Unified Theory of Oscillator Phase Noise I: White Noise

The spectral purity of every oscillator system is limited by phase noise. In this work, we extend the techniques previously used to analyze phase noise in lasers to develop an intuitive, yet powerful description of phase noise in an electromagnetic oscillator for the case when the oscillating field is sinusoidal and perturbed by white noise. The developed theory is general and unifies the understanding of phase noise in both electrical and optical oscillators. Our approach is based on partitioning the noise among the modes of the oscillator, which is analogous to the approach used to analyze phase noise in laser cavities, but has not been previously considered for electrical oscillators. We show that oscillator phase noise depends only on the oscillating power, injected noise, and round-trip delay. This result provides a theoretical foundation to and expands upon the predictions provided by Leeson's well-known empirical oscillator phase-noise model. To validate the developed theory, we compare the predicted phase noise to the experimentally measured phase noise of both a simple electrical oscillator and a hybrid opto-electronic oscillator and show excellent agreement across a wide range of operation.