## 2 Flared SBF Antenna
### Numerical Analysis
#### 2.2.1 Effect of the Flaring Angle  
During the first parametric study, the flaring angle (bf) was increased from 0\({}^{\circ}\) to 40\({}^{\circ}\) in increments of 5\({}^{\circ}\) while keeping all other variables constant. This was done to investigate the effect of increasing the flaring angle. The upper diameter of the rim (D\({}_{\rm U}\)) can be \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Description** & **Value (mm)** \\ \hline Dm & Diameter of the main reflector & 110.00 (2.02 \(\lambda\)) \\ \hline D\({}_{\rm U}\) & Upper diameter of the rim & Dm + 2. Hr. tan \(\theta\) \\ \hline D\({}_{\rm S}\) & Diameter of the sub-reflector & 38.181 (0.70 \(\lambda\)) \\ \hline Hr & Height of the rim & 32.727 (0.60 \(\lambda\)) \\ \hline H\({}_{\rm S}\) & Height of the sub-reflector & 38.181 (0.70 \(\lambda\)) \\ \hline Rchoke &
\begin{tabular}{c} Distance between the rim and \\ outer diameter of the choke \\ \end{tabular} & 5.455 (0.01 \(\lambda\)) \\ \hline dchoke & Depth of the choke & 16.064 (0.29 \(\lambda\)) \\ \hline Wchoke & Width of the choke & 16.064 (0.29 \(\lambda\)) \\ \hline a & Length of the waveguide & 40.387 \\ \hline b & Width of the waveguide & 20.193 \\ \hline \end{tabular}
\end{table} 
Table 1: Simulated dimensions of the Flared SBF antenna. Figure 1: The geometry of the flared SBF antenna. (**a**) Isometric view, (**b**) Front view, and (**c**) Top view. expressed in terms of the flaring angle as \(\rm D_{m}+2\). Hr. tan \(\rm\theta f\), where \(\rm D_{m}\) is the diameter of the main reflector and the lower diameter of the rim, and Hr is the height of the rim. All the simulations in this section used \(\rm Hr=0.6\ \lambda\) (where \(\lambda\) is the wavelength of the SBF antenna in free space), which was the optimized rim height from the unflared SBF antenna study. The case where \(\rm\theta f=0^{\circ}\) gives the results of the unflared antenna, which were compared to the results obtained at different flaring angles. The reflection coefficient (S11) results are presented in Figure 2a-c. As the flaring angle increased from 0-10\({}^{\circ}\), there was no significant change in the impedance bandwidth (Figure 2a), as it only increased from 26.4% (4.61-6.01 GHz) to 28.1% (5.85-4.41 GHz), respectively. The major change was observed when the flaring angle was increased to 15\({}^{\circ}\) (Figure 2c) and the highest impedance bandwidth of 55% (4.36-7.67 GHz) was obtained, which is more than double the result of the unflared case (26.4%). This bandwidth increase is a result of the coupling of the two resonances seen at 5.8 GHz and 6.8 GHz (1 GHz difference) for the 0\({}^{\circ}\) flaring angle (Figure 2a). Flaring the antenna to 15\({}^{\circ}\) brought the resonances together to 5.5 GHz and 6 GHz (0.5 GHz difference), causing them to overlap, thereby resulting in the larger impedance bandwidth observed. We observe that when we increased the flaring angle further to 40\({}^{\circ}\), the bandwidth decreased to 42.4% (4.77-7.34 GHz) as illustrated by Figure 2c. Figure 2: Flared SBF antenna at different flaring angles: (**a**) Reflection coefficient plot for flaring angles 0\({}^{\circ}\) and 10\({}^{\circ}\) as a function of frequency; (**b**) Reflection coefficient plot for flaring angles 20\({}^{\circ}\) to 40\({}^{\circ}\) as a function of frequency; (**c**) Impedance bandwidth as a function of the flaring angle. The simulated gain and cross-polarization ratio results for the flared SBF antenna are given in Figure 3. Figure 3a shows the peak realized gain plot as a function of frequency for flaring angles 0-40\({}^{\circ}\), while the peak realized gain trend with increasing flaring angle at a frequency of 5.5 GHz is shown in Figure 2b. As the flaring angle increased from 0\({}^{\circ}\) to 20\({}^{\circ}\), the peak realized gain increased from 14.8 dBi to 17.2 dBi (a 2.4 dB increase) at 5.5 GHz (center frequency).