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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >The determination of the optimal length of crystal blanks in quartz crystal resonators
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The determination of the optimal length of crystal blanks in quartz crystal resonators

机译：石英晶体谐振器中晶体毛坯最佳长度的确定

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摘要

It is well understood that the strong coupling of thickness-shear and flexural vibrations in piezoelectric crystal plates only occurs at specific length at which the vibration mode conversion, like the flexural mode gradually converting to thickness-shear mode while the thickness-shear mode converting to higher-order flexural mode, happens. It is important to avoid the strong coupling of modes in a crystal resonator that uses thickness-shear vibrations to enhance the energy trapping. To achieve such a design goal, the length of a crystal blank should be carefully chosen such that the coupling is at its weakest, which usually is in the middle of two strong coupling points. Through a closer examination of the frequency spectra, or the frequency-length relationship in this study, we can see that the strong coupling points appear periodically. This implies that we can find exact locations with the plate theory that predicts the resonance frequency. Based on this observation, we first use the first-order Mindlin plate theory with the precise thickness-shear frequency, which is normalized to one, to find corresponding wavenumbers. Then the length as a variable is solved from the coupled frequency equation for exact coupling points in a crystal plate of AT-cut quartz. The optimal length of a crystal blank in the simplest resonator model is calculated for the coupled thickness-shear, flexural, and extensional vibrations. The solutions and the method will be important in the determination of optimal length of a crystal blank in the resonator design process.
机译：众所周知，压电晶体板中厚度-剪切和弯曲振动的强耦合仅在振动模式转换的特定长度处发生，例如弯曲模式逐渐转换为厚度-剪切模式，而厚度-剪切模式转换为发生高阶弯曲模式。重要的是要避免晶体谐振器中的模强耦合，该谐振器使用厚度剪切振动来增强能量捕获。为了达到这样的设计目标，应仔细选择晶体坯料的长度，以使耦合处于最弱的位置，通常处于两个强耦合点的中间。通过仔细研究频谱或本研究中的频率长度关系，我们可以看到强耦合点周期性地出现。这意味着我们可以通过板理论来找到预测共振频率的精确位置。基于此观察结果，我们首先使用具有精确的厚度剪切频率（被归一化）的一阶Mindlin板理论来找到相应的波数。然后，从耦合频率方程中解出长度作为变量，以获取AT切割石英晶体板上精确的耦合点。在最简单的谐振器模型中，针对耦合的厚度剪切，弯曲和拉伸振动，计算出晶体坯料的最佳长度。解决方案和方法对于确定谐振器设计过程中晶体坯的最佳长度将很重要。

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