## 2 Design of Antenna Element and Feed Networks
Therefore, the proposed dual-polarized dual-band antenna element with shared-aperture radiation has the advantages of light weight and wide band, indicating that it is valuable for the SATCOM application. Figure 4: Simulated S-parameters of the proposed antenna element. Figure 3: Comparison of electric field distributions with and without the Via-loaded ring in Substrate 1: (**a**,**c**) Electric field amplitude and vector distribution with the Via-loaded ring; (**b**,**d**) Electric field amplitude and vector distribution without the Via-loaded ring. The massive adoption of T/R modules in phased arrays has an adverse impact on the cost and complexity of SATCOM applications [9]. In this paper, a non-uniform sub-array architecture is adopted for beam scanning. Instead of arranging a uniform planar antenna array, a sequence of subarrays with different groupings is utilized to implement the performances of low-sidelobe-level and beam-forming. The Tx- and Rx-band feed networks of a 4 \(\times\) 4 subarray are illustrated in Figure 5a,b, respectively. Specifically, a differential feed scheme based on a miniaturized ring coupler is adopted for the excitation of adjacent elements. The out-of-phase currents can suppress the unwanted leakage radiation and the cross-polarization component. A four-way corporate feed network is responsible for consistency in the amplitude and phase of the 4 \(\times\) 4 antenna array. Furthermore, the dielectric cover effect introduced by Substrate 2 increases the dielectric loss of the Tx-band feed network (i.e., Feed 1). Therefore, an SICL structure with low attenuation is adopted for the feed network design at Tx band, and the metallic Vias of the SICL are embedded in Substrate 2 and Substrate 3. The Rx-band feed network is printed on the bottom layer of Substrate 4, composed of the planar MS structure. The detailed parameters of the Tx- and Rx-band feed networks are shown in Table 2:  
The configurations of the differential feed networks based on the three-port ring coupler are illustrated in the purple box in Figure 5. The three-port coupler employs a miniaturized ring MS structure. In detail, Port 1_T1 (Port1_R1 for the Rx-band feed network) is responsible for the Tx-band input signal, and Port 2_T1 and Port 3_T1 (Port 2_R1 and Port3_R1) are utilized for feeding the adjacent elements with a 180\({}^{\circ}\) phase difference. A \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(w_{50}\) & \(w_{\text{z1}}\) & \(w_{\text{sp1}}\) & \(w_{\text{sp2}}\) & \(w_{\text{02}}\) & \(w_{\text{03}}\) & \(w_{\text{t4}}\) & \(l_{\text{t1}}\) \\ \hline
1.28 & 0.18 & 1.4 & 3.4 & 1.28 & 0.53 & 0.33 & 3.56 \\ \hline \(l_{\text{t2}}\) & \(l_{\text{t3}}\) & \(l_{\text{t4}}\) & \(w_{\text{sp6}}\) & \(r_{\text{gz1}}\) & \(w_{\text{gsp1}}\) & \(l_{\text{gsp1}}\) & \(l_{\text{gt1}}\) \\ \hline
3.9 & 3.9 & 5.36 & 1.18 & 2.59 & 0.65 & 0.25 & 3.05 \\ \hline \(l_{\text{gt2}}\) & \(l_{\text{gt3}}\) & \(l_{\text{gt4}}\) & \(w_{\text{gsp2}}\) & \(l_{\text{gsp2}}\) & \(w_{\text{sid}}\) & & \\ \hline
3.4 & 3.4 & 3.45 & 1.4 & 0.7 & 2.5 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the feed networks dimension (Unit: mm). Figure 5: The feed networks of the 4 \(\times\) 4 antenna subarray: (**a**) Tx-band feed network. (**b**) Rx-band feed network. branch-loaded transmission line with compact size and low complexity is proposed and implemented to replace the traditional quarter-wavelength transmission line between the differential output ports. In addition, the simulated S-parameter results of the three-port ring couplers of the Tx and Rx-bands feed networks are shown in Figure 6a and Figure 7a, respectively. The simulated \(\mid\)S\({}_{11}\)\(\mid\) is less than \(-20\) dB between 13.5-15 GHz and 11.5-13.0 GHz. The amplitude and phase differences between the two output ports are less than 0.7 dB and 0.25\({}^{\circ}\). In this way, the proposed three-port ring couplers are responsible for achieving the differential feed with the compact structure and suppressing the cross-polarization level.