時域有限差分法(Finite-Difference Time Domain, FDTD)是一種解決電磁問題非常有效的數值方法，然而此傳統的FDTD法屬於Explicit型式的差分方程式，它必需滿足Courant-Friedrich-Levy(CFL)穩定準則，因此最大時間步階被最小網格尺寸所限制，如果模擬的結構網格尺寸的比較細時，一個小的最大時間步階將使得計算時間變長。

Alternating-Direction Implicit(ADI)法是Implicit型式的差分方程式，因為此演算法為無條件穩定，可以選擇任意的時間步階以改善計算時間。ADI-FDTD是將ADI法與FDTD法做結合，它可以克服穩定準則的限制。本論文中我們將集總元件法和等效電流源法與ADI-FDTD結合使用，用它來模擬主或被動元件，使得這個方法的應用更為廣泛。

The Finite-Difference Time Domain (FDTD) method is a very useful numerical simulation technique for solving problems related to electromagnetism. However, as the traditional FDTD method is based on an explicit finite-difference algorithm, the Courant-Friedrich-Levy(CFL) stability condition must be satisfied when this method is used. Therefore, a maximum time-step size is limited by minimum cell size in a computational domain, which means that if an object of analysis has fine scale dimensions, a small time-step size creates a significant increase in calculation time.

Alternating-Direction Implicit (ADI) method is based on an implicit finite-difference algorithm. Since this method is unconditionally stable, it can improve calculation time by choosing time-step arbitrarily. The ADI-FDTD is based on an Alternating direction implicit technique and the traditional FDTD algorithm. The new method can circumvent the stability constraint. In this thesis, we incorporate Lumped Element and Equivalent Current Source method into the ADI-FDTD. By using them to simulate active or passive device, the application of method will be more widely.

目錄.....................................................Ⅰ
圖表目錄.................................................Ⅲ
第一章 序論..............................................1
1.1 研究背景.........................................1
1.2 論文大綱.........................................2
第二章 FDTD演算法........................................3
2.1 FDTD之公式推導.................................. 3
2.2 Courant穩定準則..................................7
2.3 激發源...........................................7
2.3.1 取代源...........................................8
2.3.2 附加源...........................................8
2.3.3 阻抗性電壓源.....................................8
2.4 吸收邊界條件.....................................9
2.4.1 Mur一階吸收界...................................10
2.5 非均勻網格之時域有限差分法......................11
2.5.1 理論............................................11
第三章 ADI-FDTD演算法...................................14
3.1 介紹............................................14
3.2 Explicit與 Implicit.............................14
3.2.1 Explicit方法.....................................14
3.2.2 Implicit方法.....................................17
3.2.3 Alternating-Direction Implicit(ADI)方法..........18
3.3 ADI-FDTD公式........................................20
3.4 ADI-FDTD穩定度分析..................................25
3.5 2D TE wave ADI-FDTD的模擬............................27
3.6 3D微帶線濾波器ADI-FDTD的模擬........................29
第四辛 集總電路元件的模擬...............................32
4.1 集總元件演算法..................................32
4.1.1 阻抗性電壓源....................................33
4.1.2 模擬矩形微帶天線................................35
4.1.3 電阻............................................36
4.1.4 電容............................................37
4.1.5 電感............................................38
4.1.6 模擬低通濾波器..................................40
4.2 等效電流源法....................................41
4.3 等效電流源法的應用..............................44
4.3.1 蕭基二極體......................................44
4.3.2 小訊號微波放大器................................48
第五章 非均勻網格的應用.................................54
5.1 2D TE mode.....................................54
5.2 微帶線的模擬....................................56
第六章 結論.............................................59
參考文獻.................................................60

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