Phase noise in oscillators: a unifying theory and numerical methods for characterization

TLDR

Phase noise is a critical phenomenon in electronic and optical circuits, yet fundamental theory and numerical characterization methods remain incomplete. This work establishes a universal foundation for phase noise analysis applicable to any oscillator, independent of its operating mechanism. We derive and solve an exact nonlinear phase‑error equation for random perturbations, enabling precise timing‑jitter and spectral‑dispersion characterization through efficient numerical techniques. The resulting methods accurately predict phase noise for diverse practical oscillators, match measurements even near the carrier, and are over three orders of magnitude faster than brute‑force Monte Carlo simulations.

Abstract

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 characterization. In this paper, we develop a solid foundation for phase noise that is valid for any oscillator, regardless of operating mechanism. We establish novel results about the dynamics of stable nonlinear oscillators in the presence of perturbations, both deterministic and random. We obtain an exact nonlinear equation for phase error, which we solve without approximations for random perturbations. This leads us to a precise characterization of timing jitter and spectral dispersion, for computing of which we have developed efficient numerical methods. We demonstrate our techniques on a variety of practical electrical oscillators and obtain good matches with measurements, even at frequencies close to the carrier, where previous techniques break down. Our methods are more than three orders of magnitude faster than the brute-force Monte Carlo approach, which is the only previously available technique that can predict phase noise correctly.