基于小波矩量法的线天线分析
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摘要
线天线的电流分布特性通常采用基本矩量法进行分析。基本矩量法的思路是将泛函方程离散成代数方程组,通过求解代数方程组对应的矩量矩阵求得原方程的解。而矩量法所形成的离散矩阵为一稠密矩阵,对于电大尺寸目标的分析,例如复杂几何结构的线天线,这个稠密矩阵求逆非常费时。矩量法就是以其大规模的计算换取了结果的高稳定性和高精度。因此,从计算时间的角度,矩量法的应用就受到了限制。
小波分析特有的消失矩、正则性和紧支撑的性质,使小波分析通过选择合适的离散基函数或离散方式能够减少二维和三维问题用矩量法求解的时间。所以本文推导了采用离散小波矩量法求解线天线电磁积分方程的方法,并用该方法分析了几种线天线的电流分布特性。
本文在推导了矩量法分析线天线问题的具体方法和步骤的基础上做了以下工作:
1.基于矩量法对三种具体的线天线进行分析求解;
2.将小波分析的思想应用于线天线问题的求解中,通过理论分析完善了小波矩量法求解计算电磁学问题的方法和步骤;
3.首次在复杂线天线的分析中引入小波分析,并对基本矩量法和小波矩量法分析同种复杂线天线的结果进行了对比。结果表明小波矩量法适用于分析任意形状线天线的电流分布特性。通过计算复杂线天线的电流分布来求解其输入阻抗和方向图等特性参数,结果验证了小波矩量法在分析复杂线天线问题时的有效性和可行性。与基本矩量法相比较,此方法不仅分析结果精确而且大大节省了计算时间。
本文的分析方法通用性强,对丰富计算电磁学的理论研究及其工程应用都具有重要的理论意义和现实意义,对小波矩量法的分析研究及其应用具有一定的理论参考价值,为进一步分析复杂线天线的传输特性以及与小波矩量法相关的其它电磁场问题奠定了一定的理论基础。
To analyses the current distribution characteristic of line-antenna usually uses the basic moment methods. Its mentality is turn continuous functional equation to discrete algebraic equation through the discretization, and to obtain the answer of original equations through solve the corresponding discrete algebraic equation. The discrete matrix which forms through the moment methods is a dense matrix. Inversion of the dense matrix is time-consuming against the objects with large electrical size, such as the line-antenna with complex geometric structure. The answers of moment methods have well stability and high accuracy at its large-scale computation, so that the application of the moment methods has been limited.
Unique nature of wavelet analysis, including vanishing moment, regularity and compact support, reduces the computation time of two-dimensional and three-dimensional problems which solved by moment methods by selecting appropriate wavelet discrete basis function or discrete way. So, this paper deduced the method of solving electromagnetic integral equation of antenna and analyzed current distribution of several line-antennas by the discrete wavelet moment methods.
This paper did the following work based on deducing the specific methods and steps of analyses the problem about line-antenna by moment methods:
1. Three kinds of specific line-antennas were analyzed based on moment methods;
2. The idea of wavelet was applied to solve the problem on line-antenna. This paper improved methods and procedures of calculating electromagnetic issues by theoretical analysis of wavelet moment methods;
3. Wavelet analysis is introduced into the analysis of complex line-antenna at first time. To analyses the same kind of complex line-antenna by basic moment methods and wavelet moment methods and the results of the analysis were compared. The results show that wavelet moment methods is applied to analyses current distribution of any shape antenna. To obtain its characteristic parameters, such as input impedance and radiation pattern, etc. by calculating the current distribution of complex line-antenna. The results of this method validate the validity and feasibility of wavelet moment methods when it analyses the complex line-antennas. Compared with basic moment methods, wavelet moment methods is not only accurate method but also greatly saves the computing time.
This analysis method is versatility and has important theoretical and practical significance to enriching the theory and its application of computational electromagnetic. It gives theoretical reference value to further analysis and application of wavelet moment methods. It lays a theoretical foundation for analyses transmission characteristics of complex line-antenna and other electromagnetic problem associated with wavelet moment methods.
