifier circuit wherein the transistor is represented by Ebers–Moll nonlinear current equations. Appropriate state variables are defined, then the linear and nonlinear parts of the Ebers–Moll current equations are separated, and a small perturbation parameter is incorporated into the nonlinear part. Now these current equations are incorporated into the set of KCL, KVL equations defined for the circuit and the state variables are perturbatively expanded. Hence, multi-variable state equations are obtained from these equations. The state variables are approximated up to first order through Fourier series expansion, as described in the proposed model. The main advantage of the proposed model is that it is simple and straightforward approach to analyze weakly nonlinear circuits, as it involves matrix computations and the calculations of exponential Fourier coefficients.