FDTD是將馬克思威方程式之微分型式利用二階中央差分法將之離散化，並配合空間網格與時間網格之電磁場配置，應用於分析時域上之各種電磁問題的一種數值方法。本論文是將FDTD的方法延伸到包含集總元件(如電阻、電感、電容)，以及非線性元件(如二極體、電晶體)，使得電路元件與電磁場能夠結合在一起，這即是所謂的LE-FDTD(Lumped-Element FDTD)演算法。首先，將先作二維(2D)的理論推導與結構的模擬說明，接著再將此種方法擴展到三維(3D)空間作全波分析，以便能符合實際的電路應用。

FDTD is a numerical method that uses the second-order central-difference method to discrete the Maxwell’s equations in differential form, and positioning electromagnetic field in space grids and time grids. It is applied to analyze many electromagnetic problems in time domain. In this report the FDTD method is extended to include lumped-elements (as resistor, inductor, capacity),and nonlinear elements(as diode, transistor) to combine the circuit elements and electromagnetic fields, it’s so called LE-FDTD algorithm. The first, we will introduce the theory derivations and simulate some circuit structures in 2D, and then in order to simulate the real circuits, we will extend this algorithm in 3D to make full-wave analysis.

論文提要.................................................................I
目錄....................................................................III
圖表目錄.................................................................V
第一章 序論............................................................1
1.1 研究背景..........................................................1
1.2 研究目的..........................................................1
1.3 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............................................................8
2.3.1 取代源............................................................8
2.3.2 附加源(穿透源) ...................................................9
2.3.3 阻抗性電壓源......................................................9
2.4 吸收邊界條件......................................................9
2.4.1 Mur一階吸收邊界..............................................11
2.4.2 完美匹配層吸收邊界...........................................12
2.5 導體與介電係數...................................................13
2.6 散射參數.........................................................14
第三章 集總電路元件的模擬.............................................15
3.1 二維LE-FDTD演算法................................................15
3.1.1 被動元件的模擬................................................18
3.1.2 電壓源及電流源的模擬..........................................18
3.1.3 主動與非線性元件的模擬........................................19
3.1.4 電路結構的模擬................................................21
3.2 三維LE-FDTD演算法................................................24
3.2.1 電阻.........................................................25
3.2.2 阻抗性電壓源.................................................26
3.2.3 電感.........................................................26
3.2.4 電容.........................................................27
3.2.5 二極體.......................................................28
3.2.6 雙載子接面電晶體.............................................31
3.3 等效電壓源法.....................................................34
3.4 等效電流源法.....................................................37
第四章 微波電路之模擬與應用...........................................39
4.1 非平衡式蕭特基二極體混頻器.......................................39
4.1.1 基本原理......................................................39
4.1.2 電路應用.........................................................40
4.2 主動迴轉器天線....................................................43
4.2.1 迴轉器操作原理............................................44
4.1.2 電路應用.........................................................47
第五章 LE-FDTD與ADS之比較.............................................51
5.1 低通濾波器的模擬.................................................51
5.2 模擬結果.........................................................52
第六章 結論...........................................................54
附錄A...................................................................55
附錄B...................................................................59
附錄C...................................................................61
附錄D...................................................................63
附錄E...................................................................65
參考文獻................................................................68

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