Tuning of the Zero Dispersion Point for Micro Electrical Mechanical Systems
Blackwell, Rebekah Mercedes
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Resonant micro-electromechanical systems (MEMS) are increasingly common in applications, including inertial sensors and frequency sources. These devices operate at resonance and take advantage of their size, ability to integrate with electronics, and light damping. The performance of these devices can be improved by operation at higher vibration amplitudes, but they often begin to exhibit frequency shifts near resonance as the amplitude is increased, due to nonlinear stiffness effects. Previous works have sought to balance nonlinearities in order extend the linear dynamic range (LDR) of these resonators. The focus of this thesis is to characterize, for design purposes, another possible operating point where the system experiences local linearity. This point, at which the frequency is locally independent of the amplitude, is called the zero dispersion (ZD) point. The present analysis considers a class of micro-mechanical beam resonators using on a first-principles model that includes mechanical and electrostatic forces. The model considers the response of the fundamental mode and is nondimensionalized to minimize the number of independent parameters. As part of this analysis, a convenient new form was found for the potential used to represent the electrostatic forces. Using this potential, the amplitude-dependent frequency of vibration is computed for the entire feasible range of amplitudes. This allows for the numerical computation of the ZD point and its dependence on system parameters, in particular, the electrode gap and a DC bias voltage that can be used for device tuning. The results are shown in graphical form, which allows one to select device parameters for achieving a desired ZD amplitude.