時域有限差分法 ( Finite-Difference Time-Domain,，FDTD )，是將馬克斯威爾方程式 ( Maxwell’s Equation )以二階中央差分法離散化，配合空間網格上之電磁場配置，在一個有限體積之計算空間內，以電生磁磁生電的跳步(leapfrog)方式，一步步計算出空間中電磁場的分佈情形。不同於頻域分析的方法(如Finite Element Method )，在頻域計算中需一個一個頻率點去分析，故當欲觀察的頻率極其寬頻時，所花費的時間將非常長；而使用時域的分析法，其好處為分析出來的數據只要透過傅利葉轉換即可得到完整的頻域響應，而不用再重新計算。

由於現今的套裝軟體，並無法將場論與電路模擬做一兩者兼具的結合，故微波電路的模擬與實做，常會因考量不夠週全而產生誤差。而時域有限差分法除了也是全波分析的技巧，經過延伸，如連結到SPICE或加入S參數等，更可在模擬結構中包含集總元件、非線性元件或主動元件等。故本論文的重點是在FDTD下發展模擬微波電路的方法，使得場論與電路模擬能有一完整的結合；並且在最後使用等效電源法分析主動天線，及使用散射參數法分析一低雜訊放大器，驗證在FDTD下模擬微波電路的可行性。

The finite-Difference Time Domain method (FDTD) is to derive the discrete form of the Maxwell’s equations by second-order central difference with the electromagnetic distribution of the Yee space lattice, and computes the value of the electric field and magnetic field in the simulation space by using leapfrog for time derivatives. This method is also different with the frequency domain method which needs to analyze its value individually (ex. Finite Element method). The frequency domain method needs to take a long time for analyzing the response on each spectrum point when the bandwidth is very wide. The advantage of time domain analysis is to obtain the complete frequency response from the simulation value through Fourier Transform method.

It’s impossible to combine the electromagnetic analysis with the lumped circuit simulation in current simulation CAD. Thereby the performance of the simulation result and the practical implementation always occurs error because of the lake of the consideration. The FDTD method is the full-wave algorithm which can also simulate the lump element, nonlinear element or active element in simulation space by linking to SPICE or S-parameter. The purpose of this thesis is to develop the method for simulating microwave circuit, and to verify the credibility between the equivalent source method and the S-parameter method in FDTD by the simulation of active antenna and low-noise amplifier.

誌謝.................................................................................................................................i
中文謫要........................................................................................................................ii
英文謫要.......................................................................................................................iii
目錄....………………………………………………………………………………...iv
圖表目錄……………………………………………………………………………...vi
第一章 序論…………………………………………………………………………1
1.1 概述…………………………………………………………………………1
1.2 論文大綱……………………………………………………………………2
第二章 FDTD演算法……………………………………………………………….3
2.1 FDTD公式推導………………………………………………………….…3
2.2 Courant穩定準則…………………. ………………………………………6
2.3 吸收邊界條件……………………. …………………………………….….6
2.3.1 Mur一階吸收邊界………………………………………………….7
2.3.2 Anisotropic PML吸收邊界…………………….…………………..8
2.4 全場/散射場公式………………………………………………………….11
2.4.1 全場/散射場公式推導…………………………...………………..11
2.4.2 模擬驗證……………………………………………………….….13
2.5 近遠場轉換………………………………..………………………………16
2.5.1 克希荷夫表面積分公式…………………..………………………16
2.5.2 2/3波長Dipole Antenna的模擬……………….…………………19
2.5.3 Patch Antenna的模擬………………………………….………….20
第三章 集總元件模擬………………………………………………..……………23
3.1 集總元件演算法………………………………………………….……….23
3.1.1 電阻………………………………………………………………..24
3.1.2 電容………………………………………………………………..24
3.1.3 電感…………………………………………….………………….25
3.1.4 阻抗性電壓源……………………………………………………..25
3.2 等效電源法………………………………………………………………..26
3.2.1 等效電流源法……………………………….…………………….26
3.2.2 等效電壓源法……………………………………………………..28
3.2.3 等效電源法的資料流程……………………………………..……30
3.2.4 模擬LC串聯電路…………………………………………………31
3.3 散射參數法………………………………………………………………..32
3.3.1 理論推導……………………………………………………..……32
3.3.2 時域導納矩陣的計算………………………………..……………34
3.3.3 模擬與比較………………………………………………………..35
3.3.4 導納矩陣之收斂探討……………………………………………..37
3.4 優缺點比較………………………………………………….…………….39
3.5 應用模擬低雜訊放大器…………………………………………………..40
第四章 主動天線分析………………………………………………………..……44
4.1 概述…………………………………………………………………..……44
4.2 天線分析…………………………………………………..………………44
第五章 模擬接收模組……………………………………………………………..49
5.1 概述………………………………………………………………………..49
5.2 元件探討…………………………………………………………………..49
5.2.1 接收天線…………………………………………………………..50
5.2.2 低雜訊放大器……………………………………………………..53
5.3 接收模擬…………………………………………………………………..55
5.3.1 x方向極化平面………………………………………………..….55
5.3.2 z方向極化平面……………………………………………………58
第六章 結論………………………………………………………………………..61
附錄A. 主動天線結構圖…………………………………………………………..62
參考文獻……………………………………………………………………………..63

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