ANALYSIS OF FREQUENCY SPECTRUM OF COUPLED T-TYPE WAVE IN AT-CUT QUARTZ VIBRATOR

In this paper we present theoretically and experimentally a study of the frequ-ancy spectrum of coupled T-type wave in AT-cut quartz vibrator. In the theoretical part of our paper, we have derived a simple wave equation of AT-cut quartz vibrator by introducing two equivalent stresses （T₁=r₁₁ S₁ and T₅ = r₅₅ S₅）. By considering also the boundary conditions of the plated and unplated regions of a plate as well as the mass loading and piezoelectric effect, a set of equations describing the propagation characteristics of coupled T-type wave are given. Form these equations we have calculated the frequency spectrum of coupled T-type wave. The energy trapping criteria of thickness/shear mode and thickness/twist mode with finite rectangular electrode are given. The relation between the best size of rectangular electrode and elastic coefficient is obtained.
In the experimental part of our paper, we have measured the frequency spectrum of AT-cut quartz vibrator with various electrode size and mass loading at fundamental frequency of about 30 MHz and 100 MHz respectively. The experimental data are in good agreement with the theoretically calculated values. Finally, an AT-cut quartz resonator with dominant single frequency characteristic is realized by using the theory developed in this paper.