Near-carrier oscillator spectrum due to flicker and white noise

The effect of device noise on oscillator phase noise in a close vicinity of average oscillator frequency is analyzed. We show that for 1/f noise, the line shape of a free-running oscillator changes from power to approximately Gaussian function very close to the oscillator frequency. The Gaussian regime occurs when the relationship between device noise and oscillator spectrum is strongly nonlinear. As this relationship approaches linear dependence at higher frequency deviation, there occurs a smooth crossover from Gaussian to well-known power line shape. The commonly used power extrapolation turns out to significantly underestimate phase noise in a part 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 dependence of the oscillator spectrum on phase fluctuations. In particular, near-carrier noise suppression of a voltagecontrolled oscillator in the second-and-higher-order phaselocked-loop is less than predicted by the linear model or even absent, unless the phase jitter is small. The proposed theory reduces to existing quantitative models of near-carrier phase noise in oscillators when the relation between noise in the oscillator phase and the output spectral density is linear.