有限周期电大尺寸频率选择面电磁散射特性的体面积分方法分析
摘要
频率选择表面(FSS)的工程应用非常广泛,但到目前为止,对FSS的研究大部分仍假定其为平面的并且是无限大周期,而在实际应用中,FSS阵列通常是有限大结构,甚至是曲面的,而且加载介质。所以对有限尺寸加载介质FSS阵列的电磁分析具有重要的实用价值。
在上述工程应用背景下,本文使用体面积分方程(VSIE)结合矩量法(MOM)来分析这种曲面有限周期加载介质FSS结构的传输特性。体面积分方程方法具有两个优点:一个是能够完全模拟任意形状FSS结构,另外就是比较容易应用多层快速多极子算法(MLFMA),来分析电大尺寸结构和加快求解速度。
本文首先分析了VSIE的基本原理及其公式推导,利用VSIE方法分析了复杂介质金属混合结构的电磁散射,其中包括曲面有限周期加载介质FSS阵列结构的散射特性。接着本文介绍了有限尺寸FSS结构传输和反射特性的分析方法和给出了传输和反射系数的求解公式,并利用VSIE结合MLFMA方法分析了曲面有限周期FSS阵列加载介质时的传输和反射特性,其基本单元为方环和十字贴片,并分别对其平面波垂直入射和斜入射情况下的透射曲线和反射曲线进行分析,将计算结果与软件仿真的无限大周期单元的结果进行对比,可以看出结果显示了较好的选频特性。
The engineering application of frequency selective surfaces (FSS) is broad. Up to now, most of the researches on the FSS still assumed that the FSS is planar and infinite-period array. But in practical applications, FSS arrays are usually finite structures, and sometimes are curved, even with dielectrics loaded. So the electromagnetic analysis on FSS with finite size and dielectric is valuable.
In the background of mentioned Engineering applications, this article present a hybrid volume-surface integral-equation(VSIE) combined with moment method (MOM) to analyze the transmission and reflection characteristics of curved and finite FSS structures which have dielectric substrate. The hybrid integral equations approach has two advantages. One is the capability of modeling arbitrarily shaped FSS structures in detail, the other one allows us to easily apply the multilevel fast multipole algorithm (MLFMA) to analyze electrically large structures and speed up the solution speed.
Firstly, this article also analysis the basic principles of VSIE and gives its formula. We use the method of VSIE to analysis the scattering of complex structure mixed with dielectrics and metal, including the curved and finite FSS structures, which FSS has dielectric substrate. This article also describes how to analysis the transmission and reflection characteristics of finite FSS, and gives the formula of transmission and reflection coefficient. The method of VSIE combined with MLFMA is used to analysis the curved and finite FSS structures loaded with dielectric substrate, these FSS are the arrays of Square-loop and Cross, then the transmission characteristics can be got from them. In the analysis, the normal incidence and oblique incidence of plane-wave are also considered in it. Then we analysis the transmission and reflection coefficient and compare them with some results got from simulating infinite-period array in a software, it can be seen that the results show a good characteristics of frequency-selective.
在上述工程应用背景下,本文使用体面积分方程(VSIE)结合矩量法(MOM)来分析这种曲面有限周期加载介质FSS结构的传输特性。体面积分方程方法具有两个优点:一个是能够完全模拟任意形状FSS结构,另外就是比较容易应用多层快速多极子算法(MLFMA),来分析电大尺寸结构和加快求解速度。
本文首先分析了VSIE的基本原理及其公式推导,利用VSIE方法分析了复杂介质金属混合结构的电磁散射,其中包括曲面有限周期加载介质FSS阵列结构的散射特性。接着本文介绍了有限尺寸FSS结构传输和反射特性的分析方法和给出了传输和反射系数的求解公式,并利用VSIE结合MLFMA方法分析了曲面有限周期FSS阵列加载介质时的传输和反射特性,其基本单元为方环和十字贴片,并分别对其平面波垂直入射和斜入射情况下的透射曲线和反射曲线进行分析,将计算结果与软件仿真的无限大周期单元的结果进行对比,可以看出结果显示了较好的选频特性。
The engineering application of frequency selective surfaces (FSS) is broad. Up to now, most of the researches on the FSS still assumed that the FSS is planar and infinite-period array. But in practical applications, FSS arrays are usually finite structures, and sometimes are curved, even with dielectrics loaded. So the electromagnetic analysis on FSS with finite size and dielectric is valuable.
