# Simulation and Design of Three 5G Antennas
## 3 Design of 5G Microstrip Array Antennas
### Dielectric Substrate Thickness (h)
#### 3.1.2 Simulation of Antenna Units  
In HFSS, the designed antenna unit is modeled and simulated. The created antenna unit model is shown in Figure 7. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Value** & **Units** \\ \hline Resonant Frequency (\(f_{0}\)) & 3.5 & GHz \\ Relative dielectric constant (\(\epsilon_{\mathrm{r}}\)) & 4.4 & \(\backslash\) \\ Substrate thickness (h) & 1.6 & mm \\ Patch width (W) & 22 & mm \\ Effective dielectric constant (\(\epsilon_{\mathrm{e}}\)) & 3.99 & \(\backslash\) \\ Equivalent radiating aperture length (AL) & 0.734 & mm \\ Patch length (L) & 19.6 & mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Antenna unit parameters. Figure 6: The influence of antenna unit length ‘L’ on S parameters. Figure 7: Antenna unit model diagram. At this point, the antenna unit model is a simple rectangular microstrip patch, and its input impedance can be calculated using empirical Formula (22). \[\Delta Z_{\text{in}}=\frac{60\lambda_{0}}{\text{W}}, \tag{22}\]  
In the equation, \(\lambda_{0}\) is the wavelength in a vacuum, and Zin is the input impedance of the antenna, which is calculated to be approximately 90 \(\Omega\). To facilitate the subsequent design of the antenna array, the microstrip antenna unit is adjusted to 50 \(\Omega\) using a feeding mechanism. Traditional end-fed methods often result in high input impedance. Therefore, this design employs the inset-fed method in microstrip feeding. This feeding method positions the feed point closer to the center, reducing the input impedance. As the current follows a sinusoidal distribution, moving a distance R from the end increases the current by \(\cos(\text{R}/\pi\text{L})\), resulting in a phase difference of \(\pi\text{R}/\text{L}\). The scale factor for the input impedance is calculated as \(\text{Z}=\text{V}/\text{I}\), where the scaling factor is Formula (23). \[Z_{\text{in}}(\text{R})=\cos^{2}(\frac{\pi\text{R}}{\text{L}})Z_{\text{in}}(0), \tag{23}\]  
In the equation, \(Z_{\text{in}}(0)\) represents the input impedance for the end-fed configuration. For example, when \(\text{R}=\text{L}/4\), it results in \(\cos(\pi\text{R}/\text{L})=\cos(\pi/4)\), making \([cos(\pi/4)]^{2}=1/2\), so a 1/8 wavelength inset reduces the input impedance by 50%. This method determines the inset length and achieves a 50\(\Omega\) input impedance. The inset-fed design effectively reduces the size of the antenna unit, enabling antenna miniaturization [22]. Moreover, the inset-fed configuration is more suitable for developing high-gain microstrip array antennas. Figure 8 depicts the model of an antenna unit with the inset-fed configuration:  
At this point, the length Y0 of the embedded feedline has the most significant impact on the antenna's input impedance. Figure 9 illustrates the resonance frequency of the embedded feed antenna unit as Y0 varies. The resonant frequency changes with the increase of Y0. Taking all factors into consideration, the performance of the antenna unit becomes optimal when it reaches Y0 = 5.25 mm. The specific dimensions of the embedded feeding structure are provided in Table 2.  
Figure 8: Antenna units with embedded feeding. The simulation of the embedded-fed antenna unit using HFSS provides the reflection coefficient VSWR as shown in Figure 10. Within the operating frequency range of 3.4 GHz to 3.6 GHz, the VSWR remains below 2. At the central frequency of 3.5 GHz, the return loss reaches \(-\)35 dB, and the VSWR \(\leq\)1.1. This indicates that the embedded-fed antenna unit achieves excellent impedance matching. As shown in Figure 11, the gain pattern of the microstrip antenna unit at a frequency of 3.5 GHz is presented. Figure 11a represents the 3D gain pattern of the antenna unit, and Figure 11b shows the gain polar pattern. From the figures, it can be observed that the maximum radiation direction of the microstrip antenna unit is perpendicular to the antenna's center, and the gain reaches 3.8 dB in the maximum radiation direction.