A hybrid moment method solution for TEz scattering fromlarge planar slot arrays

This paper develops a hybrid moment method (MM) based numerical model for electromagnetic scattering from large finite-by-infinite planar slot arrays. The model incorporates the novel concept of a physical basis function (PBF) to reduce dramatically the number of required unknowns. The model can represent a finite number of slot columns with slots oriented along the infinite axis, surrounded by an arbitrary number of coplanar dielectric slabs. Each slot column can be loaded with a complex impedance to tailor the array's edge currents. An individual slot column is represented by equivalent magnetic scattering currents on an unbroken perfectly conducting plane. Floquet theory reduces the currents to a single reference element. In the array's central portion, where the edge perturbations are negligible, the slot column reference elements are combined into a single basis function. Thus, one PBF can represent an arbitrarily large number of slot columns. A newly developed one-sided Poisson sum formula is used to calculate the mutual coupling between the PBF and the slot columns in the presence of a stratified dielectric media. The array scanning method (ASM) gives the mutual coupling between the individual slot columns. The hybrid method is validated using both numerical and experimental reference data. The results demonstrate the method's accuracy as well as its ability to handle array problems too large for traditional MM solutions     

A generalized approach to the analysis of infinite planar array antennas

In this paper a generalized expression for the complex power radiated by an element in an infinite planar array antenna is derived. Since this power formula applies to a large class of phased array antennas where the aperture field distribution can be completely specified (in normal mode form), it proves to be a powerful, unifying principle. The utility of this approach is illustrated by the simplicity with which previously known results can be derived; e.g., an infinite array of slots in a ground plane and an infinite array of flat dipoles with or without a ground plane. Further demonstrations of the usefulness of the power formula are provided by the systematic and straightforward solutions of the less-well-known problems of infinite arrays of crossed-dipole pairs and infinite arrays of open-ended rectangular waveguides. The waveguide array solution is particularly interesting because it reduces to a set of equations which are identical to those one would use to characterize an N-port network on an admittance basis (N is the number of waveguide modes). Since the power formula is derived for a parallelogram element Lattice, the resultant solution for a specific type of element is in its most general form. Expressions for the scan-dependent, dominant mode radiation admittance and the element gain function for a multimode rectangular waveguide radiator are also derived. In addition, various aspects of the waveguide array solution are investigated in the light of previous studies of infinite arrays.     

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     

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.     

Finite phased array of microstrip patch antennas: the infinitearray approach

An efficient method of analysis of large infinite arrays based on a convolution technique that allows one to obtain the finite array characteristics from the infinite array results is presented. The edge effects are taken into account by convoluting the infinite array results with the proper current amplitude window on the array. The method is based on the use of Poisson's sum formula in the case of finite arrays applied here to microstrip antennas. It is an approximate technique that can be assimilated into a perturbation method     

Analysis of finite-phased arrays of aperture-coupled stackedmicrostrip antennas

Analytical results for finite-phased arrays of aperture-coupled stacked microstrip antennas are presented. In order to evaluate the characteristics of aperture-coupled microstrip antennas in a finite array and derive the moment-method solutions for the unknown current distributions on the patches and slots, the reciprocity theorem and the spectral domain Green's functions for a dielectric slab are used. Various sized arrays are considered and compared with solutions for an infinite array. Numerical results are presented to illustrate the input impedance, mutual coupling, active reflection coefficient versus scan angle, radiation efficiency, and active-element gain patterns     

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     

Scattering from finite by infinite arrays of slots in a thinconducting wedge

The radar scattering from a finite by infinite array of slots cut into a thin conducting wedge is considered. The wedge is formed by taking a thin ground plane and applying a bend to create a sharp edge which is parallel to the columns of slots in the infinite axis. Results are derived for thin linear slots whose major axes are either parallel or perpendicular to the edge. A hybrid moment method and geometrical theory of diffraction approach is used, with magnetic current expansion functions defined using Floquet's theorem on single columns of slots. Predictions generally agree with scattering measurements of finite by finite array physical models with monostatic patterns taken in a plane orthogonal to the sharp edge     

Mutual coupling in a slotted phased array, infinite inE-plane and finite in H-plane

The mutual admittance matrix is computed for a planar phased array of thin slots with assumed single-mode cosinusoidal aperture electric field. The array is of infinite extent in the E-plane and of finite extent in the H-plane. The H-plane excitation is arbitrary and the array is phase scanned in the E-plane. Resultant active row-port admittances and H-plane aperture distribution are in agreement with large strictly finite array calculations and with a Floquet mode infinite array model, for the example case of uniform H-plane excitation     

Some experiences from FDTD analysis of infinite and finite multi-octave phased arrays

