## 4 Configuration of Proposed Double-Dielectric Antenna  
The geometry of the proposed microstrip antenna is shown in Figure 1. It was expected to achieve 3 dB more gain by narrowing the beamwidth in the elevation direction as long as we doubled the number of patches. The antenna, consisting of three patches placed above a double-layer dielectric substrate, resulted in a good trade-off between size and gain. The three units increased the antenna gain by about 4.7 dB. It was fed by a microstrip transmission line through a 50 \(\Omega\) SMA connector. Series-fed circuits were used to drive the three consecutive patches. The distance between the centers of the patches in the array equaled 199.0 mm (\(\sim\)\(\lambda_{0}\)/2 at the operation frequency). All patches were driven in phase because the radiation amplitude and phase at each patch were determined by the cumulative transmission characteristics of the preceding microstrip lines and patches. The connecting lines had the characteristic impedance of 100 \(\Omega\) and no influence on the value of the central frequency [12]. We followed a three-step approach. First, we theoretically designed the proposed antenna; second, we simulated the antenna behavior with the CST Microwave Studio electromagnetic simulator; third, we constructed and validated the antenna with some measurements. On the basis of (1) and (2), we determined \(h_{s}\) and \(h_{a}\). The upper dielectric was composed of FR4 with thickness \(h_{s}=1.6\) mm, relative permittivity \(\varepsilon_{r}=4.1\), and loss tangent tan\(\delta=0.015\)@1 GHz. The lower dielectric was composed of air with thickness \(h_{a}=3.2\) mm and relative permittivity equal to unity. Section 3 outlines how the height of the antenna influenced bandwidth. From the desired central frequency \(f_{c}=754\) MHz, we estimated each patch dimension \(W_{p}\) and \(L_{P}\) using the following equations [13]:  
\[W_{p}=\frac{\sqrt{2}}{2f_{c}\sqrt{\varepsilon_{0}\mu_{0}}\sqrt{\varepsilon_{r,eq}+1}} \tag{4}\]  
\[L_{P}=\frac{1}{2f_{c}\sqrt{\varepsilon_{0}\mu_{0}}\sqrt{\varepsilon_{r,eff}}} -2\Delta L, \tag{5}\]  
where \(\Delta L\) is given by  
\[\Delta L=\frac{0.412h\Big{(}\varepsilon_{reff}+0.3\Big{)}\Big{(}\frac{W_{p}}{ h}+0.264\Big{)}}{\Big{(}\varepsilon_{reff}-0.258\Big{)}\Big{(}\frac{W_{p}}{h}+0.8 \Big{)}}, \tag{6}\]  
and \(h\) is the total height of the antenna, equal to \(h_{s}+h_{a}\). All geometric parameters are listed in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Frequency** & \(\varepsilon_{r,eq}\) & \(W\) & \(L\) & \(W_{p}\) & \(L_{p}\) & \(L_{s}\) & \(h_{a}\) \\
**(MHz)** & \(\varepsilon_{r,eq}\) & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** \\ \hline
754 & 1.7 & 270 & 673 & 180 & 161.68 & 1.6 & 3.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometric parameters of proposed double-dielectric microstrip antenna. Figure 1: Geometry of double-dielectric microstrip antenna. Each of these three patches had a size of \(W_{p}\times L_{p}=180\times 161.7\) mm\({}^{2}\). The overall size of the antenna was \(W\times L=27.0\times 67.3\) cm\({}^{2}\). Figure 2 shows simulated reflection coefficient S\({}_{11}\) of the antenna. Assuming a return loss (RL) greater than 10 dB as the well-accepted criterion of good impedance matching, the proposed antenna was well-matched at the central frequency of 754 MHz and in channel 56 [750, 751, 752, 753, 754, 755, 756, 757, 758] MHz. The simulated bandwidth was 17 MHz, obtained at 10 dB return loss. The line length connecting patches had high impedance, and its length was equal to 164.0 mm. In total, the electrical length of the line between each consecutive patch was equal to the wavelength divided by 2, \(\lambda/2\). Therefore, the input impedance of the linear array is equivalent to the parallel connection of three patch antennas. A \(\lambda/4\) transformer was then used to convert antenna input impedance into 50 \(\Omega\). The \(\lambda/4\) transformer line had a length of 73 mm and a width of 24 mm.