Electromagnetic scattering and radiation by surfaces of arbitraryshape in layered media. I. Theory

An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces     

Electromagnetic scattering and radiation by surfaces of arbitraryshape in layered media. II. Implementation and results for contiguoushalf-spaces

For pt.I see ibid., vol.38, no.3, p.335-44 (1990). In pt.I, three mixed-potential electric field integral equations (MPIEs) for conducting surfaces of arbitrary shape residing in plane-stratified dielectric media with an arbitrary number of layers were formulated. One of the MPIEs (formulation C) was found to be particularly well suited for the application of the method of moments (MM). In pt.II, formulation C is specialized to the important case of a scatterer or antenna of arbitrary shape residing in contiguous half-spaces. This MPIE is solved by the MM employing a triangle-patch model of the surface of the object. Sample numerical results for several cases of interest are presented     

PEEC Formulation Based on Dyadic Green's Functions for Layered Media in the Time and Frequency Domains

This paper presents a novel time- and frequency-domain concept of modeling with the partial element equivalent circuit (PEEC) method, which applies the mixed potential integral equation (MPIE) with dyadic Green's functions for layered media (DGFLM-PEEC). On the one hand, it represents an exact full-wave semianalytical solution for an arbitrary configuration of traces and via holes in multilayered printed circuit boards. On the other hand, the DGFLM-PEEC model is represented in a circuit form, and thus, may be included in general-purpose circuit simulators. The paper derives a general DGFLM-PEEC formulation, which may be applied to all types of the MPIE with dyadic Green's functions. Using this concept, a particular type of layered media, namely a lossy dielectric between two grounds (stripline region), is thoroughly investigated and used to set up a particular DGFLM-PEEC model. The closed-form expressions for partial inductances and potential coefficients have been derived for this case. The time- and frequency-domain DGFLM-PEEC models for the stripline region have been validated using the measurements and the simulation by the method of moments.      

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。     

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。     

Stripline-fed arbitrarily shaped printed-aperture antennas

A full-wave analysis method is presented for modeling the radiation properties of a stripline-fed planar printed-aperture antenna element. In this formulation, both the finite length of stripline and the finite aperture may be of any arbitrary shape since their equivalent electric and magnetic currents are modeled with triangular patch basis functions. Galerkin's method is applied to numerically solve the coupled mixed-potential integral equation (MPIE). Exact spatial-domain Green's functions are used to account for all radiation, surface-wave, and mutual-coupling effects. Interactions between the stripline feed and the radiating aperture are rigorously included. Numerical analysis is presented for the following nonrectangular shapes: an exponentially tapered slot, an annular slot, an annular slot with opposing stubs, and a monofilar Archimedean spiral slot element. Results are shown for input return loss, radiation patterns, and axial ratio for the circularly polarized elements     

Fast full-wave analysis of planar microstrip circuit elements instratified media

The fast Hankel transform (FHT) algorithm is implemented in the mixed-potential integral-equation (MPIE) analysis of planar microstrip circuits in stratified media. The spatial-domain Green's functions are accurately and quickly obtained by applying the FHT algorithm to the exact spectral-domain counterparts. Therefore, the entire analysis procedure has high accuracy and efficiency. A nonuniform partition scheme is used to effectively model the rapid change of current distributions around discontinuities. A generalized supplementary equation accounting for arbitrary termination conditions at both feeding and load ends is also derived. The proposed method is used to design a single-stub band-stop filter and a compensated dc block circuit. Experimental measurements are performed to validate the computation     

任意截面非均匀各向异性阻抗柱体的电磁散射

采用矩量法(MoM)结合阻抗边界条件研究了二维无限长任意形状截面非均匀各向异性阻抗柱体的电磁散射特性。散射场通过Stratton-Chu电场积分方程、电流连续性方程和二维格林函数予以求解。当柱体截面矢径的模等于恒定值时,目标退化为二维无限长圆柱,提出的计算方法仍然有效。计算得到的散射宽度结果与解析法、物理光学法(PO)的结果进行了比较,吻合良好。     

