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.     

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     

Performance of a protruding-dielectric waveguide element in a phased array

A solution for the active array reflection coefficient in a two-dimensional array of parallel-plate-guide fed protruding-dielectric elements is presented. Analysis for this class of elements is not available in the literature. Element pattern nulls are found as in the case of dielectric-slab-covered arrays. The resonance mechanisms are also shown to be similar. Bandwidth properties of this array are briefly considered. A good agreement with experiments on two small arrays is found. Departures from infinite array theory, which take the form of a ripple on the flat portion of the element patterns and dips beyond the grating lobe angle, are shown to result from the finiteness of the arrays. These edge effects may be interpreted as arising from the interference between the "space wave," i.e., the infinite array element pattern and the fields radiated by the sources induced at the array edges by a wave traveling along the array face.     

Low-Sidelobe Pattern Synthesis Using Iterative Fourier Techniques Coded in MATLAB [EM Programmer's Notebook]

The iterative Fourier technique for the synthesis of low-sidelobe patterns for linear arrays with uniform element spacing is described. The method uses the property that for a linear array with uniform element spacing, an inverse Fourier transform relationship exists between the array factor and the element excitations. This property is used in an iterative way to derive the array element excitations from the prescribed array factor. A brief outline of the iterative Fourier technique for the synthesis of low-sidelobe patterns for linear arrays will be given. The effectiveness of this method for realizing low-sidelobe sum and difference patterns will be demonstrated for linear arrays equipped with 50 and 80 elements. This demonstration of effectiveness also involves the recovery of the original low-sidelobe patterns, as close as possible, in case of element failures. Included is a program listing of this synthesis method, coded in MATLABtrade. With a few minor modifications/additions, the included MATLAB program can also be used for the design of thinned linear arrays having a periodic element spacing. Since the computational part of the included MATLAB program is coded using vector/matrix operations, this program can easily be extended for the synthesis of low-sidelobe patterns of planar arrays with a periodic element spacing, including pattern recovery in the case of defective elements.     

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.     

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.     

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     

Asymptotic analysis of mutual coupling in concave circularcylindrical arrays. II. Near-zone

For pt.I, see ibid., vol.41, no.2, p.121-36 (1993). This work evaluates the near-zone coupling coefficients in large concave arrays. A canonical model of a circular cylindrical concave array of open-ended rectangular waveguides is analyzed. It is shown that in the paraxial region (which also includes the area close to the excited element) the coupling coefficients are identical, to lowest asymptotic order, to those in an equivalent infinite planar array. In the transition region, which lies between the paraxial and the far zone, or the ray region, two representations were developed: one, a transition function, expressed in terms of a canonical integral which must be numerically evaluated, and the other a uniform representation, which consists of a superposition of a planar array contribution and a few periodic structure rays. The uniform representation is valid in the near zone (which includes both the paraxial and the transition region) as well as in the far zone. This form is simple and may be immediately generalized to concave arrays with slowly varying curvature and periodicity     

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.     

High-frequency Green's function for a semi-infinite array ofelectric dipoles on a grounded slab .I. formulation

A uniform, high-frequency solution is presented for the electromagnetic field radiated at finite distance by a semi-infinite array of elementary electric dipoles placed on an infinite grounded dielectric slab. This solution is useful for the efficient analysis of printed arrays. The field is represented in terms of a series encompassing propagating and evanescent truncated Floquet waves together with their corresponding diffracted rays, which arise from the edge of the array. The high-frequency formulation also includes surface and leaky wave contributions excited at the array edge. The diffracted waves contain discontinuities which compensate the disappearance of surface, leaky and truncated Floquet waves at their pertinent shadow boundaries     

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.      

General relations for a phased array of printed antennas derived from infinite current sheets

Simple and general relations characterizing the behavior of infinite phased arrays of printed antenna elements are derived from a model based on infinite current sheets. The Green's function of an electric current source on a grounded dielectric slab is used in various limiting forms to treat arrays in free space, arrays above a ground plane, arrays on a semi-infinite substrate, and arrays on a grounded dielectric slab. Current sheets are selected, using the orthogonality properties of the Floquet modes of the infinite array Green's function, to excite only a few specific low-order Floquet modes. Results from this idealized model, in the form of reflection coefficient magnitudes and input resistance, are compared with rigorous moment method solutions for specific elements (dipoles and microstrip patches). It is shown how the dominant scanning characteristics of a printed phased array, such as reflection coefficient and input resistance trends, scan blindnesses, and grating lobe effects, are dictated more by factors such as element spacing and substrate parameters than by the particular element type itself.     