In the background of mentioned Engineering applications, this article present a hybrid volume-surface integral-equation(VSIE) combined with moment method (MOM) to analyze the transmission and reflection characteristics of curved and finite FSS structures which have dielectric substrate. The hybrid integral equations approach has two advantages. One is the capability of modeling arbitrarily shaped FSS structures in detail, the other one allows us to easily apply the multilevel fast multipole algorithm (MLFMA) to analyze electrically large structures and speed up the solution speed.
Firstly, this article also analysis the basic principles of VSIE and gives its formula. We use the method of VSIE to analysis the scattering of complex structure mixed with dielectrics and metal, including the curved and finite FSS structures, which FSS has dielectric substrate. This article also describes how to analysis the transmission and reflection characteristics of finite FSS, and gives the formula of transmission and reflection coefficient. The method of VSIE combined with MLFMA is used to analysis the curved and finite FSS structures loaded with dielectric substrate, these FSS are the arrays of Square-loop and Cross, then the transmission characteristics can be got from them. In the analysis, the normal incidence and oblique incidence of plane-wave are also considered in it. Then we analysis the transmission and reflection coefficient and compare them with some results got from simulating infinite-period array in a software, it can be seen that the results show a good characteristics of frequency-selective.
引文
[1]R.F.Harrington.Field Computation by Moment Methods.Malabar,Florida:Krieger Publishing Company,1983
[2]E.K.Miller,L.M.Mitschang,and E.H.Newman," Computational Electromagnetics:Frequency-Domain Method of Moments ".New York:IEEE Press,1992
[3]J.M.Song,W.C.Chew." Fast multipole method solution of three dimensional integral equations ".IEEE Antennas Propagation Symposium,1995:1528-1531
[4]J.M.Song,C.C.Lu,W.C.Chew and S.W.Lee." Introduction to Fast Illinois Solver Code(FISC) ".IEEE Antennas propagation symposium,1997:48-51
[5]M.Chen,S.N.Wang,R.S.Chen and Z.H.Fan." Electromagnetic Analysis of Electrically large and Finite periodic Frequency Selective Surfaces ",2008
[6]J.M.Song,W.C.Chew." Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering ".Microwave and Optical Tech.Lett.1995,10(10):14-19
[7]C.C.Lu and W.C.Chew," Electromagnetic scattering from material coated PEC objects:A hybrid volume and surface integral equation approach ",IEEE Antennas Propagat.Soc Int Symp,Orlando,FL,1999
[8]C.C.Lu and W.C.Chew," A coupled surface-volume integral equation approach for the calculation of electromagnetic scattering from composite metallic and material targets ",IEEE Trans.Antennas Propag.2000,48(12):1866-1868
[9]Cai-Cheng Lu and Chun Yu," Analysis of Microstrip Structures of Finite Ground Plane Using the Hybrid Volume-Surface Integral Equation Approach ",IEEE Trans.Antennas Propagation,Society Inrernational Symposium,2002:162-165
[10]C.C.Lu and C.Yu," Computation of input impedance of printed antennas with finite size and arbitrarily shaped dielectric substrate and ground plane ",IEEE Trans.Antennas Propagation.2004,52:615-619
