時域有限差分法(Finite-Difference Time-Domain，FDTD)是於1966年由K.S.Yee所提出的一種數值方法，然而FDTD法在應用上的模擬的時間較長以及延伸模擬電路的方法仍不夠完整，因此，吾人在FDTD法中加入資料外差的技巧以改進FDTD模擬微波電路的效果。

FDTD法模擬電路時所需的執行時間步階數目龐大，若是模擬的結構複雜度又高，則模擬的時間將會過長而顯得效率不彰，吾人減少FDTD法執行的步階數，將此片段的時域資料引入資料外差法重建其完整的頻域響應，由於FDTD法模擬時執行的時間步階數目減少，自然地也節省了電路模擬的時間。此外在論文中也將介紹一種結合散射參數的FDTD演算法，簡稱為散射參數法，此種演算法在進行電路模擬時省下了等效電路模型的推導，只需要將其散射參數經由向量網路分析儀或是由元件的data sheet取出，再通過傅利葉反轉換為時域的資料便可以進行FDTD法的模擬，如此解決了一般微波電路等效模型難以取得的困難，
然而先前取出的散射參數資料往往只侷限於某個頻段的範圍，吾人將此一片段頻域資料引入資料外差法重建其完整的時域響應，如此散射參數法便可以更完整的應用在電路模擬之上。

The Finite-Difference Time-Domain method ( FDTD ) is a numerical method introduced by K. S. Yee in 1966. However , it needs so much time to simulate circuits by applying the FDTD method and some extensional methods for simulating circuits are still incomplete . Therefore, the author combine the FDTD method with the data extrapolation method to improve the simulation effect.

When applying the FDTD method to simulate circuits, it needs a large number of time steps; furthermore, if the structure we simulated is complicated, the simulation time will be so much longer that the efficiency of simulation will be bad as well. The author decrease the number of time steps of the FDTD method, and then extrapolate the time-domain data to reconstruct the complete frequency response, therefore, we can save the simulation time as well because the number of the time steps of the FDTD method decreased.

Furthermore, in the thesis, we also introduce a new FDTD method combined with the S-parameter Matrix, called “S-parameter Matrix method”. People can simulate circuits without deriving the equivalent circuit by applying the S-parameter Matrix method. One only have to obtain the S-parameter Matrix by measurement, data sheet, calculation, etc, and then we translate it to time domain data by the IFT technique to apply the FDTD calculation , this way, we avoid the difficulty of deriving the equivalent circuit of general microwave circuits. However, the S-parameter data we can obtain are often limited in a finite bandwidth, we make it to be extrapolated to obtain the complete time-domain response, and this way, the S-parameter Matrix method can by apply to simulate circuits.

目 錄

目錄…………………………………………………………………………….I
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………………………………………………………..4
2.1 FDTD公式推導…………………………………………………….4
2.2 Courant穩定準則…………………………………………………...7
2.3 激發源……………………………………………………………….8
2.4 吸收邊界條件……………………………………………………….9
2.4.1 Mur一階吸收邊界……………….………………………...10
2.4.2 Anisotropic PML 吸收邊界………………………………..11
第三章 集總元件模擬……………………………………………………....15
3.1 集總元件演算法…………………………………………………...15
3.1.1 電阻…………………………………………………………17
3.1.2 電容…………………………………………………………17
3.1.3 電感…………………………………………………………18
3.1.4 二極體………………………………………………………18
3.1.5 阻抗性電壓源………………………………………………19
3.2 等效電源法………………………………………………………...21
3.2.1 等效電流源法………………………………………………21
3.2.2 等效電壓源法………………………………………………24
3.2.3 解多重根之牛頓法推導……………………………………27
3.3 模擬驗證…………………………………………………………...34
第四章 外差法的探討………………………………………………………36
4.1.1 時域響應的重建……………………………………………37
4.1.2 時域信號重建的模擬驗證…………………………………41
4.2.1 頻域響應的重建……………………………………………47
4.2.2 頻域信號重建的模擬驗證…………………………………48
第五章 外差法與FDTD之結合…………………………………………....54
5.1.1 散射參數法…………………………………………………54
5.1.2 模擬與比較…………………………………………………57
5.2 頻域重建的資料外差法與FDTD結合之模擬………………...…60
5.2.1 低雜訊放大器的模擬比較…………………………………60
5.2.2 模擬小訊號微波放大器……………………………………62
5.3 觀察與討論…………………………………………………………65
第六章 結論………………………………………………………………….66
參考文獻…………………………………………………………….67

參考文獻

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