一种新的闭式空域格林函数及其在三维互连结构电容参数提取中的应用

该文提出了一种提取分层介质中三维静态闭式空域格林函数的通用算法,并成功地运用于三维多层多导体互连结构的电容参数提取。该算法在谱域等效传输线模型的基础上,应用Krylov子空间维数缩减技术求出谱域格林函数的有理逼近表达式,再由留数定理得到闭式空域格林函数。所得闭式空域格林函数结合矩量法可以方便地用于提取三维互连结构的电容参数。数值结果验证了方法的准确性和有效性。     

一种有效计算有耗分层媒质中格林函数的方法

以两层平面分层媒质为例,讨论了不同情况下空域格林函数的计算方法,指出了有耗平面分层媒质情况下传统方法的缺点,提出采用二维离散复像法(2D-DCIM)处理有耗平面分层媒质中的格林函数,并对积分路径做了相关要求,得到了同时包含场点纵坐标z和源点纵坐标z′及场源点横向距离ρ的格林函数的空域闭式表达式。所得结果与数值积分法的结果吻合良好,证实了该文方法的正确性。     

二维直接DCIM计算分层介质空域格林函数

二维离散复镜像法(discrete complex image method,DCIM)可以有效计算分层介质中场源点位于不同介质层时的空域格林函数,但在场源点距离大于波长时的计算结果不准确。本文采用二维DCIM结合直接DCIM二级路径的方法,研究了多层微带结构中场源点位于不同介质层时空域格林函数的计算问题;通过单层和两层微带结构空域格林函数的计算实例,分析了积分路径对格林函数计算精度的影响。结果表明:采用直接DCIM二级路径的二维DCIM方法可以准确计算分层介质中场源点距离大于10倍波长时的空域格林函数。     

DCIM求解多层媒质闭式格林函数

离散复镜像方法是求解平面分层媒质格林函数的有效方法之一。本文全面系统地论述了离散复镜像法求解多层媒质空域格林函数的详细过程，并着重讨论了第 m 层为有界区域的 DCIM 处理方法、表面波提取方法和多层媒质中的三维目标空域格林函数的有效插值方法等几个关键技术，从而提高了空域格林函数的求解效率。几个典型实例的计算结果表明了本文方法的有效性。     

带有垂直接地结构的微带电路的广义多端口分析方法

该文利用矩量法(MoM)结合网络分析方法对带有垂直接地结构的微带电路进行全波分析.将垂直接地结构用边端口代替,将原电路等效成只有平面结构的广义多端口模型.将原接地的各个端口短路,得到新的网络参数即原微带电路的网络参数.此方法在矩量法计算中只需计算微带电路的平面结构部分,有效得降低了模型和格林函数计算的复杂性,数值结果表明本文方法的准确性和有效性.     

一种计算有耗媒质中跨界目标电磁散射的高效算法

为了克服传统离散复镜像法计算有耗媒质中索莫菲尔德积分的不足,提出了一种基于增强离散复镜像法的插值算法。当场点和源点位于分界面两侧时,谱域格林函数中同时包含场点和源点位置坐标,传统二级离散复镜像法无法一次拟合复指数参数,考虑将谱域核函数对场点坐标分离,然后建立复镜像参数随源点坐标的一维插值表,从而可以对复镜像参数进行插值运算;当场点和源点均位于有耗媒质中时,二级离散复镜像法的采样路径会带来错误,提出对谱域核函数进行形式变换再进行求解,从而使插值法适合有耗媒质中格林函数的计算;为了扩大传统二级离散复镜像法的横向计算距离,在对复镜像参数进行复指数级数拟合时,选择增强离散复镜像法的采样路径。该方法同传统对格林函数进行插值的方法相比,在计算复杂度降低的同时,效率和精度都获得了大大提高。     

封装微带电路网络特性的矩量法分析

该文首先对封装微带电路建立了以混合位积分方程(MPIE)描述的矩量法(MoM)分析模型,采用了复镜像技术,准确计算了Green函数并表达为简洁闭式。进而考虑了边壁对电路的影响,计算并修正了阻抗矩阵。在此研究的基础上,该文将Eleftheriades(1996)中的模型扩展为封装模型,提取出封装微带电路的网络特性,最后的数值结果表明封装效应对微带电路的网络特性有着很重要的影响。     

