Phase noise, and phase models: Recent developments, new insights and open problems

Abstract

This paper presents new insights and a review of recent results on the application of phase models to phase noise analysis in nonlinear oscillators. It is shown that an approach based on stochastic processes and the theory of stochastic differential equations offers several advantages. It is also shown that white noise is responsible for phase diffusion and frequency shift in oscillators, that is, the phase noise problem is best described as a convection diffusion process. An approach for the derivation of a reduced phase model and the associated Fokker-Planck equation is presented. These equations allow an easy determination of fundamental properties as the expectation value for the oscillation frequency, the probability distribution of the phase, the correlation function and the power spectral density.