小波分析特有的消失矩、正则性和紧支撑的性质,使小波分析通过选择合适的离散基函数或离散方式能够减少二维和三维问题用矩量法求解的时间。所以本文推导了采用离散小波矩量法求解线天线电磁积分方程的方法,并用该方法分析了几种线天线的电流分布特性。
本文在推导了矩量法分析线天线问题的具体方法和步骤的基础上做了以下工作:
1.基于矩量法对三种具体的线天线进行分析求解;
2.将小波分析的思想应用于线天线问题的求解中,通过理论分析完善了小波矩量法求解计算电磁学问题的方法和步骤;
3.首次在复杂线天线的分析中引入小波分析,并对基本矩量法和小波矩量法分析同种复杂线天线的结果进行了对比。结果表明小波矩量法适用于分析任意形状线天线的电流分布特性。通过计算复杂线天线的电流分布来求解其输入阻抗和方向图等特性参数,结果验证了小波矩量法在分析复杂线天线问题时的有效性和可行性。与基本矩量法相比较,此方法不仅分析结果精确而且大大节省了计算时间。
本文的分析方法通用性强,对丰富计算电磁学的理论研究及其工程应用都具有重要的理论意义和现实意义,对小波矩量法的分析研究及其应用具有一定的理论参考价值,为进一步分析复杂线天线的传输特性以及与小波矩量法相关的其它电磁场问题奠定了一定的理论基础。
To analyses the current distribution characteristic of line-antenna usually uses the basic moment methods. Its mentality is turn continuous functional equation to discrete algebraic equation through the discretization, and to obtain the answer of original equations through solve the corresponding discrete algebraic equation. The discrete matrix which forms through the moment methods is a dense matrix. Inversion of the dense matrix is time-consuming against the objects with large electrical size, such as the line-antenna with complex geometric structure. The answers of moment methods have well stability and high accuracy at its large-scale computation, so that the application of the moment methods has been limited.
Unique nature of wavelet analysis, including vanishing moment, regularity and compact support, reduces the computation time of two-dimensional and three-dimensional problems which solved by moment methods by selecting appropriate wavelet discrete basis function or discrete way. So, this paper deduced the method of solving electromagnetic integral equation of antenna and analyzed current distribution of several line-antennas by the discrete wavelet moment methods.
This paper did the following work based on deducing the specific methods and steps of analyses the problem about line-antenna by moment methods:
1. Three kinds of specific line-antennas were analyzed based on moment methods;
2. The idea of wavelet was applied to solve the problem on line-antenna. This paper improved methods and procedures of calculating electromagnetic issues by theoretical analysis of wavelet moment methods;
3. Wavelet analysis is introduced into the analysis of complex line-antenna at first time. To analyses the same kind of complex line-antenna by basic moment methods and wavelet moment methods and the results of the analysis were compared. The results show that wavelet moment methods is applied to analyses current distribution of any shape antenna. To obtain its characteristic parameters, such as input impedance and radiation pattern, etc. by calculating the current distribution of complex line-antenna. The results of this method validate the validity and feasibility of wavelet moment methods when it analyses the complex line-antennas. Compared with basic moment methods, wavelet moment methods is not only accurate method but also greatly saves the computing time.
This analysis method is versatility and has important theoretical and practical significance to enriching the theory and its application of computational electromagnetic. It gives theoretical reference value to further analysis and application of wavelet moment methods. It lays a theoretical foundation for analyses transmission characteristics of complex line-antenna and other electromagnetic problem associated with wavelet moment methods.
引文
[1]胡广书.现代信号处理教程[M].北京:清华大学出版社, 2007.
[2] Roger F. Harrington. Field Computation by Moment Methods[M]. New York: Macmillan, 1968: 5-7.
