Drive level dependency in quartz resonators
Drive level dependency in quartz resonators
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DOI：
10.1016/j.ijsolstr.2008.12.021
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发表时间：
2005-08
期刊：
影响因子：
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通讯作者：
M.S. Patel;Y. Yong;M. Tanaka;T. Imai
中科院分区：
文献类型：
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作者：
M.S. Patel;Y. Yong;M. Tanaka;T. Imai
普通的压电谐振器如石英谐振器具有非常高的Q和超稳定的谐振频率。然而，由于石英晶体中的小的材料非线性，谐振器是驱动电平相关的，也就是说，谐振器的活动水平及其频率取决于驱动或激励电压。这些谐振器的尺寸将在未来几年内减少到目前尺寸的四分之一，但所施加的电力不会减少那么多。因此，施加的功率与谐振器尺寸之比将更大，并且驱动电平依赖性可能在谐振器设计中发挥作用。本文利用拉格朗日非线性应力运动方程和Piola-Kirchhoff第二类应力张量研究了这一现象。用COMSOL求解了AT切、BT切、SC切和其它双旋切石英谐振器的振动问题，并与实验结果进行了比较。从驱动电压、电场、功率密度和电流密度等方面讨论了驱动电平依赖性现象。据发现，驱动电平的依赖性是最好的功率密度方面的描述。AT，BT和SC切谐振器的实验结果与我们的模型结果进行比较。新的双旋转切割的结果。分析了寄生模、品质因数和空气阻尼对DLD的影响。
Common piezoelectric resonators such as 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 motion and Piola–Kirchhoff stress tensor of the second kind. Solutions are obtained using COMSOL 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 presented. The effects of spurious modes, quality factor and air damping on DLD are presented.