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

Optimal operating points of oscillators using nonlinear resonators