Optimal operating points of oscillators using nonlinear resonators

TL;DR

This paper presents an analytical approach to optimize oscillator performance by eliminating phase noise using nonlinear resonators, with explicit parameter conditions and analysis of noise spectra.

Contribution

It introduces a method to calculate phase sensitivity and identify operating points that eliminate phase noise in nonlinear resonator oscillators.

Findings

Complete phase noise elimination is possible at specific parameters.

Operational modes can minimize feedback, thermal, and quality factor noise.

The spectrum analysis includes 1/f noise sources.

Abstract

We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources.