A fast full-wave analysis of scattering and radiation from largefinite arrays of microstrip antennas

A fast full-wave analysis technique that can be used to analyze the scattering and radiation from large finite arrays of microstrip antennas is presented. The technique discretizes the mixed potential integral equation (MPIE) in the spatial domain by means of a full-wave discrete complex image method. The del operators on the Green's functions are transferred from the singular kernel to the expansion and testing functions. The resultant system of equations is solved using the biconjugate gradient (BCG) method in which the matrix-vector product is evaluated efficiently using the fast Fourier transform (FFT). This results in an efficient and accurate computation of the scattering and radiation from finite arrays of microstrip antennas. Several numerical results are presented, demonstrating the accuracy, efficiency, and capability of this technique     

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     

微带印刷天线辐射与散射的全波分析方法

本文给出了一种分析微带印刷天线辐射与散射的数值方法。此方法将印刷天线按三角网格剖分，在导体表面建立积分方程，用全波离散镜像理论给出微带结构的空域格林函数的闭合表达式，未知电流用三角网格上的矢量电流基函数展开并用矩量法求解。与以往的矩形网格上基函数展开相比，此方法能更有效地逼近任意形状的微带结构，最后给出了几个数值结果     

Thin-stratified medium fast-multipole algorithm for solvingmicrostrip structures

An accurate and efficient technique called the thin-stratified medium fast-multipole algorithm (TSM-FMA) is presented for solving integral equations pertinent to electromagnetic analysis of microstrip structures, which consists of the full-wave analysis method and the application of the multilevel fast multipole algorithm (MLFMA) to thin stratified structures. In this approach, a new form of the electric-field spatial-domain Green's function is developed in a symmetrical form which simplifies the discretization of the integral equation using the method of moments (MoM). The patch may be of arbitrary shape since their equivalent electric currents are modeled with subdomain triangular patch basis functions. TSM-FMA is introduced to speed up the matrix-vector multiplication which constitutes the major computational cost in the application of the conjugate gradient (CG) method. TSM-FMA reduces the central processing unit (CPU) time per iteration to O(N log N) for sparse structures and to O(N) for dense structures, from O(N³) for the Gaussian elimination method and O(N²) per iteration for the CG method. The memory requirement for TSM-FMA also scales as O(N log N) for sparse structures and as O(N) for dense structures. Therefore, this approach is suitable for solving large-scale problems on a small computer     

Cubic splines as expansion functions for the current distribution of microstrip stub antennas

The current distribution on microstrip stub antennas is calculated with the appropriate Green's functions via an integral equation, which is solved with the moment method. As expansion functions for the current cubic spline functions are used. The calculated data are used for the design of a microstrip array with Chebyshev characteristics.     

Efficient electromagnetic modeling of three-dimensional multilayermicrostrip antennas and circuits

An efficient method-of-moments (MoM) solution is presented for analysis of multilayer microstrip antennas and circuits. The required multilayer Green's functions are evaluated by the discrete complex image method (DCIM), with the guided-mode contribution extracted recursively using a multilevel contour integral in the complex _ρ-plane. An interpolation scheme is employed to further reduce the computer time for calculating the Green's functions in the three-dimensional (3-D) space. Higher order interpolatory basis functions defined on curvilinear triangular patches are used to provide necessary flexibility and accuracy for the discretization of arbitrary shapes and to offer a better convergence than lower order basis functions. The combination of the improved DCIM and the higher order basis functions results in an efficient and accurate MoM analysis for 3-D multilayer microstrip structures     

A numerical formulation of dyadic Green's functions for planarbianisotropic media with application to printed transmission lines

An integral equation (IE) method with numerical solution is presented to determine the complete Green's dyadic for planar bianisotropic media. This method follows directly from the linearity of Maxwell's equations upon applying the volume equivalence principle for general linear media. The Green's function components are determined by the solution of two coupled one-dimensional IE's, with the regular part determined numerically and the depolarizing dyad contribution determined analytically. This method is appropriate for generating Green's functions for the computation of guided-wave propagation characteristics of conducting transmission lines and dielectric waveguides. The formulation is relatively simple, with the kernels of the IE's to be solved involving only linear combinations of Green's functions for an isotropic half-space. This method is verified by examining various results for microstrip transmission lines with electrically and magnetically anisotropic substrates, nonreciprocal ferrite superstrates, and chiral substrates. New results are presented for microstrip embedded in chiroferrite media     

