Nonlinearities and phase noise in electrostatically-transduced-MEMS-resonator based oscillators

Electrostatically transduced silicon microresonators have become an exciting commercial prospect as a replacement of quartz crystal resonators for timing and frequency reference applications. Several technological challenges such as stable low cost packaging, good temperature stability and low phase noise need to be tackled before a significant portion of this market can be penetrated. In this dissertation, we look at some of the phenomena related to parallel plate electrostatic transduction and other electro-mechanical effects, which have significant impact on development of low phase noise oscillators. We endeavor to study the inter-dependences and trade-offs of these effects and look at optimization of the resonator.; Linear electromechanical modeling of the resonator and oscillator design and implementation are described. Using a 1.3 MHz double-ended-tuning fork resonator a self oscillating circuit is developed and characterized. A -120 dBc/Hz phase noise floor was obtained at an offset greater than 200 Hz from the carrier. Vibration testing on this oscillator was also performed and a vibration sensitivity of 7x10-9/g was obtained.; Nonlinear models for the resonators are also developed. Particularly, the amplitude-frequency-dependence (A-f) effect and its impact on resonator performance are studied. Optimization of the resonator for maximizing the signal output is discussed. It has been found that it is possible to cancel out 3rd order electrical and mechanical nonlinearities by adjusting the DC bias voltage to these devices, increasing the linearity of the resonator. By choosing the correct bias voltage an improvement of more than two times in the current handling was observed for the 1.3 MHz resonator.; Additionally by the combined study of the linear and nonlinear electromechanical models, impact of scaling and optimization of the gap size and quality factor are also presented. By scaling down of length of the resonant beam by a factor of 5, it was found that the current handling for a DETF resonator can change by as much as 20 times as this strongly reduces the nonlinearity of the resonator. Similar scaling rules are developed for square extensional type bulk mode resonators also. General guidelines are presented on choice of resonant structure and design of fabrication processes.