Estimation of quartz resonator Q and other figures of merit by an energy sink method

One of the most important factors affecting the Q in the design of a new quartz resonator is the loss of energy from the electrode area to the base via the mountings. The acoustical characteristics of the plate resonator are changed when the plate is mounted onto a base mounting. The base affects the frequency spectra of the plate resonator. A resonator with a high Q may not have a similarly high Q when mounted on a base; hence the base is an energy sink. The frequency spectra of the quartz resonator with and without the base are presented. A scaled boundary finite element method is employed to model a semi-infinite base. Since a semi-infinite base absorbs all acoustical energies radiated from the resonator, a forced vibration analysis of such a model provides the lower bound Q values. The energy sink model could also provide other electrical parameters such as the motional capacitance, motional resistance and figure of merit, M. The model with a semi infinite base could be used for evaluating resonator and mountings designs which is important for MEMS and miniaturized devices. The effect of the mountings, plate and electrode geometries on the resonator Q and other electrical parameters are presented for AT-cut quartz resonators. Simulated results from the energy sink method were compared with experimental results and were found to be good