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 κ > 10 −2 .
Abstract-This paper describes a technical approach towards the realization of a low-power temperature-compensated micromachined resonant strain sensor. The sensor design is based on two identical and orthogonally-oriented resonators where the differential frequency is utilized to provide an output proportional to the applied strain with temperature compensation achieved to first order. Interface circuits comprising of two front-end oscillators, a mixer and low-pass filter are designed and fabricated in a standard 0.35µm CMOS process. The characterized devices demonstrate a scale factor of 2.8Hz/µε over a strain range of 1000µε with excellent linearity over the measurement range. The compensated frequency drift due to temperature is reduced to 4% of the uncompensated value through this scheme. The total continuous power consumption of the strain sensor is 3µW from a 1.2V supply. This low power implementation is essential to enable battery-powered or energy harvesting enabled monitoring applications.
This paper investigates the vibration dynamics of a closed-chain, cross-coupled architecture of MEMS resonators. The system presented here is electrostatically transduced and operates at 1.04 MHz. Curve veering of the eigenvalue loci is used to experimentally quantify the coupling spring constants. Numerical simulations of the motional resistance variation against induced perturbation are used to assess the robustness of the cross-coupled system as opposed to equivalent traditional open-ended linear one-dimensional coupling scheme. Results show improvements of as much as 32% in the motional resistance between the cross-coupled system and its onedimensional counterpart.
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