An analysis of z-strip AT-cut quartz thickness-shear resonators

This paper mainly analyzes the fundamental and third order thickness shear modes of z-strip quartz resonator with the scalar equations derived by Tiersten and Smythe. Effects of the mass ratio and the length of the electrode on the operation modes and 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 resonator application. With the mass ration increasing the vibration frequency decreases. These results are important in the understanding and design of quartz resonators.