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The calculation of electrical parameters of AT-cut quartz crystal resonators with the consideration of material viscosity

机译:考虑材料粘度的AT切石英晶体谐振器电参数计算

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Electrical parameters like resistance and quality factor of a quartz crystal resonator cannot be determined through vibration analysis without considering the presence of material dissipation. In this study, we use the first-order Mindlin plate equations of piezoelectric plates for thickness-shear vibrations of a simple resonator model with partial electrodes. We derive the expressions of electrical parameters with emphasis on the resistance that is related to the imaginary part of complex elastic constants, or the viscosity, of quartz crystal. Since all electrical parameters are frequency dependent, this procedure provides the chance to study the frequency behavior of crystal resonators with a direct formulation. We understand that the electrical parameters are strongly affected by the manufacturing process, with the plating techniques in particular, but the theoretical approach we presented here will be the first step for the precise estimation of such parameters and their further applications in the analysis of nonlinear behavior of resonators. We calculated the parameters from our simple resonator model of AT-cut quartz crystal with the first-order Mindlin plate theory to demonstrate the procedure and show that the numerical results are consistent with earlier measurements.
机译:如果不考虑材料耗散的情况,则无法通过振动分析确定诸如电阻和石英晶体谐振器的品质因数之类的电参数。在这项研究中,我们将压电板的一阶Mindlin板方程用于具有部分电极的简单谐振器模型的厚度剪切振动。我们推导出电参数的表达式,重点是与石英晶体复弹性常数或粘度的虚部相关的电阻。由于所有电参数均取决于频率,因此该程序提供了直接研究晶体谐振器频率特性的机会。我们了解到,电气参数会受到制造工艺的强烈影响,尤其是电镀技术,但是我们在此介绍的理论方法将是精确估算此类参数及其在非线性行为分析中进一步应用的第一步谐振器。我们使用一阶Mindlin板理论从AT切割石英的简单谐振器模型中计算出参数,以演示该过程,并表明数值结果与早期测量结果一致。

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