title: Optimal operating points of oscillators using nonlinear resonators.
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.
authors.affiliation: Kavli Nanoscience Institute and Condensed Matter Physics, California Institute of Technology, MC 149-33, Pasadena, California 91125, USA. eyalk@caltech.edu
authors.forename: Eyal
authors.initials: E
authors.lastname: Kenig
authors.forename: M C
authors.initials: MC
authors.lastname: Cross
authors.forename: L G
authors.initials: LG
authors.lastname: Villanueva
authors.forename: R B
authors.initials: RB
authors.lastname: Karabalin
authors.forename: M H
authors.initials: MH
authors.lastname: Matheny
authors.forename: Ron
authors.initials: R
authors.lastname: Lifshitz
authors.forename: M L
authors.initials: ML
authors.lastname: Roukes
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*