[3]张世全,葛德彪.小波矩量法及其电磁应用[J].汉中师范学院学报(自然科学), 2001, 19(1): 44-46, 65.
[4]王长清.现代计算电磁学基础[M].北京:北京大学出版社, 2005: 116-171.
[5]王秉中.计算电磁学[M].北京:科学出版社, 2002.
[6]李彦民,石雁祥.小波分析的发展及应用现状[J].伊犁师范学院学报, 2000, 1: 84-87.
[7]付芸,柳超.小波矩量法求解方环天线的电流分布[J].船舰电子工程, 2006, 26(1): 148-150.
[8]盛新庆.计算电磁学要论[M].北京:科学出版社, 2004.
[9]董辉,朱义胜,赵柏山.基于小波矩量法的平面螺旋电感的电磁辐射研究[J].电子学报, 2009.
[10]孙保华,焦永昌,刘其中.快速精确分析套筒单极子天线的一种实用新方法[J].电子学报, 2000, 28(9): 16-18.
[11]张成,郑宏兴.小波矩量法求解电磁场积分方程[J].宁夏大学学报(自然科学版)2000, 21(1): 75-78.
[12]孙保华,刘其中,尹应增.线天线的小波矩阵变换法求解[J].微波学报, 2001, 17(1): 54-59.
[13]姜光伟,曹伟,朱洪波.基于不同积分方程的线天线矩量法分析[J].南京邮电学院学报, 2005, 25(1).
[14]张钧.电磁场边值问题的积分方程解法[M].北京:高等教育出版社, 1989.
[15]屈汉章.连续小波变换及其应用[D].西安:西安电子科技大学, 2001.
[16]关海爽,马文阁,蒙彦宇.小波矩量法在电磁场数值计算中的应用[J].辽宁工学院学报, 2007, 27(3): 144-148.
[17]彭玉华,董晓龙,汪文秉等.小波变换在电磁场数值计算中的应用[J].电子学报, 1996, 24(12): 46-52.
[18]杨蕊红.小波矩算法在图象识别中的应用研究[D].西安:西北工业大学, 2002.
[19]陈挺.微波、毫米波三维空间集成电路的数值模拟研究[D].上海:上海大学, 2000.
[20]刘大良.基于小波分析的自动车牌识别算法的研究与设计[D].成都:电子科技大学, 2005.
[21]秦磊.基于矩的图象分析和快速算法[D].湖南:东南大学, 2003.
[22]魏兴昌.小波分析在电磁场数值计算中的应用[D].西安:西安电子科技大学, 2000.
[23]刘英.雷达散射截面计算方法分析与研究[D].西安:西安电子科技大学, 2001.
[24]庄丽华,孙玉宝,刘镇.基于矩量法对线天线辐射特性的仿真研究[J].舰船电子工程, 2006, 152: 111-113, 157.
[25]谢处方,饶克谨.电磁场与电磁波[M].北京:高等教育出版社, 1999.
[26]李世智.电磁辐射与散射问题的矩量法[M].北京:电子工业出版社, 1985.
[27]李玉莹,徐晓文.基于矩量法对导体板上单极天线特性研究[J].电波科学学报. 2002, 17(4): 127-129.
[28]周波,邢锋,楼建东.采用耦合Hallen方程分析八木天线[J].现代电子技术, 2008, 11.
[29]宋铮,张建华,黄冶.天线与电波传播[M].西安:西安电子科技大学出版社, 2004.
[30]刘建霞.单线背射螺旋做抛物面馈源的研究[D].太原:太原工业大学, 1997.
[31] J.D. Kraus. Antennas[M]. New York: Mc Graw-Hill, 1947, 7.
[32] H. E. King, J. L. Wong. Characteristics of 1 to 8 wave length uniform helical antennas[J]. IEEE Trans. 1980, AP(28): 291-296.
[33] H. Nakano, J. Yamauchi. Characteristics of modified spiral and helical antennas[J]. Proc. Int. Elec. Eng, 1982, 129: 232-237.
