考虑材料系数修正的石英晶体谐振器研究

Analysis of Quartz Crystal Resonator with Consideration of Correction Material Factors

基于Mindlin一阶板方程,对石英晶体板高频振动的零阶、一阶应力和电势进行了释放,获得了经修正的石英晶体材料系数。通过数值计算,绘制了更加精确的石英晶体板高频振动的色散关系和频谱关系。计算结果表明,综合考虑零阶、一阶应力和电势释放的频率漂移比只考虑零阶应力释放的频率漂移较小,这更符合谐振器频率稳定性要求。提出的修正方法可以推广到石英晶体谐振器的泛音振动,为石英晶体谐振器的精确设计和分析提供有效指导。

Based on the first-order Mindlin plate equations,correction material factors of quartz crystal were obtained by relaxation of the zeroth-order,first-order stress and electric potential for high frequency vibration of quartz crystal plate.More accurate dispersion and spectral relationships of high frequency vibration of quartz crystal plate were plotted by numerical calculation.Numerical results show that the frequency shifts with consideration of the zeroth-order,first-order stress and electric potential relaxation are smaller than that with only consideration of the zeroth-order stress relaxation which more satisfies frequency stability requirement of resonators.The correction method that proposed can be used for the overtone vibrations of quartz crystal resonator,which provides useful guidance for the precise design and analysis of quartz crystal resonators.