Resonance enhancement of micromachined resonators with strong mechanical-coupling between two degrees of freedom
A strong mechanical coupling scheme between two degrees of freedom (2-DOF) is proposed in this paper for resonance enhancement of silicon micromachined resonators. Two spring-mass-damping resonant units, with identical (or close) resonant frequency and great disparity in mass, are mechanically linked together to form a 2-DOF resonator. When the big unit (with bigger mass) is driven to resonate, a much-enlarged resonant amplitude of the small unit (with smaller mass) can be obtained, attributed to the strong mechanical coupling between the two units. PSPICE is used for simulation of the properties of the strong mechanical coupling effect. The simulation fairly verifies the mechanical coupling modeling of 2-DOF resonators and, furthermore, analyzes the effect of quality factor, which is dominated by damping, on the enlarged resonant amplitude, ratio of resonant amplitude between the two units, resonant frequency drift and resonant phase deviation. An ultra-thin silicon cantilever-shaped 2-DOF resonator consisting of a wide base-cantilever and a narrow working cantilever is fabricated with a high yield process. The 2-DOF resonator is driven in vacuum with incident laser light on the wide base cantilever. The resonant amplitude is detected with laser Doppler meter. Measurement results agree well with the strong mechanical coupling modeling of 2-DOF resonators.
resonators mechanical coupling resonant amplitude silicon cantilever