Isophoric arrays-massively thinned phased arrays withwell-controlled sidelobes

Traditional filled phased arrays have an element placed in every location of a uniform lattice with half-wavelength spacing between the lattice points. Massively thinned arrays have fewer than half the elements of their filled counterparts. Such drastic thinning is normally accompanied by loss of sidelobe control. This paper describes a class of massively thinned linear and planar arrays that show well-behaved sidelobes in spite of the thinning. The term isophoric is derived from Greek roots to denote uniform weight. In isophoric arrays, element placement based on difference sets forces uniformly weighted spatial coverage. This constraint forces the array power pattern to pass through V uniformly spaced, equal, and constant values that are less than 1/K times the main beam peak, where V is the aperture size in half-wavelengths and K is the number of elements in the array. The net result is reduced peak sidelobes, especially when compared to cut-and-try random-placement approaches. An isophoric array will exhibit this sidelobe control even when the array has been thinned to the extent that K is approximately the square root of V. Where more than one beam must be generated at a time, isophoric array designs may be used to advantage even within a traditional filled array. By “interweaving” two isophoric subarrays within a filled array and by appropriate cyclic shifting of the element assignments over time, two independent antenna power patterns can be generated, each with a sidelobe region that is approximately a constant value of 1/(2K) relative to the main beam, where K is the number of elements in the subarray     

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     

Properties of a cylindrical antenna in an infinite planar or collinear array

A solution is given for the active impedance and current distribution on a cylindrical antenna in a uniform, infinite, planar, or collinear array. The analysis is applicable to the case in which the distance in the collinear direction between the ends of adjacent elements is small. The current distribution on the collinear array is found by relating the antenna current and electric-field variation on the cylindrical surface of infinite length which contains the array. This analysis is then extended to consider a planar array. Results obtained are applicable to any combination of element length and array phasing, for arrays with or without a ground plane. Comparisons with other investigations based upon sinusoidally distributed currents reveal substantial discrepancies for some configurations.     

Mutual coupling and element efficiency for infinite linear arrays

A formulation is presented of the interrelationship among mutual coupling element efficiency, active impedance, and element radiation patterns for infinite linear (uniformly spaced) arrays. Numerical results are obtained for element efficiency and mutual coupling when the array elements are elementary dipoles. A new lower upper bonnd is obtained on element efficiency. This upper bound is expressed directly in terms of the element patterns in the open-circuit array environment.     

Phase-only synthesis of minimum peak sidelobe patterns for linearand planar arrays

Minimization of the maximum sidelobe level for a given array geometry by phase-only adjustment of the element excitations is considered. Optimum phases are obtained by using a numerical search procedure to minimize the expression for the pattern sidelobe level with respect to the element phases. Results for both linear and planar arrays of equispaced elements are presented. The data suggests that optimum sidelobe level is a logarithmic function of array size, and optimum patterns have relative efficiencies that are typically somewhat greater than for comparable-amplitude tapered arrays. An analytic synthesis algorithm is presented for use on very large arrays for which the numerical search technique for the minimization of the sidelobe level is computationally impractical. This method produces patterns with characteristics similar to arrays synthesized using the numerical search method, i.e. relatively uniform angular distribution of energy in the sidelobe region, and generally decreasing maximum sidelobe level as the array size is increased     

Large finite array analysis using infinite array data

The prediction of edge element behavior is a common problem during the design of large array antennas. The performance of the center elements can be approximated by an infinite array model, but the edge element patterns and active reflection coefficients cannot. The full element-by-element analysis of a large finite array is either excessively time consuming or impossible due to the computer power required. A study has recently been carried out to develop and test methods of fully predicting large array performance using infinite array data. The methods devised are presented, together with comparisons of predicted performance and measured data from a 163-element WG-16 array     

Theoretical and experimental study of monopole phased array antennas

A theoretical and experimental investigation of the mutual coupling in large two-dimensional periodic planar phased arrays of thin cylindrical monopoles is addressed. A plane wave representation of the active input impedance is used to analyze an infinite array of monopoles. A finite array analysis is used to compute the center element gain pattern and input impedance as a function of the array size and element position. The center element gain pattern is shown to have omnidirectional vertical polarization with a null on-axis and peak gain in the vicinity of50degfrom broadside. Measurements of the element gain pattern and mutual coupling for a 121-element passively terminated monopole square lattice array are shown to be in good agreement with the theory. The results of the infinite array analysis are compared to theoretical and experimental data in the literature for hexagonal lattice arrays.     

Scan-independent slot arrays with parasitic wire arrays in astratified medium

The effect of a parasitic wire array on the scan admittance of a slot array has been investigated. Structures considered can consist of an infinite slot array and an arbitrary number of parasitic infinite arrays of piecewise linear wires, all arrays being embedded in a stratified medium. These include, as particular cases, phased arrays of Clavin elements. Expressing the fields from the arrays as plane waves, a procedure similar to the periodic moment method for infinite periodic structures is set up to obtain the scan admittance of the slot array. Scan admittances are presented for a slot array with monopole arrays in free space, and a slot array with a tilted dipole array in a stratified medium. Blind spots at which the incident energy is mainly reflected rather than transmitted were found. Results obtained indicate the possibility of using parasitic wire arrays for scan compensation of active slot arrays