# A Compact Printed Monopole Antenna for WiMAX/WLAN and UWB Applications
## 2 Antenna Design  
The geometric configuration of the proposed antenna is shown in Figure 2. The antenna consisted of a triangle, an inverted F, and an M, which was rotated 90\({}^{\circ}\) counterclockwise to form a surface-radiating patch. This antenna was fabricated on an FR4_epoxy substrate with a relative permittivity of 4.4, a tangent of 0.02, and a height of 1.6 mm. The size of the antenna substrate was \(0.25\,\lambda\,\times\,0.14\,\lambda\,\times\,1.6\) mm (30 \(\times\) 17 mm, \(\lambda\) is the free wavelength in a 2.45-GHz space). This structure was fed by a 50-\(\Omega\) microstrip transmission line with length L\({}_{f}\) and width W\({}_{f}\). The antenna ground plate was composed of a rectangular patch with length W and width L\({}_{g}\). The two branches of the antenna increased the flow path of the surface current. In this antenna geometry model, the resonant path lengths L\({}_{11}\) and L\({}_{22}\) were approximately one-quarter of the free wavelength in air at the corresponding frequency. The proposed antenna covered the WLAN (2.4/5.2/5.8) and WiMAX high-frequency (5.25-5.85 GHz) bands. L\({}_{11}\) and L\({}_{22}\) can be described by Equations (1) and (2):  
\[\mathrm{L}_{11}=\mathrm{L}_{2}+\mathrm{L}_{7}+\mathrm{L}_{4}+\mathrm{L}_{6}+2 \mathrm{W}_{6}+\mathrm{W}_{7}+3a \tag{1}\]  
\[\mathrm{L}_{22}=\mathrm{L}_{2}+\mathrm{L}_{3}+\mathrm{L}_{4} \tag{2}\]  
From the design of the microstrip patch antenna, the theoretical dimensions were calculated as follows [18]:  
The width \(w\) of the patch is:  
\[w=\frac{c}{2f_{0}}\bigg{(}\frac{\varepsilon_{r}+1}{2}\bigg{)}^{-\frac{1}{2}} \tag{3}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**References**} & \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Size (mm\({}^{2}\))**} & \multicolumn{2}{c}{**Total Area**} & \multirow{2}{*}{**Bandwidth (GHz)**} & \multirow{2}{*}{**Relative Bandwidth**} \\  & & & & & & \\ \hline
[2] & Tri-band & 60 \(\times\) 60 & 3600 & 1.55–1.57, 2.39–2.69, 4.97–5.93 & 1.27\%, 12.00\%, 16.55\% \\
[3] & Dual-band & 35 \(\times\) 24 & 840 & 2.26–2.67, 3.00–6.78 & 16.40\%, 65.17\% \\
[4] & Dual-band & 40 \(\times\) 40 & 1600 & 3.15–3.70, 5.05–5.97 & 15.70\%, 15.86\% \\
[5] & Dual-band & 40 \(\times\) 30 & 1200 & 2.39–2.51, 5.00–6.10 & 4.80\%, 18.96\% \\
[6] & Dual-band & 34 \(\times\) 30 & 1020 & 2.30–2.50, 2.90–15.00 & **\#, \#** \\
[7] & Tri-band & 40 \(\times\) 40 & 1600 & 2.28–2.58, 3.38–3.66, 5.07–5.86 & 12.60\%, 8.00\%, 14.50\% \\
[8] & Tri-band & 35 \(\times\) 15 & 525 & 1.48–1.63, 2.25–2.48, 4.22–6.00 & 9.55\%, 9.88\%, 30.69\% \\
[9] & Dual-band & 75 \(\times\) 75 & 5625 & 2.40–2.48, 5.15–5.95 & 10.60\%, 33.8\% \\ Proposed work & Dual-band & 30 \(\times\) 17 & 510 & 2.39–2.49, 4.27–7.96 & 4.08\%, 64.31\% \\ \hline \hline \end{tabular}  
* **Notation:**\# represents information not mentioned in the reference.  
\end{table} 
Table 1: Comparison of microstrip multi-band antennas. where \(c\) represents the speed of light, \(f_{0}\) is the center frequency of the antenna, and \(\varepsilon_{r}\) is the relative permittivity of the dielectric substrate. The relative effective dielectric constant of the dielectric substrate \(\varepsilon_{re}\) is:  
\[\varepsilon_{re}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2} \bigg{(}1+\frac{12h}{w}\bigg{)}^{-\frac{1}{2}}. \tag{4}\]  
The equivalent extension length \(\Delta L\) caused by the fringe field of the antenna is:  
\[\Delta\mathrm{L}=0.412h\frac{(\varepsilon_{re}+0.3)\left(\frac{w}{h}+0.264 \right)}{(\varepsilon_{re}-0.258)\left(\frac{w}{h}+0.8\right)} \tag{5}\]  
where \(h\) represents the thickness of the dielectric substrate. From this equation, it is possible to calculate the actual length \(\mathrm{L}\) of the rectangular patch:  
\[\mathrm{L}=\frac{c}{2f_{0}}\frac{1}{\sqrt{\varepsilon_{re}}}-2\Delta\mathrm{L} \tag{6}\]  
Figure 2: Geometrical configuration of the proposed antenna: (**a**) top view, (**b**) bottom view, and (**c**) side view. The fundamental dimensions of the antenna are based on the above four equations.