[34] YU SHUAN YEN, KENNETH K.MEI. Theory of Conical Equiangular-Spiral Antennas Part I-Numerical Technique[J]. IEEE Trans. AP15(5): 364-369.
[35] Nurhan Türker, Filiz Günes, Tülay Yidirim. Artificial Neural Design of Microstrip Antennas[J]. Turk J Elec. Eng, 2006, 14(3): 445-453.
[36] K.K.MEI. On the Integral Equations of Thin Wire Antennas[J]. IEEE Trans, 1965, AP(13): 374-378.
[37] Hu Binjie, Yin Junxun. Analysis and Kernel Expression of Wire Antenna with Arbitrary Shape[J]. Journal of South China University of Technology (Natural Science Edition), 2005,33(12):52-55.
[38] HISAMATSU NAKANO, JUNJI YAMAUCHI, HIROAKI MIMAKI.Backfire Radiation from a Monofilar Helix with a Small Ground Plane[J]. IEEE Trans, 1988, AP36(10): 1359-1364.
[39] H. Nakano, Y. Samada, J. Yamauchi. Axial mode and helix antennas[J]. IEEE Trans, 1986, AP(34): 1143-1148.
[40] Wager R L, Chew W C. A study of wavelet for the solution of electromagnetic integral equations[J]. IEEE Trans, 1995, AP43(8): 802-810.
[41] Steinberg B Z, Leviathan Y. On the use of wavelet expansions in the method of moment[J]. IEEE Trans, 1993, AP4(5): 610-619.
[42]孙鹏亮.螺旋加载单极天线的矩量法计算[D].哈尔滨:哈尔滨工业大学, 2004.
[43]傅佳辉.微带天线的矩量法研究[D].哈尔滨:哈尔滨工业大学, 2000.
[44]钱小虎.线天线近场的数值分析[D].上海:华中科技大学, 2005.
[2] Roger F. Harrington. Field Computation by Moment Methods[M]. New York: Macmillan, 1968: 5-7.
[3]张世全,葛德彪.小波矩量法及其电磁应用[J].汉中师范学院学报(自然科学), 2001, 19(1): 44-46, 65.
[4]王长清.现代计算电磁学基础[M].北京:北京大学出版社, 2005: 116-171.
[5]王秉中.计算电磁学[M].北京:科学出版社, 2002.
[6]李彦民,石雁祥.小波分析的发展及应用现状[J].伊犁师范学院学报, 2000, 1: 84-87.
[7]付芸,柳超.小波矩量法求解方环天线的电流分布[J].船舰电子工程, 2006, 26(1): 148-150.
[8]盛新庆.计算电磁学要论[M].北京:科学出版社, 2004.
[9]董辉,朱义胜,赵柏山.基于小波矩量法的平面螺旋电感的电磁辐射研究[J].电子学报, 2009.
[10]孙保华,焦永昌,刘其中.快速精确分析套筒单极子天线的一种实用新方法[J].电子学报, 2000, 28(9): 16-18.
[11]张成,郑宏兴.小波矩量法求解电磁场积分方程[J].宁夏大学学报(自然科学版)2000, 21(1): 75-78.
[12]孙保华,刘其中,尹应增.线天线的小波矩阵变换法求解[J].微波学报, 2001, 17(1): 54-59.
[13]姜光伟,曹伟,朱洪波.基于不同积分方程的线天线矩量法分析[J].南京邮电学院学报, 2005, 25(1).
[14]张钧.电磁场边值问题的积分方程解法[M].北京:高等教育出版社, 1989.
[15]屈汉章.连续小波变换及其应用[D].西安:西安电子科技大学, 2001.
[16]关海爽,马文阁,蒙彦宇.小波矩量法在电磁场数值计算中的应用[J].辽宁工学院学报, 2007, 27(3): 144-148.
[17]彭玉华,董晓龙,汪文秉等.小波变换在电磁场数值计算中的应用[J].电子学报, 1996, 24(12): 46-52.
