## 2 Antenna Design Procedure
For a more exact investigation, the distance between the feed and the point where the current is 3 A/m (at the center of the geometry), is measured and summarized in Table 3. The dominant component at each frequency investigated is determined based on this distance. \begin{table}
\begin{tabular}{c c c c} \hline
**Antenna** & \(R_{in}\) **(\(\Omega\))** & \(X_{in}\) **(\(\Omega\))** & **Resonant Frequency (GHz)** & \(-\)**10 dB Bandwidth** \\ \hline Bow-tie-40 & 56.7 & 0 & 1.16 & 20.0\% \\ Bow-tie-80 & 41.2 & 0 & 1.18 & 22.0\% \\ Bow-tie-120 & 18.4 & 0 & 1.36 & X \\ Bow-tie-160 & 4.1 & 0 & 1.72 & X \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of bow ties with different flare angles. \begin{table}
\begin{tabular}{c c c} \hline
**Antenna** & \(R_{in}\) **(\(\Omega\))** & \(X_{in}\) **(\(\Omega\))** \\ \hline Bow-tie-40 & 56.7 & 0 \\ Bow-tie-80 & 37.7 & -3.7 \\ Bow-tie-120 & 13.7 & \(-\)29.6 \\ Bow-tie-160 & 2.33 & \(-\)61.5 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of input impedance of bow ties from angle study at 1.16 GHz. Figure 2: Simulated (**a**) \(S_{11}\), (**b**) \(R_{in}\), and (**c**) \(X_{in}\) for bow-tie-40, bow-tie-80, bow-tie-120, and bow-tie-160. Bow-tie-40 is shown in Figure 3a. As the frequency increases, the presence of the strong currents at the center of the antenna's geometry decreases, demonstrating the resonance at 1.16 GHz, where the strong currents (greater than 3 A/m) extend a distance of 12.51 mm from the port. The current distributions for bow-tie-80 at each of the aforementioned frequencies are shown in Figure 3b--where a trend akin to the one in bow-tie-40 is shown. This further establishes the previous observation that the bow ties with two different flare angles (40\({}^{\circ}\) and 80\({}^{\circ}\)) are similar. The difference between the two is a slight shift in the resonant frequency, with strong currents predominant at 1.18 GHz for bow-tie-80. Bow-tie-120 is shown in Figure 3c, demonstrating resonance at 1.36 GHz, with the strong currents extending to a maximum distance of 6.97 mm. At all other frequencies, strong currents are less apparent. Lastly, the current distributions for bow-tie-160 are shown in Figure 3d. The presence of strong currents on bow-tie-160 increases as the frequency increases, and dominate at 1.72 GHz, with a maximum distance of 5.24 mm, demonstrating bow-tie-160's resonance at this frequency. Thus, by increasing the flare angle, the frequency at which the largest area of the bow-tie geometry is covered in strong currents (coinciding with the resonant frequency) shifts to the right (increases). Additionally, the effect of the flare radius on the resonant frequency is investigated through an observation of the simulated \(R_{in}\) and \(X_{in}\), as shown in Figure 4a,b, respectively. In the flare radius study, a fixed flare angle of 160\({}^{\circ}\) is chosen based on the findings from the flare angle study--bow-tie-160 is important for extending the bandwidth in the upper end. Four different bow-tie antennas are investigated, having flare radii of 50 mm, 63 mm,  
Figure 3: Current distributions on (**a**) bow-tie-40, (**b**) bow-tie-80, (**c**) bow-tie-120, and (**d**) bow-tie-160 at 1.16 GHz, 1.18 GHz, 1.36 GHz, and 1.72 GHz (left to right). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Antenna** & **1.16 GHz** & **1.18 GHz** & **1.36 GHz** & **1.72 GHz** \\ \hline Bow-tie-40 & **12.51 mm** & 12.13 mm & 6.37 mm & 1.91 mm \\ Bow-tie-80 & 8.32 mm & **8.40 mm** & 5.60 mm & 2.57 mm \\ Bow-tie-120 & 6.06 mm & 6.45 mm & **6.97 mm** & 4.17 mm \\ Bow-tie-160 & 3.18 mm & 3.27 mm & 4.14 mm & **5.24 mm** \\ \hline \hline \end{tabular} The bold is to highlight the importance of each bow-tie at each frequency.  
\end{table} 
Table 3: Strong currents’ (3 A/m) distances from the feed. 73 mm, and 83 mm. These radii values are chosen arbitrarily to establish a relationship between the flare radii and antenna performance. The nomenclature for the bow ties used in this study is followed by the respective flare radius in mm.