Radiation and scattering from infinite periodic printed antennaswith inhomogeneous media

The hybrid method of moments (MoM)/Green's function method technique is applied to infinite periodic printed antenna arrays containing dielectric inhomogeneities. The solution uses an integral equation for an infinite periodic printed array on or over a homogeneous dielectric substrate, coupled with equivalent volume polarization currents for dielectric inhomogeneities on top of the homogeneous substrate. Volume pulse-basis functions were used to expand the volume polarization currents. A hybrid MoM/Green's function method solution was then obtained through the matrix form of the problem. The two-dimensional (2-D) solution of plane wave scattering from a grounded dielectric slab was used to validate the reaction impedance of the dielectric inhomogeneity. Several infinite periodic printed dipole arrays with dielectric supports and overlays were studied with this solution and good agreement was observed between the hybrid MoM/Green's function method and waveguide simulator experiments     

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.     

On the Scattering of Electromagnetic Waves by Periodic Rough Dielectric Surfaces: A BOA Solution

A new approach for the scattering of electromagnetic (EM) waves from periodic dielectric rough surfaces is addressed. The method is an extension of the buried object approach (BOA), which is developed for rough surfaces of infinite extend, to the present problem. The BOA allows to model the original problem as the scattering of EM waves from cylindrical objects located in a two-half-space medium with planar interface. Then, the problem is reduced to the solution of a Fredholm integral equation of second kind through the periodic Green's function of two-half-space medium. The periodic Green's function of two-half-space medium is calculated via the Floquet mode expansion, whose numerical evaluation can be accelerated by using effective methods. The method can also be used to solve the scattering problems of rough surfaces of infinite extend and having a localized roughness. Numerical simulations show that the method yields effective and accurate results for surfaces of arbitrary variation.      

A surface integral equation approach to the scattering andabsorption of doubly periodic lossy structures

The scattering and absorption of a doubly periodic array of absorbers, either placed in free space, backed by a perfect conductor or by a half-infinite space with the same material properties as the elements forming the array, is analyzed with a surface integral equation approach (SIE). The use of a suitable periodic Green's function as kernel of the SIE reduces the formulation of the problem to a single absorber. A set of equivalent electric and magnetic currents on the surface of the absorber is discretised using Glisson functions and the SIE is solved with Galerkin's method. The validity and flexibility of the SIE approach is exemplified by comparing numerical results with measurement data for a family of commercially available absorbers     

Cavity-Backed Aperture Antennas with Dielectric and Magnetic Overlay

A method is presented for a full wave analysis of an aperture antenna backed by a rectangular cavity. The antenna may be covered by one or more dielectric and magnetic layers. The aperture antenna may be arbitrarily shaped but must be small compared to the cross section of the cavity. The analysis includes ohmic, dielectric, and magnetic losses in the cavity as well as in the overlay. Deriving a modified magnetic field integral equation, the treatment of the cavity and of the layered overlay is separated. A dyadic Green's function describing the topology of the cavity is formulated in the space domain. Another dyadic Green's function for the layered overlay is derived in the spectral domain. Subsequently, the integral equation is solved by the method of moments. The theoretical treatment is worked out for arbitrarily shaped apertures. Finally, the proposed method is applied to narrow slot antennas backed by rectangular cavities. Some numerical results are compared with experimental data     

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     

Analysis of wraparound microstrip phased array by infinite arrayapproach

A moment method analysis of an infinite array of wraparound microstrip antennas fed with idealized current probes on a cylindrical body is presented. The integral equation is formulated through the use of periodic grounded dielectric slab Green's function. The method accounts for the blind angles and allows efficient computation of the reflection coefficient at all other angles. Illustrative results are given     

Efficient calculation of the free-space periodic Green's function

Electromagnetic scattering from periodic structures can be formulated in terms of an integral equation that has as its kernel a periodic Green's function. The periodic Green's function can be derived as a response to an array of line/point sources (spatial domain) or as a response to series of current sheets (spectral domain). These responses are a Fourier transform pair and are slowly convergent summations. The convergence problems in each domain arise from unavoidable singularities in the reciprocal domain. A method is discussed to overcome the slow convergence by using the Poisson summation formula and summing in a combination of spectral and spatial domains. A parameter study is performed to determine an optimum way to weigh the combination of domains. simple examples of scattering from a one-dimensional array of strips and two-dimensional array of plates are used to illustrate the concepts     

