On Weakly Coupled Resonant MEMS Transducers Operating in the Modal Overlap Regime

Miniaturized physical transducers based on weakly coupled resonators have previously demonstrated the twin benefits of high parametric sensitivity and the first-order common-mode rejection of environmental effects. Current approaches to sensing based on coupled resonator transducers employ strong coupling where the modal overlap of the responses is avoided. This strong coupling limits the sensitivity for such mode-localized sensors that utilize an amplitude ratio (AR) output metric as opposed to tracking resonant frequency shifts. In this article, this limitation is broken through by theoretically and experimentally demonstrating the operation of the weakly coupled resonators in the weak-coupling (modal overlap) regime. Especially, a prototype microelectromechanical systems (MEMS) sensor based on this principle is employed to detect shifts in stiffness, with a stiffness bias instability of 10.3\mu \text{N} /m (9.5 ppb) and a corresponding noise floor of 7.1\mu \text{N} /m/ \surd Hz (6.8 ppb/ \surd Hz). The linear dynamic range of such AR readout sensors is first explored and found to be defined by the dynamic range of the secondary resonator. The proposed method provides a promising approach for high-performance resonant force and inertial sensors.