Analysis of phase noise in oscillators based on nonlinear stochastic equation

Phase noise is of crucial importance in electric circuits. In this paper, we apply a generic phase noise theory to obtain an exact nonlinear stochastic equation for perturbed oscillator, then solve it and get a scalar constant c which is sufficient to describe jitter and spectral properties. By computing phase noise in a Colpitts oscillator using this theory and the time varying linearization method respectively, we get the result that the PSD has a finite value at carrier frequency and the total carrier power is preserved despite spectral spreading due to noise, whereas the result by the time varying linearization method exceeds the carrie power. Furthermore, by computing the noise contribution of each noise source, we illustrate how to reduce phase noise in circuit design.