Design analysis of miniature quartz resonator using two-dimensional finite element model

This study focused on 2-D miniature quartz plates. By assigning appropriate boundary condition using finite element modeling (FEM), the vibration of a quartz plate was analyzed for converse piezoelectric effect. The quality and stability of the resonance of a quartz plate was determined by examining changes on the response curve of resonant frequency when the length of plate was decreased or increased. A graphical user interface (GUI) was adopted to assist the finite element software to calculate the frequency responses with different length of a large number of quartz plates, and to conclude a detailed curve of resonant frequency versus size. With this diagram, changes of the resonant mode for quartz plates caused by length variation can be easily observed. An optimum size of the quartz plate is obtained from the curve. Moreover, analyses were also conducted on the electrode coverage of a quartz plate and the mass-loading effect of metallic electrodes for this study, to discuss the influence on the resonant frequencies of quartz plates.