A Capacitive Coupling Technique to Mitigate Frequency Mismatch Effects in MEMS Resonators

In this paper, a coupling technique based on series loading of arrays of frequency mismatched MEMS resonators is presented. This method exploits the poles coupling that is induced by interfacing a multi Butterworth-Van Dyke (mBVD) model in series with a capacitor. As a result, a single, spurious-free, high quality factor (Q s ) peak is generated at a tunable frequency close to the natural resonance of the system. Furthermore, this method is insensitive to the number of spurious modes, to their frequency mismatch, and to the Figure of Merit (FoM, defined as the product between Q s and the electromechanical coupling $k_t^2$) of the arrayed resonators. In the first section of this work, a simple analytical model describing the technique is presented, and its validity is verified via numerical simulations and direct measurements. In the second section, the technique is used to extract the average Q s of arrays of mismatched elements via a numerical approach. In the third and last section, it is verified that coupled arrays of mismatched elements retain their high quality factor when implemented in cutting edge applications such as high passive gain inductorless matching networks.