# A 28 GHz 5G Phased Array Antenna with Air-Hole Slots for Beam Width Enhancement
## 2 Design of the Two-Element Antenna Array  
Figure 2a illustrates the structure of the proposed two-element antenna array. The proposed antenna consists of an air-hole slot in the ground substrate in addition to two bent dipole antenna elements and a modified ground. The two-element array antenna has dimensions of 10.7 mm \(\times\) 7.8 mm \(\times\) 0.127 mm and is printed on a Taconic RF-35 substrate with a relative permittivity of 3.5 and a loss tangent of 0.0018. Figure 1: The azimuth and elevation plane versus the radiation pattern: (**a**) half power beam width (HPBW) in the elevation plane and shaded area; (**b**) hemispheric beam coverage required by mobile handsets. Figure 2: Structure of the proposed two-element array antenna: (**a**) top view (**b**) cross-sectional view. Bending of the dipole arms is applied to enhance the isolation between radiating elements and the front-to-back ratio (FBR) [13]. In addition, the ground plane is modified to improve the impedance matching of the antenna elements [14]. Figure 3 shows the reflection coefficient and isolation level of the proposed two-element array antenna. The proposed antenna exhibits a wide (15%) \(-\)10 dB reflection coefficient bandwidth from 25.8 GHz to 31 GHz and an excellent isolation level higher than 21 dB over the desired frequency band. A slot (an air-hole slot) in the ground substrate is introduced to create the complimentary current component necessary to obtain the wide beam width. Figure 4a,b shows the operating mechanism of the proposed ground slot enhancing the HPBW in the elevation plane of the two-element array. As shown in the dotted circle in Figure 4a, the slot in the ground with length L, approximately half of the guided wavelength, forms a complementary \(\lambda\)/2-dipole originating via the current distribution around the slot, as described in the following equation [15]:  
\[L\simeq\lambda_{g}/2 \tag{1}\]  
where  
\[\lambda_{g}\;=\;\frac{\lambda_{0}}{\sqrt{\varepsilon_{r}}} \tag{2}\]  
Figure 4: Implementation of the slot in the ground: (**a**) visualized mechanism of the slot as a complementary dipole source (**b**) multiplication effect of the complementary dipole source on the radiation pattern of the two-element array. Figure 3: Simulated reflection coefficient and isolation level of the proposed two-element array. Therefore, the radiation pattern of the two-element dipole array is added to that of the complementary dipole from the ground slot resulting in a wider radiation pattern in the elevation plane, as shown in Figure 4b [16; 17]. In addition, the width of the slot W is a key parameter for determining the performance of HPBW in the elevation plane. Figure 5 illustrates the parametric study of the width W. The optimized value of W is 0.5 mm since the peak gain starts to decrease at W = 0.6 mm and the HPBW becomes extremely narrow at W = 0.7 mm, which implies that the slot does not operate properly as a complementary dipole radiator. To enhance the parasitic effect of the complementary dipole, an air-hole slot in the ground is introduced, as shown in Figure 2a. The air-hole slot consists of a slot on the ground and an air-hole made by puncturing the substrate. The air-hole has an identical location and size of the slot, and is laid on the top of the slot. The effect of such an air-hole slot can be simply explained by the complementary theory in which all the materials should be completely complemented for thorough implementation [18]. Such a theory can be further expanded upon using [PERSON]'s equations as following [19]:  
\[\
abla\times H = J+\varepsilon\frac{\partial E}{\partial t}\ (\text{Ampere's Law}) \tag{3}\] \[\
abla\times E = -\mu\frac{\partial H}{\partial t}\ (\text{Faraday's Law}) \tag{4}\]  
Qualitatively, the total surface current around the slot is increased since the focusing of E field caused by the difference of relative permittivity between air hole and the substrate reinforces the second term on the right hand side of the equation of Ampere' Law.