# Broadband Microstrip Antenna for 5G Wireless Systems Operating at 28 GHz
## 5 Broadband Microstrip Antenna Designed for Use in 5G Systems  
The design process of a microstrip antenna consists of multiple stages. The main steps of the project process are presented below. The procedure for designing a single-piece rectangular microstrip antenna are the following:  
* Determine operational frequency;
* Determine operational bandwidth;
* Choose a substrate;
* Choose substrate height;
* Determine the dimensions of the patch;
* Determine the power supply;
* Determine the electrical parameters and characteristics of the antenna;
* Optimize the antenna to obtain the best possible parameters in the given frequency range. Before the development of a proper numerical model of the designed antenna could begin, it was necessary to perform preliminary calculations of its geometric parameters. These calculations were done to work out an approximate shape of the antenna, which would ensure that the structure complied with the assumptions adopted for its design. The dimensions of the individual edges of the antenna depend primarily on the resonance frequency, \(f_{r}\), and the relative permittivity, \(\varepsilon_{r}\), of the dielectric layer of the copper laminate, which are the foundation of the new antenna [24]. The antenna is designed to operate in a 5G system, on frequencies ranging from 27.50 GHz to 28.35 GHz (LMDS band) and the center frequency \(f_{r}=28.00\) GHz. Choosing the thickness of the substrate is one of the most important stages in the antenna design process, as the thickness of the substrate directly affects the efficiency and bandwidth of the microstrip antenna. One of the assumptions for this antenna is to obtain the widest bandwidth possible. As the thickness of the substrate increases, the antenna's bandwidth increases, while its efficiency decreases. The upper value of the substrate thickness was determined from the following relationship [14; 15]:  
\[h\leq\frac{0.3c}{2\pi f\sqrt{\varepsilon_{r}}}\leq\frac{0.3\times 3\times 10^{8} }{2\pi\times 28\times 10^{9}\sqrt{2.2}}\leq\frac{90\times 10^{7}}{260.8\times 10^{9}} \leq 3.45\text{ mm}. \tag{1}\]  
Taking into account the result provided above, the RT Duroid 5880 laminate was selected as a substrate, with a thickness of \(h=1.57\) mm, permittivity \(\varepsilon_{r}=2.2\), and tan\(\delta=9.0\times 10^{-4}\). In the next calculation step, the width of the radiating element should be determined from the following relationship [16; 17]:  
\[W=\frac{c}{2f_{r}}\sqrt{\frac{2}{\varepsilon_{r}+1}}=\frac{3\times 10^{8}}{2 \times 28\times 10^{9}}\sqrt{\frac{2}{2.2+1}}=4.17\text{ mm}. \tag{2}\]  
To determine the length of the radiating element, the effective permittivity \(\varepsilon_{reff}\), of the substrate must first be calculated. It is defined by the following relationship [18; 19]:  
\[\varepsilon_{reff}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2 \sqrt{1+12\frac{h}{W}}}=\frac{2.2+1}{2}+\frac{2.2-1}{2\sqrt{1+12\times\frac{1.57}{4.17}}}=1.6+0.21=1.81. \tag{3}\]  
Upon calculating \(\varepsilon_{reff}\), the effective length of the patch Le should be determined from the following relationship [20; 21]:  
\[L_{e}=\frac{c}{2f_{r}\sqrt{\varepsilon_{reff}}}=\frac{3\times 10^{8}}{2\times 2 8\times 10^{9}\sqrt{1.81}}=3.98\text{ mm}. \tag{4}\]  
Then, we calculate by how much the patch should be shortened using the following relationship [22; 25]:  
\[\Delta L=\frac{0.412\cdot h\left(\varepsilon_{reff}+0.3\right)\left(\frac{W}{ h}+0.264\right)}{\left(\varepsilon_{reff}-0.258\right)\left(\frac{W}{h}+0.8 \right)}=\frac{0.412\times 1.57(1.81+0.3)\left(\frac{417}{1.57}+0.264\right)}{(1.81-0. 258)\left(\frac{417}{1.57}+0.8\right)}=0.74\text{ mm}. \tag{5}\]  
The final patch length value is:  
\[L=L_{e}-2\Delta L=3.98-2\times 0.74=2.58\text{ mm}. \tag{6}\]  
Once the size of the radiating element is determined, the size of the reference plane also needs to be determined. The size of the reference plane is assumed to be greater than the radiating element by approximately six thicknesses of the substrate, by both width and length.