## 2 Design and Measurement of a Stacked Dual-Patch Antenna with Thick Quasi-Air Substrates  
Figure 1 illustrates the geometry of the stacked dual-patch antenna with thick quasi-air substrates and a cavity wall. To achieve the theoretical maximum bandwidth of the patch antenna, the quality factor of the system should be minimized. In this study, two techniques are employed when designing the antenna components to reduce the quality factor of the system: one is to enlarge the area of the conductive radiator as much as possible, and the other is to reduce the permittivity of the substrate within the patch to close to 1. To enlarge the conductive radiator and realize a patch antenna with this maximum bandwidth, we applied the stacked dual-patch configuration to the proposed antenna design. This stacked dual-patch configuration consists of the lower and upper rectangular patches. The width and length of the lower patch are \(w_{1}\) and \(l_{1}\), respectively, and this lower patch is directly connected to the SMA connector, as shown in Figure 1a. The upper patch, with a width \(w_{2}\) and a length \(l_{2}\), is coupled-fed from the lower patch. Thus, the proposed antenna with two radiators can achieve broadband characteristics due to the broadened area of the conductive radiators. To further broaden the antenna bandwidth, thick quasi-air substrates with low permittivity close to 1 are employed between the two radiators and the ground plate. Typically, the quasi-air substrates are implemented using Rohacell (\(\varepsilon_{r}\) = 1.08) [5; 19], but patch antennas fabricated with this material are soft and vulnerable to heat, so their durability is relatively poor. To simultaneously improve the durability and bandwidth of the antenna, square-pipe resin frames (\(\varepsilon_{r}\) = 2.9) are fabricated using a 3D printing method for implementing the quasi-air substrate structure. The square-pipe resin frame also consists of lower and upper frames, and the thicknesses of the lower and upper square-pipe resin frames are \(h_{1}\) and \(h_{2}\), respectively. Thus, the proposed quasi-air substrate has a low dielectric constant of 1.8. To increase the front-to-back ratio and suppress the leakage electric fields of the patch antenna, a metal cavity wall is placed around the square  
pipe resin frame, as shown in Figure 1b. The geometrical parameters of the proposed antenna with the stacked dual-loop design are optimized using the FEKO electromagnetic simulator [20] and the genetic algorithm (GA) [21]. The optimum parameters are listed in Table 1. These geometrical parameters of the proposed antenna were determined in the following process: First, the initial values were obtained from the basic theory for the patch antenna [8]. For example, an antenna's length is half of a wavelength (50 mm), and the thickness of the antenna is determined by less than 1/10 of a wavelength (10 mm). Next, these values are applied as the input to the GA, and the optimum design parameters are obtained through the GA. In this optimization process, a cost function is determined simply as 1/antenna bandwidth. Figure 2 shows photographs of the fabricated antenna with thick quasi-air substrates and the cavity wall. The fabrication of the proposed antenna is carried out using the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline \(w_{1}\) & 28.4 mm & \(w_{2}\) & 27 mm \\ \(l_{1}\) & 40.3 mm & \(l_{2}\) & 26.7 mm \\ \(h_{1}\) & 2.4 mm & \(h_{2}\) & 10.2 mm \\ \(f_{p}\) & 19.3 mm & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometrical parameters of the proposed antenna. Figure 1: Geometry of the proposed antenna: (**a**) isometric view of each antenna component; (**b**) isometric view of the assembled antenna; (**c**) side view of the assembled antenna. following procedures: First, two conductive radiators for the patch are printed on an RF-35 substrate (\(\epsilon_{r}\) = 3.5, tan \(\delta\) = 0.0018, thickness = 0.5 mm) using photolithography and etching techniques.