Steady-state harmonic analysis of phase shift oscillators

This paper describes an improved method for calculating the steady-state oscillation frequency and fundamental and harmonic amplitudes of phase shift oscillators (transient behaviour is not considered). The method is quite general and although the examples described in the paper relate to oscillators with RC phase shift networks, the principles apply equally to LCR-based oscillators. The method described in this paper proposes a novel extension to the method of harmonic balance to include harmonics in addition to the fundamental, as is normal practice. This is significant because the method allows a more accurate calculation of the oscillation frequency, fundamental and harmonic amplitudes in oscillators with higher signal levels, less selective phase shift networks and/or higher levels of nonlinearity than is possible with existing methods. New closed form expressions for these parameters are presented. The paper considers cubic and quadratic nonlinearities and also a general 3rd-order polynomial nonlinearity which is a weighted sum of both types, plus a linear term.