## 2 Antenna Design Methodology  
The geometrical parameters of the patch antenna are computed using conventional mathematical formulas [25; 26], and then applied to area of an octagon to derive its dimensions. An octagonal patch antenna is constructed on the basis of a circular patch antenna. The area of the octagonal and circular geometry is nearly equal, as shown in Figure 1. The dimensions of the circular and octagonal shapes are determined using Equations (1)-(4) and optimized for the better antenna performance.  
\[\pi a_{e}^{2}=2\Big{(}1+\sqrt{2}\Big{)}s^{2} \tag{1}\]  
where '\(a_{e}\)' is effective radius of circular patch due to fringing effect  
\[a_{e}=a\bigg{[}1+\frac{2h}{\pi a_{e}}\Big{\{}\ln\Big{(}\frac{\pi a}{2h}\Big{)} +1.7726\Big{\}}\bigg{]}^{\sfrac{1}{2}} \tag{2}\]  
'\(a\)' is the actual radius of the circular patch and is derived as  
\[a=\frac{F}{1+\frac{2h}{\pi Fr_{e}}\Big{[}\ln\Big{(}\frac{\pi F}{2h}\Big{)}+1.7 726\Big{]}^{\sfrac{1}{2}}} \tag{3}\]  
where  
\[F=\frac{8.791*10^{9}}{f_{r}\sqrt{\varepsilon_{r}}} \tag{4}\]  
The proposed monopole antenna with various evaluations are shown in Figure 2. The electrical dimension of the antenna is 0.16 \(\lambda\)c \(\times\) 0.18 \(\lambda\)c, where the wavelength \(\lambda\)c is the lowest operating frequency or physical size of 14 mm \(\times\) 16 mm. It is printed on Rogers RT/Duroid 5880 TM dielectric substrate with a permittivity (\(\varepsilon\)r) of 2.2 and a height (h) of 0.787 mm. The physical dimensions of substrate are Ws \(\times\) Ls, where Ws = 14 mm and Ls = 16 mm. The presented antenna has an octagonal-shaped radiating patch, tapered feed microstrip line, and partial ground plane. To achieve optimal matching, the width of the feed line is reduced linearly from W2 = 2 mm to W1 = 1.5 mm, while the length of the feed line Lf = 6.3 mm remains constant. The ground plane length Lg = 6 mm, and the radius of the circle patch (R) = 4.5 mm, from which the octagonal sides are derived. The edge of the octagon, S = 3.45 mm, and the elliptical slots D1, D2, D3, and D4 are used in the patch to construct a flower-shaped slot in the octagonal radiating patch. A very wide frequency range is also dependent on the geometry of the ground, and the time of the current path determines the lowest cut off frequency. As a result, rectangular ground becomes a partially ground plane.  
_Evaluations of SWB Monopole Antenna Configuration_  
Different evaluations of the octagonal structured proposed monopole antenna with a partial ground plane are shown in Figure 2. The octagonal radiating patch designed on Rogers RT/Duroid 5880(tm) material with partial ground geometry is shown in Figure 2a. An elliptical aperture is cut into the octagon patch to enhance its impedance bandwidth, as shown in Figure 2b. The Babinet principle is applied during this process. The elliptical slot is converted into a plus-shaped elliptical slot and embedded into the patch, as shown in Figure 2c. When the self-similar modified plus structure is merged with the preceding geometry, a new ring-slotted octagon patch is formed, as shown in Figure 2d. The octagonal structure that is carved into the flower-shaped slot is shown in Figure 2e. Furthermore, IBW and BDR are improved by switching from a rectangular 50 \(\Omega\) transmission feed line to a tapered feed line, as shown in Figure 2f. The dimensions of the evaluated geometries are listed in Table 1.  
Figure 1: Area correlation between circular and octagon geometry.  
Figure 2: Geometry of SWB antenna with different design evaluations (**a**) iteration 1, (**b**) iteration 2, (**c**) iteration 3, (**d**) iteration 4, (**e**) iteration 5, (**f**) iteration 6.