矩量法及其与IPO的混合法研究复杂目标电磁辐射与散射
摘要
本文主要应用基于电场积分方程(EFIE)的矩量法(MoM)研究复杂形状的金属载体上多种线天线的电磁辐射问题以及复杂形状金属目标的电磁散射问题。近年来，这两类问题在工程界和电磁场数值理论界得到人们的广泛重视并已成为研究的热点。随着现代天线技术的发展，在舰船上装备了大量不同频段不同类型的天线，这些天线大大提高了舰艇的通信、导航、防御、武器控制和作战指挥能力。但是如果全舰的电磁兼容性存在较大问题，它对舰艇的安全和战斗任务的完成也会构成很大威胁，其中舰船天线优化布局是研究重点之一。当通讯天线安装到舰艇或飞机上，其电磁特性会因天线本身和载体间的耦合而发生变化，考虑到载体对天线的影响，在计算时，两者应作为一个整体进行分析。另一方面，飞机、导弹和舰船等军事目标本身的雷达散射截面(RCS)也是人们十分感兴趣的问题，对该参数进行预测同样会遇到上述问题的困扰。
本文使用积分方程类方法，对一些简单和复杂金属载体上的线天线以及金属目标本身的电磁特性进行了研究，完成了有关数值方法的理论建模和程序实现，所涉及的方法主要包括基于电场积分方程的矩量法(EFIE-MoM)和迭代物理光学法(IPO)。
首先通过成熟的CAD软件进行几何建模和网格自动剖分并结合自行编制的接口程序单独提取网格数据，为矩量法程序的运算做好了前置处理工作；
应用基于电场积分方程的矩量法解决任意形状金属体在均匀平面电磁波照射下表面电流的计算及其电磁散射问题，得到了一些数据结果；
应用基于电场积分方程的矩量法和线面混合基函数解决任意形状金属载体上线天线的散射与辐射问题(包括直导线天线，螺旋天线，Koch分形天线等)，为工程中进行天线布局设计、EMC分析等应用提供了理论依据；
将矩量法与迭代物理光学法结合解决带有槽缝结构的二维电大尺寸目标的电磁散射问题，并将解决的问题范围拓展到三维电大尺寸金属目标的情况，为混合方法的研究提供了一定的参考依据。
This dissertation is focused on the radiation problems of various kinds of wire antennas mounted on the complex-shaped PEC platform and the scattering problems of complex-shaped electrically-large PEC targets based on the theory of Method of Moments. With the development of modern antenna technology, a warship is fully equipped with various kinds of antennas working in different frequency bands, which greatly improve the ability of communication, navigation, defence and weapon control. The EMC problems of a warship would heavily threaten the accomplishment of the mission and safety of the vessel itself if it were not settled properly, among which the optimized antenna distribution is the most important one. When antennas are mounted on such platform as a warship or an aeroplane, their EM characteristics will inevitably be changed a lot by the interactions between the antennas and the carrier and that between the antennas themselves. However, the problem of simulation or prediction of EM behavior of onboard antennas is very important and urgent to be solved because the antennas will not function normally when their radiation pattern is distorted severely by the structures around. On the other hand, the RCS parameters of the targets (i.e. warship, aeroplane, etc.) will also meet all the computational difficulties mentioned above.
First of all a lot of simple and complex shaped models have been analyzed to check the validity and efficiency of the methods based on EFIE-MoM. A numerical electromagnetic program is developed and its correctness is proved. Geometrical modeling and auto-meshing are made through mature CAD software, which greatly simplify the programming of MoM.
Then based on EFIE-MoM, the current computation and scattering problems of arbitrary-shaped complex PEC platform with uniform plane wave incidence are solved.
And then the radiation problems of various kinds of wire antennas (i.e. straight wire antenna, helix wire antenna, Koch fractal antenna, etc.) mounted on the complex-shaped PEC platform are solved based on the EFIE-MoM and junction basis function.
Finally the scattering problems of complex-shaped electrically-large 2D PEC targets are solved based on the hybrid method of IPO and MoM, which can be easily expanded to the 3-D condition.
