石英振盪器在電子產品中扮演著關鍵角色，其品質影響著訊號的穩定性和精確度，本研究主要討論石英振盪器的激勵功率依賴性(簡稱DLD)之效應，分析方法採用有限元素分析軟體COMSOL Multiphysics 5.6，計算石英振盪器因為輸入功率加大後的非線性頻率響應，討論特徵頻率與模態的變化；除了DLD效應以外，亦有歸納線性系統之模態判別依據與指標。 為了找出非線性的高功率下之特徵頻率，本研究中進行推導統御方程式，在有限元素模擬軟體COMSOL中寫入自訂方程式，以進一步探討了石英振盪器在高驅動功率下的穩態非線性效應，並獲得代表非線性現象的backbone頻率響應曲線，再決定頻率飄移數據與計算品質因子Q值，如此可以準確地以模擬的方式預測出高功率對石英振盪器的影響。有關於模態判別部分則是嘗試建立清楚的判別指標，以快速的自動判定所選模型是否適用。本研究的總目標為用模擬之方式，分析與討論石英振盪器的某些特性，並藉模擬結果求解最佳之設計，尋找成本與和性能間的平衡點，避免一再的製作原型與進行實驗量測，以節約開發成本。 ;Quartz oscillators play a crucial role in electronic products with their quality impacting signal stability and accuracy. This study primarily discusses the effects of drive level dependency (DLD) on quartz oscillators based on numerical results. Using the finite element analysis software COMSOL Multiphysics 5.6, the nonlinear frequency response of quartz oscillators under increased input power is calculated, and the changes in characteristic frequencies and modes are also analyzed. In addition to DLD effects, the criteria and indicators for modal discrimination in linear systems are also summarized. To identify the characteristic frequency under high-power conditions, the nonlinear governing equations are derived and customly redefined in COMSOL. This allows for further exploration of the steady-state nonlinear effects of quartz oscillators at high drive power. The numerical results then provide the backbone frequency response curve representing nonlinear phenomena. Frequency shift and the quality factor (Q) value are then calculated. These data compared well with the experimental results. For modal discrimination, clear indicators are established to quickly and automatically determine the types of selected models. The overall goal is to future establish an automatic procedure for identifying specific vibration modes of quartz oscillators to avoid repeated prototyping and experimental measurements to save development costs.
