## 5 Generation of a Complete Multiple Beam Coverage in Ka-Band  
The designed bifocal DRAA operating in dual polarization is able to generate a complete multibeam coverage with a single main aperture for transmission in the Ka-band from a GEO satellite. Figure 12 shows the contour patterns and gain levels at 20 GHz associated to the multibeam coverage. These patterns have been obtained using the commercial software SATSOFT [32], developed by Tickra. The input parameters of the software have been configured so that the designed multibeam antenna is placed on board of a GEO satellite (at a distance of 36,000 km from the Earth's surface) and it is properly pointed to illuminate part of the European and North African regions. Then, the radiation patterns of the beams generated by the proposed antenna have been projected over the Earth's surface using the advanced functionalities of SATSOFT. As can be seen in Figure 12, the resulting multibeam coverage is formed by slightly-overlapping elliptical spots arranged in a triangular lattice. The separation between the maximums of adjacent spots is around 0.56\({}^{\circ}\), which is a typical value in current multi-spot applications in Ka-band [3]. The generation of closely-spaced beams is achieved through the application of the bifocal technique to reduce the beam deviation factor in the \(xz\)-plane by 50%, and the discrimination of the orthogonal polarizations at the reflectarray element level. The proposed bifocal DRAA presents several advantages with respect to the oversized SFPB reflector designed for the same application [5]. The bifocal antenna requires a significantly smaller main aperture (an elliptical reflectarray of 3.5 m \(\times\) 1.8 m instead of a circular reflector with 4 m diameter) and a lower number of feed-horns (reduced by 50% with respect to conventional SFPB reflector systems [3; 5], thanks to the dual-polarization capability of reflectarrays). Moreover, the use of flat reflectarray panels, which can be fabricated by conventional photo-etching and processes used in multi-layer printed circuits, allows for more efficient packaging and deployment mechanisms on the satellite. Note that the largest dimension of the main RA matches the maximum aperture size that fits on the spacecraft launcher, which is around 3.5 m [33]. Beyond that size, either mesh unfurlable reflectors or deployable panel reflectors must be employed [33; 34]. The aperture efficiency of the proposed multibeam antenna is around 40%, estimated as the ratio between the simulated gain and the maximum directivity associated to the size of the elliptical aperture (3.55 m \(\times\) 1.81 m). Note that the generation of a complete multiple spot coverage with a single main aperture prevents the antenna from reaching a high radiation efficiency, because of the use of an oversized aperture. The proposed antenna presents larger aperture efficiency than the oversized SFPB reflector in [5], which shows less than 20% efficiency for a 4-m diameter aperture. Moreover, the efficiency of the proposed DRAA is similar to that of other DRAAs reported in the literature [20; 27; 35]. Note that the use of the elliptical main RA allows significant reduction of the spillover, which increases the radiation efficiency of the proposed antenna. In the case of using a circular main RA of 1.8 m diameter (instead of the elliptical one), it has been checked that the maximum gain of the beams would  
Figure 11: (**a**) Reflectarray cells formed by orthogonal sets of dipoles for controlling each linear polarization (LP): \(2\times 2\) periodic cells, (**b**) co-polar reflection phases and cross-polar reflection amplitudes at 20 GHz and under \(\theta_{i}=30^{\circ}\), \(\varphi_{i}=30^{\circ}\) oblique incidence. be around 44 dBi, which corresponds to an aperture efficiency below 20%. The antenna would still provide the same beam spacing, because of the bifocal design process, but the large spillover in the main RA would result in low radiation efficiency.