A nonlinear theory of near-carrier phase noise in free-running oscillators

A general nonlinear theory of near-carrier phase noise in oscillators is presented. It is developed in terms of the linear dependence of the instantaneous frequency of oscillations on small-signal noise. The theory is applied to a Colpitts FET oscillator in the short-channel regime. Phase noise due to amplitude to phase conversion is given special attention, since it can dominate in high-Q tunable oscillators. The theory agrees with existing linear phase noise models at frequencies where these models are valid, but predicts new phenomena at frequencies very close to the carrier. In this frequency range, the dependence of noise-induced shift in oscillator phase on noise becomes nonlinear even for small-signal noise, while the instantaneous frequency remains a linear function of noise. As a result, the oscillator line shape qualitatively differs from predictions of linear models. In particular, 1/f circuit noise results in an approximately Gaussian line shape of a free-running oscillator in the immediate vicinity of the carrier. In a significant part of this frequency region, the noise spectral density is proven to be much larger than the conventional models predict. The proposed theory gives new insights Into low noise design and is suitable for both computer and hand estimates of near-carrier phase noise.