Extension of forward‐backward method with a DFT‐based acceleration algorithm for efficient analysis of radiation/scattering from large finite‐printed dipole arrays

Abstract

In this paper, the use of reflecting microstrip arrays as stable target points, called PS as described above, is investigated for SAR interferometry applications. The reflecting surface of a reflectarray can be designed to scatter most of the incident radiation back in the direction of incidence. This goal is achieved by imposing a phase distribution (n) of the kind [5]:where n is the element position, d gives the spacing between elements, is the wavelength, and i the angle of incidence (Fig. 1). The phase contribution of each element must be chosen not only to satisfy the final distribution given by Eq. (1), but also to compensate for the phase delay ⌬ n ϭ (2/)⌬r n in the different path lengths of the incident field (Fig. 1).The overall design of microstrip reflectarray entails the use of a specified phase design curve. The phase tuning technique based on elements of different size is adopted in this work. The number of radiating elements is used to control reflectarray RCS level, which is directly related to the size of the reflecting surface. When imposing the required RCS values, the proposed planar reflector is obviously advantageous with respect to a tridimensional CR having the same face size. The use of microstrip technology gives itself significant improvements such as low cost, less weight, and easy installation. NUMERICAL RESULTSThe validity of the proposed method has been tested by realizing a reflectarray prototype with a maximum backscattering in the direction i ϭ 23Њ (typically, an incidence angle of ERS-1/2 SAR). At present, a test facility of limited size is available for far-field measurements, so that a 10-GHz array of 7 ϫ 7 elements 0.6 spaced has been designed. Figure 2 shows a photo of the reflectarray, printed on a Diclad870 substrate with r ϭ 2.33 and thickness t ϭ 0.762 mm. Square radiating elements of dimensions spanning from 5.556 mm to 10.186 mm have been chosen from the phase design curve reported in Figure 3. RCS measurements have been performed in the anechoic chamber at the Microwave Laboratory of the University of Calabria. Two X-band pyramidal horns have been used as transmitting and receiving antennas for the monostatic configuration illustrated in Figure 4. A good agreement between simulations and experimental results can be observed in Figure 5, where a maximum backscattering value exists at the required incidence angle i ϭ 23Њ. CONCLUSIONPrinted reflectarrays were proposed in this work as artificial PS for SAR applications. A maximum backscattering in a prescribed direction of incidence was obtained as in standard CR, but using a very thin and flat structure. The new planar reflector avoids the storage of unwanted materials, which usually compromises CR electromagnetic response, thus much more stability is obtained together with less cost and easier installation. The proposed method was tested on a 10-GHz reflectarray prototype. Both numerical and experimental validations show a RCS peak at i ϭ 23Њ, which is the typical ERS1/2 SAR angle of incidence. , where N tot is the to...

Efficient analysis of large phased arrays using iterative MoM with DFT‐based acceleration algorithm

“…The use of FBM in conjunction with this DFT-based acceleration algorithm shows some significant convergence problems in the analysis of printed dipole phased arrays when either the thickness of the substrate or the relative dielectric constant of the substrate (⑀ r Ͼ 1) (or both) are high [8,9]. However, such problems have not been observed in [10] nor in this study.…”

“…Therefore, in this example Q ϭ 21, although the strong region has still the same size (3 ϫ 3). Nevertheless, this is a case where FBM accelerated with a DFT-based algorithm has convergence problems, which are probably due to the nature of FBM, as claimed in [9].…”

“…It should be noted at this point that, recently, the same DFTbased acceleration technique was used in conjunction with a forward-backward method (FBM) to analyze large phased arrays of free-standing dipoles in [7] and then extended to large phased arrays of printed dipoles in [8,9]. The use of FBM in conjunction with this DFT-based acceleration algorithm shows some significant convergence problems in the analysis of printed dipole phased arrays when either the thickness of the substrate or the relative dielectric constant of the substrate (⑀ r Ͼ 1) (or both) are high [8,9].…”

Extension of forward backward method with DFT based acceleration algorithm for the efficient analysis of large periodic arrays with arbitrary boundaries

“…The DFT-based acceleration algorithm is actually well-suited for the fast and accurate analysis of rectangular arrays (freestanding and printed) [13][14][15]. Therefore, to implement this algorithm efficiently, the arrays shown in Figure 1 are mathematically extended into a rectangular array with virtual elements as shown in Figure 3.…”

“…In recent years, several MoM-based methods have been proposed to improve the operational count and memory-storage requirements of the conventional MoM [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Making use of stationary or nonstationary iterative schemes in the MoM solution reduces the operational count from O(N tot 3 ) (of order N tot 3 ) to O(N tot 2 ), where N tot is the total number of unknowns.…”