Effect of Electrodes on Force–Frequency Characteristics of Rotated Y-Cut Quartz Resonators

Abstract

The change in the resonance frequency of the thickness-shear vibration of rotated Y-cut quartz resonators using various electrode materials was studied. We used a three-dimensional finite element method to calculate the strain distribution of a circular plate and the electrodes under a pair of diametrical forces so that the anisotropy of the blank can be accurately considered. The relationship between mass-loading and force–frequency (F– f) characteristics is obtained for several types of electrode material. The results show that, for some electrode materials, the change in the F– f coefficients induced by the initial strain field distribution in the electrode through the third-order elastic constants is significant, but for others, the variations are small. We also find that the change is proportional to the thickness of the electrode. Furthermore, different materials have different effects. For most metals, such as gold, silver, copper, aluminum and nickel, with the increase in thickness, the F– f coefficient increase. However, for chromium, the increase in thickness may result in a lower F– f coefficient.

Stress-induced frequency shifts in rotated Y-cut langasite resonators with electrodes considered

“…The thicknesses of the plate and each electrode are 2h and 2h , respectively. We employ the conclusion of [6] which is used to describe the thickness vibration superposed on homogenous initial deformations with electrodes considered. For a rotated Y-cut LGS plate, we have the following frequency equations only for thickness-shear mode:…”

Study of Force-Frequency Characteristics in AT-Cut Strip Quartz Crystal Resonators with Different Rotation Angles

“…Further, Janiaud et al presented a solution to the problem of stress bias effects in anisotropic circular plates [ 17 ]. Jing et al studied the effect of electrodes on the force-frequency characteristics of QCRs [ 18 ]. Bao et al reported the first experimental measurement of the stress-induced frequency shifts of thickness-shear modes in a rotated Y-cut QCR [ 19 ].…”