Effect of air damping on quality factor of bulk mode microresonators

In this paper, the air damping effect on quality factor of bulk mode microresonators is analyzed and measured. Both the squeeze film damping and slide film damping are considered in the analysis procedure. The reactions of the resonant plate with the air flows in the transduction gaps and around the resonator plate surfaces are investigated based on the Reynolds equation and the Stoke-flow model, respectively. An electrical equivalent model has been derived for a microresonator operating in air, based on the squeeze film damping and slide film damping effect. The model is realized with resistors equivalent for the slide film damping force and frequency-dependent resistors and capacitances connected in series equivalent for the squeeze film damping force. Circuit analysis tool is employed to calculate the response of the microresonator. The simulated transmission characteristics are in good agreement with the experimental results. Consequently, this approach provides a method to estimate the effect of air damping on the dynamic response of the micromechanical devices.

Equivalent circuit for the resonator with the effect of air damping. The squeeze film damping force is modeled using series-connected R–C sections and the slide film damping forces are modeled using the resistive elements.Figure optionsDownload as PowerPoint slideHighlights
► Air damping effect on quality factor of a bulk mode microresonator is analyzed.
► An electrical equivalent model is derived for a microresonator operating in air.
► The squeeze film damping force is modeled as series-connected R–C sections.
► The slide film damping force is modeled using the resistive elements.
► The simulated result is in good agreement with the experimental one.