介质体电磁散射分析中的等效偶极矩法

在介质体电磁散射分析中,提出了一种基于等效偶极矩法的快速矩阵生成技术。该方法以矩量法和RWG基函数为基础,将源点处的电(磁)流等效为电(磁)偶极子,因而阻抗矩阵元素可以认为是源点电(磁)偶极子所产生的近区场与场点电流基函数之间的相互作用。这样等效偶极矩法避免了格林函数二重积分,使得阻抗矩阵元素的生成速度明显提高。数值结果表明该方法有较高的计算效率和精度。     

平面多层媒质中格林函数求解与应用

介绍了平面分层媒质中适用于C类混合位积分方程（MPIE）的格林函数的精确计算方法。重点讨论了空域格林函数求解过程中的表面波精确提取问题。精确定位极点之后,采用围线积分法准确计算各极点处留数值。在提取表面波后,采用二级离散复镜像（DCIM）方法求解了一个两层结构的空域格林函数,并与文献值进行了对比,结果吻合良好。文章最后结合空域矩量法（MoM）求解了微带结构的散射参数,并与商业软件CST仿真值进行了对比,结果吻合良好。     

微带天线RCS计算

在采用基于混合位积分方程的矩量法分析微带天线RCS时,首先采用二级离散复镜像法求解空域格林函数,从而大大提高了矩量法的计算效率,然后利用三角形网格剖分计算目标,也使得矩量法更适合分析复杂结构.采用本文方法的计算结果也和相关文献的计算结果相一致,从而验证了本文方法的高效性和正确性.     

Two-Dimensional Discrete Complex Image Method (DCIM) for Closed-Form Green's Function of Arbitrary 3D Structures in General Multilayered Media

The traditional discrete complex image method (DCIM) is not efficient when the source and field points are in different layers because all the spatial coordinates can not be analytically included in the image terms in spatial domain. A two dimensional method (2D-DCIM) is introduced in this paper. In the new methodology we reorganize the spectral kernel as a 2D function. We use the 2D matrix pencil method (2D-MPM) to fit this 2D function and to generate a set of complex images independent of any spatial coordinates. The closed-form spatial domain Green's function can be obtained for arbitrary locations of source and field points in general multilayered media. Compared with traditional 1D-DCIM, we do not have to run MPM for each vertical combination of source and field points. The efficiency of the matrix filling kernel of method of moments (MoM) is significantly improved.     

A Mesh-Adapted Closed-Form Regular Kernel for 3D Singular Integral Equations

The Green's functions employed in the method of moments (MoM) diverge when observation and source points coincide; this is at the origin of the difficulties in computing the MoM matrix entries, and in handling the near-field interactions in fast Fourier transform (FFT)-based fast methods and other sampling-based methods. In this paper, we show that this singularity can be avoided, and a modified regular Green's function can be used instead. This latter is obtained from the spectral representation of the usual Green's function via windowing of its spectrum; the width of the spectral window depends on the size of the mesh employed for discretizing the problem, so that the proposed regular Green's function is a mesh-adapted regular kernel. We address a general 3D problem; we relate the MoM reaction integrals to the 2D Fourier spectrum of the Green's function, that allows to discuss the necessary spectral bandwidth for the windowed Green's function. We employ a tapered window, and present a closed-form expression for the spatial Green's function. Numerical results are presented for 3D antenna and scattering problems discretized with Rao-Wilton-Glisson (RWG) functions, and for uniform and nonuniform meshing. They show that the proposed method yields accurate solutions also for the antenna input impedance. The meaning of the regularized Green's function is also discussed and put in perspective.     

Numerically efficient analysis of planar microstrip configurationsusing closed-form Green's functions

An efficient technique for the analysis of a general class of microstrip structures with a substrate and a superstrate is investigated in this paper using newly-derived closed-form spatial domain Green's functions employed in conjunction with the Method of Moments (MoM). The computed current distributions on the microstrip structure are used to determine the scattering parameters of microstrip discontinuities and the input impedances of microstrip patch antennas. It is shown that the use of the closed-form Green's functions in the context of the MoM provides a computational advantage in terms of the CPU time by almost two orders of magnitude over the conventional spectral domain approach employing the transformed version of the Green's functions     

Analytical evaluation of the MoM matrix elements

Derivation of the closed-form Green's functions has eliminated the computationally expensive evaluation of the Sommerfeld integrals to obtain the Green's functions in the spatial domain. Therefore, using the closed-form Green's functions in conjunction with the method of moments (MoM) has improved the computational efficiency of the technique significantly. Further improvement can be achieved on the calculation of the matrix elements involved in the MoM, usually double integrals for planar geometries, by eliminating the numerical integration. The contribution of this paper is to present the analytical evaluation of the matrix elements when the closed-form Green's functions are used, and to demonstrate the amount of improvement in computation time     