Emission and Susceptibility Modeling of Finite-Size Power-Ground Planes Using a Hybrid Integral Equation Method

A novel method based on hybrid integral equation for electromagnetic emission and susceptibility modeling of power-ground planes with a finite size is proposed in this paper. First, the entire computational domain is divided into the internal subdomain including the substrate sandwiched between the power and ground planes and the external subdomain surrounding the power-ground planes. The internal subdomain is modeled by using the integral equation with dyadic Green's functions of the rectangular cavity, while the free-space Green's function is used to model the outside subdomain. These two kinds of integral equations are coupled through the equivalent electric and magnetic currents that are placed on the interfaces. The key advantage of this proposed method is its ability to model both emission and susceptibility problems. This method can accurately simulate the impedance of the power-ground planes and the radiated field. In particular, it is able to predict the induced electric currents inside the power-ground planes that result from external interference sources. Therefore, this technique is able to provide a complete solution for the electromagnetic compatibility analysis of the system-level package.      

一种基于缝隙天线阻抗的带缝腔体谐振频率计算方法

电磁波经缝隙进入机箱腔体后,会在某些频率点形成驻波而发生电磁谐振,导致腔体屏蔽效能急剧下降.为快速准确预测谐振频率以指导屏蔽腔体设计,本文基于缝隙天线阻抗理论提出一种带缝腔体谐振频率的计算方法.将电磁场用自由空间和腔体格林函数表示,根据缝隙处的边界条件建立等效磁流源的积分方程.通过矩量法求解积分方程,计算出腔体输入阻抗.根据谐振发生时电抗为零或电阻最小,可从频率-阻抗曲线获得谐振频率.本文方法不仅能预测缝隙谐振和低阶模式腔体谐振,还能预测出高阶谐振.与实验和CST仿真结果对比验证了本文方法的准确性及快速性.最后用本文方法分析了腔体和缝隙尺寸以及缝隙位置对谐振频率的影响.     

Scattering from structured slabs having two-dimensional periodicity

The problem of a plane wave incident on a structured slab is examined. To analyze the problem, an electric field integral equation (EFIE) is derived that has as its unknown the equivalent surface currents on the plates in the unit cell. The integral equation is discretized and solved approximately using the method of moments with subdomain basis and testing functions. The periodic Green's function is efficiently calculated using the Poisson summation formula. The interaction of the structure with the surrounding environment is described in terms of a generalized scattering matrix. Results are presented showing the reflection coefficient as a function of frequency for arrays of zigzagging strips and honeycomb slabs     

Analysis and design of a leaky-wave EMC dipole array

An analysis of an electromagnetically coupled (EMC) dipole array is presented, in which a microstrip line is coupled to an infinite periodic linear array of microstrip dipoles, arranged perpendicular to the line. The spectral-domain immittance method is used to obtain the periodic Green's function for the two-layered structure, and the method of moments with a Galerkin testing procedure is then used to enforce the electric field integral equation (EFIE) on the line and the dipole within a unit cell of the structure to obtain the determinantal equation for the unknown leaky-wave propagation constant. One of the interesting features of this analysis is the path of integration in the complex plane used to compute the moment method reactions, which must be partly on the improper sheet for the m=-1 space harmonic when it radiates in the forward direction. Measured radiation patterns for a 10-element EMC dipole array are presented and compared with the corresponding theoretical ones     

