在由於高頻電路的結構通常都相當的小，依據CFL穩定準則的限制，傳統時域有限差分法(FDTD)的時間增量也必須非常小，在經過長時間之計算後方能達成穩定狀態，導致模擬時間大幅上揚。在本論文中，預計將實踐適用於高頻電路的ADI-FDTD演算法，推導出配合ADI-FDTD法的集總元件方程式；更進一步地研究如何將主動元件的模擬方式導入ADI-FDTD演算法當中，希望能將ADI-FDTD法應用在電路模擬的理論建構完整；使得時域有限差分法能得以突破CFL穩定準則的限制，更能適用於高頻電路的分析。

When the conventional FDTD method is applied to the high-frequency planar circuits, the time step must be very small due to the CFL stability criterion since the structural details of the circuits are usually very small. These results in a prohibitively high computation time since the simulation takes a long time to stabilize. This thesis will focus on implementing an ADI-FDTD algorithm suitable for the analysis and simulation of large-scale high-frequency planar circuits. Realization of the lumped elements befitting the ADI-FDTD algorithm will be developed. Furthermore, active devices will then be incorporated into the algorithm once the models for lumped elements are built up.

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 公式.................................................................... 3
2.2. Courant 穩定準則........................................................ 6
2.3. 激發源............................................................................ 6
2.3.1. 取代源..........................................................................7
2.3.2. 附加源..........................................................................7
2.3.3. 阻抗性電壓源..............................................................7
2.4. 吸收邊界條件................................................................ 7
2.4.1. Mur 一階吸收邊界......................................................8
第三章 ADI-FDTD 演算法..................................................10
3.1. 緣由與目的.................................................................. 10
3.2. Explicit 型式與Implicit 型式.......................................11
3.2.1. Explicit 型式..............................................................11
3.2.2. Implicit 型式.............................................................15
3.2.3. Alternating-Direction Implicit (ADI) 方法.............16
3.3. ADI-FDTD 公式.......................................................... 18
3.4. ADI-FDTD 演算法的穩定度分析.............................. 23
3.5. 2D TE mode 的自由空間模擬.................................. 27
3.6. ADI-FDTD 演算法的集總元件公式.......................... 28
3.6.1. 電阻...........................................................................30
3.6.2. 阻抗性電壓源...........................................................31
3.6.3. 電容...........................................................................33
3.6.4. 電感...........................................................................34
3.6.5. 低通濾波器的模擬...................................................35
3.7. 等效電流源法.............................................................. 36
第四章 散射參數法與ADI-FDTD的結合...........................40
4.1. 散射參數法.................................................................. 40
4.2. 在ADI-FDTD 法裡描述高頻元件.............................. 45
4.3. ADI-FDTD 法的數值色散分析.................................. 45
4.4. 低雜訊放大器(LNA)的模擬....................................... 46
第五章 結論.........................................................................50
參考文獻..............................................................................51

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