本文使用积分方程类方法，对一些简单和复杂金属载体上的线天线以及金属目标本身的电磁特性进行了研究，完成了有关数值方法的理论建模和程序实现，所涉及的方法主要包括基于电场积分方程的矩量法(EFIE-MoM)和迭代物理光学法(IPO)。
首先通过成熟的CAD软件进行几何建模和网格自动剖分并结合自行编制的接口程序单独提取网格数据，为矩量法程序的运算做好了前置处理工作；
应用基于电场积分方程的矩量法解决任意形状金属体在均匀平面电磁波照射下表面电流的计算及其电磁散射问题，得到了一些数据结果；
应用基于电场积分方程的矩量法和线面混合基函数解决任意形状金属载体上线天线的散射与辐射问题(包括直导线天线，螺旋天线，Koch分形天线等)，为工程中进行天线布局设计、EMC分析等应用提供了理论依据；
将矩量法与迭代物理光学法结合解决带有槽缝结构的二维电大尺寸目标的电磁散射问题，并将解决的问题范围拓展到三维电大尺寸金属目标的情况，为混合方法的研究提供了一定的参考依据。
This dissertation is focused on the radiation problems of various kinds of wire antennas mounted on the complex-shaped PEC platform and the scattering problems of complex-shaped electrically-large PEC targets based on the theory of Method of Moments. With the development of modern antenna technology, a warship is fully equipped with various kinds of antennas working in different frequency bands, which greatly improve the ability of communication, navigation, defence and weapon control. The EMC problems of a warship would heavily threaten the accomplishment of the mission and safety of the vessel itself if it were not settled properly, among which the optimized antenna distribution is the most important one. When antennas are mounted on such platform as a warship or an aeroplane, their EM characteristics will inevitably be changed a lot by the interactions between the antennas and the carrier and that between the antennas themselves. However, the problem of simulation or prediction of EM behavior of onboard antennas is very important and urgent to be solved because the antennas will not function normally when their radiation pattern is distorted severely by the structures around. On the other hand, the RCS parameters of the targets (i.e. warship, aeroplane, etc.) will also meet all the computational difficulties mentioned above.
First of all a lot of simple and complex shaped models have been analyzed to check the validity and efficiency of the methods based on EFIE-MoM. A numerical electromagnetic program is developed and its correctness is proved. Geometrical modeling and auto-meshing are made through mature CAD software, which greatly simplify the programming of MoM.
Then based on EFIE-MoM, the current computation and scattering problems of arbitrary-shaped complex PEC platform with uniform plane wave incidence are solved.
And then the radiation problems of various kinds of wire antennas (i.e. straight wire antenna, helix wire antenna, Koch fractal antenna, etc.) mounted on the complex-shaped PEC platform are solved based on the EFIE-MoM and junction basis function.
Finally the scattering problems of complex-shaped electrically-large 2D PEC targets are solved based on the hybrid method of IPO and MoM, which can be easily expanded to the 3-D condition.
引文
[1] S.M.Rao, D.R.Wilton, and A W.Glisson. "Electromagnetic scattering by surface of arbitrary shape". IEEE Trans. on Antennas and Propagation, Vol.30(3): 409-418,May 1982.
[2] S.M.Rao, D.R.Wilton, and A.W.Glisson. "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains". IEEE Trans. on Antennas and Propagation, Vol.32(3): 276-281 ,May 1984.
[3] K.Fujimoto and A.Henderson. 小天线．兵器工业出版社．北京，1992．
[4] R.F.Harrington. Field Computation by Moment Methods. McMillan, New York, 1968
[5] 金建铭著，王建国译，葛德彪校．电磁场有限元方法．西安电子科技大学出版社．
[6] 李世智．电磁辐射与散射中的矩量法．电子工业出版社，1985．
[7] 华夷和．基于边界积分方程的复杂金属载体上线天线的电磁特性研究．南京航空航天大学博士学位论文．2003年5月．
[8] Bhattacharya and etc. The input impedance of a monopole antenna mounted on a cubical conducting box. IEEE Trans. on Antennas and Propagation, Vol.35:756-762,1987.
[9] C. Punete el al."The koch monopole: a small fractal antenna", IEEE Trans. Antennas and Propagation,Vol-48(11): 1773-1781, 2000.
