# 臺灣博碩士論文加值系統

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 The Finite-Difference Time Domain (FDTD) method is a very useful numerical simulation technique for solving problems related to electromagnetism. However, as the traditional FDTD method is based on an explicit finite-difference algorithm, the Courant-Friedrich-Levy(CFL) stability condition must be satisfied when this method is used. Therefore, a maximum time-step size is limited by minimum cell size in a computational domain, which means that if an object of analysis has fine scale dimensions, a small time-step size creates a significant increase in calculation time.Alternating-Direction Implicit (ADI) method is based on an implicit finite-difference algorithm. Since this method is unconditionally stable, it can improve calculation time by choosing time-step arbitrarily. The ADI-FDTD is based on an Alternating direction implicit technique and the traditional FDTD algorithm. The new method can circumvent the stability constraint. In this thesis, we incorporate Lumped Element and Equivalent Current Source method into the ADI-FDTD. By using them to simulate active or passive device, the application of method will be more widely.
 目錄.....................................................Ⅰ圖表目錄.................................................Ⅲ第一章 序論..............................................11.1 研究背景.........................................11.2 論文大綱.........................................2第二章 FDTD演算法........................................32.1 FDTD之公式推導.................................. 32.2 Courant穩定準則..................................72.3 激發源...........................................72.3.1 取代源...........................................82.3.2 附加源...........................................82.3.3 阻抗性電壓源.....................................82.4 吸收邊界條件.....................................92.4.1 Mur一階吸收界...................................102.5 非均勻網格之時域有限差分法......................112.5.1 理論............................................11第三章 ADI-FDTD演算法...................................143.1 介紹............................................143.2 Explicit與 Implicit.............................14 3.2.1 Explicit方法.....................................14 3.2.2 Implicit方法.....................................17 3.2.3 Alternating-Direction Implicit(ADI)方法..........183.3 ADI-FDTD公式........................................203.4 ADI-FDTD穩定度分析..................................253.5 2D TE wave ADI-FDTD的模擬............................273.6 3D微帶線濾波器ADI-FDTD的模擬........................29第四辛 集總電路元件的模擬...............................324.1 集總元件演算法..................................324.1.1 阻抗性電壓源....................................334.1.2 模擬矩形微帶天線................................354.1.3 電阻............................................364.1.4 電容............................................374.1.5 電感............................................384.1.6 模擬低通濾波器..................................404.2 等效電流源法....................................414.3 等效電流源法的應用..............................444.3.1 蕭基二極體......................................444.3.2 小訊號微波放大器................................48第五章 非均勻網格的應用.................................545.1 2D TE mode.....................................545.2 微帶線的模擬....................................56第六章 結論.............................................59參考文獻.................................................60
 [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] A. Taflove, Computational Electrodynamics The Finite-Difference Time-Domain Method, 1995.[3] T. Namiki, “A new FDTD algorithm based on alternating direction implicit method,” IEEE Trans. Microwave Theory Tech., vol. 47, pp. 2003–2007,Oct.1999.[4] T. Namiki, “3-D ADI-FDTD Method-Unconditionally Stable Time-Domain Algor-ithm for Solving Full Vector Maxwell’s Equations,” IEEE Trans. Microwave Theory Tech., vol. 48, NO.10, pp.1743-1748,Oct.2000.[5] Fenghua Zeng , Zhizhang Chen and Jiazong Zhang , “Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method,” IEEE Trans. Microwave Theory Tech., vol. 48, pp. 1550–1558,Sep.2000.[6] 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 ,pp.1514-1523, August 1994 .[7] 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 , June 1995 , pp. 1510-1513 .[8] D. M. Sheen , S. M. Ali , M. D. Abouzahra and J. A. Kong ,“Application of the three-dimensional finite-difference time-domain method to the analysis of plannar microstrip circuits ,” IEEE Trans. Microwave Theory Tech. , vol. 38 , pp. 849-857 , July 1990.[9] An Ping Zhao, Raisanen, A.V., Cvetkovic, S.R.,” A fast and efficient FDTD algorithm for the analysis of planar microstrip discontinuities by using a simple source excitation scheme,” Microwave and Guided Wave Letters, IEEE [see also IEEE Microwave and Wireless Components Letters] , Volume: 5 , Issue: 10 , Oct. 1995 ,Pages:341 – 343[10] G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations,” Electromagnetic Compatibility, IEEE Transactions on Volume: 23 ,pp. 377 –382,Nov 1981.[11] R. Holland, “ Implicit three-dimensional finite difference of Maxwell’s equations,” IEEE Trans. Nucl. Sci., vol. NS-31, pp. 1322-1326, 1984.[12] M. Necati Őzişik, Finite Difference Methods in Heat Transfer, 1994.[13] An Ping Zhao, “Two special notes on the implementation of the unconditionally stable adi-fdtd method,” Microwave and Optical Technology Letters,vol.33,No.4,May 20 2002.[14] An Ping Zhao,” Analysis of the numerical dispersion of the 2D alternating-direction implicit FDTD method,” Microwave Theory and Techniques, IEEE Transactions on , Volume: 50 , Issue: 4 , April 2002.[15] Tae-Woo Lee, Hagness, S.C. , “Wave source conditions for the unconditionally stable ADI-FDTD method,” Antennas and Propagation Society, 2001 IEEE International Sym , Volume: 4 , pp. 142 -145 ,8-13 July 2001.[16] Jeongnam Cheon, Sooji Uh, Hyunsik Park, Hyeongdong Kim,” Analysis of the power plane resonance using the alternating-direction implicit (ADI) FDTD method,” Antennas and Propagation Society International Symposium, 2002. IEEE , Volume: 3 , 16-21 June 2002 Pages:647 – 650.[17] V. S Reddy, R. Garg, “An improved extended FDTD formulation for active microwave circuits,” Microwave Theory and Techniques, IEEE Transactions on , Volume: 47 Issue: 9 , Sep 1999.[18] 吳柏樟 , 應用時域有限差分法模擬主/被動元件 , 中山大學碩士論文 ,2003.[19] T.Namiki, and K.Ito,“Investigation of numerical errors of the two dimensional ADI–FDTD method,” Microwave Theory and Techniques, IEEE Transactions on , Volume: 48 , Issue: 11 ,pp. 1950 - 1956, Nov. 2000
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 1 應用時域有限差分法模擬微波主/被動元件

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 1 外差法與時域有限差分法的結合 2 應用時域有限差分法模擬微波主/被動元件 3 使用時域有限差分法分析大尺寸左手蘑菇型結構 4 使用Prony演算法縮減時域有限差分法之計算時間 5 利用有限時域差分法針對一維光子晶體超稜鏡效應在多工分波元件模擬量測方法之建立與分析 6 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 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 應用保形時域有限差分法探討球形體與圓柱之散射 10 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 11 使用時域有限差分法模擬與分析微帶線饋入的介質共振器天線 12 一種能快速計算封裝電源供應系統的電磁干擾之二維時域有限差分法 13 光學奈米電路之FDTD模擬 14 協助時域有限差分法之圖形化使用者介面 15 使用CNDG-FDTD演算法之混合式次網格法的分析與應用

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