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。;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.
