An analysis of z-strip at-cut quartz thickness-shear filters

This paper mainly analyzes the fundamental thickness shear modes of z-strip quartz crystal filter with the scalar equations derived by Tiersten and Smythe. Effects of the mass ratio and the distance between the electrodes on the operation modes and the resonant frequencies are also studied. Exact modes can be obtained and the results show that the operation modes without nodal lines on the electroded area are suitable for filter application. With the mass ration increasing, the vibration frequency decreases. These results are important in the understanding and design of quartz filters.