Analysis of a monolithic crystal plate acoustic wave filter

We study thickness–shear and thickness–twist vibrations of a finite, monolithic, AT-cut quartz plate crystal filter with two pairs of electrodes. The equations of anisotropic elasticity are used with the omission of the small elastic constant c56. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and the vibration confinement due to the electrode inertia are calculated and examined.

► The thickness-shear and thickness-twist vibrations of a quartz plate with two pairs of electrodes is studied.
► Modes trapped under the electrodes are found.
► The vibration distribution of these modes is sensitive to the electrode length and thickness.
► Thicker and longer electrodes lower the frequencies.