Theory of microstrip lines on artificial periodic substrates

This paper presents the theory of a microstrip line on artificial periodic substrates. A two-stage moment method in conjunction with an array-scanning scheme is proposed for the microstrip characterization. The analytic and numerical methods dealing with the interaction of microstrip components (continuous plane-wave spectrum) with artificial periodic materials (discrete plane-wave spectrum, Floquet modes) are discussed. The method of solution involves two stages of vector integral equations and moment methods. The first integral-equation formulation is to find the Green's function for a planar periodic structure. A spectral-domain moment method is applied to the second vector integral equation to determine the fields or currents on the circuit components and the associated parameters of interest. Guided-wave characteristics of a microstrip line on artificial periodic substrates, including the propagation constant and the characteristic impedance, are investigated. Propagation bandgap of a microstrip line due to periodic elements is characterized. Experiment on a three-layer microstrip-line structure with a periodic mid-layer is conducted to validate the theory     

Efficient calculation of lattice sums for free-space periodicGreen's function

An efficient method to calculate the lattice sums is presented for a one-dimensional (1-D) periodic array of line sources. The method is based on the recurrence relations for Hankel functions and the Fourier integral representation of the zeroth-order Hankel function. The lattice sums of arbitrary high order are then expressed by an integral of elementary functions, which is easily computed using a simple scheme of numerical integration. The calculated lattice sums are used to evaluate the free-space periodic Green's function. The numerical results show that the proposed method provides a highly accurate evaluation of the Green's function with far less computation time, even when the observation point is located near the plane of the array     

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.     

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     

Analysis of cavity-backed aperture antennas with a dielectricoverlay

A full-wave analysis of cavity-backed aperture antennas with a dielectric overlay is presented. The theoretical approach uses a closed-form dyadic Green's function in the spectral domain. The aperture equivalent magnetic currents are obtained using the surface equivalence theorem and an integral equation is obtained by matching the fields across the aperture. The moment method applied in spectral domain analysis is employed to solve the integral equation for the equivalent magnetic currents with proper combination of subdomain or entire domain expansion functions. Numerical results include the aperture field distribution and antenna parameters such as input impedance, bandwidth, and efficiency. A set of measurements data is compared with results based on the theoretical work     

Electromagnetic analysis of an antenna embedded in a compositeenvironment

This paper addresses the problem of an antenna embedded in a hole dug in the ground. The composite medium configuration consists of a half-space dielectric (representing the Earth-air interface) containing a cylindrical hole filled with a different dielectric medium. The wire antenna resides within this hole, on the axis. The solution strategy is based on decomposing the problem into simpler subproblems, which are treated sequentially. First we calculate a numerical dyadic Green's function for the composite medium by solving an integral equation formulated over a background consisting of the unperturbed dielectric half space (for which the Green's functions are known in a spectral integral form). This integral equation is solved via the fictitious currents method, which is a special case of the method of moments. We then solve the integral equation for the antenna currents using this numerical Green's function and determine the input impedance and radiation pattern     

Theory and experiment of the cavity-backed slot-excited dielectricresonator antenna

A slot-excited hemispherical dielectric resonator antenna backed by a rectangular cavity is studied theoretically and experimentally. The magnetic-type dyadic Green's function for the rectangular cavity is derived using the mode-matching method. An integral equation for the equivalent magnetic current is obtained by enforcing the boundary condition across the slot. The moment method with the Galerkin's procedure is then used to find the magnetic current in the slot and, hence, the input impedance of the antenna. Measurements were carried out to verify the theory and good agreement is obtained. The effects of the slot inclination angle, of the slot offset, and of the cavity size on the input impedance are discussed     

An Improved Weak-Form BCGS-FFT Combined With DCIM for Analyzing Electromagnetic Scattering by 3-D Objects in Planarly Layered Media

Fast algorithms for electrically large objects buried in layered media are mainly hindered by two time-consuming processes. One is the table filling of Green's function, and the other is the solving of the impedance matrix equation. For the first, to accelerate the evaluation of the time-consuming Sommerfeld integral in the dyadic Green's function (DGF), the discrete complex image method (DCIM) is introduced to get a closed-form DGF. To further accelerate the calculation of DGF for the volume electric field integral equation (EFIE), DGF is split before applying DCIM. For the second, the iterative solver stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) is combined with DCIM for solving the matrix equations. Meanwhile, the closed-form DGF enables the "spherical-mean" Green's function, which eliminates the singularity of Green's function. Numerical results show that the weaker singularity results in a faster and steadier convergence rate for iterative solvers