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。     

任意形状微带天线辐射特性的研究

本文从研究微带天线的积分方程出发,推导了从积分方程组到矩阵方程的全部公式,特别是对奇异积分进行了处理。提出了任意形状微带天线贴片及其附近表面的分块法,及矩形和三角形分块的自耦和互耦的计算方法,从而解决了用矩量法分析任意形状微带天线的问题。进一步利用几何绕射理论,考虑载体的绕射场影响,使载体上天线辐射方向图的计算结果与实验结果更吻合。计算了一种很有实用价值的特殊形状——双扇形微带天线的辐射方向图,并同实验结果作了比较。     

Waveguide excited microstrip patch antenna-theory and experiment

An arbitrarily shaped microstrip patch antenna excited through an arbitrarily shaped aperture in the mouth of a rectangular waveguide is investigated theoretically and experimentally. The metallic patch resides on a dielectric substrate grounded by the waveguide flange and may be covered by a dielectric superstrate. The substrate (and superstrate, if present) consists of one or more planar, homogeneous layers, which may exhibit uniaxial anisotropy. The analysis is based on the space domain integral equation approach. More specifically, the Green's functions for the layered medium and the waveguide are used to formulate a coupled set of integral equations for the patch current and the aperture electric field. The layered medium Green's function is expressed in terms of Sommerfeld-type integrals and the waveguide Green's function in terms of Floquet series, which are both accelerated to reduce the computational effort. The coupled integral equations are solved by the method of moments using vector basis functions defined over triangular subdomains. The dominant mode reflection coefficient in the waveguide and the far-field radiation patterns are then found from the computed aperture field and patch current distributions. The radar cross section (RCS) of a plane-wave excited structure is obtained in a like manner. Sample numerical results are presented and are found to be in good agreement with measurements and with published data     

A coupled surface-volume integral equation approach for thecalculation of electromagnetic scattering from composite metallic andmaterial targets

A coupled surface-volume integral equation approach is presented fur the calculation of electromagnetic scattering from conducting objects coated with materials. Free-space Green's function is used in the formulation of both integral equations. In the method of moments (MoM) solution to the integral equations, the target is discretized using triangular patches for conducting surfaces and tetrahedral cells for dielectric volume. General roof-top basis functions are used to expand the surface and volume currents, respectively. This approach is applicable to inhomogeneous material coating, and, because of the use of free-space Green's function, it can be easily accelerated using fast solvers such as the multilevel fast multipole algorithm     

Finite-Element Solution of Unbounded Field Problems

An unbounded region is divided into local picture-frame regions where a partial differential-equation solution is obtained, with the remaining unbounded region represented by an integral equation. (The method permits the use of free-space Green's functions, and thus special problem-dependent Green's functions need not be found.) The integral equation is formulated as a constraint upon the local picture-frame solutions, whence these local solutions are solved directly by a variational method, using finite elements, in a manner such that the problem of the Green's-function singularity is side-stepped. The technique is applicable where sources and media inhomogeneities and anisotropies are local, and can all be placed within one or several picture frames. It is in these cases that the integral-equation approach is at a particular disadvantage, and the use of a partial differential-equation technique is advisable if not necessary. Examples presented include the static and harmonic fields of a parallel-plate capacitor, a microstrip line on a dielectric substratum, and a radiating antenna with dielectric obstacles.     

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。     

A fast analysis of scattering and radiation of large microstrip antenna arrays

An accurate and efficient method that combines the precorrected fast Fourier transform (FFT) method and the discrete complex image method (DCIM) is presented to characterize the scattering and radiation properties of arbitrarily shaped microstrip patch antennas. In this method, the mixed potential integral equation (MPIE) is discretized in the spatial domain by means of the discrete complex image method. The resultant system is solved iteratively using the generalized conjugate residual method (GCR) and the precorrected-FFT technique is used to speed up the matrix-vector multiplication. The precorrected-FFT eliminates the need to generate and store the usual square impedance matrix and thus leads to a significant reduction in memory requirement and computational cost. Numerical results are presented for arbitrarily shaped microstrip antenna arrays to demonstrate the accuracy and efficiency of this technique.     

