Enhanced phase noise model for quartz crystal oscillators

Abstract

Leeson's model is the basic model for predicting oscillator noise. G. Sauvage [1977] has proposed a mathematical analysis of this "heuristic" model. Both models do not detail the relative importance of the amplifier transfer function associated with its own noise in regard to the resonator. In this paper, an improved version of these previous models is presented. Amplifier noise and that caused by the resonator are distinguished. Power spectral densities of phase noise at various points of the oscillator loop are calculated from their respective correlation functions. As a consequence, the influences of the amplifier and resonator inner noises on the resulting oscillator noise are predictable. Nonlinearities could also be included in this more general model. An example of phase noise modeling of the Clapp quartz crystal oscillator is simulated and discussed.