Responsive image
博碩士論文 etd-0723101-162336 詳細資訊
Title page for etd-0723101-162336
論文名稱
Title
高階時域有限差分法及分析天線場型的應用
Higher-Order FDTD Method and Application to Antenna Pattern Analysis
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
83
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2001-07-12
繳交日期
Date of Submission
2001-07-23
關鍵字
Keywords
天線場型、數值色散、高階時域有限差分法
Numerical Dispersion, Higher-Order FDTD, Antenna Pattern
統計
Statistics
本論文已被瀏覽 5658 次,被下載 73
The thesis/dissertation has been browsed 5658 times, has been downloaded 73 times.
中文摘要
使用二階中央差分近似於微分算子所產生的數值色散現象是造成Finite Difference Time Domain Method (時域有限差分法,FDTD)的主要誤差來源之一,由於數值色散條件的限制會使得空間網格的切割必須要小於λ/10,對於某些較大型的模擬結構常會因為記憶體空間的不足而無法計算,解決的方法之一就是提高中央差分的階數,便可以有效的抑止數值色散的現象。本論文主要是應用四階中央差分法於完美導體邊界上的遮蔽處理,並結合四階的APML吸收層用於天線結構的分析上。藉由使用四階的中央差分法達到放大空間網格並降低記憶體的使用量,對於某些操作於較高頻段且體積較小的天線,由於其遠場的距離較短,利用放大空間網格的方式使得遠場可以直接計算求得。在論文中以數個天線結構比較四階FDTD與透過近遠場轉換的方式計算遠場的結果,並針對相關的特性加以分析。
Abstract
Numerical dispersion resulting from using the second-order central-difference operation to approximate the differential operation is the main error source of the FDTD method. The effect of numerical dispersion can be minimized if the spatial grid size is small thanλ/10. It is difficultly to analyze the modeling of electrically large structures since a huge amount of computer memory will be needed if using a very fine grid to discretize the structure. Using higher-order FDTD is the effective alternative to reduce the effect of numerical dispersion. In this paper will discuss the handling of the discontinuous PEC boundary condition in four-order FDTD and its applications to antenna pattern analysis. Using the fourth-order FDTD can enlarge the spatial grid size and reduce the requirement of computer’s memory. The far field range of small size antenna operating at higher frequency is shorter enough to directly derive the far field pattern by enlarging the spatial size of fourth-order FDTD. It will compare the far field pattern derived by four-order FDTD with near-to-far field transformation and analyze their characteristic individually.
目次 Table of Contents
誌謝 I
論文提要 II
目錄 Ⅳ
圖表目錄 Ⅵ
第一章 緒論 1
1.1 概述 1
1.2 論文大綱 3
第二章 FDTD基本理論 5
2.1 YEE的FDTD演算法 5
2.2 穩定準則 8
2.3 非均勻正交網格 9
2.4 激發源的處理 11
2.4.1 取代源 12
2.4.2 附加源 13
2.4.3 阻抗性電壓源 14
2.5 程式的處理 15
第三章 吸收邊界條件 18
3.1 Mur吸收邊界 18
3.2 Anisotropic PML吸收邊界 19
3.2.1 APML基本理論 19
3.2.2 APML的離散化 23
3.2.3 APML角落區域處理 25
3.2.4 APML與Berenger’s PML關係 26