[11]E.H.Newman and P.Tulyathan," Wire antennas in the presence of a dielectric/ferrite inhomogeneity ",IEEE Trans.Antennas Propagation.1978,26:587-593
[12]T.K.Sarlar and E.Arvas," An integral equation approach to the analysis of finite microstrip antennas:Volume/surface formulation",IEEE Trans.Antennas Propagation.1990,38:305-312
[13]T.K.Sarlar,S.M.Rao,and A.R.Djordjevic," Electromagnetic scattering and radiation from finite microstrip structures",IEEE Trans Microwave Theory Tech.1990.38:1568-1575
[14]阮颖铮等编著,雷达截面与隐身技术,国防工业出版社,1998
[15]C.Pochini,G.Toso,G.Pelosi,and A.Roederer," A comparison between two hybrid techniques for the scattering from finite frequency-selective surfaces ",Microwave Opt Technol Let.2001,31:248-252
[16]盛新庆,计算电磁学要论[M].科学出版社,2004:16-75
[17]Xiao-Chun Nie,Ning Yuan,Le-Wei Li,Yeow-Beng Gan,and Tat Soon Yeo." A Fast Volume-Surface Integral Equation Solver for Scattering From Composite Conducting-Dielectric Objects",IEEE Trans.Antennas Propagation,2005,53(2):818-824
[18]R.Mittra,C.H.Chan,and T.Cwik," Techniques for analyzing frequency selective surfaces:A review",Proc IEEE 1988,76:1593-1615
[19]P.W.Grounds and K.J.Webb,"Numerical analysis of finite frequency selective surface with rectangular patches of various aspect ratios",IEEE Trans.Antennas Propagation.1991,39:569-575
[20]Y.Sarkar,A.Djordjevic,and E.Arvas,"On the choice of expansion and weighting functions in the numerical solution of operator equations",IEEE Trans.Antennas Propagation,1985(33):988-996
[21]L.Gurel,K.Sertel,and I.K.Sendur,"On the choice of basis functions to model surface electric current densities in computational electromagnetic",Radio Science,1999(34):1373-1387
[22]R.F.Harrington." Field Computation by Moment Methods".Krieger Publishing Company,Malabar,Florida,1983
[23]C.F.Wang and J.M.Jin,"A fast full-wave analysis of scattering and radiation from large finite arrays of microstrip antennas",IEEE Trans.Antennas Propagation.1998,46(10):1467-1474
[24]史为民,方大纲,陶玉明.毫米波/红外频率选择表面研究[J].电波科学学报,1995,10(1):183-187
[25]PELTON E L and MUNK B A."Scattering from periodic arrays of crossed dipoles".IEEE Trans.Ante nnas Propagation,1979,27(3):323-330
[26]SAVIA S B,PARKER E A,PHILIPS B."Finite planar and curved-ring-element frequency selective surfaces".IEEE Trans.Antennas Propagation.1999,146(6):401-406
[27]YU C,LU C-C." Analysis of finite and curved frequency-selective surfaces using the hybrid volume-surface integral equation approach ".Microwave and Optical Technology Letters,2005,45(2):107-112
[28]WU T K."Frequency Selective Surface and Grid Array ".New York:Wiley,1995.
[29]D.R.WILTON,S.M.RAO,A.W.GLISSON,D.H.SCHAUBERT,AL-BUNDAK and C.M.BUTLER," Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains",IEEE Trans.Antennas Propagation,1984,AP-32(3):276-281
[30]YU C,LU C-C."Analysis of Curved Frequency Selective Surfaces Using the Hybrid Volume-Surface Integral Equation Approach".IEEE Trans.Antennas Propagation,Sociery Inrernational Symposium,2003:809-812
[31]R.S.Chen,Edward.K.N.Yung,C.H.Chan,D.X.Wang and D.G.Fang."Application of the SSOR preconditioned conjugate gradient algorithm to the vector FEM for 3-dimensional full-wave analysis of Electromagnetic-field boundary value problems".IEEE Trans.on Microwave Theory and Tech,2002,50(4):1165-1172
[32]樊振宏,电磁散射分析中的快速方法.南京理工大学,博士论文,2006.
