# Quad-Beam 4 \(\times\) 2 Array Antenna for Millimeter-Wave 5G Applications
## 3 Array Antenna Design
### A 2 \(\times\) 1 Array Antenna  
A \(2\times 1\) array structure (Ant2), as shown in Figure 9a, is designed and analyzed for its radiation pattern. The interelement spacing (Es1) along the x-axis is 0.6\(\lambda_{1}\), which is slightly greater than a half-wavelength. Equal power is split between A1 and A2 with the aid of a T-junction stub having an impedance of \(Z_{1}\). The splitting stub length is half of the injection stub. To feed the power to the T-splitter, a feed line length is tuned to \(Z_{2}\) (where \(Z_{1}=50\)\(\Omega\) and \(Z_{2}=100\)\(\Omega\)).  
The radiation pattern is well described by the array factor (AF). For a two-element linear array, \(AF=I_{1}e^{i(0)}+I_{2}e^{i(\mathbf{r})}\). Since both antennas are provided with equal power, where \(k\) is the wavenumber, \(\beta\) is the phase difference between elements and \(I=I_{1}=I_{2}\). Applying [PERSON]'s rule and simplifying leads to the following:  
\[AF=I\Big{(}1+e^{i(kEs1 cos(\theta)+\beta}\Big{)}, \tag{14}\]  
where \(k\) is the wavenumber, \(\beta\) is the phase difference between elements, and \(I=I_{1}=I_{2}\). Applying [PERSON]'s rule and simplifying leads to the following:  
\[AF=2I\Big{|}cos\Big{(}\frac{kEs1 cos(\theta)+\beta}{2}\Big{)}\Big{|}\ \ . \tag{15}\]  
Since the parallel feed mechanism is used, the phase difference \((\beta)\) between the elements will be zero. Equation (15) is fed to the Matlab tool to study the radiation behaviors for the different distances of \(Es1\). Further, with a 0.6\(\lambda_{1}\) distance, the desired dual  
Figure 9: (**a**) The \(2\times 1\) array antenna (Ant2) with elements separated by a distance of Es1 = 6 mm, where SW2 = 8 mm and SL2 = 10 mm. (**b**) A pictorial representation of the wave formation by the \(2\times 1\) Ant2 due to the Es1 spacing.  
constructive beam is obtained, for which the feed network is designed and simulated using the FEM method.  
Generally, when array elements are considered along the x-axis, the radiation pattern must form a narrow beam pattern in the xz-plane. However, in this case, it is quite different. A pictorial representation of the wave-formation of the \(2\times 1\) array is shown in Figure 9. As Es1 \(>0.5\lambda_{1}\), the beam is stretched along the x-axis, forming an elongated pattern between A1 and A2. However, between these two elements, the wave cancels due to the phase difference, causing a null at the center. Thus, an \(\varepsilon\)-shaped pattern can be seen in the xz-plane. It is also worth noting that, due to the dual-elliptical structure of each element, a narrow beam is formed in the yz-plane. The 3D radiation pattern shown in Figure 10 illustrates this phenomenon. It is also worth noting, as shown in Figure 10, that with the \(2\times 1\) array, the X-polarization in the yz-plane is improved compared to the single-element antenna shown in Figure 4. The limitation with Es1 \(>0.5\lambda_{1}\) is that the radiation energy is spread along the x-axis, resulting in a marginal increase in gain. In the case of the \(  
The pair (A1, A2) and (A3, A4) form a constructive pattern in the broadside; however, due to Es2 = \(1.01\lambda_{1}\), two additional beams are formed at the different elevation angles (\(\theta\)), as shown in Figure 12. The gain of Ant3 is increased by 19% and 22.72% compared to Ant2 and Ant1, respectively. Ant2 has a main feed line impedance (\(Z_{1}\)) of 50 \(\Omega\), connected to a 100 \(\Omega\)\(Z_{2}\) line. Here, no transformation is required because, at the point of injection, the \(Z_{2}\) line is considered as two 100 \(\Omega\) lines; thus, its parallel impedance becomes 50 \(\Omega\). Therefore, the main feed line is connected directly to the 100 \(\Omega\) line.