Phase noise and timing jitter in oscillators

Phase noise is a topic of theoretical and practical interest in electronic circuits, as well as in other fields such as optics. Although progress has been made in understanding the phenomenon, there still remain significant gaps, both in its fundamental theory and in numerical techniques for its characterisation. We present a rigorous nonlinear analysis for phase noise in oscillators and reach the following conclusions: the power spectrum of an oscillator does not blow up at the carrier frequency as predicted by many previous analyses. Instead, the shape of the spectrum is a Lorentzian (the shape of the squared magnitude of a one-pole lowpass filter transfer function) about each harmonic. The average spread (variance) of the timing jitter grows exactly linearly with time. A single scalar constant suffices to characterise both the timing jitter and spectral broadening due to phase noise. Previous linear analyses of phase noise make unphysical predictions such as infinite noise power. We develop efficient computational methods in the time and frequency domains for predicting phase noise. Our techniques are practical for large circuits. We obtain good matches between spectra predicted using our technique and measured results, even at frequencies close to the carrier and its harmonics, where most previous techniques break down.