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

Abstract

This two-part sequence deals with the formulation of an efficient method for the full wave analysis of large phasedarray 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 (FW's) 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 for 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 recently described by other authors. The second part of this paper deals with the appropriate generalization of this method to three-dimensional (3-D) arrays.

Time-domain Green's function for an infinite sequentially excited periodic line array of dipoles

“…The and paired TD-FW wavefield observables are, to the best of our knowledge, new findings that are likely to have broad implications. The perspectives gained from this highly idealized canonical problem are expected to facilitate application to more realistic TD periodic array configurations, as demonstrated in [8], [9] for slot arrays. This will be the subject of future investigations, as is the TD generalization of the FD results for smooth line source arrays on slabs and truncated ground planes in [22], [23].…”

“…Such waves on semi-infinite and finite rectangular arrays of dipoles have been and are being studied in the FD [4]- [7] and furnish the models for the explorations in the TD. The truncated array Green's functions lead to efficient parameterization of realistic arrays with slot elements, as demonstrated in [8] and [9]. Our initial aim is to understand the dispersive TD wave physics on simple canonical geometries, utilizing various methods that synthesize the solution from different perspectives.…”

Semi-Infinite Arrays of Isotropic Point Scatterers. A Unified Approach

“…Recently, methods based on integral equations have been devised in which the basic idea is to formulate an integral equation for the difference between the infinite array and finite array solutions; see [26,21], for example. For large finite one-dimensional arrays this leads to problems formulated on semi-infinite arrays.…”

Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

“…Neto solves a truncated array of slits in a ground plane by a method of moments solution of an integral equation where the unknown is the difference between the exact current distribution on the truncated array and the current distribution of the infinite array [25]. Neto follows essentially the same procedure as Munk in setting up the problem, but calculates the field due to the infinite array solution that exists on A * asymptotically using the techniques developed by Capolino [21].…”

“…To determine the number P of necessary p-terms used in the Taylor expansion in (25), the percentage 1.E-11…”