分形与多频天线的研究
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摘要
分形是通过迭代产生的具有自相似性的分数维结构，分形的概念可用于天线设计以实现天线的尺寸减缩与多频特性，这在军用和民用方面有着广泛应用前景。本文介绍了分形的基本概念和分形结构的迭代算法。对于分形微带天线结构使用基于矩量法的ADS商业软件的电磁仿真工具Momentum进行了分析研究。首先用微带馈电的单层微带贴片天线进行仿真和验证。在此基础上，着重分析了微带线耦合馈电的Sierpinski等边三角形微带分形贴片天线以及Sierpinski方形微带分形贴片天线的多频特性，给出了介质参数、贴片尺寸、分形的阶数以及减少分形贴片数对微带线耦合馈电的Sierpinki等边三角和Sierpinski方形微带分形贴片天线特性的影响；其次基于微带线耦合馈电的半圆双频微带贴片天线和矩形双频微带贴片天线的性能分析和比较，提供了尺寸缩减的依据；最后对以上天线的频带扩展进行了探论。
A 'fractal' is a recursively generated structure having a fractional dimension and self-similarity property. The concept of a 'fractal' has been applied to antenna design in order to reduce the size of antenna and obtain multi-band frequency operation. Fractal antennas have broad application prospect in military and civil application.
In this thesis, the concept of 'fractal' and the recursive algorithm of fractal structure are depicted. For the case of microstrip fractal patch antenna structure, the MoM based EM tool Momentum of commercial software ADS is used for analysis and research. Firstly a microstrip-fed microstrip patch antenna has been emulated and validated. On the base of this, the multi-band property of Sierpinski equilateral triangle and squareness microstrip fractal patch antennas are carefully studied, and the effect of antenna's property by the permittivity, the size of patch, the order of the fractal and the decrease of fractal patches is depicted; secondly on the base of analysis and comparison of performance of microstrip-fed semicircle and rectangle double-band microstrip patch antennas, warranty of dimension curtailment is offered; finally expansion of band of those antennas above is discussed.
A 'fractal' is a recursively generated structure having a fractional dimension and self-similarity property. The concept of a 'fractal' has been applied to antenna design in order to reduce the size of antenna and obtain multi-band frequency operation. Fractal antennas have broad application prospect in military and civil application.
In this thesis, the concept of 'fractal' and the recursive algorithm of fractal structure are depicted. For the case of microstrip fractal patch antenna structure, the MoM based EM tool Momentum of commercial software ADS is used for analysis and research. Firstly a microstrip-fed microstrip patch antenna has been emulated and validated. On the base of this, the multi-band property of Sierpinski equilateral triangle and squareness microstrip fractal patch antennas are carefully studied, and the effect of antenna's property by the permittivity, the size of patch, the order of the fractal and the decrease of fractal patches is depicted; secondly on the base of analysis and comparison of performance of microstrip-fed semicircle and rectangle double-band microstrip patch antennas, warranty of dimension curtailment is offered; finally expansion of band of those antennas above is discussed.
引文
[1] 齐东旭，分形及其计算机生成．北京科学出版社，1994．
[2] (美)R. F.哈林登，计算电磁场的矩量法．北京-国防工业出版社，1981
[3] 李世智，电磁辐射与散射问题的矩量法．北京．电子工业出版社，1985
[4] 刘英，龚书喜，傅德民，“用于多频通信的微带分形贴片天线”，微波学报，vol．17(4)，200 1，pp．76-79．
[5] 刘英，龚书喜，傅德民，“分形天线德研究进展”，电波科学学报，vol．17(4)，2002，pp．54-58．
[6] C. Puente-Baliarda, et al. "On the behavior of the Sierpinski fractal antenna", IEEE Trans, AP-46(6), 1996, pp.517-524.
[7] Emmanuel Tronect et al. "Microwave characterization and modeling of the surface impedance of fractal structure copper films", IEEE AP-46(3), 1998, pp434-441.
[8] C. Puente, et al. "Small but long koch fractal monopole. IEE Electronics Letters, 34(1), 1998, pp.9-10.
[9] C. Punete el al. "The koch monopole: a small fractal antenna", IEEE Trans., AP-48(11), 2000, pp. 1773-1781.
[10] R. V. HaraPrasad, et al.. "Microstrip fractal patch antenna for multiband communication", IEE Electronics Letters, 36(14), 2000, pp. 1179-1180.
[11] Zhengwei Du, et al. "Analysis of microstrip fractal patch antenna muli-band communication", IEE Electronics Letters, 37(13), 2001, pp805-806.
[12] IJ鲍尔，P布哈蒂亚"Microstrip Antennas" 1980
[13] 唐世军，顾长青“分形天线的电磁特性研究”[学位论文]南京航空航天大学2003
[14] F. Alonso-Monferrer, A. Kishk, A. Glisson, "Green's Function Analysis of Planar Circuits in a Two_Layer Grounded Medium", IEEE Trans. On APS, vol. 40, no. 6, pp. 690-696, June 1992.
[15] Shih-Chang Wu, N. Alexopoulos, O. Fordham, "Feeding Structure Contributions to Radiation by Patch Antennas with Rectangular Boundaries", IEEE Trans. On AP, vol. 40, no. 10, pp. 1245-49, October 1992
[16] 王丽萍，许峰，傅德民，龚书喜，“Minkowski分形天线分析”，西安电子科技大学学报， vol．29，no．6，pp．753-755
[17] C. Borja et al.. "High directivity fractal boundary microstrip patch antenna", IEE Electronics Letters, 36(9), 2000, pp.778-779.