3.2.5 PML相關參數設計 28
3.2.6 APML吸收效果比較 29
3.2.7 APML於程式上的實作 32
第四章 FDTD降低色散處理 34
4.1 數值波傳播特性 34
4.2 NJL演算法 39
4.3 高階FDTD 41
4.3.1 四階FDTD原理 41
4.3.2 S24 FDTD分析 42
4.3.3 NJL、S22與S24比較 44
4.4 高階FDTD的特殊處理 48
4.4.1 PEC的特殊處理 48
4.4.2 PML截斷區間的特殊處理 51
第五章 近遠場轉換 52
5.1 概述 52
5.2 克希荷夫表面積分式 52
5.3 基本電偶極天線的模擬 54
第六章 天線特性分析 56
6.1 微帶天線分析 56
6.1.1 吸收邊界比較 58
6.1.2 粗細網格比較 59
6.1.3 遠場場型模擬 60
6.1.4 同軸線饋入 63
6.2 平面型倒F天線(PIFA)分析 65
6.3 CBCPW饋入平面型倒F天線 69
6.3.1 CBCPW激發源的處理 69
6.3.2 散射參數的處理 70
6.3.3 天線的模擬 71
第七章 結論 76
參考文獻 77
附錄A Anisotropic PML於角落處差分方程式 81

圖表目錄
圖2-1 FDTD單位網格空間電磁場配置圖 6
圖2-2 FDTD電磁場計算時間配置圖 7
圖2-3 非均勻網格電磁場空間配置圖 10
圖2-4 微帶線邊緣激發電壓源 12
圖2-5 穿透源放置位子表示圖 13
圖3-1 平面波入射示意圖 20
圖3-2 微帶線橫截面表示圖 29
表3-1 微帶線結構相關參數 29
圖3-3 APML與Mur吸收邊界吸收效果比較 30
圖3-4 改變R(0)對吸收效果的影響 31
圖3-5 改變m對吸收效果的影響 31
圖3-6 改變厚度對吸收效果的影響 32
圖4-1 數值波速與空間網格解析度的關係 36
圖4-2 以脈衝電源激發的粗格模擬 36
表4-1 各演算法所需的浮點運算與最小穩定因子 37
圖4-3a 數值誤差對傳播角度 38
圖4-3b 最大誤差對空間解析 38
圖4-4a 相速誤差對傳播角度以及空間網格大小的關係 39
圖4-4b 相速誤差對傳播角度以及 大小的關係 39
圖4-5a 二階中央差分示意圖 41
圖4-5b 四階中央差分示意圖 41
圖4-6 正規化相速度與傳播角度的關係 44
圖4-7 自由空間中平面波入射 44
圖4-8 、 =0.1m 及T=1ns時的時域響應 45
表4-2 NJL、S22、S24的比較 46
圖4-9 、 =0.05m及T=0.5ns時的時域響應 46
圖4-10 、 =0.1m及T=0.5ns時的時域響應 47
圖4-11a S24演算法更新電場分量空間配置圖 48
圖4-11b S24演算法更新磁場分量空間配置圖 48
圖4-12 PEC平板由點源激發的散色問題 49
圖4-13a 不對金屬板做遮蔽處理(高斯脈衝激發) 50
圖4-13b 對金屬板做遮蔽處理(高斯脈衝激發) 50
圖4-14a 不對金屬板做遮蔽處理(高斯脈衝+正弦函數激發) 50
圖4-14b 對金屬板做遮蔽處理(高斯脈衝+正弦函數激發) 50
圖4-15 高階PML截斷處理 51
圖5-1 近場與遠場時間步階示意圖 54
圖5-2 基本電偶極示意圖 54
圖5-3a Dipole天線E-Plane場型 55
圖5-3b Dipole天線H-Plane場型 55
圖6-1 微帶線饋入矩型patch天線 56
表6-1 微帶線饋入矩型patch天線參數 56
圖6-2 矩型微帶天線z方向電場分佈圖 57
圖6-3 Mur、APML與量測值的回返損耗比較 58
表6-2 兩種空間網格切割 59
圖6-4 粗細格的回返損耗比較 59
圖6-5 三種遠場的標準與天線電性尺寸( )的關係 60
圖6-6a 矩型微帶天線E-Plane場型 61
圖6-6b 矩型微帶天線H-Plane場型 61
表6-3 三種空間網格分割 62
圖6-7a 改變空間解析對E-Plane的場型 62
圖6-7b 改變空間解析對H-Plane的場型 62
圖6-8 同軸饋入微帶天線 63
圖6-9 同軸饋入微帶天線的反射係數 63
圖6-10a 同軸線饋入矩型微帶天線E-Plane場型 64
圖6-10b 同軸線饋入矩型微帶天線H-Plane場型 64
圖6-11 同軸饋入PIFA的結構圖 65
表6-4 同軸饋入PIFA相關結構參數 65
圖6-12 同軸饋入PIFA的回返損耗 66
圖6-13 同軸饋入PIFA的輸入阻抗 67
圖6-14 同軸饋入PIFA的史密斯圖 67
圖6-15a 同軸饋入PIFA的天線E-Plane場型 68
圖6-15b 同軸饋入PIFA的天線H-Plane場型 68
圖6-16 Ericsson藍芽模組 69
圖6-17 CBCPW結構電場分佈圖 69
圖6-18 CBCPW饋入PIFA結構圖(俯視圖) 71
表6-5 CBCPW饋入PIFA相關結構參數 72
圖6-19 不使用貫孔接地的S參數 72
圖6-20 使用貫孔接地的S參數 73
圖6-21 CBCPW饋入PIFA的輸入阻抗 73
圖6-22 CBCPW饋入PIFA的史密斯圖 74
圖6-23a CBCPW饋入PIFA的天線E-Plane場型 74
圖6-23b CBCPW饋入PIFA的天線H-Plane場型 74
參考文獻 References
[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] 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.