Some experiences from finite-differences time-domain (FDTD) analysis of infinite and finite multi-octave phased arrays are presented. First, a more unified derivation of equations suitable for unit-cell analysis of phased arrays or other types of periodic structures using FDTD is presented. Second, results from FDTD calculations of small to very large multi-octave finite arrays are summarized in order to answer the question of how large an array model must be in order to capture the characteristics of both the interior and the edge elements of a large multi-octave phased array. It is found that a considerably larger number of elements is required in the broad-band case than in the normal narrow-band case, and it is also found that FDTD is well suited for such calculations. Third, simple methods to save computer memory using locally fine grids in an otherwise coarse FDTD grid to model finite-phased arrays are explored. The two local grid methods tested were found in our application to suffer from numerical instabilities.     

大型波导纵缝阵列天线的分析与设计

本文利用矩量法和等效网络法对矩形波导宽边纵缝阵列进行了精确的理论分析，严格计算阵中缝隙的内部和外部互耦，并利用等效网络法提取阵中缝隙的等效导纳特性。在此基础上，提出模型阵列和模型缝隙的大型波导缝隙阵的设计方法．理论结果与实验比较吻合。     

Multiport scattering analysis of general multilayered printedantennas fed by multiple feed ports. I. Theory

A general solution is given for a class of printed antenna geometries composed of multiple dielectric layers or ground planes, radiating patches, dipoles, or slots, and an arbitrary configuration of multiple transmission lines proximity-coupled or aperture-coupled to the radiating elements. The solution uses a full-wave spectral-domain moment method approach, and a new generalized multiport scattering formulation to model the excitation from the multiple feed lines. This method treats infinite phased arrays as well as isolated elements. The general theory using the new multiport scattering formulation is elaborated, with details of the key analytical and numerical aspects. Considering the unified nature of the multiport scattering analysis, and its simplicity, this analysis is appropriate for computer simulation of a large variety of multilayered microstrip antennas involving radome layers, dual polarized feeds, proximity-coupled or aperture-coupled elements, multifeed stacked or parasitic patches, and several related configurations for integrated phased array applications     

On the use of metallized cavities in printed slot arrays with dielectric substrates

A detailed analysis of infinite slot arrays excited by delta-function current sources is presented. The existence of severe array blindness is proved for most of the cases of slots without metallic cavity separators.     

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.     

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 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 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     

Mutual coupling between parallel columns of periodic slots in aground plane surrounded by dielectric slabs

Arrays of slots with arbitrary orientation in an infinite conducting plane that are infinitely periodic in one dimension and finitely periodic in another dimension are considered. The plane is bounded on each side of dielectric slabs of finite thickness and infinite extent. Single columns of slots are represented by equivalent magnetic scattering currents, which are solved for by the moment method. The mutual coupling (admittance) between slot columns in the presence of the stratified media is found by the array scanning method, which expresses the admittance as the average of the scan admittance of an artificially constructed doubly infinite array of slots over all real scan angles. The technique avoids the use of Sommerfeld integrals, but still gives rise to singularities at scan angles corresponding to the resonant excitation of surface waves. An analytical approximation removes these surface wave singularities, making numerical implementation of the method practical     

Phased array theory and technology

This review of array antennas highlights those elements of theory and hardware that are a part of the present rapid technological growth. The growth and change in array antennas include increased emphasis on "special-purpose" array techniques such as conformal and printed circuit arrays, wide angle scanning arrays, techniques for limited sector coverage, and antennas with dramatically increased pattern control features such as low sidelobe, adaptively controlled patterns. These new topics have substantially replaced large radar arrays in the literature and constitute a major change in the technology. The paper presents a tutorial review of theoretical developments emphasizing techniques appropriate to finite arrays, but indicating parallel developments in infinite array theory, which has become the useful tool for analysis of large arrays. A brief review of the theory of ideal arrays is followed by a generalized formulation of array theory including mutual coupling effects, and is appropriate to finite or infinite arrays of arbitrary wire elements or apertures in the presence of a conducting ground screen. Some results of array tolerance theory are summarized from the literature and retained as reference throughout discussions of array component requirements and device tolerance for low sidelobe arrays. Examples from present technology include conformal and hemispherical coverage arrays, lightweight printed circuit arrays, systems for use with reflectors and lenses in limited sector coverage applications, and wide-band array techniques.     

Scattering parameters of surface-wave multistrip directional couplers: a field approach

A field solution for the acoustic-surface-wave modes in infinite arrays of metal strips is applied to multistrip directional couplers consisting of a finite number of strips. Particular emphasis is put on the behaviour close to resonance, where the period in the array is one halfwavelength of the acoustic surface wave. Experiments on an array of 120 strips show good agreement with the theory.