# Simulation and Design of Three 5G Antennas
## 3 Design of 5G Microstrip Array Antennas
### Dielectric Substrate Thickness (h)  
When designing microstrip antennas, parameters such as the dielectric substrate thickness (h), relative permittivity (\(\text{e}_{r}\)) and dielectric loss tangent (tan8) have a significant impact on antenna performance [20]. A lower relative permittivity (\(\text{e}_{r}\)) can lead to a notable increase in antenna bandwidth, but also results in larger antenna dimensions. However, a higher dielectric loss tangent (tan8) can reduce antenna efficiency, so it should be minimized. Choosing a thicker dielectric substrate can improve the antenna's bandwidth to some extent  
Figure 3: (**a**) Antenna top view and (**b**) antenna side view. but can also increase the excitation of surface waves, thus decreasing antenna performance. Therefore, selecting an appropriate thickness is crucial. Taking all these factors into account, this design opts for FR4-epoxy, which is an epoxy glass fiber board with a relative permittivity (\(\mathrm{e_{r}}\)) of 4.4 and a dielectric loss tangent (tan\(\delta\)) of 0.02. This material offers stable electrical insulation, standard thickness tolerance, heat and moisture resistance, and good mechanical processability, making it suitable for crafting high-performance antennas. Commonly used thicknesses include 0.8 mm, 1.0 mm, 1.2 mm, 1.6 mm, 1.8 mm, and 2.0 mm. Figure 4 illustrates the impact of the dielectric substrate thickness (h) on the S\({}_{11}\) parameter. It is evident that, as the dielectric substrate thickness (h) increases from 0.8 mm to 2.0 mm, the antenna's resonant frequency gradually decreases. The S\({}_{11}\) initially decreases and then increases, and the S\({}_{11}\) curve becomes smoother, resulting in a broader bandwidth. When the dielectric substrate thickness is set to h = 1.6 mm, the antenna's resonant frequency aligns with the 3.5 GHz requirement for this design. Therefore, the choice of a 1.6 mm thick FR4-epoxy substrate material is confirmed to meet the design specifications. Antenna Element Width (W)  
Once the dielectric substrate thickness (h), relative permittivity (\(\mathrm{e_{r}}\)), and dielectric loss tangent (tan\(\delta\)) for the selected substrate material are determined, the initial calculation of the width W of the rectangular patch element can be made using empirical Formula (17). However, it is essential to limit the range of W, as an excessively large width can generate higher-order modes and affect the antenna's performance. \[\mathrm{W}\leq\frac{\mathrm{c}}{2\mathrm{f_{0}}}\bigg{(}\frac{\mathrm{\varepsilon _{r}+1}}{2}\bigg{)}^{-\frac{1}{2}}, \tag{17}\]  
In the formula, c represents the speed of light, \(c=3.0\times 10^{8}\) m/s. \(f_{0}\) is the resonant frequency and is set to 3.5 GHz in this design. The relative permittivity (\(\mathrm{\varepsilon r}\)) is fixed at 4.4. Through calculations, it is found that W should be limited to \(\leq\)26.082 mm. As shown in Figure 5, it illustrates the impact of the antenna element width (W) on the S\({}_{11}\) parameter. Within the range of antenna element widths from 18 mm to 27 mm, it is evident that changes in the antenna element width W significantly affect the S11  
Figure 4: The influence of dielectric substrate thickness on S parameters. parameter. Additionally, the antenna achieves the best matching at around 22 mm. Further optimization of W will be carried out in subsequent simulations. Antenna Element Length (L)  
In theory, the length (L) of the rectangular microstrip patch antenna is approximately half-wavelength [21]. It can be calculated using Equation (18). \[\text{W}\leq\frac{\text{c}}{2\text{f}_{0}}\bigg{(}\frac{\epsilon_{\text{r}}+1}{ 2}\bigg{)}^{-\frac{1}{2}}, \tag{18}\]  
where \(\lambda_{0}\) is the wavelength in a vacuum area that can be found by Equation (3), and \(\epsilon_{e}\) is the effective dielectric constant of the substrate material that can also be given by Equation (19).