## 3 Design of Array Antenna
### Application of SP Feed in 2 \(\times\) 2 Antenna Array  
To illustrate the presented SP feed with applications to 2 \(\times\) 2 arrays, we employed a CP patch for an antenna element with a 0.35\(\lambda_{g}\)\(\times\) 0.35\(\lambda_{g}\) SP feed. The array performance is optimized with the compact size that has the distance between the centers of the elements, 19.73 mm (0.535\(\lambda_{0}\)). Figure 4b shows the geometry of the optimized design of the \(2\times 2\) arrays with the SR phase feeding structure. Figure 5 shows the improved performance of the 2 \(\times\) 2 array, compared to the single patch antenna. The IBW of the single patch is from 7.95-8.32 GHz that covers the uplink band for satellite application. The maximum realized gain of the antenna is 5.4 dBi and the overlapping ARBW is from 8.12-8.22 GHz. In the case of array, the AR and gain level performances both appeared to undergo improvements. The IBW of the 2 \(\times\) 2 array is 7.88-8.42 GHz and the ARBW of 7.92-8.42 GHz with the peak LHCP gain of 11.5 dBic. In this illustration, the impedance is designed at 50 \(\Omega\) for the antenna elements and the input ports. The plots of co-pol radiation patterns at five frequency samples in the bandwidth are given in Figure 6. It can be seen that there is asymmetry in the radiation patterns with respect to the broadside direction in two planes, which is caused by the non-uniformity in the structure of the array due to the feed line. The asymmetry gets decreases at high frequencies in the band. However, the peak gain of the main lobe is along the broadside directions. The side lobe levels lie near \(-\)10 dBic. Table 2 summarizes the comparison of our work with earlier studies in terms of 3 dB ARBW, CP gain, and compactness (C-to-C distance). The gain in [17; 18; 20] is lower as compared to the proposed compact design. Unlikely, the size of the [21] is comparatively smaller as compared to the proposed work, but it results in a very low gain. The gain of 13.5 dBic in [19] is higher because of the larger distance between the centers of the elements. Similarly, the gain of 14.25 dBic is achieved in [22] by using the air gap in multiple layers. Thus, the design is bulky as well as a larger C-to-C distance among the elements. The ARBW of the design in [18] is 7.6%, which is just greater by 0.66% than the ARBW of the proposed design. Unlikely, the ARBW in [19] is very low that is 1.3%. In all of the above literature, the designs have higher gain at the expense of the size. Finally, the design in [23] is very compact that has a higher 3 dB ARBW but the gain is low as compared to the proposed work. Despite the compact structure, the gain is improved by using parasitic patches to increase the radiation surface. The main issue of this compact structure is that the main beam at different frequencies has deviated from the broadside direction. Second, this design cannot be extended to 4 \(\times\) 4 array with this configuration on a single layer to achieve high gain. For this purpose, the feed should be on the second layer, which increases the fabrication cost. On the other hand, the proposed structure can easily be extended to 4 \(\times\) 4 array on a single layer. Furthermore, the main beam of the proposed design is along the broadside direction. The aim of our work is to maintain a certain level of gain in \(\pm\)10\({}^{\circ}\) range with respect to the broadside direction. Otherwise, the tilt in the main beam degrades the gain in desired direction. Figure 5: Comparison of the performance between single element and 2 \(\times\) 2 array: **(a)** Reflection coefficient. **(b)** AR and LHCP gain. In practical applications, like small satellites for next-generation, just a 3 dB ARBW criteria is not acceptable. The AR must be lower than 1.5 dB with an acceptable level of gain up to 12 dBic in the angular width of \(\pm 10^{\circ}\).