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首页> 外文期刊>Journal of thermal stresses >EFFECTS OF THERMAL STRESSES ON THE FREQUENCY-TEMPERATURE BEHAVIOR OF PIEZOELECTRIC RESONATORS
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EFFECTS OF THERMAL STRESSES ON THE FREQUENCY-TEMPERATURE BEHAVIOR OF PIEZOELECTRIC RESONATORS

机译：热应力对压电谐振器频率-温度行为的影响

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摘要

The frequency-temperature behavior of a piezoelectric crystal resonator can be predicted quite accurately if the resonator is under a stress-free and steady-state uniform temperature condition. The condition is however seldom achieved practically. Most practical resonators are subjected to thermal stresses. Conventional finite element analytical tools such as ANSYS cannot provide a sufficiently accurate model for the frequency-temperature behavior of piezoelectric quartz resonators. A new dynamic frequency-temperature model which accurately predicted the frequency-temperature behavior of quartz resonators affected by transient and steady state temperature changes was presented. Lagrangean equations for small vibrational (incremental) displacements superposed on initial thermal stresses and strains were employed. The initial thermal stresses and strains were obtained from the uncoupled heat and thermoelastic equations. The constitutive equations for the incremental displacements incorporated the temperature derivatives of the material constants. Numerical results were compared with the experimental results for a 50MHz AT-cut quartz resonator mounted on a glass package. Good comparisons between the experimental results and numerical results from our new model were found. The differences between the thermal expansion coefficients of glass and quartz gave rise to the thermal stresses that had adverse effects on the frequency stability of resonators. Different optimal crystal cut angles of quartz, and resonator geometry were found to achieve stable frequency-temperature behavior of the resonator in a glass package. The dynamic frequency-temperature model was used in the theoretical analyses and designs of high Q, 3.3 GHz, quartz thin film resonators.
机译：如果谐振器处于无应力且稳定的稳态均匀温度条件下，则可以非常准确地预测压电晶体谐振器的频率温度行为。但是，实际上很少达到该条件。大多数实用的谐振器都承受热应力。传统的有限元分析工具（例如ANSYS）无法为压电石英谐振器的频率-温度行为提供足够准确的模型。提出了一种新的动态频率温度模型，该模型可以准确预测受瞬态和稳态温度变化影响的石英谐振器的频率温度行为。拉格朗日方程组用于较小的振动（增量）位移，它叠加在初始热应力和应变上。初始热应力和应变是从解耦的热和热弹性方程获得的。增量位移的本构方程包含了材料常数的温度导数。将数值结果与安装在玻璃封装上的50MHz AT切割石英谐振器的实验结果进行了比较。在我们的新模型的实验结果和数值结果之间找到了很好的比较。玻璃和石英的热膨胀系数之间的差异导致了热应力，这对谐振器的频率稳定性产生了不利影响。发现石英的不同最佳晶体切割角和谐振器几何形状可以在玻璃封装中实现谐振器的稳定的频率-温度特性。动态频率-温度模型用于高Q，3.3 GHz石英薄膜谐振器的理论分析和设计中。

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