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首页> 外文会议>IEEE(Institute of Electrical and Electronics Engineers) International Frequency Control Symposium and Exhibition; 20050829-31; Vancouver(CA) >Drive Level Dependency in Quartz Resonators
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Drive Level Dependency in Quartz Resonators

机译：石英谐振器的驱动电平依赖性

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摘要

Common piezoelectric resonators such as the quartz resonators have a very high Q and ultra stable resonant frequency. However, due to small material nonlinearities in the quartz crystal, the resonator is drive level dependent, that is, the resonator level of activity and its frequency are dependent on the driving, or excitation, voltage. The size of these resonators will be reduced to one fourth of their current sizes in the next few years, but the electrical power which is applied will not be reduced as much. Hence, the applied power to resonator size ratio will be larger, and the drive level dependency may play a role in the resonator designs. We study this phenomenon using the Lagrangian nonlinear stress equations of morion and Piola-Kirchhoff stress tensor of the second kind. Solutions are obtained using FEMLAB for the AT-cut, BT-cut, SC-cut and other doubly rotated cut quartz resonators and the results compared well with experimental data. The phenomenon of the drive level dependence is discussed in terms of the voltage drive, electric field, power density and current density. It is found that the drive level dependency is best described in terms of the power density. Experimental results for the AT-, BT- and SC-cut resonators in comparison with our model results are presented. Results for new doubly rotated cuts are also presented.
机译：诸如石英谐振器之类的普通压电谐振器具有很高的Q值和超稳定的谐振频率。但是，由于石英晶体中材料的非线性很小，谐振器取决于驱动电平，也就是说，谐振器的活动电平及其频率取决于驱动电压或激励电压。在未来几年中，这些谐振器的尺寸将减小到其当前尺寸的四分之一，但是所施加的电能将不会减小太多。因此，所施加的功率与谐振器尺寸之比将会更大，并且驱动电平的依赖性可能会在谐振器设计中发挥作用。我们使用morion的拉格朗日非线性应力方程式和第二种Piola-Kirchhoff应力张量来研究此现象。使用FEMLAB针对AT切割，BT切割，SC切割和其他双旋转切割石英谐振器获得了解决方案，并将结果与​​实验数据进行了比较。根据电压驱动，电场，功率密度和电流密度来讨论驱动电平依赖性现象。已经发现，就功率密度而言，最好地描述了驱动电平的依赖性。与我们的模型结果比较，给出了AT，BT和SC切谐振器的实验结果。还显示了新的双倍旋转切割的结果。

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