Dispersive coupling and dual-mode sensing of a micromechanical resonator

Dual-mode sensing represents a highly promising strategy for resonant sensors to achieve in-situ compensation and high-accuracy parameter detection. Micromechanical resonators typically exhibit multiple vibration modes, each with distinct sensitivities to external parameters. By employing different modes for sensing and simultaneously reading out their respective frequencies, cross-sensitivity in multi-parameter detection can be effectively mitigated while fully exploiting the advantages of frequency output in resonant sensors. To address the challenges of inter-modal interaction and vibration signal coupling in dual-mode vibration, this paper investigates dispersive coupling in a double-clamped microbeam, and analyzes the mutual influence between the amplitudes and frequencies of the modes under dual-mode excitation, as well as the implications for sensing applications. Based on constant-amplitude automatic gain control (AGC) and dual differential detection, a dual-mode vibration signal decoupling and stable closed-loop control approach is proposed, achieving a simple and efficient decoupled detection of the dual-mode vibration signals and enabling real-time, synchronous readout of the dual-mode frequencies. The effectiveness of the proposed method was experimentally validated using a resonant pressure sensor. Test results of the pressure sensor demonstrate excellent in-situ temperature compensation effects, with a fitting accuracy of ±0.009% full scale (FS), a maximum repeatability error of 0.0042% FS, a maximum pressure hysteresis error of 0.0068% FS, and an overall pressure accuracy of ±0.012% FS. Furthermore, this dual-mode sensing scheme shows significant potential for multi-parameter measurements and contributes to the advancement of resonant sensors toward miniaturization and intelligence.