Micromechanical resonator reference oscillators for wireless communications.

Abstract

This dissertation explores the performance capabilities, limitations, and theoretical analysis of micromechanical resonator reference oscillators for wireless communications applications, particularly focusing on amplitude limiting mechanisms and phase noise. A modified Pierce circuit topology has been used to first demonstrate a 9.75 MHz high-<italic>Q</italic> micromechanical reference oscillator, which exhibits excessive 1/<italic>f</italic><super>3</super> dependence that limits the phase noise performance to -80 dBc/Hz at a 1 kHz offset from the carrier. In order to investigate the effect of vibration amplitude on phase noise, two different types of automatic level control (ALC) based on adjustment of resonator dc-bias and amplifier gain have been used to remove the 1/<italic> f</italic><super>3</super> phase noise seen in non-ALC'ed oscillators. In addition, reductions in phase noise by more than 26 dB have been obtained by replacing the single resonator normally used in such oscillators with a mechanically-coupled array of them to effectively raise the power handling ability of the frequency selective tank by a factor equal to the number of resonators used in the array, and all with virtually no increase in volume or cost, given that all resonators are integrated onto a single die using batch processed MEMS technology. Due to their low power handling capabilities, micromechanical resonators exhibit a <italic>hard-limit</italic> phenomenon by which an oscillator limits its output. Hard-limiting in micromechanical resonators has been approximately modeled as piecewise linear or quadratic nonlinear oscillation system with severe damping, and solved by Krylov-Bogoliubov-Mitropolskii's slowly varying amplitude and phase averaging method in the first order, revealing that the vibration frequency is significantly affected by amplitude fluctuation in hard-limited resonators. Amplitude noise measurements by self multiplication with a double balanced mixer are consistent with analytical formulations relating AM noise to PM noise, suggesting that the AM to PM conversion is a dominant phase noise generation mechanism in hard-limit resonator oscillators. In some cases, deterioration of the quality factor by hard-limiting shapes the noise function that governs AM-induced phase noise at midrange offset frequencies, resulting in 1/<italic> f</italic><super>2</super> noise. But more commonly, the measured amplitude noise exhibits a 1/<italic>f</italic> dependency at low frequency that converts into excessive 1/<italic>f</italic><super>3</super> phase noise.