# A Wideband Reflectarray Antenna for Satellite Application with Low Cross-Polarization
## 3 Reflectarray Antenna Implementation and Results  
Based upon the new design of the unit cell, an RA is constructed as shown in Figure 7. An offset pyramidal horn is employed to illuminate the RA located at the mirror image of the beam at 30\({}^{\circ}\). The horn is fixed at the phase center of the RA at \(F=R_{0}=350\) mm  
Figure 5: Normalized reflection phase curves at 11.725 GHz for various oblique incidence. Figure 6: Surface current on the unit cell at 11.725 GHz when the dipole is not shorted with iterations: (**a**) Top layer. (**b**) Middle Layer. and surface current on the unit cell at 11.725 GHz when the dipole and iterations are shorted with each other: (**c**) Top layer. (**d**) Middle Layer. [\(I_{x}\) and \(I_{y}\) represents the co- and x-pol currents]. with coordinates \((x_{p},y_{p},z_{p})=(-175,0,303.108)\) mm that point to the center of the RA. The aperture of the RA is an octagonal shape with a maximum dimension of D = 456 mm. To avoid spillover losses, F/D = 0.765 is chosen to provide proper aperture illumination with an E-field edge taper of about \(-\)10 dB. The octagonal aperture is adapted because it has proper E-field edge tapering as compared to the rectangular aperture. To design the RA, the realized phase reflection of each element on the aperture regarding the specific direction of the beam can be obtained by the following equation [1]:  
\[\phi_{i}=k_{0}(R_{i}-(x_{i}\cdot sin(\theta_{b})\cdot cos(\phi_{b})+y_{i}\cdot sin (\theta_{b})\cdot sin(\phi_{b})))-k_{0}\cdot R_{0} \tag{1}\]  
where \(k_{0}\) is the wave number in free space, \(R_{i}\) is the spatial phase delay from the phase center of the array to the \(i\)th element. \(x_{i}\) and \(y_{i}\) are the coordinates of the \(i\)th element on the aperture. \(\theta_{b}\) and \(\phi_{b}\) are the required beam directions in the space. \(R_{0}\) is the distance between the phase center of the RA and the reference point (center of the RA aperture). In our case \(\phi_{b}=0^{\circ}\), thus Equation (1) becomes  
\[\phi_{i}=k_{0}(R_{i}-(x_{i}\cdot sin(\theta_{b})))-k_{0}\cdot R_{0} \tag{2}\]  
Figure 8a shows the mechanical setup of the reflectarray antenna and its geometry. An 8 mm thick octagonal metallic jig of the same area as the reflectarray aperture is designed, and polycarbonate screws were used to assemble the reflectarray and jig. To rotate the horn antenna along the circular path, a rectangular strut that consists of parallel vertical arms made of steel holds the jig, and the horizontal arm which holds the horn antenna is made of plastic. The vertical steel arms have no significant effect on the co- and x-pol pattern. However, the horizontal arm has a considerable effect on the reflectarray performance. Therefore, it is made of non-conductive material. A fabricated prototype of the RA in the near-field measurement environment is shown in Figure 8b. The horn is mounted on the strut with the help of a holder. Figure 9 presents the simulated and measured co- and x-pol patterns in the azimuthal and elevation plane at 11.725 GHz. The measured radiation patterns agree very well with the simulated patterns. The x-pol levels in the main beam direction lie at around \(-\)10 dBi. The measured side lobe levels (SLL) are around 6 dB in both the azimuthal and elevation planes. The aperture efficiency and comparison of the measured and simulated gains of the proposed RA are plotted in Figure 10 for only the desired bandwidth. Figure 7: Schematic representation of the reflectarray antenna and co-ordinate system. This shows that the measured peak gains of 31.2 dBi are achieved across the bandwidth. The differences in the measurements and simulations can be attributed to the fabrication tolerances and beam alignment during measurements. The RA peak aperture efficiency of 42% at 11.35 GHz is noted. Moreover, the simulated GBWs of 32% (3 dB) and 25.2% (1 dB) are obtained. Figure 8: (**a**) Mechanical setup and (**b**) Near-field measurement setup of the proposed reflectarray.