## 2 Antenna Design and Development
However, the AR of the inverted L-shaped antenna on the resized partial ground plane was greater than 3 dB (>3 dB) in the L-band, as shown in Figure 4. To realize an AR below 3 dB (\(\leq\)3 dB), a diagonally adjoining branch was integrated into the proposed antenna scheme as part of the partial ground plane. Figure 3: The reflection coefficient of the inverted L-shaped planar monopole antenna on a partial ground plane in vacuum and with FR-4 substrate. Figure 2: Inverted L-shaped planar monopole antenna on the partial ground plane: (**a**) in vacuum, (**b**) with FR-4 substrate. A transmission-line model was introduced to analyze a microstrip patch antenna using a series and parallel resonant circuit, where the bandwidth is given by Equations (2) and (3), respectively, and the resonant frequency can be calculated using Equation (4) [20]. \[BW=\ \frac{1}{Q}=\ \frac{R}{\omega_{0}L}=2\frac{\Delta\omega}{\omega_{0}}, \tag{2}\]  
\[BW=\ \frac{1}{Q}=\ \frac{1}{\omega_{0}RC}=2\frac{\Delta\omega}{\omega_{0}}, \tag{3}\]  
\[\omega_{0}=1/\sqrt{LC}. \tag{4}\]  
Figure 5 shows the equivalent circuit model of the inverted L-shaped planar monopole antenna on a partial ground plane in vacuum and with the FR-4 substrate. In the figure, the microstrip patch can be considered as a parallel resonant circuit of inductor (\(L_{p}\)), capacitor (\(C_{p}\)), and finite resistance (\(R_{p}\)) [1]. The corner feeding to the patch can be modeled as a series inductor (\(L_{s}\)) with a capacitor (\(C_{s}\)) and resistance (\(R_{s}\)). In vacuum, the initial values of \(R\), \(L\), and \(C\) can be calculated using Equations (2)-(4) for the operating frequency of 1.5 GHz. The equivalent circuit model was subsequently optimized using the Keysight Advanced Design System (ADS) software for optimal component values. The introduction of the FR-4 substrate (replacing vacuum with FR-4) and resizing of the partial ground plane altered the optimal component values of the equivalent circuit, as tabulated in Table 2; therefore, double resonance can be obtained. Meanwhile, the wider bandwidth could be achieved by increasing \(R_{s}\) and decreasing \(R_{p}\). Figure 6 compares the simulated reflection coefficient of an equivalent circuit using ADS in vacuum and with an FR-4 substrate. Figure 4: The axial ratio of the inverted L-shaped planar monopole antenna on a partial ground plane in vacuum and with FR-4 substrate. Figure 5: The equivalent circuit model of an inverted L-shaped planar monopole antenna on a partial ground plane in vacuum and with FR-4 substrate. Figure 7 shows the evolutionary stages of the inverted L-shaped patch antenna with a branch structure diagonally adjoining the partial ground plane: Antennas I, II, III, and IV. Each of Antenna I-IV was simulated with CST for investigating mainly the CP. In Antenna I, the diagonally adjoining branch is of symmetrical L-shaped type and located at the farthest corner of the ground plane [15; 16], as shown in Figure 7a. The adjoining branch was used to perturb the LP field (from the inverted L-shaped patch antenna) to generate a CP field. In Antenna II, the diagonally adjoining branch of the square ring shape was used to excite CP in the upper L-band frequency (Figure 7b). In Antenna III, the adjoining branch of the solid square shape was used to mitigate the coupling effect between the inverted L-shaped radiating patch and the adjoining branch (Figure 7c). In Antenna IV, the corner-truncated partial ground plane was introduced to enhance ARBW, as shown in Figure 7d. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & \(R_{s}\) & \(C_{s}\) & \(L_{s}\) & \(R_{p}\) & \(C_{p}\) & \(L_{p}\) \\ \hline In vacuum (initial value) & 4 & 5.9 & 1.9 & 46 & 5.9 & 1.9 \\ With FR-4 substrate & 42 & 5.9 & 3 & 23 & 15.5 & 1.1 \\ Unit & \(\Omega\) & pF & nH & \(\Omega\) & pF & nH \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal component values of an equivalent circuit model of inverted an L-shaped planar monopole antenna on a partial ground plane in vacuum and with FR-4 substrate.