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     

TM scattering by an impedance sheet extension of a paraboliccylinder

An integral equation and method of moments (MM) solution are presented for the two-dimensional (2-D) problem of transverse magnetic (TM) scattering by an impedance-sheet extension of a perfectly conducting parabolic cylinder. An integral equation is formulated for a dielectric cylinder of general cross section in the presence of a perfectly conducting parabolic cylinder. It is then shown that the solution for a general dielectric cylinder considerably simplifies for the special case of TM scattering by a thin multilayered dielectric strip that can be represented as an impedance sheet. The solution is termed an MM/Green's function solution, where the unknowns in the integral equation are the electric surface currents flowing in the impedance sheet; the presence of the parabolic cylinder is accounted for by including its Green's function in the kernel of the integral equation. The MM solution is briefly reviewed, and expressions for the elements in the matrix equation and the scattered fields are given. Sample numerical results are provided     

Current induced by TE excitation on a conducting cylinder located near the planar interface between two semi-infinite half-spaces

An analysis is presented for determining the current induced by a known transverse electric excitation on a perfectly conducting cylinder located near the planar interface separating two semi-infinite, homogeneous half-spaces of different electromagnetic properties. The conducting cylinder of general cross section is of infinite extent and the excitation is transverse electric to the cylinder axis. Two types of integral equations, the magnetic field integral equation and the electric field integral equation, are formulated, and the Green's functions for the integral equations are derived in an appendix. Numerical solution methods for solving the integral and integrodifferential equations are presented. For a strip parallel or perpendicular to the interface, a circular cylinder, and a rectangular cylinder, data are presented and discussed for selected parameters, including the case of a cylinder resting on the interface.     

Diffraction of an H-polarized electromagnetic wave by a circular cylinder with an infinite axial slot

A comparison of three methods of solution for the problem of scattering and diffraction of a transverse electric (TE) polarized plane wave by an infinite circular cylinder having an infinite axial slot is presented. In one method of solution, the aperture field integral equation (AFIE) method, the fields in and around the cylinder are found from the apertureE-field and the Green's functions for the interior and exterior of a cylinder. In the other two methods, the fields are determined from the surface current, which is obtained by solution of theH-field integral equation (HFIE) or theE-field integral equation (EFIE). The field in the aperture of the cylinder is found from the three methods, and the advantages and disadvantages of each method of solution are discussed. In addition, it is also shown that for shell thickness less than 1/20 of a wavelength, the aperture fields do not differ signifcantly from those of an infinitely thin shell cylinder.     

Application of a new MPIE formulation to the analysis of adielectric resonator embedded in a multilayered medium coupled to amicrostrip circuit

A new mixed-potential integral-equation (MPIE) formulation is developed for the analysis of electromagnetic problems due to conducting or dielectric objects of arbitrary shape embedded in a planarly stratified medium. In the new MPIE formulation, the dyadic kernel of the vector potential is kept in the simple form originally developed by Sommerfeld. The scalar potential, which is related to the vector potential via the Lorenz gauge, is then represented by a double dot product of a dyadic kernel with a dyadic charge density. An extra line integral term, which is well behaved and nonsingular, will appear when the object penetrates an interface. The numerical implementation of the double dot product is found to be trivial if one takes advantage of the well-established basis functions in which the unknown current density is expressed. The new MPIE formulation is employed in conjunction with the triangular patch model to treat the problem of a dielectric resonator (DR) excited by microstrip circuit. A matched-load simulation procedure has been used to extract the network S-parameters of a DR microstrip circuit. The diameters of the Q circles have been measured to determine the coupling coefficients and the Q factors of the DR excited by a microstrip circuit. The validity of the new MPIE formulation and the numerical procedure have been verified by comparing the obtained S-parameters, with available measurement data     

Prediction of the shielding and resonant behavior of multisectionenclosures based on magnetic current modeling

