## 3 Parametric Study
### Parametric Sweep of the Antenna Scheme  
This section investigates the effect of variable antenna parameters on the impedance bandwidth of the proposed portable wideband directional antenna scheme. The results are graphically presented in Figures 12-15. Figure 12a,b shows the simulated impedance bandwidth (\(1\,S_{11}\,1\leq-10\) dB) under various widths of the folded bowtie radiator (\(W_{\text{di}}\); 20, 25, 30, 35, and 40 mm) and angles of the folded bowtie radiator (\(AG_{\text{dp}}\); 0, 7.5, 15, 22.5, and 30\({}^{\circ}\)). As shown in Figure 12a,b, the optimal \(W_{\text{di}}\) and \(AG_{\text{dp}}\) were 30 mm and 15\({}^{\circ}\), respectively. In addition, the optimal length of the triangular section of the folded bowtie radiator (\(D_{\text{dp}}\)) was 18.7 mm, and the optimal height of the folded bowtie radiator (\(h_{\text{mi}}\)) was 15 mm. The optimal width of the first and second sections of the folded bowtie radiator (\(W_{\text{mi}}\)) were 15.2 and 15.2 mm, while the optimal width of the final section of the folded bowtie radiator (\(W_{\text{r}}\)) was 6.9 mm. The optimal length of one arm of the folded bowtie radiator was thus 101 mm. In other words, the optimal overall length of the folded bowtie radiator was 202 mm. Figure 13a,b shows the simulated impedance bandwidth (\(1\,S_{11}\,1\leq-10\) dB) under variable distance from the center of the supporting plate to the reflector (\(D_{\text{ref}}\)) and reflector length (\(L_{\text{ref}}\)). As shown in Figure 13a,b, the optimal \(D_{\text{ref}}\) and \(L_{\text{ref}}\) were 78.61 mm and 226.42 mm, respectively, covering the target operating frequency band of 470-890 MHz. Figure 13c shows the simulated impedance bandwidth under variable reflector height (\(l_{\text{ref}}\)) (25, 45, 65, and 85 mm), and Figure 13d illustrates the corresponding simulated radiation pattern at 890 MHz. The larger \(l_{\text{ref}}\) improved the back lobe level (i.e., front-to-back ratio), especially in the upper frequency band. In Figure 13d, despite the high back lobe level of \(-21.3\) dB under \(l_{\text{ref}}=85\) mm, the final antenna was bulky. As a result, the reflector height (\(l_{\text{ref}}\)) of 45 mm, with a back lobe level of \(-14.14\) dB, was selected for compactness. Figure 11: Simulated surface current distribution of the proposed portable wideband directional antenna scheme at: **(a)** 470 MHz, **(b)** 680 MHz, and **(c)** 890 MHz. Figure 12: Simulated impedance bandwidth (\(1\,S_{11}\,1\leq-10\) dB) under variable parameters: **(a)** width of folded bowtie radiator (\(W_{\text{di}}\)), **(b)** angle of the folded bowtie radiator (\(AG_{\text{dp}}\)). Figure 14: Simulated impedance bandwidth (\(\left.1\,S_{\mathrm{11}}\right.\leq-10\) dB) under variable parameters: (**a**) distance between the director and center of the supporting plate (\(D_{\mathrm{dil}}\)), (**b**) director’s arm length (\(L_{\mathrm{di}}\)), and (**c**) angle of the director’s arm (\(AG_{\mathrm{di}}\)). Figure 13: Simulated impedance bandwidth under variable parameters: (**a**) distance from center of the supporting plate to the reflector (\(D_{\mathrm{rel}}\)), (**b**) reflector length (\(L_{\mathrm{rel}}\)), (**c**) reflector height (\(h_{\mathrm{rel}}\)), and (**d**) radiation pattern at 890 MHz under variable \(h_{\mathrm{rel}}\). Figure 14a-c shows the simulated impedance bandwidth (\(\left\lvert\,S_{11}\,\right\rvert\leq-10\) dB) under variable distance between the director and the center of the supporting plate (\(D_{\text{di}}\)), the director's arm length (\(L_{\text{di}}\)), and the angle of the director's arm (\(AG_{\text{di}}\)). The optimal \(D_{\text{di}}\), \(L_{\text{di}}\), and \(AG_{\text{di}}\) were 25 mm, 43.34 mm, and 34.6 mm, respectively, covering the target operating frequency band of 470-890 MHz. Figure 15a,b shows the simulated impedance bandwidth (\(\left\lvert\,S_{11}\,\right\rvert\leq-10\) dB) under variable balun height (\(H_{\text{balun}}\)) and distance from the center to the center of the balun (\(D_{\text{balun}}\)).