Mode selection for electrostatic beam resonators based on motional resistance and quality factor
Jeong H. Ryou, Jason J. Gorman
An analytical comparison between the fundamental mode and higher modes of vibration for an electrostatic beam resonator is presented. Multiple mode numbers can be matched to a desired resonant frequency through the appropriate scaling. Therefore, it is necessary to determine which mode yields the best performance in terms of the lowest motional resistance and highest quality factor. A nonlinear dynamic model of the resonator is derived and then used to determine the motional resistance for each mode. The resulting nist-equation, along with accepted models for quality factor in beam resonators, provides the basis for comparing performance between modes. Numerical results show that for the frequencies, materials, and geometric parameters of interest, the fundamental mode always provides the lowest motional resistance and typically results in the highest quality factor, although with some exceptions. Further experimental results are required to validate the quality factor models and provide more definitive results for selecting the highest performing mode.