非等厚电极对石英晶体板高频振动影响分析

Influence of Unequal Thickness Electrode on High Frequency Vibrations of Quartz Crystal Plate

利用Mindlin一阶板理论分析了覆盖非等厚电极层的AT切石英晶体板的高频振动,获得了包含厚度剪切振动模态、弯曲振动模态、面剪切振动模态、拉伸振动模态和厚度扭转振动模态的色散关系和频谱关系。研究结果表明由于上下电极层的非等厚性,过去认为不耦合的两组振动模态变得相互耦合,必须进行联合求解。计算结果表明由于非等厚电极层的质量效应,各振动模态的频率均有所降低。根据石英晶体板高频振动的频谱关系图,可以选取石英晶体板的最佳长厚比作为谐振器的制造尺寸。获得的电极层厚度与频率变化关系可以用来指导谐振器电极层厚度设计。

Based on Mindlin's first-order plate theory,the high-frequency vibrations of AT cut quartz crystal plate covered with unequal thickness electrode layers was analyzed.The dispersion relation and frequency spectrum of vibration modes including thickness-shear vibration mode,flexural vibration mode,face-shear vibration mode,extension mode and thickness-twist modes were obtained.The research results show that due to unequal thickness of the upper and lower electrode layers,the two originally groups of vibration modes that were previously considered uncoupled are now coupled and must be solved jointly.The computing results show that the frequency of every vibration mode decrease due to the mass effect of the unequal thickness electrode layer.According to the frequency spectrum of high frequency vibration of quartz crystal plate,the optimal length/thickness ratio of quartz crystal plate can be selected as the manufacturing size of resonator.The relationship between the thickness of the electrode layer and the frequency variation can be used to guide the design of the electrode layer thickness of the resonator.