[33]Sergey N.Makarov,Shashank D.Kulkarni,Andrew G.Marut,and Leo C.Kempel," Method of Moments Solution for a Printed Patch/Slot Antenna on a Thin Finite Dielectric Substrate Using the Volume Integral Equation" IEEE Trans.Antennas Propagation,2006,54(4):818-824
[34]C.-C.Lu," Volume-surface integral equation",in Fast and eficient algorithms in computational electmmagnetics,E.M.W.C.Chew,J.-M.Jin,and J.Song,Eds.Boston-London:Artech House,2001:487-540
[35]Ning Yuan,Tat Soon Yeo,Xiao Chun Nie,Le Wei Liand Yeow Beng Gan " Efficient analysis of electromagnetic scattering and radiation from patches on finite,arbitrarily curved,grounded substrates",Radio Science,2004,39
[36]Cai-Cheng Lu," Multilevel Fast Multipole Algorithm for Electromagnetic Scattering from Conducting Objects with Material Coating" IEEE Trans.Antennas Propagation,2001,49(2):770-773
[37]Xiao-Chun Nie,Le-Wei Li,Ning Yuan,Tat Soon Yeo,and Yeow-Beng Gan,"Precorrected-FFT Solution of the Volume Integral Equation for 3-D Inhomogeneous Dielectric Objects" IEEE Trans.Antennas Propagation,2005,53(1):313-320
[38]陈晓光,金亚秋,三维电磁波体积分方程中的快速多极子算法,电子科学学刊,2000,22(6):1007-1015
[39]王浩刚.电大尺寸含腔体复杂目标矢量电磁散射一体化精确建模与高效算法研究.四川成都:电子科技大学博士学位论文,2001
[40]万继响,张玉,项铁铭,梁昌洪,FMM结合改进自适应MBPE技术快速求解单站RCS,电波科学学报,2004(19):72-76
[41]J.M.Song,C.C.Lu,W.C.Chew,S.W.Lee." Fast Illinois solver code(FISC)".IEEE Transactions on Antennas and Propagation,1998,40(3):27-34
[42]T.K.Shark,S.M..Rao,and A.R.Djordievic,"Electromagnetic scattering and radiation from finite microstrip structures",IEEE Trans.Micro.Theory Tech,1990,38(11):1568-1575
[43]CWIK T and MITTRA R."The effects of the truncation and curvature of periodic surfaces:a strip grating".IEEE Trans.Antennas Propagation,1988,36(5):612-622
[44]M.RAO,R.WILTON,W.GLISSON," Electromagnetic Scattering by Surfaces of Arbitrary Shape" IEEE Trans.Antennas Propagation,1982,AP-30(3):409-418
[45]D.H.Schaubert,D.R.Wilton,and A.W.Glisson,"A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies," IEEE Trans.Antennas and Propagation,1984,AP-32(1):77-85
[46]Paolo Arcioni,Marco Bressan,and Luca Perregrini."On the Evaluation of the Double Surface Integrals Arising in the Application of the Boundary Integral Method to 3-D Problems",IEEE Transactions On Microwave Theory And Techniques,1997,45(3):436-439
[2]E.K.Miller,L.M.Mitschang,and E.H.Newman," Computational Electromagnetics:Frequency-Domain Method of Moments ".New York:IEEE Press,1992
[3]J.M.Song,W.C.Chew." Fast multipole method solution of three dimensional integral equations ".IEEE Antennas Propagation Symposium,1995:1528-1531
[4]J.M.Song,C.C.Lu,W.C.Chew and S.W.Lee." Introduction to Fast Illinois Solver Code(FISC) ".IEEE Antennas propagation symposium,1997:48-51
[5]M.Chen,S.N.Wang,R.S.Chen and Z.H.Fan." Electromagnetic Analysis of Electrically large and Finite periodic Frequency Selective Surfaces ",2008
[6]J.M.Song,W.C.Chew." Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering ".Microwave and Optical Tech.Lett.1995,10(10):14-19
[7]C.C.Lu and W.C.Chew," Electromagnetic scattering from material coated PEC objects:A hybrid volume and surface integral equation approach ",IEEE Antennas Propagat.Soc Int Symp,Orlando,FL,1999