Estimation of spurious radiation from microstrip etches usingclosed-form Green's functions

The problem of spurious radiation from electronic packages is considered by investigating the power radiated from microstrip etches that are excited by arbitrarily located current sources and terminated by complex loads at both ends. The first step in the procedure is to compute the current distribution on the microstrip line by using the method of moments (MoM). Two contributions of this paper are: (i) employing the recently derived closed-form Green's functions in the spatial domain, which permits an efficient computation of the elements of the MoM matrix; and (ii) incorporating complex load terminations in a convenient manner with virtually no increase in the computation time. The computed current distribution is used to calculate the spurious radiated power, and the result is compared with that derived by using an approximate, transmission line analysis     

Derivation of closed-form Green's functions for a generalmicrostrip geometry

The derivation of the closed-form spatial domain Green's functions for the vector and scalar potentials is presented for a microstrip geometry with a substrate and a superstrate, whose thicknesses can be arbitrary. The spatial domain Green's functions for printed circuits are typically expressed as Sommerfeld integrals, which are inverse Hankel transforms of the corresponding spectral domain Green's functions and are time-consuming to evaluate. Closed-form representations of these Green's functions in the spatial domains can only be obtained if the integrands are approximated by a linear combination of functions that are analytically integrable. This is accomplished here by approximating the spectral domain Green's functions in terms of complex exponentials by using the least square Prony's method     

Efficient analysis of planar microstrip geometries using aclosed-form asymptotic representation of the grounded dielectric slabGreen's function

A newly developed closed-form asymptotic representation of the grounded dielectric slab Green's function is used in a moment-method formulation to calculate the propagation constant of an infinite microstrip transmission line and the input impedance of a finite-length, center-fed printed dipole. In these problems, source and field points are laterally rather than vertically separated with respect to the substrate. The conventional Sommerfeld integral and the plane wave spectral integral (PWS) representations of the microstrip Green's function converge very slowly in this case. However, the asymptotic closed-form representation of the Green's function does not have this limitation, and it remains accurate even for very small lateral separation between source and observation points. A modified form of the Sommerfeld integral representation is used only for observation points in the immediate vicinity of the source, while the asymptotic form is used elsewhere. Some numerical results based on this approach are presented and are shown to compare very well with previous results based on the corresponding exact-integral or PWS forms of the Green's function     

An asymptotic closed-form microstrip surface Green's function forthe efficient moment method analysis of mutual coupling in microstripantennas

A relatively simple closed-form asymptotic representation for the single-layer microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air-dielectric interface. This asymptotic solution remains surprisingly accurate even for very small (a few tenths of a free-space wavelength) lateral separation of the source and field points. Thus, using the present asymptotic approximation of the Green's function can lead to a very efficient moment method (MM) solution for the currents on an array of microstrip antenna patches and feed lines. Numerical results based on the efficient MM analysis using the present closed-form asymptotic approximation to the microstrip surface Green's function are given for the mutual coupling between a pair of printed dipoles on a single-layer grounded dielectric slab. The accuracy of the latter calculation is confirmed by comparison with numerical results based on a MM analysis which employs an exact integral representation for the microstrip Green's function     

Efficient analysis of input impedance and mutual coupling of microstrip antennas mounted on large coated cylinders

An efficient and accurate hybrid method, based on the combination of the method of moments (MoM) with a special Green's function in the space domain is presented to analyze antennas and array elements conformal to electrically large material coated circular cylinders. The efficiency and accuracy of the method depend strongly on the computation of the Green's function, which is the kernel of the integral equation that is solved via MoM for the unknown equivalent currents representing only the antenna elements. Three types of space-domain Green's function representations are used, each accurate and computationally efficient in a given region of space. Consequently, a computationally optimized analysis tool for conformal microstrip antennas is obtained. Input impedance of various microstrip antennas and mutual coupling between two identical antennas are calculated and compared with published results to assess the accuracy of this hybrid method.     

A numerically efficient technique for the analysis of slots inmultilayer media

A numerically efficient technique for the analysis of slot geometries in multilayer media is presented using closed-form Green's functions in spatial domain in conjunction with the method of moments (MoM). The slot is represented by an equivalent magnetic-current distribution, which is then used to determine the total power crossing through the slot and the input impedance. In order to calculate power and current distribution, spatial-domain closed-form Green's functions are expanded as power series of the radial distance ρ, which makes the analytical evaluation of the spatial-domain integrals possible, saving a considerable amount of computation time