# Quasi-Yagi Slotted Array Antenna with Fan-Beam Characteristics for 28 GHz 5G Mobile Terminals
## 2 Antenna Design and Performance
### Analysis of Human Body Effect  
At mm-wave frequencies, since most of the energy is absorbed within a short distance from the skin, the power density is used as a basic restriction in RF exposure to the human body, instead of the specific absorption rate (SAR) [16]. Currently, the World Health Organization (WHO) recommends a standard established by the International Commission on Non-Ionizing Radiation Protection (ICNIRP). In addition, South Korea adopted the WHO recommended standard [17]. Therefore, in this paper, the RF exposure standard established by the ICNIRP was used [18]. According to the standard, in 10-300 GHz frequency band, the spatial power density averaged over any 1 and 20 cm\({}^{2}\) on the reference plane shall not exceed 200 and 10 W/m\({}^{2}\), respectively. The spatial-average power density can be calculated using the Poynting vector, as shown in Equation (1) [19; 20; 21]. Figure 14a shows the evaluation model of the power density. The power density is assessed over an averaging area \(A\), which is perpendicular to the unit vector \(\hat{n}\), with a separation distance \(h\) away from the antenna. As shown in Figure 14b, the power density of the proposed \(1\times 8\) array antenna is simulated with  
Figure 13: The \(1\times 8\) array antenna: (**a**) without directors, (**b**) with directors, (**c**) with simulated S-parameters with directors, (**d**) showing simulated radiation patterns at 28 GHz, and (**e**) showing simulated beam steering performances in the \(yz\) plane at 28 GHz, with directors. \(A=1\) cm\({}^{2}\) and \(h=10\) mm by using the Fields Calculator of the HFSS software [22]. Assuming that the mobile terminal is located at a distance of 10 mm away from the head in talk mode, the separation distance \(h\) was determined to be 10 mm [23]. The simulated spatial-average power density of the proposed array antenna is 138.53 W/m\({}^{2}\) with 20 dBm input power at each lumped port [19]. \[S=\frac{1}{2A}\int_{A}Re[\overrightarrow{E}\times\overrightarrow{H}^{*}]\cdot nA dA \left[\text{W}/\text{m}^{2}\right] \tag{1}\]  
To investigate the impacts of the human body on the antenna performance at 28 GHz, S-parameters and radiation patterns of the proposed \(1\times 8\) array antenna with a simplified skin phantom were simulated as in Figure 15. As we mentioned, since skin penetration depth of the energy is less than 2 mm at 15 GHz and less than 1 mm at 30 GHz [16], a simplified skin phantom of 2 mm thickness with a relative dielectric constant of 16.6 and conductivity of 25.8 S/m at 28 GHz was used [24]. Since a full human body phantom model is very time-consuming to analyze in the simulation software, a simplified skin layer was introduced. The dimensions of the phantom are \(28\times 70\) mm and this size is enough to cover the radiators. As shown in Figure 15a, the simulations were performed using a simplified skin phantom spaced vertically from the antenna with the gap distance of \(g\). A slot antenna is complementary to a planar electric dipole and is called a magnetic-type antenna since the electric source **J** on the planar electric dipole is replaced by the magnetic source M on the slot antenna by [PERSON]'s principle [25]. In Equation (2), \(Z\) is the intrinsic impedance of the surrounding medium (air), and \(Z_{1}\) and \(Z_{2}\) are the input impedances of the two complementary antennas (slot and planar electric dipole), respectively. The slot antenna has a constant impedance of \(60\pi\,\Omega\) (in air) that is independent of frequency since \(Z_{1}\) is equal to \(Z_{2}\) for ideal complimentary structures [12; 13]. In other words, when the slot antenna operates in free space, the variation of the input impedance of the slot antenna is less sensitive even if an object is present around the antenna. Simulated S-parameters when \(g=5\), 10, and 20 mm are shown in Figure 15c-e. The simulated reflection coefficients of all cases fully cover the target band. However, the mutual coupling levels are slightly degraded due to the existence of the skin phantom.