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研究生:賴威成
研究生(外文):Wei-cheng Lai
論文名稱:適用於模擬具曲線結構的時域有限差分法
論文名稱(外文):The modification of Yee’s FDTD method for the simulation of curved structures
指導教授:郭志文郭志文引用關係
指導教授(外文):Chih-Wen Kuo
學位類別:碩士
校院名稱:國立中山大學
系所名稱:通訊工程研究所
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:2004
畢業學年度:92
語文別:中文
論文頁數:50
中文關鍵詞:時域有限差分曲線結構
外文關鍵詞:Conformal FDTDCurved structuresFinite-Difference Time Domain
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很多的電磁問題可以藉FDTD來獲得模擬,而在處理電磁問題時,一般情形我們皆以cartesian正交座標系為主,因為大部分的情況下,所要模擬的結構純粹是規則的矩形結構,但有時我們會有需要模擬不規則的結構,如弧形、圓形等等,對於諸如此類的問題,傳統的FDTD演算法已經無法處理,所以原本的演算法公式必須被修改,才可以滿足模擬不規則結構的需求。

除了上述的CFDTD演算法,我們更結合了非均勻網格法來做更進一步的應用,而應用的時機就是當模擬物同時具有曲線結構及矩形結構,像是同軸饋入微帶線時;像這樣的情況會是應用的好時機。
Many electromagnetic problems can be simulated by FDTD method. Mainly, we use orthogonal cartesian coordinate in normal situations when we deal with the electromagnetic problems. Because in most situations, the structures simulated are simply rectangular. But sometimes we may need to simulate the structures which are not rectangular like the sharps of arc and circle. For this kind of problems, the tranditional FDTD method no longer works, so the tranditional FDTD method must be modified to fit the simulation of irregular structures.

Besides the FDTD method we mention above, we even combine it with non-uniform grid method in more applications. And the time to apply it is when the object simulated both has the rectangular and curved structures in the same time like the microstrip fed by the coaxial cable. The situations like that would be a good time to apply it.
目錄…………………………………………………………………………………I
圖表目錄……………………………………………………………………………II
第一章 序論………………………………………………………………………1
1.1 概述…………………………………………………………………………1
1.2 論文大綱……………………………………………………………………3
第二章 適用於模擬具曲線結構之數值方法……………………………………4
2.1 基本數值方法………………………………………………………………4
2.2 Conformal FDTD……………………………………………………………8
2.3 Conformal FDTD的公式組…………………………………………………13
第三章 Conformal FDTD的實現………………………………………………15
3.1 彎曲型微帶線的色散情形………………………………………………15
3.2 180° HYBRID的實現……………………………………………………23
3.2.1 結構說明…………………………………………………………………23
3.2.2 CFDTD的模擬…………………………………………………………24
3.2.3 階梯法(Staircase)的模擬……………………………………………26
3.2.4 實作……………………………………………………………………28
3.2.5 各S參數之分析比較…………………………………………………29
第四章 非均勻網格與conformal FDTD的結合…………………………………32
4.1 非均勻網格法………………………………………………………………32
4.1.1 理論………………………………………………………………………32
4.1.2 非均勻網格公式組………………………………………………………35
4.2 非均勻網格法與conformal FDTD的結合…………………………………36
4.2.1 理論……………………………………………………………………36
4.2.2 CFDTD和非均勻網格法的公式組…………………………………38
4.3 非均勻網格法與conformal FDTD的實現………………………………39
4.3.1 Wilkinson Divider之結構圖…………………………………………39
4.3.2 CFDTD的模擬…………………………………………………………40
4.3.3 實做……………………………………………………………………42
4.3.4 以階梯法模擬……………………………………………………43
4.3.5 比較……………………………………………………………………43
4.3.6 網格縮小化的影響……………………………………………………45
第五章 結論………………………………………………………………………48
參考文獻……………………………………………………………………………49
[1] Y. Hao and C. J. Railton,“Analyzing electromagnetic structures withcurved
boundaries on Cartesian FDTD meshes,”IEEE Trans. Microwave Theory
Tech.,vol.46,pp.82-88,Jan.1998.

[2] W. Yu and R. Mittra,“A conformal FDTD algorithm for modeling perfectly conducting objects with curve-shaped surfaces and edges,”Microwave Opt. Technol.Lett.,vol.27,pp.136-138, 2000.

[3] T.I. Kosmanis and T.D. Tsiboukis,“A systematic conformal finite-difference time-domain(FDTD) technique for the simulation of arbitrarily curved interfaces between dielectrics,”IEEE Trans. Microwave Theory Tech.,vol.38,pp.645-648., Mar. 2002.

[4] Liang, X.-P.; Chang, H.-C.; Zaki, K.A.,“Modeling of cylindrical dielectric resonators in rectangular waveguides and cavity,”IEEE Trans. Microwave Theory Tech.,vol.41,pp.2174-2181,Dec.1993.

[5] N. Kaneda, B. Houshm, and T.Itoh,“FDTD analysis of dielectric resonators with curved surfaces,”IEEE Trans. Microwave Theory Tech.,vol.45,pp.1645-1649, Sept. 1997.

[6] Wenhua Yu and Raj Mittra,“Accurate modelling of planar microwave circuit using conformal FDTD algorithm,”IEE Electronics Letters.,vol.36,pp.618-619, March. 2000.

[7] Dey, S. and Mittra, R.,“A locally conformal finite difference time domain (FDTD) algorithm for modeling three-dimensional perfectly conducting objects,”Microwave and Guided Wave Letters, vol.7,p.273-275, Sept. 1997.

[8] Wenhua Tu and Raj Mittra,“A comformal Finite Difference Time Domain Technique for Modeling Curved Dielectric Surfaces,”IEEE microwave and wireless components letters. vol.11,pp.25-27. January. 2001.

[9] S. Dey and R. Mittra,“A conformal finite difference time-domain technique for modeling cylindrical dielectric resonators,”IEEE Trans. Microwave Theory Tech.,vol.47,pp.1737-1739, Sept 1999.

[10] J. Fang and J. Ren,“A locally conformed finite-difference time-domain algorithm of modeling arbitrary shape planar metal strips,”IEEE Trans Microwave Theory Tech.,vol.41,pp.830-838, May 1993.

[11] S. Dey, R. Mittra, and S. Chebolu,“A technique for implementing the FDTD algorithm on a nonorthogonal grid,”Microwave Opt. Technol. Lett.,vol.14,
pp.213-215,Mar 1997.

[12] J. Anderson, M. Okoniewski, and S. S. Stuchly,“Practical 3-D
contour/staircase treatment of metal in FDTD,”IEEE Microwave Guided Wave Lett.,vol.6,pp.146-148,Mar 1996.

[13] David M. Pozar, Microwave Engineering,second edition.,1998.
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