二維有限元素模型在小型化石英振盪器之設計分析

The Design and Analysis on Miniature Quartz Resonators Using the 2-D FEM Model

陳政宇(Zheng-Yu Chen)

指導教授 ： 黃自貴

國立虎尾科技大學/工程學院/機械設計工程研究所/碩士(2011年)

https://doi.org/10.6827/NFU.2011.00131

摘要

石英振盪器為目前3C產業中使用最廣泛的被動元件之一，在我們日常生活中常見的電腦及電子儀器都能見其蹤跡。石英振盪器的振盪來源出自於振盪器中的石英晶體薄板及其與生俱有的壓電特性，在迴路中透過電壓的施加而輸出綿綿不絕的振盪。石英晶體為異向性材料，因此不同的切割方式會產生不同的材料特性，應用領域也不盡相同。AT切面的石英薄板具高材料Q值及穩定的溫度效應特性使其在高頻元件的應用上最具獨占性。
本研究針對AT切面的石英晶體薄板來探討其振盪特性。AT切面的薄板為利用厚度剪切的形式產生振動，因此厚度剪切頻率的高低主要決定於厚度。但薄板的長度在特定尺寸變化下會使得厚度剪切模態附近的彎曲振動模態或耦合模態變得十分接近，導致厚度剪切模態的振盪能量被分散。影響石英平板振動頻率的因素還包含覆蓋於薄板表面的電極面積以及電極材料的質量加載效應；不同的溫度變化下亦會造成振盪頻率的飄移。本研究利用有限元素法探討薄板在長度的變化下厚度剪切模態、彎曲振動模態及耦合振動模態的變化趨勢，並且針對電極覆蓋比例及電極質量加載進行分別的比較，另外，石英振盪器受電壓激振產生的激振頻及導致的失效頻，還有石英平板在溫度效應下產生的頻率飄移也有進一步的探討。

關鍵字

石英振盪器 ； AT-cut ； 厚度剪切模態 ； 激振頻 ； 失效頻 ； 溫度效應

並列摘要

This study focused on 2-D miniature quartz plates. By assigning appropriate boundary condition using finite element modeling (FEM), the vibration of a quartz plate was analyzed for converse piezoelectric effect. The quality and stability of the resonance of a quartz plate was determined by examining changes on the response curve of resonant frequency when the length of plate was decreased or increased. A graphical user interface (GUI) was adopted to assist the finite element software to calculate the frequency responses with different length of a large number of quartz plates, and to conclude a detailed curve of resonant frequency versus size. With this diagram, changes of the resonant mode for quartz plates caused by length variation can be easily observed. An optimum size of the quartz plate is obtained from the curve. Moreover, analyses were also conducted on the electrode coverage of a quartz plate and the mass-loading effect of metallic electrodes for this study, to discuss the influence on the resonant frequencies of quartz plates. This study also further discussion excitation and dead vibration modes in quartz resonators, and temperature effect cause frequency drift of quart plate.

並列關鍵字

Quartz resonator ； AT-cut ； thickness shear mode ； excitation vibration ； dead vibration ； temperature effect

參考文獻

[1]R. D. Mindlin, 1951, "Thickness-Shear and Flexural Vibrations of Crystal Plates", Journal of Applied Physics, Volume 22, Number 3, pp. 316-323

[2]R.D. Mindlin, 1952, "Forced Thickness-Shear and Flexural Vibrations of Piezoelectric Crystal Plates", Journal of Applied Physics, Volume 23, Number 1, pp. 83-88

[3]R. Bechmann, 1958, "Elastic and Piezoelectric Constants of Alpha-Quartz", Physical Review, Volume 110, Number 5, pp. 1060-1061

[4]Y.K. Yong, Masako Tanaka, Tsutomu Imai, 2003, "Finite Element Prediction of Q and Equivalent Electrical Parameters of Quartz Resonators", Ultrasonics, 2003 IEEE Symposium on, Volume 1, pp. 80-83

[5]Y.K. Yong, Masako Tanaka and Tsutomu Imai, 2004, "Dedicated finite elements for electrode thin films on quartz resonators", Ultrasonics Symposium, 2004 IEEE, Volume 1, pp. 274-277