Wavelet-based simulations of electromagnetic scattering fromlarge-scale two-dimensional perfectly conducting random rough surfaces

Simulations of electromagnetic waves scattering from two-dimensional perfectly conducting random rough surfaces are performed using the method of moment (MoM) and the electric field integral equation (EFIE). Using wavelets as basis and testing functions, the resulting moment matrix is generally sparse after applying a threshold truncation. This property makes wavelets particularly useful in simulating large-scale problems, in which reducing memory storage requirement and CPU time are crucial. In this paper, scattering from Gaussian conducting rough surfaces of a few hundred square wavelengths are studied numerically using Haar wavelets. A matrix sparsity less than 10% is achieved for a range of root mean square (RMS) height at eight sampling points per linear wavelength. Parallelization of the code is also performed. Simulation results of the bistatic scattering coefficients are presented for different surface RMS heights up to 1 wavelength. Comparisons with sparse-matrix/canonical-grid approach (SM/CG) and triangular discretized (RWG basis) results are made as well. Depolarization effects are examined for both TE and TM incident waves. The relative merits of the SM/CG method and the present method are discussed     

Flexibility in the choice of Green's function for the boundaryelement method

Several useful Green's functions are derived for the quasi-static analysis of shielded planar transmission lines by the boundary element method. These newly employed Green's functions satisfy forced boundary conditions in a rectangular region. The integral equation does not have a singular point and the integrand contains only the normal derivative of the electric potential. The present method is proposed to characterize multilayered and multi-conductor structures. Numerical results are presented for a microstrip, a suspended line, and a coplanar waveguide. For the coplanar waveguide, a combined Green's function is also studied. This combined Green's function further reduces the memory size in computation. All of these Green's functions are represented in infinite series. The resulting matrix equation has slowly convergent matrix elements. To reduce the computation time of matrix elements, we split the original series in two parts. The geometric series method is employed to convert one part into a fast convergent form (4 terms). For the other part, only a few terms (less than 20) require computation     

Quick quasi-TEM analysis of multiconductor transmission lines withrectangular cross section

This paper presents an efficient and accurate procedure for computing the quasi-static matrix parameters ([C], [L], [G], and [R]) of rectangular-shaped conductors embedded in a multilayered dielectric medium over an infinite ground plane. An additional top ground plane can also be considered., The problem is formulated in terms of the space-domain integral equation for the free-charge distribution on the slab conductor surfaces. The spatial Green's function is computed from its spectral counterpart using system identification techniques [Prony's method or matrix pencil method (MPM)]. The integral equation is solved by means of a Galerkin scheme employing entire domain basis functions. This results in a small matrix size. In addition, the quasi-analytical evaluation of the entries of the Galerkin matrix leads to a very efficient and accurate computer code. A detailed study on the convergence and accuracy of the method has been included     

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     

全等效电流积分方程法分析微带天线

提出了一种分析微带天线的新方法——全等效电流积分方程法。根据等效原理，用等效表面电流表示金属导体影响，用等效体极化电流来取代介质结构影响，建立全等效电流积分方程，结合空域矩量法来求解整个微带结构的电流分布。采用该方法可以分析任意结构的微带天线，只需用最简单的自由空间格林函数而无须求解复杂的谱域或空域格林函数，避免了无穷积分或Sommerfeld积分，且在分析中精确考虑了有限尺寸金属接地板的影响。用该方法分析了矩形微带天线，计算结果与其它文献给出的结果一致，证实了该方法的有效性。     

Full wave analysis of microstrip floating line structures bywavelet expansion method

A full wave analysis of microstrip floating line structures by wavelet expansion method is presented. The surface integral equation developed from a dyadic Green's function is solved by Galerkin's method, with the integral kernel and the unknown current expanded in terms of orthogonal wavelets. Using the orthonormal wavelets (and scaling functions) with compact support as basis functions and weighting functions, the integral equation is converted into a set of linear algebraic equations, with the matrices nearly diagonal or block-diagonal due to the localization, orthogonality, and cancellation properties of the orthogonal wavelets. Limitations inherited in the traditional orthogonal basis systems are released: The problem-dependent normal modes have been replaced by the problem-independent wavelets, preserving the orthogonality; the trade-off between orthogonality and continuity (e.g. subsectional basis functions including pulse functions, roof-top functions, piecewise sinusoidal functions, etc.) is well balanced by the orthogonal wavelets. Numerical results are compared with measurements and previous published data with good agreement