Frequency Stabilization in an Encapsulated High-Q Micromechanical Resonator via Internal Resonance

The frequency stability is a key parameter to determine the performance of a micro-electro-mechanical (MEM) resonator. In this study, we utilized the mechanism of 1:2 internal resonance (IR) in a hermetically encapsulated beam resonator with a high Q-factor (>4000) to improve the frequency stability. When a MEM resonator is driven by a single-frequency actuation and conditions for IR are satisfied, two engaged modes are simultaneously resonated with their phases locked together through a strong and effective intermodal energy transfer. The increased inertia of these two active resonant modes leads to the frequency stabilization in both frequency outputs. In an open-loop experimental setting, we demonstrated that the IR achieved a six-fold improvement in the frequency stability. This paper reports the first implementation of IR in an encapsulated high-Q beam resonator.