## 2 2-D Phased Array Design
### Novel CORPSs Feeding System of 4 \(\times\) 9  
As set out in previous sections, the proposed 2-D configurations use 4 \(\times\) 9 CORPSs feeding networks to generate the required phase plane at the antenna elements and to reduce the number of phase shifters employed in the antenna system. Figure 5 illustrates the novel feeding system based on four inputs and nine outputs using crossovers and 2 \(\times\) 3 CORPSs networks [25] by the ring power dividers/combiners. The dimension values of this feeding system are shown in Figure 5. This feeding system has been proposed to have a more stable transmission power, achieving better control of the output amplitude. This new 4 \(\times\) 9 structure incorporates different division and recombination nodes (ring type), reducing by 50% the number of the resistors used in the feeding system with respect to previous works [26]. Furthermore, this new structure provides better phase control and has a number of recombination nodes lower than conventional feeding systems, and therefore, less losses by energy dissipation. The crossovers are used in the feeding system to avoid high values of phase difference at the input ports and to make more feasible the utilization of the raised cosine distribution. Figure 6 illustrates the behavior of the reflection coefficients (Figure 6a) and the behavior of the impedance of the feeding network system in the Smith chart format (Figure 6b). The reflection coefficients illustrate the good performance of the feeding system in a wide band with values of \(-\)15 dB in the operation range of 5.5-6.0 GHz. The behavior of the impedance of the feeding network illustrates adequate values to be matched in this operation frequency range. Figure 7 illustrates the behavior of the transmission coefficients of the novel 4 \(\times\) 9 feeding network. The transmission characteristics obtained are adequate, considering the losses in each element of the network system and the SMA connectors. This new 4 \(\times\) 9 CORPSs feeding network presents better features in terms of the reflection and transmission coefficients. This is because the crossovers of the new structure have a better performance with respect to the previous 4 \(\times\) 9 feeding network. Figure 8 shows the crossover design [29] employed in the feeding network system, considering the (a) top view, (b) manufactured prototype, (c) rear view, and (d) reflection and transmission coefficients. As shown in this figure, the crossovers of the new structure have better behavior in terms of the bandwidth with respect to the previous 4 \(\times\) 9 feeding network. The feeding structure is sensitive to the behavior of the crossovers. The proposed crossover design helps the new 4 \(\times\) 9 CORPSs feeding structure to have a better performance with respect to the previous design. Figure 5: CORPSs feeding system of 4 inputs and 9 outputs, including the dimension values. Figure 8: Crossover design of the novel 4 \(\times\) 9 feeding system: (**a**) top view, (**b**) manufactured prototype, (**c**) rear view, and (**d**) reflection and transmission coefficients. Figure 6: Behavior of the (**a**) reflection coefficients and the (**b**) match impedance of the feeding system. Figure 7: Behavior of the transmission coefficients of the novel 4 \(\times\) 9 feeding system. Figure 9 illustrates the ring type used as a divider or combiner in the new feeding network. This ring configuration offers a compact structure and better operation features with respect to a traditional power divider [30]. The dimensions set for our configuration are shown in Figure 9. The operation features (in bandwidth) are interesting and very adequate for the 4 \(\times\) 9 CORPSs feeding network and can be in observed in the behavior of the transmission and reflection coefficients shown in Figure 10.  
Output Phase States Using Phase Control (Input PSs)  
The behavior of the phase through the proposed 4 \(\times\) 9 feeding network is as follows.