Energy trapping behavior of AT-cut quartz crystal resonators with a groove ring on main electrodes

Abstract

This paper considers an energy trapping AT-cut quartz crystal resonator, and proposes a quartz crystal resonator with a groove ring having a cutoff frequency higher than that of the periphery, located near the outer periphery of the electrode. A numerical analysis is performed from the viewpoint of the purely elastic and isotropic cases. The results are verified by numerical calculation by the three-dimensional finite-element method. It is shown that the following properties are realized for any geometrical parameters of the main electrodes by providing the groove ring structure. (1) The frequency difference between the main resonant frequency and the anharmonic spurious component can be increased on the order of 10%. (2) If the frequency difference between the anharmonic spurious components is kept the same, the displacement of the quartz crystal substrate edge can be reduced by several tens of percent. These properties help to reduce vibration energy leakage from the edge support, and to reduce the size of the quartz crystal resonator. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(4): 48–55, 1999