Near-carrier oscillator spectrum due to flicker and white noise

The effect of device noise on oscillator phase noise close to the average oscillator frequency is analyzed. We show that for 1/f (flicker) noise, the line shape of a free-running oscillator changes from a power law to a Gaussian function very close to the oscillator frequency. The Gaussian regime occurs when the relationship between device noise and oscillator spectrum is strongly nonlinear. At higher frequency offsets, this relationship becomes linear, and there occurs a smooth crossover from Gaussian to the well-known power-law line shape. The extrapolation of the power law to small frequency offsets significantly underestimates phase noise in parts of the near-carrier frequency range. We also analyze how the near-carrier spectrum of the phase-locked oscillator is affected by the nonlinearity in the conversion of phase fluctuations to voltage noise. In particular, near-carrier noise suppression of a voltage-controlled oscillator in the second-and-higher-order phase-locked loops can be less than predicted by the linear model or even absent. The proposed theory reduces to the existing quantitative models of near-carrier phase noise in oscillators when the phase-to-voltage noise conversion is linear