## 2 Antenna Design Methodology  
The proposed configuration of the UWB antenna without band elimination features is fabricated on an FR4 substrate with the dimensions 0.19\(\lambda\)\(\times\) 0.13\(\lambda\)\(\times\) 0.01\(\lambda\), where \(\lambda\) is computed using the lower frequency of 3.7 GHz. An antenna's step-by-step evolution with its reflection coefficient (S11) is depicted in Figure 1. Antenna 1 is a fundamental circular monopole antenna with a complete ground plane that offers no frequency range below \(-\)10 dB in the S11 curve. Antenna 2's ground plane is reduced to half, resulting in no frequency range below \(-\)10 dB in the S11 curve. The further ground plane is lowered to 1.9 mm in antenna 3, which provides an S11 curve ranging from 5.1 to 11.5 GHz. The reduction in the ground plane influences the quality factor, thereby increasing the impedance bandwidth. The impedance bandwidth is further improved in antenna 4 by modifying the radiating plane. Embedding ellipses with the circle arrangement provides an S11 of 4.3-13.6 GHz. Although antenna 4 provides a UWB spectrum, the ground plane of the antenna structure is further analyzed for a stable and broader S11 curve, especially at the lower frequency. Finally, in antenna 5, arc shapes are embedded onto the edges of the ground plane. This configuration exhibits an impedance bandwidth ranging from 3.7 to 13.3 GHz, well below \(-\)11 dB. Figure 1: UWB antenna. (**a**) Antenna evolution representing the radiator (**left**) and ground pane (**right**) in each antenna configuration. (**b**) Reflection coefficient curve. The circular monopole of antenna 1 is designed with a substrate thickness (\(h\)) of 1.6 mm, resonant frequency (\(f_{r}\)) of 13 GHz, and dielectric constant (\(\epsilon_{r}\)) of 4.4. The design equations used for determining the patch dimensions are as described in Equations (1)-(3) [27]. The radius (\(r\)) of the circular patch is determined by:  
\[r=\frac{F}{\sqrt{1+\frac{2h}{\pi\epsilon_{r}F}\left[\ln\left(\frac{\pi F}{2h} \right)+1.7726\right]}}, \tag{1}\]  
where \(F\) is given by  
\[F=\frac{8.791\times 10^{9}}{f_{r}\sqrt{\epsilon_{r}}}. \tag{2}\]  
The effective radius results from the fringing field spreading from the patch border to the ground plane. The fringing field around the circular patch may increase the radius of the circle. Therefore, the effective radius (\(r_{eff}\)) is determined as shown below:  
\[r_{eff}=\frac{1.8412\ c}{2\pi f_{r}\sqrt{\epsilon_{r}}}, \tag{3}\]  
where \(c=3\times 10^{11}\) mm/s. Parametric analysis is carried out on every design to find an optimum value for the UWB antenna's geometry. The final dimension for the proposed design is shown in Figure 2. The optimized physical dimension of the proposed UWB configuration is depicted in Table 1.  
The frequency band notching is realized by perturbing the radiating plane. This perturbation should not disturb the UWB antenna radiation characteristics over the impedance \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Parameters/Antenna Design** & **W\({}_{\text{S}}\)** & **Ls** & **P1** & **P2** & **P3** & **P4** & **P5** & **P6** & **P7** & **P8** & **P9** \\ \hline UWB & 11 & 16 & 3 & 6 & 1.6 & 2 & 5 & 1.9 & 0.2 & 4.7 & 2.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimized physical parameters of the proposed UWB antenna (dimensions in mm). Figure 2: Geometry details of the proposed UWB antenna: (**a**) radiator, and (**b**) ground plane. bandwidth. Consequently, dual-band notch features are attained with the help of an inverted U-shaped slot on the radiator. The inverted U-shaped slot enables a frequency notch ranging from 5 to 5.6 GHz, covering WLAN and IEEE 802.11a/b/j/n/ac/ax standards. Inserting the slots results in an open circuit, avoiding impedance matching and current propagation at the notched frequency. The inverted U-shaped slot radiating-plane configuration helps frequency band elimination from 7.3 to 8.3 GHz, covering the entire X-band satellite communication.