空域MPIE/MoM全波分析三维微带电路

矩量法在空域分析三维微带电路的关键是闭式格林函数的求解。本文首先介绍谱域格林函数一种新的表达式,使得源点和场点在同一层时,离散复镜像法可提取出与它们无关的闭式,从而避免了插值;不在同一层时,可提取与场点无关的闭式,此时只须对源点进行一维插值,因而提高了计算效率。然后,利用闭式格林函数和RWG基函数,基于混合位积分方程的矩量法就可以在空域精确、有效地分析三维任意形状微带电路。给出了几个典型实例,表明本文方法的有效性。     

基于固定实镜像平面波展开的快速多极子方法计算微带结构问题

将快速多极子算法应用于微带结构的一个关键技术是将矩量法中描述远区单元相互作用的Green函数用加法定理进行平面波展开.本文提出用固定实镜像方法拟合微带结构谱域Green函数进行平面波展开,对比目前常用的复镜像闭式平面波展开方法,该方法具有展开收敛性好,物理概念清晰,Green函数宽频插值方便等特点.计算实例表明了该方法的有效性和可靠性.     

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     

An efficient algorithm for analyzing large-scale microstripstructures using adaptive integral method combined with discretecomplex-image method

An efficient algorithm combining the adaptive integral method and the discrete complex-image method (DCIM) is presented in this paper for analyzing large-scale microstrip structures. The arbitrarily shaped microstrips are discretized using triangular elements with Rao-Wilton-Glisson basis functions. These basis functions are then projected onto a rectangular grid, which enables the calculation of the resultant matrix-vector product using the fast Fourier transform. The method retains the advantages of the well-known conjugate-gradient fast-Fourier-transform method, as well as the excellent modeling capability offered by triangular elements. The resulting algorithm has the memory requirement proportional to O(N) and the operation count for the matrix-vector multiplication proportional to O(N log N), where N denotes the number of unknowns. The required spatial Green's functions are computed efficiently using the DCIM, which further speeds up the algorithm. Numerical results for some microstrip circuits and a microstrip antenna array are presented to demonstrate the efficiency and accuracy of this method     

An efficient method for electromagnetic characterization of 2-Dgeometries in stratified media

A numerically efficient technique, based on the spectral-domain method of moments (MoM) in conjunction with the generalized pencil-of-functions (GPOF) method, is developed for the characterization of two-dimensional geometries in multilayer planar media. This approach provides an analytic expression for all the entries of the MoM matrix, explicitly including the indexes of the basis and testing functions provided that the Galerkin's MoM is employed. This feature facilitates an efficient modification of the geometry without the necessity of recalculating the additional elements in the MoM matrix. To assess the efficiency of the approach, the results and the matrix fill times are compared to those obtained with two other efficient methods, namely, the spatial-domain MoM in conjunction with the closed-form Green's functions, and a fast Fourier transform algorithm to evaluate the MoM matrix entries. Among these, the spectral-domain MoM using the GPOF algorithm is the most efficient approach for printed multilayer geometries     

Full-Wave Solver for Microstrip Trace and Through-Hole Via in Layered Media

This paper reports major improvements to a 3-D full wave solver for a microstrip line and through-hole via in layered media. The interior layer problem, consisting of vias between two reference planes, is solved using the Foldy-Lax multiple scattering equations. The exterior layer problem is solved using the method of moments (MoM) with the layered media Green's functions. The exterior layer and interior layer problems are combined to obtain the S-parameters of the trace and through-hole via. A fast approach for calculating the layered-medium Green's functions using the numerical modified steepest descent path method is utilized. The Green's functions require milliseconds to compute per point. Schemes for efficiently computing image contributions for the static portion of the mixed potential Green's function are also implemented to solve the neighboring or self-RWG (basis function) interaction in the MoM problem. To validate the accuracy of the solution, extensive comparison with Ansoft's HFSS versions 9 and 11 for different pad sizes and antipad sizes are presented. The CPU per frequency is also tabulated to demonstrate the speed of the approach in this paper.     

Application of DCIM to MPIE-MoM analysis of 3D PEC objects inmultilayered media

The Formulation-C Green's functions for multilayered media are reformulated in this paper to extract z-dependent part when the source and observation points are in different layers. The discrete complex image method (DCIM), is applied to obtain complex images independent on z but dependent on z´. For simulation of three-dimensional (3-D) perfectly electrical conduction (PEC) objects penetrating two or more layers, tables of complex images are built in a z´-grid. During the matrix-filling stage of the mixed-potential integral equation, together with method of moments (MPIE-MoM), the spatial-domain Green's functions are interpolated from values in the z´-grid, while these values are calculated from complex images in the z´-grid. This interpolation scheme is more efficient than those directly storing the spatial-domain Green's functions. Numerical examples are given for analyzing a dipole in a two-layered media     

Efficient Analysis of Phased Arrays of Microstrip Patches Using a Hybrid Generalized Forward Backward Method/Green's Function Technique With a DFT Based Acceleration Algorithm

A hybrid method based on the combination of generalized forward backward method (GFBM) and Green's function for the grounded dielectric slab together with the acceleration of the combination via a discrete Fourier transform (DFT) based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation/scattering from electrically large, irregularly contoured two-dimensional arrays consisting of finite number of probe-fed microstrip patches. In this method, unknown current coefficients corresponding to a single patch are first solved by a conventional Galerkin type hybrid method of moments (MoM)/Green's function technique that uses the grounded dielectric slab's Green's function. Because the current distribution on the microstrip patch can be expanded using an arbitrary number of subsectional basis functions, the patch can have any shape. The solution for the array currents is then found through GFBM, where it sweeps the current computation element by element. The computational complexity of this method, which is originally ( being the total number of unknowns) for each iteration, is reduced to using a DFT based acceleration algorithm making use of the fact that array elements are identical and the array is periodic. Numerical results in the form of array current distribution are given for various sized arrays of probe-fed microstrip patches with elliptical and/or circular boundaries, and are compared with the conventional MoM results to illustrate the efficiency and accuracy of the method.     

