# Modeling and Analysis of Vibration Coupling in Differential Common-Based MEMS Resonators

## TL;DR

This paper studies how vibrations in tiny sensor devices interfere with each other and proposes a method to model and reduce this interference.

## Contribution

A novel modeling and analysis approach for vibration coupling in differential common-based MEMS resonators is introduced.

## Key findings

- Theoretical and experimental coupling stiffness values for two resonator structures were determined and matched closely.
- A validated model enables evaluation of vibration coupling intensity for design optimization.

## Abstract

In differential MEMS resonant sensors, a pair of resonators are interconnected with other structural components while sharing a common substrate. This leads to mutual coupling of vibration energy between resonators, interfering with their frequency outputs and affecting the sensor’s static performance. This paper aims to model and analyze the vibration coupling phenomena in differential common-based MEMS resonators (DCMR). A mechanical model of the DCMR structure was established and refined through finite element simulation analysis. Theoretical calculations yielded vibration coupling curves for two typical silicon resonant accelerometer (SRA) structures containing DCMR: SRA-V1 and SRA-V2, with coupling stiffness values of 2.361 × 10−4 N/m and 1.370 × 10−2 N/m, respectively. An experimental test system was constructed to characterize the vibration coupling behavior. The results provided coupling amplitude-frequency characteristic curves and coupling stiffness values (7.073 × 10−4 N/m and 1.068 × 10−2 N/m for SRA-V1 and SRA-V2, respectively) that validated the theoretical analysis and computational model. This novel approach enables effective evaluation of coupling intensity between 5resonators and provides a theoretical foundation for optimizing device structural designs.