[8]C.C.Lu and W.C.Chew," A coupled surface-volume integral equation approach for the calculation of electromagnetic scattering from composite metallic and material targets ",IEEE Trans.Antennas Propag.2000,48(12):1866-1868
[9]Cai-Cheng Lu and Chun Yu," Analysis of Microstrip Structures of Finite Ground Plane Using the Hybrid Volume-Surface Integral Equation Approach ",IEEE Trans.Antennas Propagation,Society Inrernational Symposium,2002:162-165
[10]C.C.Lu and C.Yu," Computation of input impedance of printed antennas with finite size and arbitrarily shaped dielectric substrate and ground plane ",IEEE Trans.Antennas Propagation.2004,52:615-619
[11]E.H.Newman and P.Tulyathan," Wire antennas in the presence of a dielectric/ferrite inhomogeneity ",IEEE Trans.Antennas Propagation.1978,26:587-593
[12]T.K.Sarlar and E.Arvas," An integral equation approach to the analysis of finite microstrip antennas:Volume/surface formulation",IEEE Trans.Antennas Propagation.1990,38:305-312
[13]T.K.Sarlar,S.M.Rao,and A.R.Djordjevic," Electromagnetic scattering and radiation from finite microstrip structures",IEEE Trans Microwave Theory Tech.1990.38:1568-1575
[14]阮颖铮等编著,雷达截面与隐身技术,国防工业出版社,1998
[15]C.Pochini,G.Toso,G.Pelosi,and A.Roederer," A comparison between two hybrid techniques for the scattering from finite frequency-selective surfaces ",Microwave Opt Technol Let.2001,31:248-252
[16]盛新庆,计算电磁学要论[M].科学出版社,2004:16-75
[17]Xiao-Chun Nie,Ning Yuan,Le-Wei Li,Yeow-Beng Gan,and Tat Soon Yeo." A Fast Volume-Surface Integral Equation Solver for Scattering From Composite Conducting-Dielectric Objects",IEEE Trans.Antennas Propagation,2005,53(2):818-824
[18]R.Mittra,C.H.Chan,and T.Cwik," Techniques for analyzing frequency selective surfaces:A review",Proc IEEE 1988,76:1593-1615
[19]P.W.Grounds and K.J.Webb,"Numerical analysis of finite frequency selective surface with rectangular patches of various aspect ratios",IEEE Trans.Antennas Propagation.1991,39:569-575
[20]Y.Sarkar,A.Djordjevic,and E.Arvas,"On the choice of expansion and weighting functions in the numerical solution of operator equations",IEEE Trans.Antennas Propagation,1985(33):988-996
[21]L.Gurel,K.Sertel,and I.K.Sendur,"On the choice of basis functions to model surface electric current densities in computational electromagnetic",Radio Science,1999(34):1373-1387
[22]R.F.Harrington." Field Computation by Moment Methods".Krieger Publishing Company,Malabar,Florida,1983
[23]C.F.Wang and J.M.Jin,"A fast full-wave analysis of scattering and radiation from large finite arrays of microstrip antennas",IEEE Trans.Antennas Propagation.1998,46(10):1467-1474
[24]史为民,方大纲,陶玉明.毫米波/红外频率选择表面研究[J].电波科学学报,1995,10(1):183-187
[25]PELTON E L and MUNK B A."Scattering from periodic arrays of crossed dipoles".IEEE Trans.Ante nnas Propagation,1979,27(3):323-330
[26]SAVIA S B,PARKER E A,PHILIPS B."Finite planar and curved-ring-element frequency selective surfaces".IEEE Trans.Antennas Propagation.1999,146(6):401-406
[27]YU C,LU C-C." Analysis of finite and curved frequency-selective surfaces using the hybrid volume-surface integral equation approach ".Microwave and Optical Technology Letters,2005,45(2):107-112
[28]WU T K."Frequency Selective Surface and Grid Array ".New York:Wiley,1995.
