Phased array antenna analysis with the hybrid finite element method

A new analysis technique for infinite phased array antennas was developed and demonstrated. It consists of the finite element method (FEM) in combination with integral equation radiation conditions and a novel periodic boundary condition for 3-D FEM grids. Accurate modeling of rectangular, circular and circular-coaxial feeds is accomplished by enforcing continuity between the FEM solution and several waveguide modes across an aperture in the array's ground plane. The radiation condition above the array is enforced by a periodic integral equation in the form of a Floquet mode summation, thus reducing the solution to that of a single array unit cell. The periodic boundary condition at unit cell side walls is enforced through a matrix transformation. That mathematically “folds” opposing side walls onto each other with a phase shift appropriate to the array lattice and scan angle. The unit cell electric field is expanded in vector finite elements. Galerkin's method is used to cast the problem as a matrix equation, which is solved by the conjugate gradient method. A general-purpose computer code was developed and validated for cases of open-ended waveguides, microstrip patches, clad monopoles and printed flared notches, showing that the analysis method is accurate and versatile     

Analysis of a microstrip array and feed network

An analysis technique for a microstrip array is presented. The array elements and mutual coupling between elements are analyzed by a method of moments (MM) solution of the exact integral equation. The combination of the microstrip array elements, plus the microstrip transmission line feed network is analyzed using a generalized Thévenin theorem. The method is applied to the specific problem of the series fed microstrip array.     

Analysis of infinite arrays of substrate-supported metal stripantennas

An electric field integral equation method is applied to a metal strip antenna on an electrically thick dielectric substrate of finite size in a uniform infinite array environment. An efficient solution is found using the method of moments. Metal strip folded dipole antennas are analyzed both with and without a coplanar strip feed line, and the effects of the substrate and feed line are investigated. A technique for minimizing the effect of feed line scattering is presented, and arrays of these elements are shown to be capable of good scanning performance over a wide range of beam-steer angles. A phased array simulator experiment is described and the measured results show good agreement with those obtained by analysis. The class of antenna elements studied may be fabricated using monolithic microwave integrated circuit (MMIC) technology, and the analysis described illustrates the expected characteristics for millimeter-wavelength phased arrays of this type     

Scattering from a finite array of microstrip patches

A full-wave solution to the problem of plane wave scattering by a finite array of rectangular microstrip patches printed on a grounded dielectric slab is presented. The electric field integral equation is solved using the spectral-domain Green's function/moment method approach. Derivations for the elements of the impedance and voltage matrices are presented. An efficient massively parallel computer implementation of the moment method solution is described. Computed radar cross section (RCS) data for microstrip patch antenna arrays are presented as a function of incident signal frequency and angle of incidence     

Fast spectral domain algorithm for rapid solution of integralequations

A fast spectral domain algorithm is presented for rapid solution of planar surface integral equations. The method of moments coupling integral matrix is formulated in the spectral domain but not explicitly calculated. Thus, in conjunction with an iterative equation solver, the pertinent matrix/vector products are evaluated with complexity O(n) where n is the number of unknowns. Validation and timing results are presented for an array analysis approach using a hybrid finite element (FE)-boundary integral implementation     

Matching and mutual coupling characteristics of the elements of a finite waveguide array with an impedance flange

Matching and mutual coupling characteristics of the elements of a waveguide antenna array consisting of a finite number of aperture radiators with a finite flange are analyzed. The radiators are formed by semi-infinite cylindrical waveguides of an arbitrary cross section. The array radiates into a plane-layered medium. The solution procedure is based on the single-mode variational approach. Numerical results are presented for an array consisting of nine apertures of rectangular waveguides.     

A hybrid symmetric FEM/MOM formulation applied to scattering byinhomogeneous bodies of revolution

A new symmetric formulation of the hybrid finite element method (HFEM) is described which combines elements of the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) for the exterior region along with the finite element solution for the interior region. The formulation is applied to scattering by inhomogeneous bodies of revolution. To avoid spurious modes in the interior region a combination of vector and nodal based finite elements are used. Integral equations in the exterior region are used to enforce the Sommerfeld radiation condition by matching both the tangential electric and magnetic fields between interior and exterior regions. Results from this symmetric formulation as well as formulations based solely on the EFIE or MFIE are compared to exact series solutions and integral equation solutions for a number of examples. The behaviors of the symmetric, EFIE, and MFIE solutions are examined at potential resonant frequencies of the interior and exterior regions, demonstrating the advantage of this symmetric formulation     

