Estimation of Quartz Resonator Q and other Figures of Merit by an Energy Sink Method

Abstract

An important determinant of the quality factor Q of a 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 substrate. The base substrate 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 and the Q will be affected by the shape and size of this base. A lower bound Q will be obtained if the base is a semi-infinite base since it will absorb all acoustical energies radiated from the resonator. A scaled boundary finite element method is employed to model a semi-infinite base. The frequency spectra of the quartz resonator with and without the base are presented. In addition to the loss of energy via the base, there are other factors which affect the resonator Q, such as, for example, material dissipation, and damping at the interfaces of quartz and electrodes. The energy dissipation due to material damping increases with the resonant frequency and the reduction of resonator size; hence material damping becomes important in the current and future miniaturized resonators operating at very high frequencies. An energy sink model along with material dissipation would provide realistic Q, motional capacitance, motional resistance, and other figures of merit useful for designing resonators. The model could be used for evaluating resonator and mountings designs of microelectromechanical systems and miniaturized devices. The effect of the mountings, and plate and electrode geometries on the resonator Q and other electrical parameters are presented for AT-cut quartz resonators. Model results from the energy sink method were compared with experimental results and were found to be good.

Si-based MEMS resonant sensor: A review from microfabrication perspective

“…Whereas poly-crystalline Si material shows low level intrinsic Q-factors in contrast to single-crystalline Si, but possess good characteristics as these poly-Si resonant sensors structures can be fabricated in precise dimensions. Quartz is widely utilized material for the fabrication of resonant sensor as these are piezo-electric material; suitable candidate for the excitation and detection of vibration [73]. Bio-compatibility, chemical inertness, and hydrophilicity, as well as residual stress, etching sensitivity and selectivity along with the fabrication cost, are some of the parameters for when choosing a resonator material.…”

Identification of Vibration Modes of Quartz Crystal Plates with Proportion of Strain and Kinetic Energies

“…TSh,F, AT -cut, two modes, TSh,F,FS, AT -cut, three modes, TSh,TT, TSt, E, F, FS, SC -cut, six modes; (23) whereŨ is total of the strain energy of the plate which excludes the coupling energy parts as:…”

“…We use Eqs. (23) and (29) for the calculation and the energy distributions of each frequency and the results are given in Table 1.…”

“…20 For piezoelectric plate vibrations, the energy calculations were often used to describe the energy trapping and harvest effect. 21,22 Through the research of Yong, et al, 23 the ratios of the trapped energies can be calculated to evaluate the quality of resonators.…”

Effects of mode coupling on the admittance of an AT-cut quartz thickness-shear resonator

“…Recently, there has been growing interest in the computation of resonator admittance, e.g., Refs. [14]- [21]. However, usually only the dependence of the admittance on the driving frequency of the applied voltage was examined.…”