[29]D.R.WILTON,S.M.RAO,A.W.GLISSON,D.H.SCHAUBERT,AL-BUNDAK and C.M.BUTLER," Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains",IEEE Trans.Antennas Propagation,1984,AP-32(3):276-281
[30]YU C,LU C-C."Analysis of Curved Frequency Selective Surfaces Using the Hybrid Volume-Surface Integral Equation Approach".IEEE Trans.Antennas Propagation,Sociery Inrernational Symposium,2003:809-812
[31]R.S.Chen,Edward.K.N.Yung,C.H.Chan,D.X.Wang and D.G.Fang."Application of the SSOR preconditioned conjugate gradient algorithm to the vector FEM for 3-dimensional full-wave analysis of Electromagnetic-field boundary value problems".IEEE Trans.on Microwave Theory and Tech,2002,50(4):1165-1172
[32]樊振宏,电磁散射分析中的快速方法.南京理工大学,博士论文,2006.
[33]Sergey N.Makarov,Shashank D.Kulkarni,Andrew G.Marut,and Leo C.Kempel," Method of Moments Solution for a Printed Patch/Slot Antenna on a Thin Finite Dielectric Substrate Using the Volume Integral Equation" IEEE Trans.Antennas Propagation,2006,54(4):818-824
[34]C.-C.Lu," Volume-surface integral equation",in Fast and eficient algorithms in computational electmmagnetics,E.M.W.C.Chew,J.-M.Jin,and J.Song,Eds.Boston-London:Artech House,2001:487-540
[35]Ning Yuan,Tat Soon Yeo,Xiao Chun Nie,Le Wei Liand Yeow Beng Gan " Efficient analysis of electromagnetic scattering and radiation from patches on finite,arbitrarily curved,grounded substrates",Radio Science,2004,39
[36]Cai-Cheng Lu," Multilevel Fast Multipole Algorithm for Electromagnetic Scattering from Conducting Objects with Material Coating" IEEE Trans.Antennas Propagation,2001,49(2):770-773
[37]Xiao-Chun Nie,Le-Wei Li,Ning Yuan,Tat Soon Yeo,and Yeow-Beng Gan,"Precorrected-FFT Solution of the Volume Integral Equation for 3-D Inhomogeneous Dielectric Objects" IEEE Trans.Antennas Propagation,2005,53(1):313-320
[38]陈晓光,金亚秋,三维电磁波体积分方程中的快速多极子算法,电子科学学刊,2000,22(6):1007-1015
[39]王浩刚.电大尺寸含腔体复杂目标矢量电磁散射一体化精确建模与高效算法研究.四川成都:电子科技大学博士学位论文,2001
[40]万继响,张玉,项铁铭,梁昌洪,FMM结合改进自适应MBPE技术快速求解单站RCS,电波科学学报,2004(19):72-76
[41]J.M.Song,C.C.Lu,W.C.Chew,S.W.Lee." Fast Illinois solver code(FISC)".IEEE Transactions on Antennas and Propagation,1998,40(3):27-34
[42]T.K.Shark,S.M..Rao,and A.R.Djordievic,"Electromagnetic scattering and radiation from finite microstrip structures",IEEE Trans.Micro.Theory Tech,1990,38(11):1568-1575
[43]CWIK T and MITTRA R."The effects of the truncation and curvature of periodic surfaces:a strip grating".IEEE Trans.Antennas Propagation,1988,36(5):612-622
[44]M.RAO,R.WILTON,W.GLISSON," Electromagnetic Scattering by Surfaces of Arbitrary Shape" IEEE Trans.Antennas Propagation,1982,AP-30(3):409-418
[45]D.H.Schaubert,D.R.Wilton,and A.W.Glisson,"A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies," IEEE Trans.Antennas and Propagation,1984,AP-32(1):77-85
[46]Paolo Arcioni,Marco Bressan,and Luca Perregrini."On the Evaluation of the Double Surface Integrals Arising in the Application of the Boundary Integral Method to 3-D Problems",IEEE Transactions On Microwave Theory And Techniques,1997,45(3):436-439