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.     

Capacitance computations in a multilayered dielectric medium usingclosed-form spatial Green's functions

An efficient method to compute the 2-D and 3-D capacitance matrices of multiconductor interconnects in a multilayered dielectric medium is presented. The method is based on an integral equation approach and assumes the quasi-static condition. It is applicable to conductors of arbitrary polygonal shape embedded in a multilayered dielectric medium with possible ground planes on the top or bottom of the dielectric layers. The computation time required to evaluate the space-domain Green's function for the multilayered medium, which involves an infinite summation, has been greatly reduced by obtaining a closed-form expression, which is derived by approximating the Green's function using a finite number of images in the spectral domain. Then the corresponding space-domain Green's functions are obtained using the proper closed-form integrations. In both 2-D and 3-D cases, the unknown surface charge density is represented by pulse basis functions, and the delta testing function (point matching) is used to solve the integral equation. The elements of the resulting matrix are computed using the closed-form formulation, avoiding any numerical integration. The presented method is compared with other published results and showed good agreement. Finally, the equivalent microstrip crossover capacitance is computed to illustrate the use of a combination of 2-D and 3-D Green's functions     

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     

Analysis of microstrip filters using efficient MoM approach

An efficient approach for the analysis of microstrip filters is proposed. The computation is based on the method of moments (MoM) in which rooftop basis functions on non-uniform meshes, an analytical integration technique and numerical matched loads are combined. The resulting MoM matrix is then compressed and computation time is considerably reduced     

电大尺寸微带天线的并行矩量法分析

为了能够有效地求解大规模微带天线阵列,首先对微带天线建立了以混和位积分方程（MPIE）描述的矩量法（MoM）分析模型,采用了离散复镜像技术,将Sommerfeld积分形式的格林函数并表达为简洁闭式。进而采用并行矩量法对大规模微带天线阵进行了求解,该方法可以有效地提高矩量法分析微带结构的规模,数值结果表明本文方法的准确性和有效性。     

Fast multipole method for scattering from an arbitrary PEC targetabove or buried in a lossy half space

The fast multipole method (FMM) was originally developed for perfect electric conductors (PECs) in free space, through exploitation of the spectral properties of the free-space Green's function. In the work reported here, the FMM is modified, for scattering from an arbitrary three-dimensional (3-D) PEC target above or buried in a lossy half space. The “near” terms in the FMM are handled via the original method-of-moments (MoM) analysis, wherein the half-space Green's function is evaluated efficiently and rigorously through application of the method of complex images. The “far” FMM interactions, which employ a clustering of expansion and testing functions, utilize an approximation to the Green's function dyadic via real image sources and far-field reflection dyadics. The half-space FMM algorithm is validated through comparison with results computed via a rigorous MoM analysis. Further, a detailed comparison is performed on the memory and computational requirements of the MoM and FMM algorithms for a target in the vicinity of a half-space interface     

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     

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。     

A Novel Analysis of Microstrip Structures Using the Gaussian Green's Function Method

A novel closed form expression is derived for spatial Green's functions of microstrip structures by expanding the spectral Green's function into a Gaussian series. This innovative method is called the Gaussian Green's function (GGF) method due to the Gaussian form in the closed form Green's function representation. The main advantage of the GGF method lies in its precision as well as rapid convergence. To demonstrate the versatility of this method, the current distribution of a microstrip antenna is achieved via the combination of the method of moments (MoM) and GGF method. It is shown that this method can be computationally very efficient with less than 1% error compared to the numerical integration of the spectral integral. Also, the results of the GGF method have been compared to the results of the commercial full-wave software of Agilent ADS.      

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.     

平面分层媒质空域Green 函数快速计算

格林函数法是电磁场数值分析中的一种基本方法,平面分层媒质的空域格林函数通常表达成Sommer-feld积分形式。文中针对该问题快速求解的几种基本方法进行了系统分析,对各种分析方法进行了分类,根据研究进展情况,概述了传统离散复镜像法(DCIM)、二阶DCIM、增强型DCIM(EDCIM)、柱面波逼近和支割线积分以及其他方法,阐明了各种方法的优缺点;对计算得到的闭式Green函数在具体电磁散射与辐射计算中产生的误差控制、定阶、维数、媒质有耗问题进行了分析,给出了一种简便的有耗媒质DCIM方法,数值计算结果显示文中方法的正确性。     

Efficient evaluation of spatial-domain MoM matrix entries in theanalysis of planar stratified geometries

An efficient hybrid method for evaluation of spatial-domain method-of-moments (MoM) matrix entries is presented in this paper. It has already been demonstrated that the introduction of the closed-form Green's functions into the MoM formulation results in a significant computational improvement in filling up MoM matrices and, consequently, in the analysis of planar geometries. To achieve further improvement in the computational efficiency of the MoM matrix entries, a hybrid method is proposed in this paper and, through some examples, it is demonstrated that it provides significant acceleration in filling up MoM matrices while preserving the accuracy of the results