## 3 Parametric Study  
### Conceptualization of the Portable Directional Antenna Scheme  
Figure 3a-c illustrates the conceptualization of the proposed portable wideband directional antenna scheme for digital terrestrial television reception, starting with the Yagi-Uda antenna (model I), the modified antenna with the U-shaped reflector and director (model II), and the proposed antenna scheme (model III). Model I is the Yagi-Uda antenna of a wire-type structure. The main advantages of the Yagi-Uda antenna are unidirectionality and high gain. However, model I suffered from a narrow impedance bandwidth. Given the center frequency of 680 MHz, the length of the radiator element was \(\lambda_{\rm C}/2\) (220.58 mm), where \(\lambda_{\rm C}\) was the wavelength of the center frequency. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Description** & **Physical Size,** & **Electrical Size** \\  & **mm** & **at 680 MHz** \\ \hline \(h\) & Spacing between the lower base plate and the reflector & 139.00 & 0.315 \(\lambda_{\rm C}\) \\ \(p\) & Thickness of the supporting plate and the base plate & 5.00 & 0.011 \(\lambda_{\rm C}\) \\ \(H_{\rm balun}\) & Balun height & 140.32 & 0.318 \(\lambda_{\rm C}\) \\ \(h_{\rm di}\) & Antenna height & 156.00 & 0.353 \(\lambda_{\rm C}\) \\ \(D_{\rm balun}\) & Distance between center to center of the balun & 19.24 & 0.043 \(\lambda_{\rm C}\) \\ \(h_{\rm ref}\) & Reflector height & 45.00 & 0.102 \(\lambda_{\rm C}\) \\ \(L_{\rm ref}\) & Reflector length & 226.42 & 0.513 \(\lambda_{\rm C}\) \\ \(D_{\rm ref}\) & Distance from center of the supporting plate to the reflector & 78.61 & 0.178 \(\lambda_{\rm C}\) \\ \(AG_{\rm dp}\) & Angle of the folded bowtie radiator (degree) & 15.00 & - \\ \(W_{\rm di}\) & Width of the folded bowtie radiator & 30.00 & 0.068 \(\lambda_{\rm C}\) \\ \(D_{\rm dii}\) & Distance between director and center of the supporting plate & 25.00 & 0.056 \(\lambda_{\rm C}\) \\ \(L_{\rm di}\) & Director’s arm length & 43.34 & 0.098 \(\lambda_{\rm C}\) \\ \(AG_{\rm di}\) & Angle of the director’s arm (degree) & 34.60 & - \\ \(D_{\rm dp}\) & Length of triangular section of the folded bowtie radiator & 18.70 & 0.042 \(\lambda_{\rm C}\) \\ \(h_{\rm mi}\) & Height of the folded bowtie radiator & 15.00 & 0.034 \(\lambda_{\rm C}\) \\ \(W_{\rm mi}\) & Width of the 1 st and 2 nd sections of the folded bowtie radiator & 15.20 & 0.034 \(\lambda_{\rm C}\) \\ \(W_{\rm r}\) & Width of the final section of the folded bowtie radiator & 6.90 & 0.015 \(\lambda_{\rm C}\) \\ \hline \hline \end{tabular} \(\lambda_{\rm C}\) is the wavelength at the center frequency of the target operation band (470–890 MHz).  
\end{table} 
Table 1: The optimal dimensions of the portable wideband directional antenna for digital terrestrial television reception. In model II, to improve the impedance bandwidth, the radiator element of model I was replaced with the folded bowtie radiator. The wire reflector was replaced with the stainless-steel U-shaped reflector, and the director was reshaped into the U shape. In model III, the U-shaped reflector was corrugated to reduce the overall physical size of the antenna while increasing the electrical size. Moreover, the corrugated reflector improved the electromagnetic reflection of the proposed antenna scheme [32,33]. The U-shaped director was reshaped into the V shape for the antenna compactness without compromising the antenna performance. Figure 4 compares the simulated impedance bandwidth (\(1S_{11}\)\(\,\)\(\leq-10\) dB) of the antenna models I, II, and III. Model I achieved a narrow impedance bandwidth, covering 620-700 MHz. The narrow impedance bandwidth rendered model I operationally unsuitable for digital television reception. Model II experienced an impedance mismatch between 590-780 MHz, rendering it operationally inapplicable. Model III achieved the simulated impedance bandwidth of 63.85%, covering 468-907 MHz, which encompassed the target frequency band (470-890 MHz). Figure 5 compares the antenna gain of models I, II, and III.