[4] 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.
[5] 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.
[6] J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computat. Phys., vol. 114, pp. 185-200, 1994.
[7] 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.
[8] J. B. Schneider, “Faster-Than-Light Propagation,” IEEE Microwave and Guided Wave Lett., vol.9, No.2, pp.54-56, Feb. 1999.
[9] J. B. Schneider and R. J. Kruhlak, “Inhomogeneous Waves and Faster-Than-Light Propagation in the Yee FDTD Grid,” Antennas and Propagation Society International Symposium 1999, vol.1, pp.184-187, July 1999.
[10] A. C. Cangellaris and R. Lee, “On the accuracy of numerical wave simulations on finite methods,” J. Electromagn. Waves Applicat., vol. 6, no. 12, pp. 1635-1653, 1992.
[11] K. L. Shlager, J. G.Maloney, S. L. Pay, and A. F. Peterson, “Relative accuracy of several finite-difference time-domain methods in two and three dimensions,” IEEE Trans. Antennas Propagat., vol. 41, pp.1732-1737, Dec. 1993.
[12] J. Fang, “Time-domain finite difference computations for Maxwell’s equations,” Ph.D. dissertation, EECS Dept., Univ. California, Berkeley, 1989.
[13] T. Deveze, L. Beaulieu, and W. Tabbara, “A fourth order scheme for the FDTD algorithm applied to Maxwell’s equations,” in IEEE APS Int. Symp. Proc., Chicago, IL, July 1992, pp. 346-349.
[14] T. Deveze, L. Beaulieu, and W. Tabbara, “An absorbing boundary condition for the fourth order FDTD scheme,” in IEEE APS Int. Symp. Proc., Chicago, IL, July 1992, pp. 342-345.
[15] P. G. Petropoulos, “Phase error control for FD-TD methods of second- and fourth-order accuracy,” IEEE Trans. Antennas Propagat., vol.42, pp.859-862, June 1994.
[16] C. W. Manry, Jr., S. L. Broschat, and J. B. Schneider, “Higher order FDTD methods for large problems,” ACES J., vol. 10, pp. 17-29, July 1995.
[17] M. F. Hadi and M. Piket-May, “A modified FDTD (2,4) scheme for modeling electrically large structures with high-phase accuracy,” IEEE Trans. Antennas Propagat., vol.45, pp. 254-264, Feb. 1997.
[18] K. Lang, Y. Liu and W. Lin, “A higher order (2,4) scheme for reducing dispersion in FDTD algorithm,” IEEE Trans. Electromag. Compat., vol. 41, pp. 160-165, May 1999.
[19] M. Krumpholz and L. P. B. Hatehi, “MRTD: New Time-Domain Schemes Based on Multiresolution Analysis,” IEEE Trans. MTT, vol. 44, pp. 555-571, April 1996.
[20] J. B. Cole, “A High-Accuracy Realization of the Yee Algorithm Using Non-Standard Finite Differences,” IEEE Trans. MTT, vol. 45, pp. 991-996, June 1997.
[21] E. A. Forgy, “A Time-Domain Method for Computational Electromagnetics with Isotropic Numerical Dispersion on an Overlapped Lattice,” Master’s thesis, University of Illinois an Urbana-Champaign, 1998.
