## 2 Antenna Configuration  
This study designed 1 \(\times\) 2 antenna Palm Tree Coplanar Vivaldi antenna in the E-plane, as shown in Figures 1 and 2, using the same type and size of the substrate. The antenna is designed with an FR-4 substrate with a thickness of 1.6 mm, while the radiator and feeding shape is made of copper with a thickness of 0.035 mm. The dimensions of the patch element are 250 mm \(\times\) 250 mm \(\times\) 0.035 mm but it has an additional substrate width of 12.5 mm on both sides of the antenna width to reduce the mutual coupling. The antenna was simulated in the frequency range between 500 MHz-4.5 GHz with the dimension as illustrated in Table 1. Equation (1) is used to determine the tapered side on the bottom of PT CVA, the flared region, and the ESE structure. The \(C_{1}\) and \(C_{2}\) are constants, and \(R\) is the exponential growth rate with the value of \(R_{1}\), \(R_{2}\), \(R_{3}\), and \(R_{4}\) shown in Table 1 (based on Figure 1a. The beginning and ending points of an exponential curve are \(x_{1}\), \(y_{1}\), \(x_{2}\), and \(y_{2}\)[44].  
\[y=C_{1}e^{Rx}+C_{2}\,,\ \ \ \ \ C_{1}=\frac{y_{2}-y_{1}}{e^{Rx_{2}}-e^{Rx_{1}}}\,,\ \ \ \ \ C_{2}=\frac{y_{1}e^{Rx_{2}}-y_{2}e^{Rx_{1}}}{e^{Rx_{2}}-e^{Rx_{1}}} \tag{1}\]  
Figure 1h delivers the Hilbert curve structure in the third iteration with the total length of the slot (\(l_{h}\)), the line segment (\(dd\)), and iteration (\(in\)) follows Equation (2) [47]. In this case, we use 3 rd iteration.  
\[dd=\frac{l_{h}}{2^{in}-1} \tag{2}\]  
Figure 2c,d show the vertical and horizontal wave slots. The Constant of the wavy slot in Equation (3) is \(B_{1}=2\), \(B_{2}=1\), \(B_{3}=1\), \(B_{4}=5\), and \(B_{5}=36\). The depth of the wave, the number of waves, and the length of the wave slot can all be modified by changing the value of \(B_{\rm{n}}\)[48].  
\[A(t)=B_{1}\bigg{(}B_{2}+B_{3}\ \cos\,\bigg{(}\frac{B_{4}\pi t}{B_{5}}\bigg{)} \bigg{)} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{**Dimension (mm)**} & & & \\ \hline
**Par** & **Dim** & **Par** & **Dim** & **Par** & **Dim** & **Par** & **Dim** & **Par** & **Dim** \\ \hline a & 550 & k & 100 & u & 25 & E & 10 & O & 12 \\ b & 250 & 1 & 50 & v & 93.53 & F & 188 & P & 120\({}^{\circ}\) \\ c & 135 & m & 99.78 & w & 6 & G & 30 & Q & 12 \\ d & 55 & n & 38 & x & 17.9 & H & 150 & R & 10 \\ e & 0.5 & o & 30\({}^{\circ}\) & y & 162 & I & 50 & S & 16 \\ f & 90 & p & 30\({}^{\circ}\) & z & 25.11 & J & 51 & R\({}_{1}\) & 0.03 \\ g & 14 & q & 35 & A & 25 & K & 1 & R\({}_{2}\) & 0.05 \\ h & 1005 & r & 25 & B & 62.39 & L & 6 & R\({}_{3}\) & \(-\)0.2 \\ i & 50 & s & 41 & C & 5 & M & 0.7 & R\({}_{4}\) & \(-\)02 \\ j & 25 & t & 5 & D & 25 & N & 0.4 & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter dimension of the antenna.  
Figure 1: The 1 \(\times\) 2 Coplanar Vivaldi Antenna of (**a**) Regular Palm Tree (RPT-CVA), (**b**) Front Cut Palm Tree (FCPT-CVA), (**c**) Middle Cut Palm Tree (MCPT-CVA), (**d**) Back Cut Palm Tree (BCPT-CVA), (**e**) Complete Cut Palm Tree (CCPT-CVA), (**f**) Left Tilt Palm Tree (LTPT-CVA), (**g**) Right Tilt Palm Tree (RTPT-CVA), (**h**) Hilbert Fractal Structure Palm Tree (HFSPT-CVA).