Analysis of a Class of Self-Biased Multimode Oscillators

A mathematical model is obtained for a class of oscillators having two nonlinearities. Although many features of the model and the allowable nonlinearities are chosen to conform to basic characteristics of common self-biased oscillator circuits, the basic procedures employed are applicable to a much larger class of nonlinear problems. The system of nonlinear differential equations describing the original model is approximated by a new, more tractable system chosen by the method of Krylov and Bogoliubov. This approximating system is second order and thus amenable to a phase-plane solution. The phase-plane solutions of the approximating system are shown to predict several common modes of self-biased oscillator behavior, including CW oscillation, squegging, amplitude modulation and multimode operation. The results of the theoretical analysis are then shown to be in very close agreement with the actual behavior of an experimental oscillator.