## 2 Antenna Array Design
### Hybrid Feeding Network  
To construct a CP antenna array based on the proposed antenna element, a sequential phase rotated feeding network is required. The impedance matching and phase-adjusting duties were performed by the hybrid feeding network shown in this section. A sequential feeding strategy was used to achieve CP radiation in both the element orientation and phase distribution.  
To obtain the required wideband phase differences between the elements, three Schiffman phase shifters and Wilkinson power dividers were used. Wilkinson power dividers help isolate the element antennas from each other, whereas the Schiffman phase shifters create a 90\({}^{\circ}\) phase difference between adjacent antennas and maintain this difference over a wide frequency spectrum [29]. First, ports 4 and 5 were separated from ports 2 and 3 with the first Wilkinson power divider. Then, each pair of ports was separated by another power divider. Each path of the power divider was incorporated with a half-wavelength and quarter-wavelength couple line to create the 90\({}^{\circ}\) phase difference. The proposed feeding  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Para.** & **Val. (mm)** & **Para.** & **Val. (mm)** & **Para.** & **Val. (mm)** \\ \hline \(L_{d}\) & 80 & \(W_{g}\) & 8.85 & \(W_{s}\) & 2.3 \\ \(L_{m}\) & 6 & \(W_{m}\) & 18 & \(a\) & 18 \\ \(H_{d}\) & 21.5 & \(W_{d}\) & 2.9 & \(W_{e}\) & 2.9 \\ \(H_{m}\) & 20 & \(w_{m}\) & 1.8 & \(L\) & 38 \\ \(W_{h}\) & 2 & \(H_{e}\) & 19 & \(w\) & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The dual-dipole antenna dimensions.  
Figure 2: (a) Effect of \(H_{e}\) on the reflection coefficient; (b) effects of \(H_{m}\) on the reflection coefficient.  
network for the 2 \(\times\) 2 array antenna is shown in Figure 4. The Wilkinson power dividers are designed to have an equal power division ratio in order to supply all four antennas with similar amplitude. The feeding network was designed on a RO4003C substrate of 0.8 mm thickness. As the input port, the feed point was connected to a SMA connector at the opposite side of the substrate.  
The reflection coefficient of the feeding network is shown in Figure 5a. At 2.3 GHz, a minimum reflection coefficient of \(-26\) dB was obtained. The excitation of four dual-dipole elements had an amplitude close to the predicted \(-7\) dB as shown in Figure 5b. In addition, they were nearly equal to each other from 1.8 GHz to 3.0 GHz. The power was distributed evenly between the four ports by the feeding network; however, some losses in the isolation resistors and long transmission lines cause the output phases to shift. The achieved output  
Figure 4: Schematic of hybrid feed network based on the Schiffman phase shifter.  
Figure 3: (a) Simulated and measured reflection coefficient; (b) simulated and measured antenna gain.  
phases for four elements are shown in Figure 5c. The phase delay between two inputs of four pairs port 2/port 3, port 3/port 4, and port 4/port 5 was roughly 90\({}^{\circ}\). This phase difference was 107\({}^{\circ}\) of maximum at 1.8 GHz and 72\({}^{\circ}\) of minimum at 2.45 GHz. It interprets why the proposed antenna array has the CP at this band.