A new method of moments (MoM) formulation is proposed to evaluate the shielding efficiency of metallic rectangular enclosures. To this end, a mixed potential integral equation (MPIE) is formulated for the magnetic currents in the apertures using the exact Green's function of the enclosure. The accuracy of the method is demonstrated by a number of examples. The method allows the quality factor of the resonances to be predicted. Finally, the effect of partitioning the enclosure by metallic planes is also investigated     

Scattering by arbitrarily cross-sectioned layered, lossy dielectric cylinders

The scattering properties of TM or TE illuminated lossy dielectric cylinders of arbitrary cross section are analyzed by the surface integral equation techniques. The surface integral equations are formulated via Maxwell's equations, Green's theorem, and the boundary conditions. The unknown surface fields on the boundaries are then calculated by flat-pulse expansion and point matching. Once the surface fields are found, scattered field in the far-zone and radar cross section (RCS) are readily determined. RCS thus obtained for circular homogeneous dielectric cylinders and dielectric coated conducting cylinders are found to have excellent agreements with the exact eigenfunction expansion results. Extension to arbitrary cross-sectioned cylinders are also obtained for homogeneous lossy elliptical cylinders and wedge-semicircle cross-sectioned cylinders, with and without a conducting cylinder in its center. RCS dependences on frequency and conductivity as well as the matrix stability problem of this surface integral equation method are also examined.     

Studies on Fast Algorithm for the Scattering of a Large Array of Waveguide-Fed Wide-Slot Antennas in Millimeter Wave Region

We present an effective numerical technique to characterize the scattering of wide-slot antennas fed by waveguides with arbitrary terminations in terms of the method of moment (MoM) and the mixed potential integral equation (MPIE). In particular, the precorrected-fast Fourier transform (P-FFT) eliminates the need to generate and store the usual square impedance matrix andthus leads to speed up the matrix-vector multiplication in the resultant system. This property makes the Rao-Wilton-Glisson (RWG) functions to be useful in simulating electrically large-scale problems. In addition, the scattering from the finite ground surfaces is accounted for in the total scattered field by using the method of equivalent edge currents. The numerical results are presented and compared with both the traditional method of moment results obtained using the entire-domain basis functions and the experimental results, to demonstrate the proposed method to be a good candidate for study on the scattering of arbitrary wide-slot large array.     

SOLUTION OF ARBITRARY CROSS-SECTION WAVEGUIDE USING METHOD OF EIGEN WEIGHTED BOUNDARY INTEGRAL EQUATION

Based on the second kind of Green's identity,a boundary integral equation forarbitrary cross-section waveguide is transformed to a system of linear homogeneous algebraicequations by means of expansion of boundary bases and by using the eigenfunctions of a fictitiousregular boundary as weighting functions,which corresponds to less algebraic equations than BEMand simpler coefficients than the modified BEM.The numerical results for some typical metallicwaveguides are given by using the method of eigen-weighted boundary integral equation,and theyare accurate enough with fast convergence.     

TM and TE scattering by a dielectric/ferrite cylinder in the presence of a half-plane

An integral equation solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by an isotropic dielectric/ferrite material cylinder in the presence of a perfectly conducting half-plane is presented. The technique is termed a method of moments (MM)/Green's function solution since the method of moments is used to determine the electric and magnetic polarization currents representing the material cylinder, while the presence of the half-plane is accounted for by including the half-plane Green's function in the kernel of the integral equations. Numerical results are presented for the echo width, material cylinder interior fields, and the surface impedance of a material slab on the surface of a half-plane.     

TM scattering by a dielectric cylinder in the presence of a half-plane

The problem considered is the transverse magnetic (TM) scattering by a dielectric cylinder in the presence of a perfectly conducting half-plane. An integral equation, involving the half-plane Green's function in its Kernel, is obtained for the equivalent volume currents representing the dielectric cylinder. This integral equation is solved by the method of moments. Numerical results are compared with measurements for the echo width of a dielectric slab on a half-plane. The dielectric slab surface impedance and the fields inside the dielectric are also shown.