Dispersive Resonance Modulation Based on the Mode-Coupling Effect in a Capacitive Micromechanical Resonator

Abstract

This paper presents a theoretical and experimental investigation into the electrostatic coupling mechanism between different nonlinear modes inside a single resonator. Nonlinear intermodal coupling allows an arbitrary mode to be used as a modulator for the resonance of the coupled mode, presenting an efficient method to tune the frequency of a specific vibration mode. Here, a capacitive micromechanical resonator is developed, in which different modes exhibit different nonlinear characteristics. Inside this resonator, interactions between different nonlinear modes induced by electrostatic fields are observed and accurately modeled. It demonstrates that resonance modulation control can be achieved by activating the coupled modes based on the dispersive parametric coupling effect. Meanwhile, the resonance modulation is jointly determined by coupled modes, providing a theoretical basis and approach for modal manipulation technology. The dispersive coupling between intrinsic modes enables the probe resonance to be tuned by nearly 100 times its bandwidth, and its range and polarity can also be controlled by selecting the resonance of the pump mode. It is proven that resonance modulation control induced by the modal coupling effect can efficiently tune the resonator's resonance frequency over a wide range, which presents a promising voltage-frequency transduction scheme with high sensitivity and low noise for the precision instrument. Its pull range exhibits a great potential of more than 20% as a voltage-controlled oscillator and can be customized to satisfy different requirements, paving the way toward advanced mechanics.