## 2 Antenna Design and Development  
Figure 1 illustrates the proposed square-branch corner-truncated partial ground plane patch antenna on an FR-4 substrate (TLM140, Thai Laminate Manufacturer, Bangkok, Thailand). The TLM140 was selected because of its availability in the local market. To design the proposed antenna for 1.5 GHz (center of L-band), the relative permittivity (\(\varepsilon_{r}\)), loss tangent (\(tan\delta\)), and thickness (\(h\)) of the substrate were 4.3, 0.015, and 1.6 mm,  
respectively. It is noted that the relative permittivity was not readily provided in the TLM140 datasheet at the desired frequency [18]. The curve fitting from available data with a power function was introduced to estimate the relative permittivity at 1.5 GHz. The thickness of the substate was chosen to optimize the reflection coefficient and axial ratio. The substrate was inserted between the inverted L-shaped radiating patch and the corner-truncated partial ground plane with a diagonally adjoining square branch. The radiating patch was connected to the 50 \(\Omega\) SMA feeding point and the square branch was diagonally adjoined with the corner-truncated ground plane. The proposed inverted L-shape patch antenna was 92 \(\times\) 96 \(\times\) 1.6 mm (W \(\times\) L \(\times\) H) in dimension. The inverted L-shaped radiating patch generated linear polarization (LP) field and adjoining square branch was used to perturb the LP field to generate a CP field. The corner-truncated partial ground plane was utilized to realize a wide CP frequency band (L-band frequency spectrum). Table 1 tabulates the optimal dimension of the inverted L-shaped patch antenna with a corner-truncated partial ground plane diagonally adjoined with a square branch. Prior to the antenna development, the lower resonant frequency (\(f_{L}\) in GHz) of the inverted L-shaped planar monopole antenna (radiating patch) on the partial ground plane in vacuum (Figure 2a) was determined using Equation (1), where \(W\) and \(L\) are the width and length (in unit of cm) of the rectangular patch of the monopole antenna and \(p\) is the distance (in unit of cm) between the rectangular patch and the partial ground plane (i.e., probe length) [19]. \[f_{L}=7.2/(L+p+(W/2\pi))\ \mathrm{GHz}. \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Parameters** & \(\mathbf{S_{1}}\) & \(\mathbf{S_{2}}\) & \(\mathbf{P_{1}}\) & \(\mathbf{P_{2}}\) & \(\mathbf{L_{1}}\) & \(\mathbf{L_{2}}\) & \(\mathbf{L_{3}}\) & \(\mathbf{L_{4}}\) & \(\mathbf{b}\) & \(\mathbf{t}\) & \(\mathbf{d}\) & \(\mathbf{h}\) \\ \hline Optimal value (mm) & 92 & 96 & 45 & 68 & 76 & 2 & 12 & 29 & 26 & 27 & 19 & 1.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The optimal dimension of the inverted L-shaped patch antenna with corner-truncated partial ground plane diagonally adjoined with a square branch (in mm). Figure 1: The geometry of the square-branch corner-truncated partial ground plane patch antenna: (**a**) front view, (**b**) side view. To realize the lower (first) resonant frequency (\(f_{L}\)) close to the center frequency of the L-band, \(W\), \(L\), and \(p\) were thus equal to 4, 3, and 1.15 cm, so the calculated \(f_{L}\) was equal to 1.504 GHz. In Figure 2b, an FR-4 substrate was inserted between the radiating patch and the resized partial ground plane. The FR-4 substrate nevertheless shifted the center frequency. As a result, the partial ground plane was resized (i.e., downsized) to restore the center frequency of the L-band. Figure 3 compares the CST simulated reflection coefficient or return loss bandwidth (RLBW) of the inverted L-shaped planar monopole antenna on a partial ground plane in vacuum with that on an FR-4 substrate. The resizing of the partial ground plane resulted in two resonant frequencies within the L-band (1-2 GHz).