PIECEWISE-LINEAR ANALYSIS OF THE WIEN BRIDGE OSCILLATOR

This paper presents a quantitative analysis of the Wien bridge oscillator based on a piecewise-linear approximation of the op-amp characteristic. Usually the circuit parameters are chosen in such a way that the linearized circuit has a pair of complex conjugate natural frequencies which lie slightly to the right of the j omega-axis. The frequency of oscillation is assumed to coincide with the value omega(0) at which the poles cross the j omega-axis. However, this simplified approach is unable to predict the true frequency of oscillation and the amount of distortion. The aim of the present analysis is to determine the exact waveform, frequency and spectral content corresponding to the steady state behaviour. The phase plane is partitioned into three regions, in each of which the vector field is linear. The limit cycle corresponding to the steady state oscillation is reconstructed by using the Poincare map method. Expressions for the frequency of oscillation and the Fourier coefficients are given which depend on a critical parameter representing the voltage gain of the amplifier.