以有限元素法決定石英振盪器之共振特性

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姓名

楊盈瑜(Ying-Yu Yang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

以有限元素法決定石英振盪器之共振特性
(Determining the Resonance Characteristics of a Quartz Oscillator via the Finite Element Method)

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至系統瀏覽論文 (2025-7-31以後開放)

摘要(中)

石英振盪器在現今電子產品中，扮演著舉足輕重的地位，主要用於頻率控制，其功能為穩定訊號的頻率，應用範圍由一般的石英鐘錶，衍生至通訊、資訊、工業、軍事等領域，石英振盪器頻率的精準及穩定相當重要。石英振盪器的品質好壞取決於振盪器的穩定度，石英晶片的尺寸變化、整體結構以及環境溫度都是影響振盪品質的重要參考因素。為了求解石英自然頻率，本文中使用有限元素軟體給予適當的邊界條件藉由頻域分析計算。
本論文將完成下列事項：(1) 建立石英振盪器結構之有限元素模型；(2)以MATLAB撰寫黃金比例法及擬牛頓法腳本，並命令COMSOL執行計算之程式，以尋找石英之自然頻率；(3)以模擬所得之電抗-頻率曲線，估算石英等效電路中之電容、電感與電阻數值；以及(4)探討各參數對石英振盪器自然頻率的影響。

摘要(英)

Quartz oscillators, mainly used for frequency control, play an important role in electronic products. The scope of applications of Quartz oscillators is from quartz clocks, communications, industry, military and other fields. The quality of the quartz oscillator depends on the frequency stability which can be affected by the temperature, the size of the quartz crystal, and the size of the electrodes. For solving the natural frequency of quartz, finite element analysis software were used to calculate the natural frequency of the quartz oscillator.
This thesis completes the following items.
(1) Establish the finite element model of the quartz oscillator structure.
(2) Use MATLAB to write a script based on the Golden Section Method and Quasi - Newton Method for controlling the finite element software to calculate the admittance of the quartz system. The frequency corresponding to maximum admittance is the natural frequency.
(3) Estimate the capacitance, inductance and resistance of the quartz equivalent circuit from the reactance-frequency curve obtained by simulation.
(4) Discuss the influence of varying system parameters on the natural frequency of a quartz oscillator.

關鍵字(中)

★ 石英振盪器
★ 以MATLAB控制COMSOL結合數值方法求解
★ 石英共振頻率計算
★ 石英等效電路計算
★ 石英溫度效應模擬

關鍵字(英)

★ Quartz Oscillator

論文目次

摘要 i
Abstract ii
目錄 iii
圖目錄 vi
表目錄 ix
1 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 1
1.3 論文架構 4
2 基本理論 6
2.1 石英晶體特性 6
2.2 石英壓電效應 8
2.2.1 正壓電效應 9
2.2.2 逆壓電效應 9
2.3 石英壓電方程式 10
2.4 石英振動原理 12
2.5 石英等效電路 13
2.6 數值方法 16
2.6.1 牛頓法 17
2.6.2 黃金比例法 19
3 數值模擬方法 21
3.1 有限元素方法簡介 21
3.2 數值模擬軟體簡介 22
3.3 模擬手法與流程 22
3.4 石英模型前處理設定 23
3.4.1 石英模型建立 23
3.4.2 石英旋轉座標系統設定 24
3.4.3 材料設定 26
3.4.4 邊界條件設定 28
3.4.5 網格劃分 30
4 MATLAB控制COMSOL之數值模擬方法 32
4.1 COMSOL連結MATLAB設定 32
4.2 路徑設定 34
4.3 呼叫COMSOL程式庫與檔案讀取 35
4.4 模擬手法與流程 35
4.5 COMSOL指令介紹 36
5 石英數值模擬結果與討論 38
5.1 數值方法應用與分析 38
5.1.1 數值方法- COMSOL步階法 38
5.1.2 數值方法-擬牛頓法 42
5.1.3 數值方法-黃金比例法 44
5.2 網格收斂性分析 47
5.3 石英等效電路 48
5.4 石英參數敏感度分析 50
5.4.1 參數一:石英晶片尺寸 50
5.4.2 參數二:銀膠尺寸與位置 52
5.4.3 參數三:電極尺寸 55
5.5 石英副波分析 57
5.6 石英溫度效應分析 65
6 結論與未來展望 71
6.1 結論 71
6.2 未來展望 72
參考文獻 74
附錄 78

參考文獻

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指導教授

黃以玫(Yi-Mei Huang)

審核日期

2020-7-23

推文