[18] Caries Puente Baliarda, et al.. "An iterative model for fractal antenna: application on the Sierpinski gasket antenna", IEEE AP-48(5), 2000, pp.713-719.
[19] Richards, et al.. "An improved theory for microstrip antennas and applications", IEEE
Trans, AP-29(1), 1981, pp.38-46.
[20] C. Puente, etc. "Fractal Multiband Antenna Based on Sierpinski Gasker", IEE Electronics Letters, 32(1), 1996, pp. 1-2.
[21] C. Puente, et al.. "Multiband properties of a fractal tree antenna generated by electrochemical deposition", IEE Electronics Letters, 32(25), 1996, pp. 2298-2299.
[22] Douglas H. Wemer, et al.. "Fractal antenna engineering: The theory and design of fractal antenna arrarys", IEEE Antennas and Propagation Magazine, 41(5), 1999, pp.37-59.
[23] M. Sindou, et al.. "Multiband and wideband properties of printed fractal branched antennas", IEE Electronics Letters, 35(3), 1999, pp. 181-182.
[24] J. Romeu Y. Rahmat-Samii "Dual band FSS with fractal elements", IEE Electronics Letters, 35(9), pp.702-703.
[25] ADS Documentation, A Theory of Operation of Momentum
[26] http://www.fractenna.com
[27] http://www.fracus.com
[28] http://www.imst.de
[29] http://eesof.tm.agilent.com/docs/
[2] (美)R. F.哈林登，计算电磁场的矩量法．北京-国防工业出版社，1981
[3] 李世智，电磁辐射与散射问题的矩量法．北京．电子工业出版社，1985
[4] 刘英，龚书喜，傅德民，“用于多频通信的微带分形贴片天线”，微波学报，vol．17(4)，200 1，pp．76-79．
[5] 刘英，龚书喜，傅德民，“分形天线德研究进展”，电波科学学报，vol．17(4)，2002，pp．54-58．
[6] C. Puente-Baliarda, et al. "On the behavior of the Sierpinski fractal antenna", IEEE Trans, AP-46(6), 1996, pp.517-524.
[7] Emmanuel Tronect et al. "Microwave characterization and modeling of the surface impedance of fractal structure copper films", IEEE AP-46(3), 1998, pp434-441.
[8] C. Puente, et al. "Small but long koch fractal monopole. IEE Electronics Letters, 34(1), 1998, pp.9-10.
[9] C. Punete el al. "The koch monopole: a small fractal antenna", IEEE Trans., AP-48(11), 2000, pp. 1773-1781.
[10] R. V. HaraPrasad, et al.. "Microstrip fractal patch antenna for multiband communication", IEE Electronics Letters, 36(14), 2000, pp. 1179-1180.
[11] Zhengwei Du, et al. "Analysis of microstrip fractal patch antenna muli-band communication", IEE Electronics Letters, 37(13), 2001, pp805-806.
[12] IJ鲍尔，P布哈蒂亚"Microstrip Antennas" 1980
[13] 唐世军，顾长青“分形天线的电磁特性研究”[学位论文]南京航空航天大学2003
[14] F. Alonso-Monferrer, A. Kishk, A. Glisson, "Green's Function Analysis of Planar Circuits in a Two_Layer Grounded Medium", IEEE Trans. On APS, vol. 40, no. 6, pp. 690-696, June 1992.
[15] Shih-Chang Wu, N. Alexopoulos, O. Fordham, "Feeding Structure Contributions to Radiation by Patch Antennas with Rectangular Boundaries", IEEE Trans. On AP, vol. 40, no. 10, pp. 1245-49, October 1992
[16] 王丽萍，许峰，傅德民，龚书喜，“Minkowski分形天线分析”，西安电子科技大学学报， vol．29，no．6，pp．753-755
[17] C. Borja et al.. "High directivity fractal boundary microstrip patch antenna", IEE Electronics Letters, 36(9), 2000, pp.778-779.
[18] Caries Puente Baliarda, et al.. "An iterative model for fractal antenna: application on the Sierpinski gasket antenna", IEEE AP-48(5), 2000, pp.713-719.
[19] Richards, et al.. "An improved theory for microstrip antennas and applications", IEEE
Trans, AP-29(1), 1981, pp.38-46.
[20] C. Puente, etc. "Fractal Multiband Antenna Based on Sierpinski Gasker", IEE Electronics Letters, 32(1), 1996, pp. 1-2.
[21] C. Puente, et al.. "Multiband properties of a fractal tree antenna generated by electrochemical deposition", IEE Electronics Letters, 32(25), 1996, pp. 2298-2299.
[22] Douglas H. Wemer, et al.. "Fractal antenna engineering: The theory and design of fractal antenna arrarys", IEEE Antennas and Propagation Magazine, 41(5), 1999, pp.37-59.
[23] M. Sindou, et al.. "Multiband and wideband properties of printed fractal branched antennas", IEE Electronics Letters, 35(3), 1999, pp. 181-182.
[24] J. Romeu Y. Rahmat-Samii "Dual band FSS with fractal elements", IEE Electronics Letters, 35(9), pp.702-703.
[25] ADS Documentation, A Theory of Operation of Momentum
[26] http://www.fractenna.com
[27] http://www.fracus.com
[28] http://www.imst.de
[29] http://eesof.tm.agilent.com/docs/