# A Ka-Band Cylindrical Paneled Reflectarray Antenna
## 3 Implementation  
The validation of the proposed cylindrical reflectarray was done by taking, as a reference, the parabolic cylindrical reflector proposed in [15]. In this antenna (see Figure 1 in [15]) a parabolic cylindrical reflector was illuminated by a hat-feed placed on its focus. The hat-feed was, in turn, excited through a TEM (transverse electro-magnetic) wave launched by a parallel plate waveguide (PPW), which was located along the reflector longitudinal axis (see Figure 1a). The reference antenna focus, \(f\), was equal to 7.5 cm, thus implying an overall aperture \(D\) equal to 30 cm. The radiating aperture length, \(L\), was equal to 40 cm. In this work, the feeding structure of the antenna (hat-feed and PPW) was left unchanged while the cylindrical parabolic reflector was replaced with the proposed paneled reflectarray in order to enlarge the aperture without modifying the overall antenna height. For the case at hand, the cylindrical reflectarray geometry was optimized to operate in the Ka Rx band (19-21 GHz) while the antenna aperture was set to 44 cm, thus making the \(f\)/\(D\) equal to 0.34. It is worth noticing that larger apertures and higher efficiencies could be achieved by redesigning the hat-feed. Although not optimal in terms of illumination efficiency, adapting the feeding structure from another antenna provides a direct comparison with a similar radiating structure while allowing a reduction of the experimental validation costs. Table 1 shows the final dimensions of the segmented reflector calculated with the designing principle described in Section 2; no further optimization stages were needed. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(D\) & 44 cm & \(M_{4}\) & 6 \\ \(f\) & 7.5 cm & \(M_{5}\) & 6 \\ \(L\) & 40 cm & \(M_{6}\) & 6 \\ \(N\) & 7 & \(M_{7}\) & 7 \\ \(W\) & \(\lambda/3\) & \(\theta_{1}\) & \(2.72^{\circ}\) \\ \(W_{1}\) & 3.0462 cm & \(\theta_{2}\) & \(5.11^{\circ}\) \\ \(W_{2}\) & 3.0736 cm & \(\theta_{3}\) & \(13.37^{\circ}\) \\ \(W_{3}\) & 3.1276 cm & \(\theta_{4}\) & \(18.40^{\circ}\) \\ \(W_{4}\) & 3.2069 cm & \(\theta_{5}\) & \(23.16^{\circ}\) \\ \(W_{5}\) & 3.3097 cm & \(\theta_{6}\) & \(27.60^{\circ}\) \\ \(W_{6}\) & 3.4338 cm & \(\theta_{7}\) & \(31.71^{\circ}\) \\ \(W_{7}\) & 3.5771 cm & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions of the segmented reflector shown in Figure 1.  
The gain of the proposed structure was numerically evaluated for three different reflectarray configurations: planar, oblique, and paneled. The paneled curvature was defined by a virtual focus \(f=16\) cm. Table 2 reports the gain and radiation efficiency obtained simulating an \(L^{\prime}\times D\) portion of the proposed reflectarray (\(L^{\prime}=5\) mm) using Equation (3) and a full-wave model [14] (see Figure 3). As it can be seen, the paneled configuration provided higher gain than the planar one due to the possibility to reduce spillover losses. Furthermore, the increased aperture provided higher gain with respect to the cylindrical case, as expected. To better understand how the segmented reflectarray works, the electric field amplitude and phase was evaluated along the aperture transversal plane and compared with the ones of the conventional cylindrical reflector presented in [15] (see Figure 4). The two behaviors were similar along the entire aperture but, in the vicinity of the PPW feed, the gaussian vertex employed in the cylindrical reflector generated a smoother amplitude distribution. Furthermore, the phase profile of the reflectarray was less uniform in the vicinity of the border, which would cause a higher side lobe level.