Investigating vibration dyanmics of cross-coupled MEMS resonators for reduced motional resistance

Abstract

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.

Numerical Study of the Impact of Vibration Localization on the Motional Resistance of Weakly Coupled MEMS Resonators

“…The topology of Fig. 2d has been practically implemented in [14] using a DETF configuration. Additional coupling paths can be implemented by using resonators coupled to a common base as it is the case in Fig.…”

“…More specifically, two-dimensional coupling [7] [8] [9] and [10], higher order [11] as well as cyclic coupling architectures [12] and [13] have been shown experimentally and numerically to provide improved insertion loss and ripple characteristics, indicating an enhancement in robustness against vibration localization effects relative to their 1D-κ counterparts. Similarly a cross coupled topology [14] has been shown to improve the robustness of the R x to external stiffness perturbations compared to the traditional 1D-κ chain.…”

Mode Localization and Tunable Overlap in a Closed-Chain Micromechanical Resonator Array

“…The combination of the three drive voltages and three coupling voltages provide a number of options for generating unique dynamic behavior. This closed-chain concept has previously been explored theoretically [9] and a closed chain of mechanically coupled tuning fork resonators has been presented previously [10]. However, to our knowledge, resonators with tunable electrostatic coupling in a closed chain has not been demonstrated experimentally to date.…”

“…Coupled micromechanical resonators have received significant attention over the last decade for both their ability to enhance measurement sensitivity in sensors and to demonstrate complex nonlinear behavior that may be useful for both classical and quantum computing [1][2][3][4][5][6][7][8][9][10][11][12]. Mode localization in coupled resonators has in particular been shown to be a powerful approach for improving the precision of microelectromechanical (MEMS) sensors, where the relative vibration amplitudes between resonators are used to measure external perturbations [1,2].…”

“…(b) Optical micrograph of a fabricated array. Inset: Electrical connections for the drive and coupling voltages.with a few exceptions [9][10][11].Here, we present a new design for resonator arrays that combines piezoelectric actuation and sensing with electrostatic coupling. This results in large vibration amplitudes that are transduced with high sensitivity while also having continuous coupling tunability.…”