Electromagnetic scattering by a perfectly conducting patch array ona dielectric slab

The scattering characterization of an infinite and truncated periodic array of perfectly conducting patches on a dielectric slab is discussed. In particular, an approximate solution for the truncated array scattering that is based on the exact solution for the corresponding infinite array is presented. The latter is obtained numerically by solving for the patch currents using a conjugate-gradient fast Fourier transform (FFT) technique, eliminating the need to generate and store the usual square impedance matrix. The scattering pattern of the finite array is then computed approximately by integrating the infinite-period-array currents over the given finite array. Numerical results are presented for the infinite and finite arrays, and the accuracy of the approximate solution for the finite array is examined and discussed in relation to some available exact data. It is found that the approximate solution is of reasonable accuracy in predicting the scattering by the truncated array     

The design of large waveguide arrays of shunt slots

It is shown that the method of moments (MM) solution can determine the active admittance of each slot in a finite array and that the infinite array model is quite accurate for the design of large waveguide arrays of shunt slots. Active admittances computed by an infinite array model agree favorably with that of slots in sufficiently large finite arrays. Measured results verify the MM solution, thereby validating the infinite array model accuracy     

Analysis of finite phase arrays of microstrip patches

A method for the analysis of large phased arrays of microstrip patches is presented. It is based on an infinite array approach where the edge effects are taken into account through the convolution with a proper window function. In the first step, a rigorous Green's function corresponding to a finite array of elementary sources is derived. This Green's function is then used to analyze the finite phased array of microstrip patches. Results are shown for the active impedance and element patterns of several arrays, and compared with measurements or, in the case of small arrays, with results obtained by a rigorous element-by-element approach. It is shown that the method, even if developed for the analysis of large arrays, is able to handle small arrays. Indeed, the results obtained are good even for single patches. Although the method has been developed for the microstrip phased array case, the results are general and are valid for any phased array with a rectangular grid     

MoM simulation of signal-to-noise patterns in infinite and finite receiving antenna arrays

An approach based on the method of moments is presented for the computation of the sensitivity of infinite and finite receiving phased arrays with active beamforming networks. The sensitivity is characterized in terms of signal-to-noise element patterns. Coupling of noise through the array is included in the analysis, as well as noise resulting from losses in the antennas. Simulation results are shown for arrays consisting of tapered-slot antennas made of metallic plates. For finite arrays, the average signal-to-noise ratio per element is not necessarily smaller than in the infinite-arraycase. For an 8/spl times/8 array, the average signal-to-noise element pattern is somewhat more narrow than for the infinite array. At broadside, the sensitivity of relatively small arrays (4/spl times/4 to 8/spl times/8) is described within order 1 dB by the infinite-array solution.     

Edge effects in finite arrays of uniform slits on a ground plane

The results obtained by modeling a linear array as an infinite periodic structure can be used for the analysis of finite arrays as the zero-order approximation of a perturbation technique. This idea is utilized to investigate the edge effects in two arrays of uniform slits fed by parallel-plate waveguides terminated on a ground plane. It is shown that the realized gain pattern of an element depends substantially upon its position in the array. This is true particularly for the deep resonance notches in the patterns which are present for certain element spacings. When the array is excited with uniform magnitude and linear phase, the aperture voltages are the superposition of a term, corresponding to the infinite array model, plus another correction term (a "spatial transient") representing the edge effect. The influence of this term is particularly relevant when the array is scanned at endfire. In such a case, the method introduced here allows the prediction of the element terminal admittances and the array pattern, while according to the infinite array model no radiation would be permitted.     

Analysis of printed array antennas

A simple but efficient analysis tool for printed antenna arrays is presented. It relies on a perturbation approach, which starts from the infinite periodic array assumption to ultimately take into account effects due to finite size, nonperiodicity, double-periodicity in a multilayer case, complex excitation with nonlinear phase shifts between elements, etc. The technique is an approximation, as are most of the array analysis tools. However, it gives good results for arrays presenting a relatively smooth variation of the antenna characteristics between adjacent cells. Results will be shown for several arrays, including nonperiodic and multilayered cases. The method is validated through the comparison with results obtained by a rigorous element-by-element method     

