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研究生:李志信
研究生(外文):Chih-Hsin Lee
論文名稱:時域有限差分法於微波電路分析之應用
論文名稱(外文):The Application of Finite Difference Time Domain Method to Microwave Circuit Analysis
指導教授:蔡智明蔡智明引用關係
指導教授(外文):Chih-Ming Tsai
學位類別:碩士
校院名稱:國立成功大學
系所名稱:電機工程學系碩博士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:103
中文關鍵詞:普羅尼法品質因數入射波與反射波分離時域有限差分同軸完美匹配層頻率相關時域有限差分介質損耗輪廓路徑法邊界銜接場源激發微帶線電路
外文關鍵詞:Seperation of the Incident Wave and the ReflectiProny's MethodQuality FactorMicrostrip CircuitContour Path MethodSource ExcitationBoundary ConnectionDielectric LossesFrequency-Dependent Finite Difference Time DomaiFinite Difference Time DomainUniaxial Perfect Match Layer
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  近年來由於電腦計算能力越來越強,使得採用時域有限差分法來分析微波電路的相關研究越來越多。在計算過程中,需要吸收邊界條件將無窮空間截斷成有限計算範圍,並將散射的電磁波吸收,其中以完美匹配層的效果最為顯著。在時域模擬介電質損耗並不容易,因為常用來描述介電質損耗的形式為複數常數。不過,透過適當的曲線逼近技巧,在某頻帶範圍內,可用時域有限差分法模擬出相同的效果。

  本論文是由基本的理論開始,介紹時域有限差分法的演算結構,使用同軸完美匹配層做為吸收邊界條件,並結合多階Debye介質與導電率去近似複數常數的介電係數,配合傳輸線原理解離出入射波與反射波,來分析具有介電質耗損的微波電路。此外,利用Prony’s Method來計算諧振電路的品質因素,以及外差時域資料,減少計算時間,並得到相同結果。
Finite difference time domain (FDTD) method is an effective method that provides accurate analysis of microwave circuits. In the process of numerical computation of FDTD, absorbing boundary condition (ABC) must be introduced to truncate the infinite space and prevent wave from reflecting at the outer boundary. Among various ABC, perfectly matched layer, a highly effective absorber material, works well.

Lossy dielectrics are usually described by a constant complex permittivity which can not be directly used in transient FDTD calculations. However, frequency- dependent FDTD can accommodate a better approximation to a constant complex permittivity over a band of frequencies.

In this thesis, the research is based on the usage of FDTD with uniaxial perfectly matched layer in the analysis of microwave circuits. In the frequency-dependent FDTD, multi-order Debye material associated with conductivity is used to approximate a constant complex permittivity. A method to separate the incident wave and the reflective wave without extra input port simulation is adapted to compute scattering parameters of microwave circuits. Besides, the Prony’s method is combined with FDTD to calculate the quality factor of resonant circuits, and to reduce the computation time by extrapolating the transient data without losing the accuracy.
第一章 序論 1
第二章 時域有限差分法. 3
2.1 有限差分架構與原理 3
2.2 馬克斯威爾方程式的時域有限差分法演算結構 6
2.3 網格色散現象與穩定性條件 12
第三章 吸收邊界條件. 13
3.1 吸收邊界條件的演進. 13
3.2 異方向性完美吸收層 18
3.3 同軸完美匹配層的差分方程式推導 24
3.4 完美匹配層用於離散空間的修正 29
第四章 介電質耗損與介質接面處理. 32
4.1 介電係數為頻率函數的介質 32
4.1.1 引用導電率來減少對記憶體使用量 34
4.1.2 與同軸完美吸收層的有限差分演算法整合 37
4.2 介質接面處裡 38
4.2.1 輪廓路徑法 39
4.2.2 介質接面的時域有限差分公式 40
第五章 場源激發. 42
5.1 激發源截面的空間分佈 42
5.2 激發源的時間變化 43
5.3 激發源的演算程序 44
第六章 微帶線電路特性的計算 47
6.1 傅立葉轉換的注意事項 47
6.2 微帶線特性的計算 48
6.2.1 微帶線的電壓與電流 48
6.2.2 等效介電常數 49
6.2.3 微帶線的特性阻抗 49
6.2.4 50Ω微帶線的模擬 50
6.3 S參數 54
6.3.1 入射波與反射波區分方式 54
6.3.2 電路模擬與比較 58
6.4 介電質損耗的電路模擬與量測結果比較 72
第七章 諧振電路的品質因數計算與時域資料外插. 75
7.1 品質因數 75
7.2 品質因數的數值計算模式 77
7.3 使用Prony's Method計算品質因數 80
7.3.1 Prony's Method 80
7.3.2 計算模式 81
7.3.3 程式模擬與比較 83
7.4 使用Prony’s Method外插時域資料 90
7.4.1 外插時域資料的實驗結果 90
第八章 結論與展望 96
參考文獻 98
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