Integral equation analysis of artificial media

This paper presents an integral equation and method of moments (MM) solution to determine the effective permittivity and permeability of an artificial medium. The artificial medium is modeled as a triple infinite periodic array of identical scattering elements. A plane wave of unknown phase constant is assumed to propagate in the periodic medium in a given direction, and the periodic moment method (PMM) is used to set up a matrix equation for the currents on the center element of the periodic array. By setting the determinant of the PMM impedance matrix to zero, one can determine the phase constant of the plane wave, and then the effective permittivity and permeability of the artificial medium     

Analysis of finite phased arrays of circular microstrip patches

A method is presented for analyzing a finite planar array of circular microstrip patches fed by coaxial probes. The self- and mutual impedances between array elements are calculated using the method of moments with the dyadic Green's function for a dielectric layer on a ground plane. The patch circuits are determined by using the reaction integral equation. The active input impedance as well as the active element pattern of the array are computed from a knowledge of the resultant patch currents. The calculated results for two-element and eight-element linear arrays are in good agreement with experimental data. The active reflection coefficient and element pattern for the center and edge elements of a two-dimensional array as a function of scan angle are also presented     

A truncated Floquet wave diffraction method for the full waveanalysis of large phased arrays. I. Basic principles and 2-D cases

This two-part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas. This is based on the method of moments (MoM) solution of a fringe integral equation (IE) in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array. The unknown currents can be interpreted as produced by the field diffracted at the array edge, which is excited by the Floquet waves (FWs) pertinent to the infinite configuration. Following this physical interpretation, the unknown in the IE is efficiently represented by a very small number of basis functions with domain on the entire array aperture. In order to illustrate the basic concepts, the first part of this sequence deals with the two-dimensional example of a linearly phased slit array. It is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted-ray-shaped unknown functions. This also permits a simple interpretation of the element-by-element current oscillation, which was described by other authors     

一种快速有限周期阵列特征模分析法北大核心CSCD

周期特征模分析(PCMA)方法是一种有限周期阵列特征模分析数值算法。该方法使用特征向量在每个阵元上定义若干组全域基函数,然后基于全域基函数得到一个压缩广义特征值方程。利用该方程可实现该阵列的特征模分析。与传统方法相比,该方法未知数量显著减少,节省了存储成本和求解时间。然而,广义特征值方程中的矩阵元素计算涉及二重面积分,非常耗时。文章采用等效偶极矩法计算矩阵元素,避免了二重面积分运算,从而节省了计算时间。数值结果表明新方法的结果与PCMA法以及传统分析法结果吻合很好,验证了所提方法的精度。同时,该方法显著降低了求解时间。     

Hybrid numerical method for harmonic 3-D Maxwell equations:scattering by a mixed conducting and inhomogeneous anisotropicdielectric medium

This article deals with a hybrid numerical method for solving harmonic Maxwell equations in the classical electrodynamic context. This formulation can be used with any body of arbitrary three-dimensional geometry, of perfectly conducting material or dielectric, with locally inhomogeneous and anisotropic behavior laws, and with or without dielectric losses. The mathematical formulation is presented along with applications validating it. The exterior problem is treated by the integral equation method while local equations are used for the dielectric parts of the body. A global variational formulation of the coupled problem is developed for use in discretization by the finite element method. Boundary finite elements are used for integral operators connected with the exterior problem. Localized finite elements are used for the interior problem. Difficulties of irregular frequencies, also called resonant frequencies in the perfectly conducting case, arising from the integral formulation are analyzed in detail and an efficient solution is developed     

Mutual coupling analysis of a finite planar waveguide array

This paper deals with mutual coupling in a finite planar array antenna, composed of open-ended circular waveguides in a ground plane. The element-by-element approach is used and the problem is formulated as an integral equation, by requiring the transverse electric and magnetic fields to be continuous across the apertures. The equation is then solved by the method of moments and the mutual coupling in a 127-element array is computed. Excellent agreement with measurements and with the active reflection coefficient for the corresponding infinite array is found. The presented method of coupling analysis can be considered as a supplement to the established periodic-structure approaches for infinite arrays and may be useful for the analysis of small or nonperiodic arrays.     

