# Slotted Circular-Patch MIMO Antenna for 5G Applications at Sub-6 GHz
## 2 Evolution of Single Antenna Element
### Antenna Design  
In CST Microwave Studio, we expertly designed a circular patch antenna specifically tailored for the 5G sub-6 GHz spectrum at a central frequency of 4 GHz. To achieve optimal signal integrity and minimize losses for reliable performance, we selected an RT5880 substrate with an overall size of 30 \(\times\) 46 \(\times\) 1.57 mm\({}^{3}\). This remarkable material offers a dielectric constant of 2.2, an exceptionally low loss tangent of 0.0009, and a thickness of 1.57 mm, making it an excellent choice for electrical and mechanical applications. ROGER's superior electrical characteristics in RF and microwave circuits significantly diminish signal loss and distortion, which are critical components for cutting-edge communication systems, radar technologies, and high-frequency electronics. Its stable dielectric properties across a wide frequency range make it an ideal candidate for vital industries such as aerospace and telecommunications.  
The patch and ground layers are constructed from copper, measuring 0.035 mm thickness. The patch is excited using a Microstrip line feeding technique, and to ensure broadband operation, we have included a partial ground plane on the substrate's rear side. The initial task is to compute the radius (r) of the circular patch with Equations (1) and (2) [29], setting the groundwork for effective performance.  
\[\mathrm{r}=\frac{\mathrm{F}}{\sqrt{1+\frac{2h}{\pi\mathrm{F}_{tr}}\left[\ln \left(\frac{\pi\mathrm{F}}{2h}\right)+1.7726\right]}} \tag{1}\]  
\[\mathrm{F}=\frac{8.791\times 10^{9}}{\mathrm{f}_{tr}\sqrt{\mathrm{\varepsilon}_{ r}}} \tag{2}\]The parameters h, \(\varepsilon_{\mathrm{r}}\) and f\({}_{\mathrm{r}}\) represent the configuration's thickness, relative permittivity, and resonance frequency. Table 1 provides the actual design dimensions.  
To ensure a compact structure while ensuring the desired operational bandwidth, we strategically minimized the patch's dimensions by adjusting the partial ground plane length. Our design utilizes a defective circular stub patch antenna. To enhance the antenna's reflection coefficient (S11), we also expanded the antenna's bandwidth and increased the aperture area by adding a circular slot at the lower section of the patch.  
Figure 1 presents the simulated design and fabricated prototype antenna. This well-considered design not only fulfils performance requirements but also excels in efficiency and effectiveness. The design's input impedance is around 50 ohms at the central frequency, as shown in Figure 1e.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Parameter** & **Substrate Width** & **Substrate Length** & **r1** & **r2** & **Lf1** & **Lf2** & **Wf** & **c** & **Wg** & **Lg** \\ \hline (mm) & 30 & 46 & 12 & 5 & 17.35 & 1 & 4.21 & 4 & 30 & 15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Single element dimensions.  
Figure 1: The single antenna simulated design: (**a**) top view and (**b**) back view, fabricated prototype element, (**c**) top view and (**d**) back view, and (**e**) input impedance over frequency.