## 2 Antenna Design  
### Dual Band-Notched UWB Antenna  
The conventional circular monopole is modified to attain operational frequency in the UWB range. The UWB antenna structure evolution is illustrated in Figure 1a. The simulated S-parameters curve at every stage (ant 1, ant 2,..., ant 5) is depicted in Figure 1b. In the first step, the radius of the circular patch is calculated using the Equations (1)-(3) with a microstrip feedline [20]. This configuration shows the S11 curve below \(-10\) dB from 12 GHz onwards, as shown in Figure 1b for ant 1. To accomplish wider impedance bandwidth, the ground plane of the circular monopole antenna is lowered in response to the impedance bandwidth. The alteration of the ground plane disturbs the uniform current distribution affecting the transmission line properties and quality factor, which helps to attain the broader bandwidth, as shown in Figure 1 for ant 2, and 3, and ant 5. Following the reduced ground plane, the radiator is modified by integrating a rectangular shape between the circle and feedline, as shown in Figure 1 for ant 4. This arrangement provides simulated impedance bandwidth below \(-20\) dB from 3.5 to 12.4 GHz, except for the middle frequencies, where it is below \(-17\) dB. The ant 5 in Figure 1 provides the required UWB spectrum having overall physical dimensions of 21.5 \(\times\) 13 \(\times\) 1.6 mm\({}^{3}\), and uses FR4 as a substrate. The dimensions of the antenna element, stub, slot, ground plane, and feedline of the UWB antenna (ant 5) are represented in Figure 2, and their values are listed in Table 1.  
Figure 1: Evolution of UWB antenna: (**a**) structure (**b**) simulated S-parameters curve. Figure 2: The geometrical information of the projected UWB antenna. 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 a circle. Therefore, the effective radius (\(r_{eff}\)) is determined as shown below  
\[r_{eff}=\frac{1.8412\ c}{2\pi r_{r}\sqrt{\epsilon_{r}}} \tag{3}\]  
where \(c=3\ \times\ 10^{11}\) mm/s, \(f_{r}\) is the resonating frequency, and \(\epsilon_{r}\) is the dielectric constant of the FR4 substrate. In the first stage, a circular monopole antenna is designed using Equations (1)-(3) with the specification of \(\epsilon_{r}=4.4\), \(h=0.16\) cm, and \(f_{r}=7.5\) GHz. \[F=\frac{8.791\ \times\ 10^{9}}{7.5\ \times\ 10^{9}\ \times\ \sqrt{4.4}}=0.6\]  
\[r=\frac{F}{\sqrt{1+\frac{2h}{\pi\epsilon_{r}F}\left[\ln\left(\frac{\pi F}{2h} \right)+1.7726\right]}}=\frac{0.6}{\sqrt{1+\frac{2\ \times\ 0.16}{\pi\ \times\ 4.4\ \times\ 0.6}\ \left[\ln\left(\frac{\pi\ \times\ 0.6}{2\ \times\ 0.16}\right)+1.7726\right]}}\]  
\[r=5.6\ \mathrm{mm}\]  
\[r_{eff}=\frac{1.8412\ c}{2\pi f_{r}\sqrt{\epsilon_{r}}}=\frac{1.8412\ \times\ 3\ \times\ 10^{11}}{2\ \times\ \pi\ \times 7.5\ \times\ 10^{9}\times\sqrt{4.4}}\ 5.6\ \mathrm{mm}\]  
The radius and effective radius are 5.6 mm. Therefore, a circle with a 5.6 mm radius is chosen with the 50 \(\Omega\) matched feedline for ant 1 in Figure 1a. The UWB spectrum covers the current X-band, WLAN, WiMAX, and other small frequency bands. To prevent interference with the UWB spectrum, narrow-band frequency notching is necessary. In the designed UWB antenna, dual-frequency band-notching is attained using U-shape and inverted U-shape slots on the radiator. The first notching covers the WLAN band from 4.3 to 5.4 GHz, and the second frequency notching from 7.3 to 8.5 GHz covers both the uplink and downlink of X-band satellite communication, as represented in Figure 3a,b. The band notching is performed without affecting the impedance bandwidth other than the intended notch frequencies.