# A Compact Monopole Wideband Antenna Based on DGS
## 2 Antenna Design Methodology and Optimization Process  
### Initial Antenna Design  
The antenna is constructed on a Taconic TLY dielectric substrate with a dielectric constant of \(\varepsilon_{\mathrm{r}}\) = 2.2, a loss tangent of (tan \(\delta\)) = 0.0009, and a thickness of 1.524 mm. A 50 \(\Omega\) microstrip line is connected to excite the antenna and to reduce incident wave rejection. The center frequency was set to 11.5 GHz. Equations (1)-(7), Ref. [23] are used to determine the initial dimensions of the antenna radiators' width (w) and length (L). In this design we used half of the center frequency to calculate the width and length of the patch or ground plane by considering the DGS. Here also L\({}_{\mathrm{S}}\) is used as W\({}_{\mathrm{S}}\) and vice versa for the substrate or ground plane for convenience of the design. Patch width (w) and effective permittivity (\(\varepsilon_{\mathrm{reff}}\)):  
\[\mathrm{w}=\frac{c}{2f_{c}}\sqrt{\frac{2}{\varepsilon_{r}+1}} \tag{1}\]  
\[\varepsilon_{\mathrm{reff}}=\ \frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1 }{2}\bigg{[}1+12\frac{h}{w}\bigg{]}^{-1/2} \tag{2}\]  
Patch length (L) and length for fringing fields, \(\Delta\)L is written as follows:  
\[\mathrm{L}=\mathrm{L}_{\mathrm{eff}}-2\Delta\mathrm{L} \tag{3}\]  
\[\mathrm{L}_{\mathrm{eff}}=\frac{c}{2f_{\mathrm{c}\sqrt{\varepsilon_{r\prime \prime f}}}} \tag{4}\]  
\[\Delta\mathrm{L}=0.421\mathrm{h}\frac{\left(\varepsilon_{reff}+0.3\right)}{ \left(\varepsilon_{reff}-0.258\right)}\frac{\left(\frac{w}{2}-0.246\right)}{ \left(\frac{w}{2}-0.813\right)} \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Stages of Evolution** & **Type of Shaped Slots to DGS** & **Obtained Grequencies (GHz)** & **3D Gain Plot (dBi)** & **Bandwidth (GHz)** & **Total Bandwidth (GHz)** & **Total Bandwidth (\%)** \\ \hline \multirow{2}{*}{1} & Standard ground plane & 8.85 & \multirow{2}{*}{6.8} & 8.79–8.93 & \multirow{2}{*}{2.71} & \multirow{2}{*}{20.5} \\ \cline{3-3} \cline{5-6}  & & 15.57 & & & 15.03–17.60 & \\ \hline \multirow{4}{*}{2} & \multirow{4}{*}{L-slot} & 6.77 & \multirow{4}{*}{4.32} & 4.18–7.64 & \multirow{4}{*}{9.35} & \multirow{4}{*}{77.8} \\ \cline{3-3} \cline{5-6}  & & 8.2 & & 8.12–8.37 & & \\ \cline{3-3} \cline{5-6}  & & 13.57 & & 12.9–17.45 & & \\ \cline{3-3} \cline{5-6}  & & 19.51 & & 18.77–19.86 & & \\ \hline
3 & Semi-circular segment & 16.90 & 4.18 & 4.08–18.92 & 14.84 & 129.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance analysis of a compact monopole wideband antenna based on DGS evolution. Substrate dimension is calculated as follows:  
\[\mathrm{L_{S}=L+6h} \tag{6}\]  
\[\mathrm{W_{S}=W+6h} \tag{7}\]  
where W refers to the patch width, c refers to the vacuum light speed, fc is the center frequency, \(\epsilon_{\mathrm{r}}\) is the relative dielectric permittivity, \(\epsilon_{\mathrm{reff}}\) is the effective permittivity of the substrate, h is the substrate height, and L is the patch length. It is important to consider the transmission line width (\(W_{f}\)) when calculating radiation intensity because it directly impacts the signal's bandwidth. By plugging in values for the desired impedance (\(Z_{0}\)), thickness of copper (t), dielectric thickness (h), and relative dielectric constant (\(\epsilon_{\mathrm{r}}\)), the fundamental Equation (8) can be used to calculate the width of the microstrip line [23]. \[W_{f}=\frac{7.48\times\mathrm{h}}{e^{\frac{2\epsilon_{\mathrm{r}}\times\sqrt{ \epsilon_{\mathrm{r}}\times\mathrm{L}}}{8\pi}}}-1.25\times\mathrm{t} \tag{8}\]  
In accordance with the fundamental equation, the width of the transmission line was calculated to be 4 mm when the impedance is 50 \(\Omega\), copper thickness is 0.035 mm, dielectric thickness is 1.524 mm, and dielectric constant is 2.2. By using the basic monopole antenna Equations (1)-(7), the antenna's initially optimized dimensions were derived at the beginning of the design as W = 23 mm, L = 20 mm, L\({}_{\mathrm{S}}\) = 28 mm, and W\({}_{\mathrm{S}}\) = 34 mm (Figure 1a).