Parameters Extraction and Design Optimization for AT-cut Quartz Resonator based on Mindlin's 2D Model

For miniaturized strip AT-cut quartz resonator, the demand of performance is higher and higher, so the design ability is more important than before. But to get a precise simulation electrical response of the AT-cut quartz plate by a common commercial FEM tool is not easy and time consuming also. Base on Mindlin's (1961) 2D model and Lee-Brebbia's (1978) FEA method, Pao (2004) et al. presented an efficient numerical method in calculating the electrical response different modes of AT-cut strip quartz crystal resonator with electrode. Base on weak coupling of quartz material and mass loading effect of electrode, this problem was solved by separating the mechanical vibration and electrical coupling effects. The method considers not only the pure mechanical vibration but also the electrical response, so different modes can be identified effectively and efficiently. However, to be a practical design tool, the parameters used in the simulation better come from real samples. In this paper, the works was extended to parameters extraction for design optimization. A blank with electrode was built and its acoustic and electrical material parameters (including damping coefficient) of the quartz resonators could be extracted by fitting to few measured sample admittance curves. The extracted parameters could be used for design optimization purpose. To examine the effectiveness of the parameters extraction, another blank with electrode quartz resonator was built and the results showed the calculated impedance curves could match the measured ones, and a practical AT-cut strip quartz resonator design tool could be made based on extended Mindilin's 2D model