Infinite phased dipole array

By means of a Poisson sum formula and an integral-equation technique, an accurate solution for an infinite phased dipole array is obtained. The elements of the array are spaced uniformly and are excited with increasing phases. The technique can be applied to an infinite collinear array and to an infinite planar array either in free space or over a ground plane. The integral equation is solved both by a Fourier method and by an approximate five-term procedure. It is found that the latter is as good as the former. The current distributions and the active admittances are investigated.     

Equivalent Network of a Multimode Planar Grating

In this paper a plane-parallel, perfectly conducting, zero-thickness grating is analyzed by an integral equation procedure. This procedure generalizes the well-known single-mode method by taking multimode propagation into account. The grating is located in free space; viewed transversely to the plane of the structure, it is a zero-thickness shunt discontinuity in the free-space waveguide. The solution of the integral equation is obtained for E (or TM) mode excitation, when the spacing between conducting strips is small compared to a period, and it is interpreted in network terms. Finally, an explicit equivalent network is presented for the grating under multimode conditions.     

Multimode Equivalent Networks for the Design and Analysis of Frequency Selective Surfaces

A modular technique originally proposed for waveguide junctions, the multimode equivalent network approach based on the integral equation formulation (IEMEN), is extended to the analysis of multilayer frequency selective surfaces integrated with waveguide array antennas. This technique represents each layer and transition between layers in terms of a generalized impedance or admittance matrix, obtained directly from the solution of an integral equation with reduced kernel. Thanks to the adopted formulation, the integral equation needs to be solved only in a limited set of frequency points. The IEMEN method is validated by comparison with results available in literature.     

A reactively loaded aperture antenna array

The use of variable reactive loads to control the beam direction of an antenna array consisting ofNclosely spaced waveguide-backed dielectric-filled rectangular slots is considered. Only the center waveguide is driven (no complex feed network is required for the array), and the other waveguides are short circuited at specified distances to provide reactive loading. The solution uses the method of moments applied to the integral equation for the equivalent magnetic current in the aperture region. The initial, design of the array is obtained by resonating the complex excitation voltages required for maximum gain with all of the elements driven. This is then improved by an optimum seeking univariate search method. Computed results are given for seven- and fifteen-element aperture arrays.     

细线结构时域电场积分方程的有限差分求解

提出一种求解基于细线结构的时域电场积分方程 ( TDEFIE)的方法 -有限差分方法。与传统求解时域电场积分方程的时域矩量法相比 ,该方法易于数值实现。文中还利用该方法研究了电磁辐射、散射的三个经典问题 ,并将结果与时域矩量法的结果进行了比对 ,研究表明 ,该方法求解细线结构的 TDEFIE非常有效。     

一种考虑互耦的脉冲天线阵列快速计算方法

基于有源单元方向图思想, 提出了一种可用于计算脉冲天线阵列时域辐射场的快速方法.该方法在考虑单元间互耦的情况下, 将大型阵列的时域辐射场计算问题转化为一个小型阵列的计算问题, 大大地减少了计算量.采用文中的阵列综合方法, 结合有限积分法软件, 仅对一个5×5元阵列进行模拟, 即可推算出大型阵列的远场方向图, 其计算时间不超过全波模拟时的十分之一.计算结果与仿真软件的仿真结果吻合较好, 验证了方法的正确性.       

Reflector Antenna Analysis Using the Complex Equivalent Length Concept: Reciprocity and Coupling Between Feeds

This work presents a procedure for analyzing multiply fed reflector antennas in both transmission and reception modes, by using the Reflector Antenna Complex Equivalent Length (RA-CEL) concept. The RA-CEL is derived by combining the Feed Element Complex Equivalent Length (FE-CEL) Method with an Equivalent Current (EC) model on the reflector surface. This formulation, in terms of both electric and magnetic equivalent currents, is consistent with the reciprocity theorem. Its application to reflector antenna far-field pattern analysis, in both the transmission and reception modes, is presented. The proposed method accurately considers the mutual coupling among feeding array elements through the reflector surface, and its computational cost is substantially lower than required by a full-wave analysis. Some applications investigating the mutual coupling among feeding elements of reflector antennas are presented, and are compared with a reference solution given by the Method of Moments - Physical Optics hybrid method, and a numerical evaluation of the integral equation.