Nonisochronous Oscillations in Piezoelectric Nanomechanical Resonators

Citation

Matheny, Matthew Hayward (2012) Nonisochronous Oscillations in Piezoelectric Nanomechanical Resonators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2P71-JT64. https://resolver.caltech.edu/CaltechTHESIS:06082012-140554238

Abstract

Nanoelectromechanical systems (NEMS) have proven an excellent test bed for exploring nonlinear dynamics due to short decay times, weak nonlinearities, and large quality factors. In contrast to previous research in nonlinear dynamics involving driven or phase fixed NEMS, where time is referenced by an external source, we describe phenomena classified by phase free phenomena. Here we describe NEMS embedded into feedback oscillators with weak nonlinearities.

We make measurements of this mechanical nonlinearity by developing a transduction scheme, the piezoelectric/piezoresistive (PZE/PZR) transduction, which emphasizes the detector dynamic range over absolute sensitivity. Using these measurements, projections on quantum nondemolition schemes involving the mechanical nonlinearity as a detector are made. These measurements also are important for understanding the detection limits of NEMS sensor technology, which uses a mechanical resonator as a frequency reference in a phase locked loop (PLL).

This work identifies ways to reduce noise within ‘nonlinear’ feedback oscillators, and these results have implications for sensing systems using nonlinear mechanical resonators embedded in PLLs. Since the mechanical nonlinearity of PZE/PZR resonators can be accurately calibrated, we make predictions for the behavior of these dynamical systems based on the given mechanical and electrical parameters. We show, theoretically, that local isochronicity above critical nonlinear amplitudes can create special operating points in feedback oscillators at which parametric fluctuations may cause less phase noise in the oscillator than in feedback oscillators driven below critical amplitudes. For these predictions, we present data that show quantitative agreement for the amplitude and frequency, and qualitative agreement for the phase noise.

Finally, we show synchronization, assisted by nonisochronicity, between two feedback NEMS oscillators. We develop a general theoretical framework for two saturated feedback oscillators which use resonators with nonlinear stiffness. In the limit of small coupling, we show that the system obeys the Adler equation with analytical predictions for the oscillators’ individual amplitudes and net frequency difference. We develop an experiment in which the three important parameters of the system (detuning, nonisochronicity, and coupling) can be tuned, and show data that agrees with the predictions for a large range of coupling. We include data on phase slipping between two oscillators in which the aperiodic frequency difference is clearly observed. Finally, we present data on phase noise in synchronized oscillators.

Thesis Files