# Quad-Beam 4 \(\times\) 2 Array Antenna for Millimeter-Wave 5G Applications
## 2 Single-Element Antenna  
### Design Procedure  
The single-element antenna is a highly compact structure etched on a Rogers 5880 substrate, which has a relative permittivity of 2.2 and thickness of 0.254 mm. The design operates at a wavelength of \(\lambda_{1}\) (where \(\lambda_{1}\) is a wavelength at 30 GHz). The base design is a dual-ellipse configuration derived from a conventional circular patch [23]. A typical circular patch antenna with a radius of 1.82 mm generates resonance at \(\lambda_{1}\), resulting in a total area of 10.40 mm\({}^{2}\). This circular area is divided into two elliptical sections to form a dual-ellipse structure in the proposed design. Each elliptical section has a major axis (\(Eh1\)), which determines the resonance of the antenna, the dimension of which is derived from the cavity model Equation (1) for the TM\({}_{10}\) operation mode. The dimension of the minor axis (\(Ev1\)) significantly affects the impedance matching and tuning the resonance, which is judicially chosen. \[f_{1}=\frac{c}{2\pi\sqrt{\varepsilon_{eff}}}\cdot\sqrt{\left(\frac{m}{Eh1} \right)^{2}+\left(\frac{n}{Ev1}\right)^{2}}, \tag{1}\]  
where \(c\) is \(3\times 10^{8}\) (m/s) and \(\varepsilon_{eff}\) is the relative permittivity, which is approximately 1.6 in this case. The \(m\) and \(n\) are fundamental modes along the x-axis and y-axis, respectively. In this case, \(m=1\) and \(n=0\), and then the resulting \(Eh1\) is equal to 3.95 mm for 30 GHz. Further, this is tuned to 3.74 mm to obtain a better result with a minor axis (\(Ev1\)) of 1.7 mm, providing an individual area of approximately 5 mm\({}^{2}\). Together, the two elliptical sections closely match the area of the original circular patch. As illustrated in Figure 1a, the dual-ellipse design is implemented to increase the effective antenna aperture, thereby enhancing gain. The antenna achieves improved surface current distribution and overall performance by redistributing the area in two elliptical structures. A quarter-wave transformer with a guided wavelength of \(\lambda_{g}\) long at 30 GHz and having an impedance of 75 \(\Omega\) is used to feed the antenna, aiming to match the antenna impedance with the port. However, a significant impedance mismatch is observed, as depicted by the surface current distribution shown in Figure 1b. Figure 1: Initial design of the antenna (Antl) (a), and its surface current representation (b). The antenna's initial impedance is measured to be \(2.84-\)j2.38 \(\Omega\), indicating a short current path and low reactance. This low impedance suggests that the patch antenna presents minimal resistance to the surface currents. To address this issue, the impedance is adjusted by increasing the electrical length of the oscillating current. This is achieved by introducing elliptical slots within both elliptical structures of the antenna, as shown in Figure 2. Now, due to the slot, the electrical length is close to 3.74 mm, which results in improved resonance at 30 GHz, as evidenced by the cavity model in Equation (1). The slots extended the current path, resulting in a substantial increase in reactance. The modified antenna impedance is measured as \(59.32-j21.74\)\(\Omega\), bringing it closer to the target of 50 \(\Omega\). This improvement is further illustrated through the surface current distribution shown in Figure 3a. Despite these modifications, the bandwidth remains relatively narrow, ranging from 30.12 to 30.56 GHz. Efforts to enhance the impedance match and current distribution have contributed to improved antenna performance within this frequency range. The single-element antenna (Ant1) achieved a peak gain of 7.8 dBi, as shown in Figure 4a. With a fully grounded structure at the bottom, the radiation is directed in the broadside direction.