柱面多层结构快速格林函数法研究
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摘要
圆柱面共形天线作为一种最简单的曲面共形结构，受到学术界越来越广泛的重视，在工程上也得到了越来越多的应用。然而，目前还缺少关于该类结构的高效精确分析方法，已有的各类商业电磁仿真软件计算效率还不够高。鉴于以上研究现状，本文在已有研究的基础上，对基于柱面分层媒质格林函数的矩量法进行了详细和系统的研究。
首先，本文详细和完整地推导了ejω t体制下柱面分层结构场型并矢格林函数各分量（EDGFs）的显式表示式，从而克服已有研究存在的表达式不完整、定义不清晰、推导不简洁等缺点。为后续研究打下基础。
为了克服柱面分层结构场型并矢格林函数在数值计算时出现溢出问题，本文将场型并矢格林函数改写成关于贝塞尔函数比值式的表示式，从而避免直接计算高阶大自变量贝塞尔函数，有效克服数值溢出问题。与已有研究相比，本文结果更加简明、通用、易于算法实现。
为了进一步提高已有算法计算空域场型并矢格林函数远区场的精度和效率，本文提出了一种基于有理函数逼近（RFFM）的表面波提取方法。该方法能够快速精确计算场型并矢格林函数近区和远区场，将已有快速方法场源距离的适用值提高一个数量级，从而有效提高精确分析电大尺寸问题的能力。
为了能够采用RWG基函数等性能良好的空域基函数对柱面共形天线进行矩量法分析，本文对柱面空域混合位并矢格林函数作了进一步的研究。首先，在已有研究的基础上进一步研究了柱面谱域混合位并矢格林函数（MPDGFs）的表达式，对已有文献中存在的两组不同表达形式进行了重新推导和进一步的验证。同时，本文将RFFM方法推广到空域混合位并矢格林函数远区场的快速精确计算中。
针对已有方法在计算空域混合位型并矢格林函数时存在轴线发散问题。本文提出了一种解析二阶渐近项提取方法，将谱域格林函数中与轴线相关的奇异项完全提取出来，并应用Sommerfeld恒等式解析变换到空域中，从而使得剩余数值计算部分快速收敛。与已有方法相比，该方法对基函数没有限制，收敛性和稳定性也更好。
最后，在以上研究的基础上，本文采用基于屋顶基的空域矩量法，对柱面振子天线、矩形贴片天线的输入阻抗、表面电流、辐射方向图以及阵元间的互耦特性进行了分析。通过与其它算法结果及商业仿真软件相对比，说明本算法的准确性、高效性和适用性。
本文相关研究结果可为圆柱面共形天线结构的快速、准确分析提供一套有效解决方案。
As the simplest conformal strucuture, cylindrical surface has received more andmore attention. Now, cylindrically conformal antennas have been widely applied inpractice. However, until now, there has no efficient and accurate analysis method forthis type of structure, the efficiency of the commercial software for electromagneticsimulation is not very satisfying. Due to this situation, in this thesis, an efficient andaccurate method, which is based on the method of moments (MoM) combined with thelayered Green’s functions for cylindrically stratified structure, is studied exhaustivelyand systematically.
First, to overcome the problem in the literature for deriving the formula of theelectric dyadic Green’s functions (EDGFs) for cylindrically stratified structure, such asthe incomplete equations, the unclear definitions, and the complicated derivation, theexplicit formula of EDGFs is thoroughly rederived, which provides a foundation for thefollowing study.
In order to avoid possible overflow/underflow problems in the numericalcalculations of EDGFs for cylindrically stratified media, the explicit expressions of thecomponents of EDGFs are rewritten in the ratios of Bessel and Hankel functions, whichavoids directly calculating Bessel and Hankel functions with high order and largearguments. Compared with other method, the procedure in this thesis is simpler, andeasier for programming and application.
In order to further improve the accuracy and efficiency of the numerical method inthe calculation of the components of EDGFs in spatial domain. A surface-waveextraction method based on the rational function fitting method (RFFM) is proposed.The method can calculate both the near and far field of the components of EDGFsefficiently and accurately. The accuracy range between the source and field points isincreased by about one order, which can enhance the ability for analyzing theelectrically large antennas mounted on cylindrical surface.
In the analysis of cylindrically stratified structure, in order to make use of theRWG basis function in the MoM procedure, the mixed potential dyadic Green’sfunctions (MPDGFs) for cylindrically stratified media are further studied in this thesis.Two different forms of MPDGFs reported in the literature are rederived anddemonstrated. Meanwhile, the RFFM is extended to calculate the far fields of thecomponents of MPDGFs.
From the literature, it is found that the method proposed for the calculation ofspatial-domain MPDGFs can not be valid when the source and field points are locatedon the same axial line, which will make the MoM Procedure more complex. In order toovercome this problem, a two order analytical asymptotic term extraction method is proposed in this thesis. In this method, the singular parts related to the axial line arecompletely extracted, and then transformed into the spatial domain with the aid ofSommerfeld identities. After this extraction, the remaining parts in the spectral domainare fast convergent and can be easily transformed into the spatial domain using thenumerical method such as the generalized pencil of function method (GPOF). Unlikethe other method, this method need not choose special basis functions to cancel thesingularity in the spectral-domain MPDGFs. The performance of convergence andstability are significantly improved.
At last, based on the above study, the MoM procedure combined with the roof-topbasis function is applied for analyzing dipole and rectangular antennas mounted on thecylindrical surface. The input impedance, surface current, radiation pattern and themutual coupling coefficients between antenna array elements are calculated. Incomparison to the results obtained by other algorithms and the simulation software, it isdemonstrated that the method in this thesis has a good performance of accuracy,efficiency and easy applicability.