[10] R.F.Harrington. Time Harmonic Electromagnetics. Mchill Press, 1960
[11] J.A. Stratton. Electromagnetic Theory. McGraw-Hill,NY, July 1941
[12] F. Obelleiro, J.M.Taboada, J.L.Rodriguez, J.O.Rubinos, and A.M.Arias. Hybrid moment-method physical-optics formulation for modeling the electromagnetic behavior of on-board antennas. Microwave and Optical Technique Letters,Vol.27(2):88-93, Oct 2000.
[13] C.C.Lu and W.C.Chew. Electromagnetic scattering from material coated pec objects: a hybrid volume and surface integral approach. IEEE Antennas Propagation Symposium, 1999.
[14] 华夷和，徐金平．金属载体上线天线阻抗与辐射特性的矩量法分析．南京航空航天大学学报，34(3)：298-301，2002．
[15] N.C.Albertsen, J.E.Hansen, and N.E.Jensen. Computation of radiation from wire antnnas on conducting bodies. IEEE Trans Antennas and Propagation, Vol. 22:200-205,1974.
[16] 聂小春，葛德彪，阎玉波．IPO-MoM混合方法分析开槽电大目标的电磁散射，电子学报Vol．27，No．9，1999．
[17] R.F.Harrington and J.R.Mautz. A Generalized network formulation for aperture problem. IEEE Trans. on. AP, 1976, 24(6):870～873.
[18] J.M.Jin, S.S.Ni and S.W.Lee. Hybridization of SBR and FEM for scattering by large bodies with cracks and cavities. IEEE Trans. on. AP, 1995, 43(10): 1130～1138.
[19] Fermando Obelleiro Basteiro, Jose Luis Rodriguez and Robert J.Burkholder. An iterative physical optics approach for analyzing the electromagnetic scattering by large open-ended cavities. IEEE Trans. on AP, 1995,43(4):356～361.
[20] M.Kaye,P.K. Murthy and G.A.Thiele. An iterative method for solving scattering problems. IEEE Trans. on AP, 1985,33(11):1272～1279.
[21] Shyh-Kang Jeng. Scattering from a Cavity-Backed Slit in a Ground Plane——TE Case. IEEE Trans. on AP, 1990,38(10): 1523～1529.
[22] 王竹溪，郭敦仁，特殊函数概论．2000年5月，第1版．
[23] Ibrahim Tekin and E.H.Newman. Method of moment solution for a wire attached to an arbitrary faceted surface. IEEE Trans. on Antennas and Propagation, Vol.46(4), April 1998.
[24] Lee, L. Martin, and J. P. Castillo. Limitations of wire grid modelling of a closed surface. IEEE Trans. EMC, Vol.16:172, 1974.
[25] 姚海英，聂在平，三维矢量散射分析中奇异积分的准确计算方法．电子科学学刊，Vol．22(3)：471-477，2000．
[26] G. W. Hohmann. Three-dimensional em modelling. Geophysical Surveys, Vol.6:27-53,1983.
[27] R. A. Mittra. Computer Techniques for Electromagnetics. Hemisphere Publishing Corporation, 1973.
[28] S. A. Schelkunof. Advanced Antenna Theory. John Wiley and Sons, New York, 1952
[29] 盛剑霓．电磁场数值计算．电子工业出版社，1983．
[30] 华夷和，徐金平，电场积分方程矩量法中具有局部连续性的基函数积分奇异性降阶处理，电子与信息学报，Vol．25，No．8：
[31] E.H. Newman and P.Tulyatha. A surface patch model for polygonal plates. IEEE Trans. AP, Vol.30(4):588-593, July 1982.
[2] S.M.Rao, D.R.Wilton, and A.W.Glisson. "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains". IEEE Trans. on Antennas and Propagation, Vol.32(3): 276-281 ,May 1984.
