# A Compact Planar Wi-Fi Antenna with Optimized Radiation Patterns for Small UAV Applications
## 2 Antenna Design and Analysis
### Antenna Design for 5.8 GHz  
Figure 4 shows the simulated surface current density at 5.8 GHz, where the areas with higher surface current densities are the main radiation areas. The outer conductor forms four monopole antennas from each triangle vertex to its adjacent corners. These four \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Dimension**} & **Ratio to the** & **Ratio to the** & \multirow{2}{*}{**Angle**} \\  & & **Wavelength of** & **Wavelength of** & **Angle** \\  & **(mm)** & **2.4 GHz in** & **5.8 GHz in** & **(Degree)** \\  & & **Vacuum** & **Vacuum** & \\ \hline W & 30.3 & 0.24 & 0.59 & N/A \\ W\({}_{\rm i}\) & 27.3 & 0.22 & 0.53 & N/A \\ L & 16.5 & 0.13 & 0.32 & N/A \\ L\({}_{\rm i}\) & 12.5 & 0.10 & 0.24 & N/A \\ W\({}_{\rm I}\) & 12.1 & 0.10 & 0.23 & N/A \\ W\({}_{\rm 2}\) & 1.5 & 0.01 & 0.03 & N/A \\ L\({}_{\rm I}\) & 2 & 0.02 & 0.04 & N/A \\ L\({}_{\rm 2}\) & 5.75 & 0.05 & 0.11 & N/A \\ L\({}_{\rm 3}\) & 5.5 & 0.04 & 0.11 & N/A \\ a & 8.5 & 0.07 & 0.16 & N/A \\ b & 8.5 & 0.07 & 0.16 & N/A \\ c & 1 & 0.01 & 0.02 & N/A \\ T\({}_{\rm h}\) & 5.7 & 0.05 & 0.11 & N/A \\ T\({}_{\rm w}\) & 1.5 & 0.01 & 0.03 & N/A \\ W\({}_{\rm f}\) & 2.5 & 0.02 & 0.05 & N/A \\ g & 0.3 & 0.00 & 0.01 & N/A \\ C\({}_{\rm t}\) & 0.035 & 0.00 & 0.00 & N/A \\ h & 1.6 & 0.01 & 0.03 & N/A \\ Beta & N/A & N/A & N/A & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The values of geometrical parameters for the proposed antenna. Figure 3: The main design steps of the proposed antenna. monopoles have the same wavelength, \(\lambda_{\rm H}\), and the upper resonance frequency, \(\rm f_{H}\), can be approximated using (1), where c is the speed of light in a vacuum (\(3\times 10^{8}\) m/s). \[\rm f_{H}\cong\frac{c}{\lambda_{H}}=\frac{c}{(L_{2}+L_{3}+L_{1}/2)/0.23}=5.63\;GHz, \tag{1}\]  
Higher surface current densities exist at the four corners inside the outer conductor, which approximate four point sources named Element A, Element B, Element C, and Element D. The radiation pattern is mainly synthesized from these four point sources. Due to the electric field that radiates between the inner and outer conductors, the proposed antenna approximates a two-element array of two point sources, Elements 1 and 2, as shown in Figure 5.  
The radiation patterns of Elements 1 and 2 equal the sum of Elements A and C and the sum of Elements B and D, respectively. Furthermore, since the cross-sectional area of the inner conductor used as the reference plane is very small, the radiation patterns of Elements 1 and 2 approximate a vertical infinitesimal dipole. Based on the directivity of the  
Figure 4: The simulated surface current density at 5.8 GHz. Figure 5: Far-field observation of a two-element array consisting of two point sources, Elements 1 and 2, positioned along the \(z\)-axis. vertical infinitesimal (Hertzian) dipole [17], the normalized pattern function of the vertical infinitesimal dipole is \(\sin^{2}\!\theta\). The normalized array factor of Elements 1 and 2, \(\left(\mathrm{AF_{12}}\right)_{\mathrm{n}}\), is adapted from (2) [18], where k is the wave number equal to \(2\pi/\lambda_{0\;5\;\mathrm{sG}}\), and d is the distance between Elements 1 and 2, approximately equal to \(\mathrm{L_{i}}+\left(\mathrm{L_{i}}/2\right)\times 2\). In addition, \(\lambda_{0\;5\;\mathrm{sG}}\) is the wavelength of 5.8 GHz in vacuum, \(\theta\) is the elevation angle, and \(\pi\) is the ratio of a circle's circumference to its diameter (\(180^{\circ}\)).