Analysis of finite parallel-plate waveguide arrays

An analysis has been carried out to determine the edge effects in finite parallel-plate waveguide arrays. The method used in the evaluation is to compare the element patterns and reflection coefficients versus scan for finite arrays with the corresponding results for hypothetical infinite arrays. It is found that, in arrays of empty waveguides, an element has to be about four or five elements removed from the edge in order to be regarded as being in an infinite array environment. On the other hand, when the waveguides are loaded with dielectric plugs having suitable combination of parameters, considerably more elements are needed for the simulation of an infinite array environment due to the appearance of the resonant null in the array transmission coefficient. It is found, moreover, that even though there may be substantial variation in the radiation properties from element to element in finite arrays, particularly so in the case of moderately sized arrays, this variation does not seem to severely degrade the array performance in terms of beamwidth and sidelobe levels.     

Analysis of finite arrays-a new approach

A novel method for the analysis of finite arrays is presented. The method is based on a global array concept where the array problem (for single-mode elements) is reduced to a solution of a single Fredholm integral equation of the second kind. This formulation offers several types of solutions (not all explored yet) with illuminating results. The approximate solution of this integral equation, for example, yields finite array characteristics in terms of equivalent infinite array scattering parameters and mutual admittances. The method is general, i.e., applicable to any element-type and periodic array geometry. Presently, the method applies to single-mode elements (one unknown per element), however, it can be extended to a multimode analysis     

曲面阵列结构散射与辐射特性的迭代分析

建立了一种适用于曲面有限阵列结构辐射与散射特性分析的迭代方法。首先根据阵列结构相同单元电流分布的相似性,对曲面有限阵列单元几何形状和表面电流分布作了两个假定,将有阵阵格林函数法推广应用于曲面有限阵列结构的分析;然后给出曲面有限阵列结构迭代分析的一般公式,通过迭代运算来消除两个假定近似的影响;最后迭代运算来消除两个假定近似的影响;最后以有两曲面带栅的散射和线源激励曲面带栅结构的辐射分析为例,验证了方法的有效性,并同逐元法作了比较,给出了有关的数值计算结果。结果表明：这种迭代法不受阵面曲率变化、单元数量和分布情况的限制,对有限周期和非周期阵列的分析都有着较高的计算效率和稳定性。     

Finite periodic structure approach to large scanning array problems

There are two conventional techniques dealing with mutual coupling problems for antenna arrays. The "element-by-element" method is useful for small to moderate size arrays. The "infinite periodic structure" method deals with one cell of infinite periodic structures, including all the mutual coupling effects. It cannot, however, include edge effects, current tapers, and nonuniform spacings. A new technique called the "finite periodic structure" method, is presented and applied to represent the active impedance of an array, it involves two operations. The first is to convert the discrete array problem into a series of continuous aperture problems by the use of Poisson's sum formula. The second is to use spatial Fourier transforms to represent the impedance in a form similar to the infinite periodic structure approach. The active impedance is then given by a convolution integral involving the infinite periodic structure solution and the Fourier transform of the equivalent aperture distribution of the current over the entire area of the array. The formulation is particularly useful for large finite arrays, and edge effects, current tapers, and nonuniform spacings can also be included in the general formulation. Although the general formulation is valid for both the free and forced modes of excitation, the forced excitation problem is discussed to illustrate the method.     

Analysis of finite phased arrays of printed dipoles

The problem of a finite array of printed dipoles is treated, and results are presented in the form of reflection coefficient magnitudes, element patterns, and efficiency (based on power lost to surface waves). Various sized arrays are considered, and are compared with infinite array solutions. The excitation of surface waves is discussed in relation to the scan blindness phenomenon and the transition to an infinite array. Techniques for computational efficiency are also presented.     

Experimental Study of Planar Finite Grid Oscillator Arrays

Results of an experimental study on finite grid oscillator arrays and the effects of the edge element loading stubs in such arrays are presented. Three finite grid oscillator arrays, based on the same unit cell, with different number of unit were fabricated on RT/Duroid 5870 substrate and tested in terms of the oscillation frequencies, radiated power and radiation patterns. It is observed that the oscillation frequency of a finite grid array differs from the theoretically prediction based on the infinite array assumption and is strongly affected by the edge element loading stubs. The measurement also indicates that mode-jumping and multi-frequency (spurious) oscillation can exist in grid oscillator arrays.     

