An Analysis of Frequency-Temperature Relations of At-Cut Quartz Crystal Resonators By Finite Element Method With Comsol

机译：用康索尔有限元方法分析石英晶体谐振腔的频温关系

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In order to study the frequency-temperature relations of AT-cut quartz crystal resonators, vibrations of the quartz crystal blank in the temperature field is analyzed by incremental thermal field theory. With the incremental thermals field equations, the mathematical models of thermal expansion coefficients and temperature, thermal elasticity coefficient and temperature, and density temperature coefficient and temperature are used. The thermal coefficient function model of quartz crystal is established by using the parametric model with the finite element simulation software COMSOL, and the impedance relations and harmonic frequency are analyzed at a given ambient temperature.

机译：为了研究AT切石英晶体谐振器的频率-温度关系，利用增量热场理论分析了石英毛坯在温度场中的振动。通过增量热场方程，使用热膨胀系数和温度，热弹性系数和温度以及密度温度系数和温度的数学模型。利用有限元仿真软件COMSOL的参数模型建立了石英晶体的热系数函数模型，并在给定的环境温度下分析了阻抗关系和谐波频率。

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《Symposium on Piezoelectricity, Acoustic Waves and Device Applications》|2019年|1-4|共4页
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Juan WEN; Xiao-ming SUN; Chao ZHAN; Yuan-hua ZHONG; Ji WANG;
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关键词
Quartz crystals; Resonant frequency; Resonators; Mathematical model; Impedance; Vibrations;

机译：石英晶体;谐振频率;谐振器;数学模型;阻抗;振动;

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专利

1. A finite element analysis of frequency-temperature relations of AT-cut quartz crystal resonators with higher-order Mindlin plate theory [J] . Wang J, Yu JD, Yong YK, Acta Mechanica . 2008,第1a4期

机译：基于高阶Mindlin板理论的AT切石英晶体谐振器频率-温度关系的有限元分析
2. A finite element analysis of frequency–temperature relations of AT-cut quartz crystal resonators with higher-order Mindlin plate theory [J] . Ji Wang, J.-D. Yu, Y.-K. Yong, Acta Mechanica . 2008,第s1a4期

机译：基于高阶Mindlin板理论的AT切石英晶体谐振器频率-温度关系的有限元分析
3. Development of SMD 32.768 kHz tuning fork-type crystals - Part IV: Finite element method design of quartz tuning fork resonators - Significant design parameters affecting motional capacitance C{sub}1 [J] . Sungkyu Lee, Yangho Moon, Jae-Hwan Ahn, Zeitschrift fur Metallkunde . 2008,第11期

机译：SMD 32.768 kHz音叉型晶体的开发-第IV部分：石英音叉谐振器的有限元方法设计-影响运动电容C {sub} 1的重要设计参数
4. An Analysis of Frequency-Temperature Relations of At-Cut Quartz Crystal Resonators By Finite Element Method With Comsol [C] . Juan WEN, Xiao-ming SUN, Chao ZHAN, Symposium on Piezoelectricity, Acoustic Waves, and Device Applications . 2019

机译：COMSOL有限元法通过有限元法升温晶体谐振器频率 - 温度关系分析
5. Nonlinear finite element modeling of quartz crystal resonators. [D] . Beerwinkle, Austin Dale. 2011

机译：石英晶体谐振器的非线性有限元建模。
6. A Comparison of Frequency Pullability in Oscillators Using a Single AT-Cut Quartz Crystal and Those Using Two Single AT-Cut Crystals Connected in Parallel with a Series Load Capacitance or Series Load Inductance [O] . Vojko Matko 2006

机译：使用单个AT-Cut石英晶体的振荡器和使用两个带有串联负载电容或串联负载电感并联的单个AT-Cut晶体的振荡器的频率可拉性的比较
7. Higher-order Plate Theory Based Finite Element Analysis of the Frequency-temperature Relations of Quartz Crystal Resonators [O] . Ji Wang, Yook-kong Yong, Tsutomu Imai 1998

机译：基于高阶板理论的石英晶体谐振器频率-温度关系有限元分析
8. Initial Stress Field and Resonance Frequencies of Incremental Vibrations in Crystal Resonators by Finite Element Method [R] . Lee, P. C., Tang, M. S. 1986

机译：有限元法求解晶体谐振器增量振动的初始应力场和共振频率

An Analysis of Frequency-Temperature Relations of At-Cut Quartz Crystal Resonators By Finite Element Method With Comsol

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