[3] K.Fujimoto and A.Henderson. 小天线．兵器工业出版社．北京，1992．
[4] R.F.Harrington. Field Computation by Moment Methods. McMillan, New York, 1968
[5] 金建铭著，王建国译，葛德彪校．电磁场有限元方法．西安电子科技大学出版社．
[6] 李世智．电磁辐射与散射中的矩量法．电子工业出版社，1985．
[7] 华夷和．基于边界积分方程的复杂金属载体上线天线的电磁特性研究．南京航空航天大学博士学位论文．2003年5月．
[8] Bhattacharya and etc. The input impedance of a monopole antenna mounted on a cubical conducting box. IEEE Trans. on Antennas and Propagation, Vol.35:756-762,1987.
[9] C. Punete el al."The koch monopole: a small fractal antenna", IEEE Trans. Antennas and Propagation,Vol-48(11): 1773-1781, 2000.
[10] R.F.Harrington. Time Harmonic Electromagnetics. Mchill Press, 1960
[11] J.A. Stratton. Electromagnetic Theory. McGraw-Hill,NY, July 1941
[12] F. Obelleiro, J.M.Taboada, J.L.Rodriguez, J.O.Rubinos, and A.M.Arias. Hybrid moment-method physical-optics formulation for modeling the electromagnetic behavior of on-board antennas. Microwave and Optical Technique Letters,Vol.27(2):88-93, Oct 2000.
[13] C.C.Lu and W.C.Chew. Electromagnetic scattering from material coated pec objects: a hybrid volume and surface integral approach. IEEE Antennas Propagation Symposium, 1999.
[14] 华夷和，徐金平．金属载体上线天线阻抗与辐射特性的矩量法分析．南京航空航天大学学报，34(3)：298-301，2002．
[15] N.C.Albertsen, J.E.Hansen, and N.E.Jensen. Computation of radiation from wire antnnas on conducting bodies. IEEE Trans Antennas and Propagation, Vol. 22:200-205,1974.
[16] 聂小春，葛德彪，阎玉波．IPO-MoM混合方法分析开槽电大目标的电磁散射，电子学报Vol．27，No．9，1999．
[17] R.F.Harrington and J.R.Mautz. A Generalized network formulation for aperture problem. IEEE Trans. on. AP, 1976, 24(6):870～873.
[18] J.M.Jin, S.S.Ni and S.W.Lee. Hybridization of SBR and FEM for scattering by large bodies with cracks and cavities. IEEE Trans. on. AP, 1995, 43(10): 1130～1138.
[19] Fermando Obelleiro Basteiro, Jose Luis Rodriguez and Robert J.Burkholder. An iterative physical optics approach for analyzing the electromagnetic scattering by large open-ended cavities. IEEE Trans. on AP, 1995,43(4):356～361.
[20] M.Kaye,P.K. Murthy and G.A.Thiele. An iterative method for solving scattering problems. IEEE Trans. on AP, 1985,33(11):1272～1279.
[21] Shyh-Kang Jeng. Scattering from a Cavity-Backed Slit in a Ground Plane——TE Case. IEEE Trans. on AP, 1990,38(10): 1523～1529.
[22] 王竹溪，郭敦仁，特殊函数概论．2000年5月，第1版．
[23] Ibrahim Tekin and E.H.Newman. Method of moment solution for a wire attached to an arbitrary faceted surface. IEEE Trans. on Antennas and Propagation, Vol.46(4), April 1998.
[24] Lee, L. Martin, and J. P. Castillo. Limitations of wire grid modelling of a closed surface. IEEE Trans. EMC, Vol.16:172, 1974.
[25] 姚海英，聂在平，三维矢量散射分析中奇异积分的准确计算方法．电子科学学刊，Vol．22(3)：471-477，2000．
[26] G. W. Hohmann. Three-dimensional em modelling. Geophysical Surveys, Vol.6:27-53,1983.
[27] R. A. Mittra. Computer Techniques for Electromagnetics. Hemisphere Publishing Corporation, 1973.
[28] S. A. Schelkunof. Advanced Antenna Theory. John Wiley and Sons, New York, 1952
[29] 盛剑霓．电磁场数值计算．电子工业出版社，1983．
[30] 华夷和，徐金平，电场积分方程矩量法中具有局部连续性的基函数积分奇异性降阶处理，电子与信息学报，Vol．25，No．8：
[31] E.H. Newman and P.Tulyatha. A surface patch model for polygonal plates. IEEE Trans. AP, Vol.30(4):588-593, July 1982.