典型的類比電路自動化設計方法大致可分為兩大類：模擬基礎
(simulation-based)以及方程式基礎(equation-based)方法。模擬基礎的方法有高度的準確性，但需要消耗大量的模擬時間。方程式基礎方法雖然執行速度快，但因為估計公式無法考慮到較高階的電路效應使得結果不準確。因此，本論文提出一套結合方程式基礎與模擬基礎優點的類比電路自動化設計方法。利用本論文提出的「全域性方程式設計參數空間化簡方法」，能快速地縮減設計參數空間，留下小部分最佳解可能存在的區域。之後，再用模擬基礎的最佳化方法，對剩下的小部分區域作搜尋。在實驗中，所提出的演算法用於兩級式運算放大器自動化設計與鎖相迴路行為模型參數設計上。在第一階段的演算法中，原本的設計參數空間被化簡為小範圍的設計參數空間，然後再用模擬基礎的搜尋方法對化簡後的設計參數空間作搜尋。從實驗結果可以看出，提出的演算法能有效地提高模擬基礎最佳化方法的效率，且結果也保有高度的準確性。

Traditional analog design automation approaches can be classified into two categories. One is simulation-based optimization. It has high accuracy but requires more simulation time to find the global optimal solution. The other is equation-based optimization. It has short execution time but the accuracy is often limited due to the simplified equations. In this thesis, a combined method is proposed to take the advantages of both simulation-based and equation-based approaches for analog design automation. By using the proposed “global equation-based design space reduction” method, the design space with the global optimal can be simplified to a small region quickly in the first stage of the proposed algorithm. Then, simulation-based optimization is applied to search the small region to accurately identify the global optimal point. As shown in the experimental results on several analog circuits, the proposed method has higher efficiency than traditional global search approaches without sacrifice on accuracy.

摘要 iv
Abstract v
目錄 vi
圖目錄 ix
表目錄 xi
1 第一章、緒論 1
1-1 研究動機 1
1-2 相關研究 3
1-3 論文結構 8
2 第二章、背景 9
2-1 單純形基礎最佳化方法 9
2-1-1 單純形定義 9
2-1-2 演算法參數定義 10
2-1-3 單純形取樣與切割 10
2-1-4 初始分割 11
2-1-5 最佳化流程 13
2-1-6 實驗結果 14
2-1-7 演算法總結 15
2-2 gm/ID兩級式運算放大器效能估測方法 16
2-2-1 兩級式放大器估測公式 16
2-2-2 電晶體操作偏壓限制 17
2-2-3 gm/ID方法 18
2-2-4 gm/ID的特性 19
2-2-5 線性迴歸(regression) 21
3 第三章、 24
3-1 演算法主要想法 24
3-2 演算法流程 25
3-2-1 縮減單純形 26
3-2-2 蒐集單純形 28
3-3 演算法驗證 28
3-4 提高模擬基礎搜尋方法效率 30
4 第四章、實驗結果與分析 31
4-1 兩級式運算放大器自動化設計 31
4-2 實驗環境與方法 32
4-2-1 模擬退火演算法參數設定 34
4-2-2 放大器設計參數範圍 34
4-2-3 模擬退火演算法搜尋間隔 35
4-2-4 實驗三第一階段演算法停止條件 35
4-2-5 實驗三第一階段目標效能設定 36
4-3 實驗結果與討論 37
4-3-1 規格一實驗結果 37
4-3-2 規格二實驗結果 39
4-4 鎖相迴路行為模型參數設計 41
4-4-1 實驗流程與實驗參數設定 42
4-4-2 實驗結果 43
5 第五章、結論 45
6 參考文獻 46

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