Frequency and amplitude modulations in crystal resonators due to transient thermal effects

被引：4

作者：

Cui, Jing ^{[1
]}

Du, Jianke ^{[1
]}

Wang, Ji ^{[1
]}

Yang, Jiashi ^{[1
,2
]}

机构：

[1] Ningbo Univ, Sch Mech Engn & Mech, Piezoelect Device Lab, Ningbo 315211, Zhejiang, Peoples R China

[2] Univ Nebraska, Dept Mech & Mat Engn, Lincoln, NE 68588 USA

来源：

JOURNAL OF APPLIED PHYSICS | 2014年 / 115卷 / 05期

基金：

中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

THICKNESS-SHEAR VIBRATIONS; PIEZOELECTRIC RESONATORS; ELECTROELASTIC EQUATIONS; BIASING DEFORMATIONS; PLATE;

D O I：

10.1063/1.4863643

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

We show through a theoretical analysis that when a crystal resonator is subjected to a transient temperature change, in addition to the known frequency shift or modulation, there always exists an accompanying amplitude modulation. The theory for small fields superposed on finite initial fields is employed and reduced to an ordinary differential equation with a time-dependent coefficient. An approximate analytical solution is obtained. The solution shows that the frequency modulation is a first-order effect, and the amplitude modulation is a second-order effect. The results are useful to the understanding and design optimization of crystal resonators. (c) 2014 AIP Publishing LLC.

引用

页数：4

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