# 臺灣博碩士論文加值系統

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 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………………………………………………………………….11.1 概述…………………………………………………………………11.2 論文大綱……………………………………………………………2第二章 FDTD演算法………………………………………………………..42.1 FDTD公式推導…………………………………………………….42.2 Courant穩定準則…………………………………………………...72.3 激發源……………………………………………………………….82.4 吸收邊界條件……………………………………………………….92.4.1 Mur一階吸收邊界……………….………………………...102.4.2 Anisotropic PML 吸收邊界………………………………..11第三章 集總元件模擬……………………………………………………....153.1 集總元件演算法…………………………………………………...153.1.1 電阻…………………………………………………………173.1.2 電容…………………………………………………………173.1.3 電感…………………………………………………………183.1.4 二極體………………………………………………………183.1.5 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[1]K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equation in isotropic media,” IEEE Trans. Antennas Propagat., vol.14, No.3, pp.300-307, May 1966.[2] Athanasios Papoulis,”A New Algorithm in spectral Analysis and Band-Limited Extrapolation”,IEEE Transactions on circuits and systems, vol. CAS-22, NO.9, September 1975[3] Ramadan, A.; Omar, A.S.,”A new algorithm for the reconstruction of band-pass signles”, IEEE AP-S Int. Symp. vo1.,8-13,pp 292-295 July 2001[4] Sarkar, T.K., Pereira ,O.:Using the matrix pencil method to estimate the parameters of a sum of complex exponentials. Antennas and Propagation Magazine,IEEE, Vol.37(1995)48-55[5] Xing-Wie Zhou , Xiang-Gen Xia,”The extrapolation of High-Dimensional Band-limited functions”,IEEE Trans.Acoustics ,Speech,and Signal processing ,vol.37,No.10pp.1576-1580.October 1989[6] Richard G. Wiley ,”On an iterative technique for recovery of bandlimited signals”, Proc,of the IEEE letters,vol.66,NO.4,April 1978[7] Jiazong Zhang, Yunyi Wang, “FDTD Analysis of Active Circuits Based on the S-parameters.” in 1997 Asia Pacific Microwave Conference, 5A18-4, pp.1049-1052[8]A. Taflove, Computational Electrodynamics The Finite-Difference Time-Domain Method, 1995.[9]G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagnetic Compatibility, vol. EMC-23, pp. 377-382, Nov. 1981.[10]Z. Bi, K. Wu, C. Wu, and J. Litva, “ A dispersive boundary condition for microstrip component analysis using the FD-TD method,” IEEE Trans. Antennas and Propagat., vol. MTT-40, no. 4, pp. 774-777, Apr. 1992.[11]O. M. Ramahi, “Complementary operators: A method to annihilate artificial reflections arising from the truncation of the computational domain in the solution of patial differential equations,” IEEE Trans. Antennas and Propagat., vol. 43, pp. 697-704, Jul. 1995.[12]J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computat. Phys., vol. 114, pp. 185-200, 1994.[13]Z.S. Sacks, D.M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas and Propagat., vol. 43, pp. 1460 –1463, Dec. 1995.[14]S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas and Propagat., vol. 44, pp. 1630 -1639, Dec. 1996.[15]W. Sui , D. A. Christensen , and Carl H. Durney , “Extending the Two-Dimensional FDTD Method to Hybrid Electromagnetic System with Active and Passive Lumped Elements ,” IEEE Transactions on Microwave Theory Tech. , vol. 40 , NO. 4 , April 1992 .[16]M. P. May , A. Taflove , and J. Baron , “FD-TD Modeling of Digital Signal Propagation in 3-D Circuits with Passive and Active Loads ,” IEEE Transactions on Microwave Theory and Techniques , vol. 42 , No. 8 , August 1994 .[17]B. Toland, B.Houshmand, and T. Itoh, “Modeling of nonlinear active regions with the FDTD method,” accepted for publication in IEEE Microwave and Guided Wave Letters.[18]Vincent A. Thomas, Michael E. Jones, Melinda Piket-May, Allen Taflove, and Evans Harrigan, “The use of SPICE lumped circuits as sub-grid models for FDTD analysis.” accepted for publication in IEEE Microwave and Guided Wave Letters, Vol. 4, No. 5, May 1994.[19]Vincent A. Thomas, Michael E. Jones, Melinda Piket-May, Allen Taflove, and Evans Harrigan, “The use of SPICE lumped circuits as sub-grid models for FDTD analysis.” accepted for publication in IEEE Microwave and Guided Wave Letters, Vol. 4, No. 5, May 1994.[20]Chien-Nan Kuo , Ruey-Beei Wu , Bijan Houshmand , and Tatsuo Itoh ,”Modeling of Microwave Active Devices Using the FDTD Analysis Based on the Voltage-Source Approach ,” IEEE Microwave and Guided Wave Letters , Vol. 6 , No. 5 , pp. 199-201 , May 1996.[21]Chien-Nan Kuo , Bijan Houshmand , and Tatsuo Itoh ,”FDTD analysis of active circuits with equivalent current source approach , ” in 1995 IEEE AP-S Int. Symp. Dig. , Newport Beach , CA , pp. 1510-1513 , June 1995 .
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 1 以表面電漿效應提升氮化銦鎵/氮化鎵發光二極體之效能 2 運用光子晶體結構於太陽能電池之分析 3 使用CNDG-FDTD演算法之混合式次網格法的分析與應用 4 時域有限差分法與時域偽譜法結合之探討 5 利用光配向研製液晶偏振光柵及其光學模擬之研究 6 行動通訊基地台及手機訊號對人體頭部SAR值分佈之影響 7 以有限差分時域法分析光子晶體及色散現象 8 時域有限差分結合等效電源法之分析與應用 9 運用時域有限差分法模擬微波電路

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 1 ADI-FDTD法應用於平面型電路之研究 2 使用Prony演算法縮減時域有限差分法之計算時間 3 結合散射參數之時域有限差分法在微波電路模擬上的應用 4 應用時域有限差分法模擬微波主/被動元件 5 使用時域有限差分法分析大尺寸左手蘑菇型結構 6 平行化時域有限差分法應用於電磁相容問題的模擬與分析 7 計算具表面黏著技術去耦合電容之電腦封裝電源供應系統特性的快模速型 8 時域有限差分法之非均勻網格分析與應用 9 利用FDTD光電模擬方法研究提昇電致發光顯示元件發光效率 10 有限時域差分法電磁波源特性 11 時域有限差分法完全吸收層的最佳化 12 利用IBIS模型鏈結有限時域差分法模擬及分析訊號品質和電磁輻射 13 小型化天線的分析與模擬 14 以時域有限差分法研究高速數位電路接地彈跳效應對信號完整性及電磁輻射干擾的影響 15 應用於金屬物之RFID標籤天線設計與量測

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