# Design and Analysis of Dual-Band High-Gain THz Antenna Array for THz Space Applications
## 2 Proposed Antenna Structure
THz antenna with elliptical metallic addition of size 30 \(\upmu\)m \(\times\) 131.5 \(\upmu\)m \(\times\) 1 \(\upmu\)m. While the Step 4 antenna is shown in Figure 2d, this is the proposed and reference novel shape dual-band THz antenna supported by three elliptical shape metallic additions of size 30 \(\upmu\)m \(\times\) 131.5 \(\upmu\)m \(\times\) 1 \(\upmu\)m, and each of them is separated by an angle of 40\({}^{\circ}\) from each other. Later, it will be observed from the results in the simulations section that the Step 4 antenna provides better performance than the remaining three models; the parameters of the THz antenna are calculated by utilizing a very famous planar antenna theory [38] for the resonance frequency (\(f_{r}\)) in the unit of Terahertz (THz), a relative permittivity (\(e_{r}\)), and the height of the substrate (\(h_{s}\)) in units of micrometers (\(\upmu\)m). The effective length (\(L_{p}\)) and width (\(W_{p}\)) are calculated by using the following equation [39]:  
\[W_{p}=L_{p}=2P\bigg{[}1+\frac{2h_{s}}{\pi P}\bigg{(}\ln\frac{P}{2h_{s}}+1.7726 \bigg{)}\bigg{]}^{\frac{1}{2}} \tag{2}\]  
where radius (\(P\)) is representing the actual radius of microstrip circular antenna, it is calculated by using the following equations [39]:  
\[P=\frac{J}{[1+\frac{2h_{s}}{J\pi e_{r}}+\ln(\frac{J\pi}{2h_{s}})+1.772]^{\frac {1}{2}}} \tag{3}\]  
where the magnitude of \(J\) is determined by using the following equation:  
\[J=\frac{8.8\times 10^{9}}{f_{r}(e_{r})^{\frac{1}{2}}} \tag{4}\]  
The effective area of the antenna (\(A_{e}\)) is calculated by using the following equation:  
\[A_{e}=\frac{\pi W_{p}L_{p}}{4} \tag{5}\]  
The corporate feed line network is adopted for THz antenna array due to structure simplicity. However, unwanted radiations are created due to feed-resistive loss, which results in the form of side lobe radiations. The corporate feed line is designed for two purposes: to control the directivity and power radiation of antenna by using the equal power distribution among the radiating elements, and to avoid unwanted radiations by matching the driven elements input resistance with a wave guide port input impedance of 50 \(\Omega\) value [28]. The impedance of the feed line is controlled by a feed line width \(W_{f}\), where \(W_{f}\) is given by using the formula [30]. \[W_{f}=e^{\big{[}\frac{Z_{e}}{87\sqrt{4}r+124}\big{]}}\bigg{[}\frac{0.8}{5.98h_ {s}}\bigg{]} \tag{6}\]  
where, \(Z_{e}\), \(h_{s}\), and \(e_{r}\) denote the impedance of the feed line, the height of the substrate, and the relative dielectric constant of the substrate material, respectively. The structure of the proposed novel shape antenna is displayed below in Figure 1. While, the dimensions of the proposed novel shape antenna are listed in the Table 2.  
The step by step development of the proposed dual-band THz antenna is designed as mentioned in Figure 2; the group of these shapes is responding in the form of different return losses, as shown in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values (\(\mathbf{\mu}\))** & **Parameters** & **Values (\(\mathbf{\mu}\))** \\ \hline \(W_{p}\) & 263.5704698 & \(L_{p}\) & 263.6738427 \\ \(W_{e}\) & 2920 & \(L_{g}\) & 1055 \\ \(W_{f1}\) & 45 & \(L_{f1}\) & 132 \\ \(W_{f2}\) & 1594 & \(L_{f2}^{\prime}\) & 132 \\ \(W_{f3}\) & 25 & \(L_{f3}\) & 132 \\ \(W_{f4}\) & 797 & \(L_{f4}\) & 132 \\ \(W_{f5}\) & 15.3020458 & \(L_{f5}\) & 132 \\ \(W_{f6}\) & 1558 & \(\theta\) & 40\({}^{\circ}\) \\ \(C\) & 5 & \(d\) & 533 \\ \(W_{f}\) & 20 & \(h_{s}\) & 10 \\ \(h_{g}\) & 1 & \(h_{p}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of parameters used in THz antenna array designing. Figure 1: The proposed novel shape dual-band THz antenna: (**a**) Front view (**b**) Side view. Figure 2: The development process of dual-band THz antenna: (**a**) Step 1; (**b**) Step 2; (**c**) Step 3; and (**d**) Step 4.