[22] J. W. Nehrbass, J. O. Jetvic, and R. Lee, “Reducing the Phase Error for Finite-Difference Methods Without Increasing the Order,” IEEE Trans. AP, vol. 46, pp. 1194-1201, Aug. 1998.
[23] E. Turkel, Advances in Computational Electrodynamics: The Finite Difference Time Domain Method, 1998.
[24] K. L. Shlager and J. B. Schneider, “Relative Accuracy of Several Finite-Difference Time-Domain Schemes,” Antennas and Propagation Society International Symposium 1999, vol. 1, pp.168-171, July 1999.
[25] N. V. Kantarzis and T. D. Tsiboukis, “A Higher-Order FDTD Technique fot the Implementation of Enganced Dispersionless Perfectly Matched Layers Combined with Efficient Absorbing Boundary Conditions,” IEEE Trans. Magnetics, vol. 34, pp.2736-2739, Sep. 1998.
[26] G. Haussmann and M. Piket-May, “Modeling Interface Discontinuities and Boundary Conditions for a Dispersion-Optimized Finite-Difference Time-Domain Method,” Antennas and Propagation Society International Symposium, vol. 4, pp.1820-1823, June 1998.
[27] J. L. Young, D. Gaitonde, and J. J. S. Shang, “Toward the Construction of a Fourth-Order Difference Scheme for Transient EM Wave Simulation: Staggered Grid Approach,” IEEE Trans. AP., vol. 45, pp.1573-1580, Nov. 1997.
[28] O. M. Ramahi, “Near- and Far-field calculation in FDTD simulations using Kirchhoff Surface Integral Representation,” IEEE Trans. AP., Vol. 45, pp. 753-759, May. 1997.
[29] 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 planar microstrip circuit” IEEE Trans. MTT., vol. 38, pp. 849-857, 1990.
[30] A. P. Zhao, “Application of a simple and efficient source excitation technique to the FDTD analysis of waveguide and microstrip circuits,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 1535-1539, July 1996.
[31] M. Piket-May, A. Taflove, and J. Baron, “FD-TD modeling of digital signal propagation in 3-D circuits with passive and active loads,” IEEE Trans. Microwave Theory Tech., vol. 42, no. 8, pp. 1514-1523, Aug. 1994.
[32] S. D. Gedney, “An Anisotropic Perfectly Matched Layer-Absorbing Medium for the Truncation of FDTD Lattices,” IEEE Trans. AP., vol. 44, no. 12, pp. 1630-1639, Dec. 1996.
[33] D. Kingsland, R. Dycziz-Edlinger, J. F. Lee, and R. Lee, “Performance characterization of a perfectly matched anisotropic absorber for frequency domain FEM applications,” URSI Symp. Dig., Newport Beach, CA, p. 339. June 1995.
[34] R. Bansal, “The Far-Field: How Far is Far Enough?,” Applied Microwave & Wireless., vol. 11, pp. 58-60, Nov. 1999.
[35] M. Ali, and G. J. Hayes, “Analysis of integrated inverted-F antennas for bluetooth applications,” 2000 IEEE-APS Conference, pp. 21-24, June 2000.
[36] K. P. Ma, Y. Qian, and Tatsuo Itoh, “Analysis and Applications of a New CPW-Slotline Transition,” IEEE Trans. MTT., vol. 47, no. 4, pp. 426-432, April, 1999.
[37] E. A. Navarro, N. T. Sangary, and J. Litva, “Some considerations on the accuracy of the nonuniform FDTD method and its application to waveguide analysis when combined with the perfectly matched layer technique,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 1115-1124, July 1996.
電子全文 Fulltext
本電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。
論文使用權限 Thesis access permission:校內一年後公開,校外永不公開 campus withheld
開放時間 Available:
校內 Campus: 已公開 available
校外 Off-campus:永不公開 not available

您的 IP(校外) 位址是 35.153.134.169
論文開放下載的時間是 校外不公開

Your IP address is 35.153.134.169
This thesis will be available to you on Indicate off-campus access is not available.

紙本論文 Printed copies
紙本論文的公開資訊在102學年度以後相對較為完整。如果需要查詢101學年度以前的紙本論文公開資訊,請聯繫圖資處紙本論文服務櫃台。如有不便之處敬請見諒。
開放時間 available 已公開 available

QR Code