Semi-analytical modeling of substrate loss of miniature resonators

Abstract eng:
In this paper, a new semi-analytical technique for estimating the energy loss in a miniature resonator mounted on a substrate is presented. Recent high quality factor resonators typically have resonant frequencies up to several hundred kilohertz, and therefore, the substrate is best treated as a plate. The only traveling waves in a plate are Lamb waves, which leads to a simplified characterization of the energy carried away from a vibrating source on the plate surface. In the presented approach, absorbing boundary elements of standard finite element (FE) models are replaced with the analytical expressions for Lamb waves. The method of stitching together the FE model and analytical expressions is extended to include modal analysis in order to determine quality factors of the resonator modes. The semianalytical approach is demonstrated for a cantilever bonded to a plate, and eigenmode parameters are determined. Good agreement with conventional FE simulations is shown.

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