阵列结构辐射与散射特性分析的迭代方法

给出一种适用于有限阵列结构辐射及特性分析的迭代方法。该法不受阵列单元排布形式、单元电流分布情况和单元数量的限制，对有限周期和非周期阵列的分析都有着较高的计算效率和稳定的收敛性。文中着重以有限周期及非周期带栅的散射分析为例，验证了方法的有效性，并同有限阵格林函数法和逐元法作了比较，给出了有关的数值计算结果。     

Efficiency as a measure of size of a phased-array antenna

This communication addresses the problem of estimating the minimum size a phased-array antenna must have in order that analyses based on simple infinite-array models yield meaningful results. The measure of array size proposed herein is an efficiency parameter defined for an infinite array with truncated excitations. Numerical results are presented for arrays of slots and dipoles, showing the rate of convergence of the efficiency parameter for various spacings and scan angles. The conclusions deduced from this analysis as to the minimum array size are in substantial agreement with exact computations dealing with finite arrays published in the literature.     

Pseudopotentials: A Simplified Model for Certain Types of Array Elements

The results obtained by modeling an infinite linear array of electrically short dipoles by an array of pseudopotentials (the pseudopotential is a quantum-mechanical analog of the dipole) can be used for the analysis of finite linear dipole arrays. This idea is utilized to investigate properties of finite arrays such as resonances, grating lobes, and end effects. For a wide range of parameter values, it is found that the pseudopotentials can quantitatively describe all aforementioned properties of the actual finite array. Certain extensions to waveguide arrays are discussed.      

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     

On the size requirement for finite phased-array models

The question considered is how large an array model must be in order to capture approximately the characteristics of both the interior and the edge elements of a large multi-octave phased array. Arrays with tapered slot elements and with top-loaded dipoles are analyzed at element spacings as small as 0.1λ and it is concluded that at any frequency, a finite array model with this type of element should be at least 5λ×5λ in size. This suggests the generalization of the 10×10 element model often used as an engineering "rule of thumb" in the normal narrow-band case with 0.5λ element spacing. An array model with a 5:1 bandwidth thus needs about 25 times more elements than a narrow-band model. The array feed impedance is considered and it is found that the array active reflection coefficient in finite arrays but not in infinite arrays is dependent on the matching condition at the feed. The finite-difference time-domain (FDTD) technique is used to analyze arrays up to 49×49 elements, demonstrating that computer power now makes feasible the full wave solution for large phased arrays with complex geometry     

Scan blindness phenomenon in conformal finite phased arrays of printed dipoles

Scan blindness phenomenon for finite phased arrays of printed dipoles on material coated, electrically large circular cylinders is investigated. Effects on the scan blindness mechanism of several array and supporting structure parameters, including curvature effects, are observed and discussed. A full-wave solution, based on a hybrid method of moments/Green's function technique in the spatial domain, is used to achieve the aforementioned goals. Numerical results show that the curvature affects the surface waves and hence the mutual coupling between array elements. As a result, the array current distribution of arrays mounted on coated cylinders are considerably different compared to similar arrays on planar platforms. Therefore, finite phased arrays of printed dipoles on coated cylinders show different behavior in terms of scan blindness phenomenon compared to their planar counterparts. Furthermore, this phenomenon is completely different for axially and circumferentially oriented printed dipoles on coated cylinders suggesting that particular element types might be important for cylindrical arrays.     

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.     

A 3-D hybrid finite element/boundary element method for the unifiedradiation and scattering analysis of general infinite periodic arrays

We present a rigorous frequency domain variational 3-D electromagnetic formulation for the general nonself-adjoint infinite periodic array problem. The hybrid method described combines the vector finite element and Floquet boundary element techniques. It is general in the sense that it is applicable to infinite periodic arrays of the open or aperture-types. It is thus effective for modeling both the scattering and radiation performance of diverse FSS, absorber, and phased-array structures. The technique accurately handles arbitrarily complicated 3-D geometries, lossy inhomogeneous media and internal as well as external excitations. These analyses can be applied to general skewed grids under arbitrary scan and polarization conditions