Numerical Study of the Impact of Vibration Localization on the Motional Resistance of Weakly Coupled MEMS Resonators
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This paper presents a numerical study of the impact of process-induced variations on the achievable motional resistance Rx of one-dimensional, two-dimensional, cyclic and cross-coupled architectures of weakly coupled, electrostatically transduced MEMS resonators operating in the 250 kHz range. We use modal analysis to find the Rx of such coupled arrays and express it as a function of the eigenvectors of the specific mode of vibration. Monte Carlo numerical simulations, which accounted for up to 0.75% variation in critical resonator feature sizes, were initiated for different array sizes and coupling strengths, for the four distinct coupling architectures. Improvements in the mean and standard deviation of the generated Rx distributions are reported when the resonators are implemented in a cross-coupled scheme, as opposed to the traditional one-dimensional chain. The two-dimensional coupling scheme proves to be a practical and scalable alternative to weakly coupled one-dimensional chains to improve the immunity to process variations. It is shown that a 75% reduction in both the mean and standard deviation of the Rx is achieved as compared to the traditional one-dimensional chain for a normalized internal coupling k > 10-2.
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1941-0158
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Engineering and Physical Sciences Research Council (EP/K000314/1)
Engineering and Physical Sciences Research Council (EP/L010917/1)