Impact of mode localization on the motional resistance of coupled MEMS resonators

This paper investigates the effect of mode-localization that arises from structural asymmetry induced by manufacturing tolerances in mechanically coupled, electrically transduced Si MEMS resonators. We demonstrate that in the case of such mechanically coupled resonators, the achievable series motional resistance (R_x) is dependent not only on the quality factor (Q) but also on the variations in the eigenvector of the chosen mode of vibration induced by mode localization due to manufacturing tolerances during the fabrication process. We study this effect of mode-localization both theoretically and experimentally in two pairs of coupled double-ended tuning fork resonators with different levels of initial structural asymmetry. The measured series R_x is minimal when the system is close to perfect symmetry and any deviation from structural symmetry induced by fabrication tolerances leads to a degradation in the effective R_x. Mechanical tuning experiments of the stiffness of one of the coupled resonators was also conducted to study variations in R_x as a function of structural asymmetry within the system, the results of which demonstrated consistent variations in motional resistance with predictions.