## 2 Wideband Antenna Designing  
### Design Methodology  
Figure 1 depicts the structure of the suggested design of an antenna operating over 28 GHz. The antenna is designed over substrate material Roger RT/Duroid 6002 with a loss tangent of 0.0012 and relative permittivity of 2.2. The antenna has an overall size of L \(\times\) W \(\times\) H = 15 mm \(\times\) 10 mm \(\times\) 1.52 mm. The antenna has a simplified structure with a rectangular and circular patch loaded with arm-shaped stubs. These stubs are loaded to the antenna to improve antenna performance in terms of bandwidth and return loss. Moreover, the antenna is designed on the commercially available electromagnetic (EM) software tool high frequency structure simulator (HFSSv9). The optimized value of antenna parameters is given below. W = 10; L = 15; H = 1.52; A = 2; B = 2.58; C = 4; D = 4; E = 1; F\({}_{\rm X}\) = 6; F\({}_{\rm Y}\) = 0.75; and R = 2. All units are in millimeters (mm).  
To obtain the optimized results, few design steps are performed. Initially, an antenna with rectangular stub is design in first step for 28/38 GHz wireless applications. The length and width of the antenna are obtained from the below formula [42; 43]:  
\[{\rm L_{eff}}=\frac{c}{2{\rm F}\sqrt{erff}} \tag{1}\]  
\[\epsilon_{\rm{reff}}= \frac{\varepsilon r+1}{2}+\frac{\varepsilon r-1}{2}\Bigg{[}\frac{ 1}{1+12\ \frac{H}{W}}\Bigg{]} \tag{2}\] \[\Delta{\rm L}=0.412{\rm H}\ \frac{(\varepsilon{\rm{reff}}+0.3)\ \Big{(}\frac{W}{H}+0.264 \Big{)}}{(\varepsilon{\rm{reff}}-0.258\Big{)}\Big{(}\frac{W}{H}+0.8\Big{)}} \tag{3}\]  
The resultant antenna operates at 28 GHz and 37 GHz with a return loss of \(-\)10.25 dB and \(-\)8.5 dB, respectively. After that, in the second step, a circular radiator of radius R = 2 mm is loaded to the antenna in order to improve the return loss, which will help in the enhancement of bandwidth. The antenna obtained from this step offers multiple resonances at 25 GHz, 29 GHz, 38 GHz, and 42 GHz with return losses of \(-\)12.5 dB, \(-\)15 dB, \(-\)16 dB, and \(-\)14.35 dB, respectively. In the third stage, an arm-shaped stub is added as given in the figure. This step improves the return loss of the antenna, which leads the antenna to operate over a wideband. In the final stage, the length of the arm is improved to get further improvement in the bandwidth of the antenna. The improvement is possible until the length of 4 mm. The antenna obtained from the final stage offers ultra-wideband from 26.5 to 43.7 GHz, as given in Figure 2.  
Figure 1: Geometrical configuration of proposed a dual-band millimeter wave antenna: (**a**) top view, (**b**) back view, and (**c**) side view.  
Figure 2: (**a**) Designing steps; (**b**) corresponding results.  
Parametric analysis of key parameters is performed to get an optimized value. For the proposed antenna, the parametric analysis radius of the circular patch and length of the lower stub is analyzed. At an optimal value of R = 1.8 mm, the antenna offers the ultra-wideband of 26.5-43.7 GHz with a minimum value of return loss around \(-\)38 dB. If the value is increased to 2.0 mm, the antenna stops operating over wideband and only offers dual band with a minimum return loss of \(-\)18 dB and \(-\)11 dB at a resonant frequency of 29.5 GHz and 38.5 GHz, respectively. If the value is decreased to 1.6 mm, again the return loss and bandwidth is compromised, as given in Figure 3a. Another key parameter is the length of lower stub D. At optimal value of D = 4 mm, the antenna offers the required operational band. If the value is fixed at D = 6 mm, the antenna offers a 30-37 GHz bandwidth with a return loss of around \(-\)15 dB. If the value is fixed at D = 2 mm, the antenna offers 31.5-42.5 GHz with a return loss of around \(-\)20 dB, as given in Figure 3b.