The procedure introduced in this thesis will provide a possibility for analyzingcylindrically conformal antennas more efficiently and accurately.
首先，本文详细和完整地推导了ejω t体制下柱面分层结构场型并矢格林函数各分量（EDGFs）的显式表示式，从而克服已有研究存在的表达式不完整、定义不清晰、推导不简洁等缺点。为后续研究打下基础。
为了克服柱面分层结构场型并矢格林函数在数值计算时出现溢出问题，本文将场型并矢格林函数改写成关于贝塞尔函数比值式的表示式，从而避免直接计算高阶大自变量贝塞尔函数，有效克服数值溢出问题。与已有研究相比，本文结果更加简明、通用、易于算法实现。
为了进一步提高已有算法计算空域场型并矢格林函数远区场的精度和效率，本文提出了一种基于有理函数逼近（RFFM）的表面波提取方法。该方法能够快速精确计算场型并矢格林函数近区和远区场，将已有快速方法场源距离的适用值提高一个数量级，从而有效提高精确分析电大尺寸问题的能力。
为了能够采用RWG基函数等性能良好的空域基函数对柱面共形天线进行矩量法分析，本文对柱面空域混合位并矢格林函数作了进一步的研究。首先，在已有研究的基础上进一步研究了柱面谱域混合位并矢格林函数（MPDGFs）的表达式，对已有文献中存在的两组不同表达形式进行了重新推导和进一步的验证。同时，本文将RFFM方法推广到空域混合位并矢格林函数远区场的快速精确计算中。
针对已有方法在计算空域混合位型并矢格林函数时存在轴线发散问题。本文提出了一种解析二阶渐近项提取方法，将谱域格林函数中与轴线相关的奇异项完全提取出来，并应用Sommerfeld恒等式解析变换到空域中，从而使得剩余数值计算部分快速收敛。与已有方法相比，该方法对基函数没有限制，收敛性和稳定性也更好。
最后，在以上研究的基础上，本文采用基于屋顶基的空域矩量法，对柱面振子天线、矩形贴片天线的输入阻抗、表面电流、辐射方向图以及阵元间的互耦特性进行了分析。通过与其它算法结果及商业仿真软件相对比，说明本算法的准确性、高效性和适用性。
本文相关研究结果可为圆柱面共形天线结构的快速、准确分析提供一套有效解决方案。
As the simplest conformal strucuture, cylindrical surface has received more andmore attention. Now, cylindrically conformal antennas have been widely applied inpractice. However, until now, there has no efficient and accurate analysis method forthis type of structure, the efficiency of the commercial software for electromagneticsimulation is not very satisfying. Due to this situation, in this thesis, an efficient andaccurate method, which is based on the method of moments (MoM) combined with thelayered Green’s functions for cylindrically stratified structure, is studied exhaustivelyand systematically.
First, to overcome the problem in the literature for deriving the formula of theelectric dyadic Green’s functions (EDGFs) for cylindrically stratified structure, such asthe incomplete equations, the unclear definitions, and the complicated derivation, theexplicit formula of EDGFs is thoroughly rederived, which provides a foundation for thefollowing study.
In order to avoid possible overflow/underflow problems in the numericalcalculations of EDGFs for cylindrically stratified media, the explicit expressions of thecomponents of EDGFs are rewritten in the ratios of Bessel and Hankel functions, whichavoids directly calculating Bessel and Hankel functions with high order and largearguments. Compared with other method, the procedure in this thesis is simpler, andeasier for programming and application.
In order to further improve the accuracy and efficiency of the numerical method inthe calculation of the components of EDGFs in spatial domain. A surface-waveextraction method based on the rational function fitting method (RFFM) is proposed.The method can calculate both the near and far field of the components of EDGFsefficiently and accurately. The accuracy range between the source and field points isincreased by about one order, which can enhance the ability for analyzing theelectrically large antennas mounted on cylindrical surface.
In the analysis of cylindrically stratified structure, in order to make use of theRWG basis function in the MoM procedure, the mixed potential dyadic Green’sfunctions (MPDGFs) for cylindrically stratified media are further studied in this thesis.Two different forms of MPDGFs reported in the literature are rederived anddemonstrated. Meanwhile, the RFFM is extended to calculate the far fields of thecomponents of MPDGFs.
From the literature, it is found that the method proposed for the calculation ofspatial-domain MPDGFs can not be valid when the source and field points are locatedon the same axial line, which will make the MoM Procedure more complex. In order toovercome this problem, a two order analytical asymptotic term extraction method is proposed in this thesis. In this method, the singular parts related to the axial line arecompletely extracted, and then transformed into the spatial domain with the aid ofSommerfeld identities. After this extraction, the remaining parts in the spectral domainare fast convergent and can be easily transformed into the spatial domain using thenumerical method such as the generalized pencil of function method (GPOF). Unlikethe other method, this method need not choose special basis functions to cancel thesingularity in the spectral-domain MPDGFs. The performance of convergence andstability are significantly improved.
At last, based on the above study, the MoM procedure combined with the roof-topbasis function is applied for analyzing dipole and rectangular antennas mounted on thecylindrical surface. The input impedance, surface current, radiation pattern and themutual coupling coefficients between antenna array elements are calculated. Incomparison to the results obtained by other algorithms and the simulation software, it isdemonstrated that the method in this thesis has a good performance of accuracy,efficiency and easy applicability.
The procedure introduced in this thesis will provide a possibility for analyzingcylindrically conformal antennas more efficiently and accurately.
引文
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