[18]杨蕊红.小波矩算法在图象识别中的应用研究[D].西安:西北工业大学, 2002.
[19]陈挺.微波、毫米波三维空间集成电路的数值模拟研究[D].上海:上海大学, 2000.
[20]刘大良.基于小波分析的自动车牌识别算法的研究与设计[D].成都:电子科技大学, 2005.
[21]秦磊.基于矩的图象分析和快速算法[D].湖南:东南大学, 2003.
[22]魏兴昌.小波分析在电磁场数值计算中的应用[D].西安:西安电子科技大学, 2000.
[23]刘英.雷达散射截面计算方法分析与研究[D].西安:西安电子科技大学, 2001.
[24]庄丽华,孙玉宝,刘镇.基于矩量法对线天线辐射特性的仿真研究[J].舰船电子工程, 2006, 152: 111-113, 157.
[25]谢处方,饶克谨.电磁场与电磁波[M].北京:高等教育出版社, 1999.
[26]李世智.电磁辐射与散射问题的矩量法[M].北京:电子工业出版社, 1985.
[27]李玉莹,徐晓文.基于矩量法对导体板上单极天线特性研究[J].电波科学学报. 2002, 17(4): 127-129.
[28]周波,邢锋,楼建东.采用耦合Hallen方程分析八木天线[J].现代电子技术, 2008, 11.
[29]宋铮,张建华,黄冶.天线与电波传播[M].西安:西安电子科技大学出版社, 2004.
[30]刘建霞.单线背射螺旋做抛物面馈源的研究[D].太原:太原工业大学, 1997.
[31] J.D. Kraus. Antennas[M]. New York: Mc Graw-Hill, 1947, 7.
[32] H. E. King, J. L. Wong. Characteristics of 1 to 8 wave length uniform helical antennas[J]. IEEE Trans. 1980, AP(28): 291-296.
[33] H. Nakano, J. Yamauchi. Characteristics of modified spiral and helical antennas[J]. Proc. Int. Elec. Eng, 1982, 129: 232-237.
[34] YU SHUAN YEN, KENNETH K.MEI. Theory of Conical Equiangular-Spiral Antennas Part I-Numerical Technique[J]. IEEE Trans. AP15(5): 364-369.
[35] Nurhan Türker, Filiz Günes, Tülay Yidirim. Artificial Neural Design of Microstrip Antennas[J]. Turk J Elec. Eng, 2006, 14(3): 445-453.
[36] K.K.MEI. On the Integral Equations of Thin Wire Antennas[J]. IEEE Trans, 1965, AP(13): 374-378.
[37] Hu Binjie, Yin Junxun. Analysis and Kernel Expression of Wire Antenna with Arbitrary Shape[J]. Journal of South China University of Technology (Natural Science Edition), 2005,33(12):52-55.
[38] HISAMATSU NAKANO, JUNJI YAMAUCHI, HIROAKI MIMAKI.Backfire Radiation from a Monofilar Helix with a Small Ground Plane[J]. IEEE Trans, 1988, AP36(10): 1359-1364.
[39] H. Nakano, Y. Samada, J. Yamauchi. Axial mode and helix antennas[J]. IEEE Trans, 1986, AP(34): 1143-1148.
[40] Wager R L, Chew W C. A study of wavelet for the solution of electromagnetic integral equations[J]. IEEE Trans, 1995, AP43(8): 802-810.
[41] Steinberg B Z, Leviathan Y. On the use of wavelet expansions in the method of moment[J]. IEEE Trans, 1993, AP4(5): 610-619.
[42]孙鹏亮.螺旋加载单极天线的矩量法计算[D].哈尔滨:哈尔滨工业大学, 2004.
[43]傅佳辉.微带天线的矩量法研究[D].哈尔滨:哈尔滨工业大学, 2000.
[44]钱小虎.线天线近场的数值分析[D].上海:华中科技大学, 2005.