# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 3 Results
### Horn Antenna  
The characteristics of a horn antenna from [347] were also calculated using the developed Wire-Grid and Triangle-Grid codes. Here, the obtained results were compared with the measured results of the prototype from the same reference. The geometrical parameters of the antenna structure were as follows: \(ap=80\) mm, \(bp=60\) mm, \(a=23\) mm, \(b=10\) mm, \(ar=23\) mm, \(br=10\) mm, \(l=150\) mm, and \(lr=10\) mm (Figure 30a). The antenna was modeled using Triangle-Grid with \(\lambda/15\) cells per wave-length (Figure 30b). In Wire-Grid, the initial segment length was considered to be as \(\lambda/40\) (Figure 30c). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Code** & **Frequency (GHz)** & **Impedance (Ohm)** & **Memory (GB)** & **Time (ms)** & \(N\) & **Cond (Z)** \\ \hline Wire-Grid & 0.1 & \(192.31-58.89\) & * \(\approx\)0.18 & 91 & 513 & \(2.17\times 10^{6}\) \\ (\(\lambda/20\)) & 0.5 & \(102.02+j33.36\) & \(\approx\)0.59 & 1579 & 2177 & \(5.74\times 10^{5}\) \\  & 1 & \(88.28+56.82\) & \(\approx\)1.19 & 7002 & 4353 & \(1.60\times 10^{5}\) \\ \hline Wire-Grid & 0.1 & \(28.01+j25.59\) & \(\approx\)0.22 & 317 & 897 & \(3.15\times 10^{5}\) \\ (\(\lambda/40\)) & 0.5 & \(90.44+j48.18\) & \(\approx\)1.89 & 8004 & 4353 & \(9.56\times 10^{6}\) \\  & 1 & \(84.62+j71.55\) & \(\approx\)3.91 & 36,214 & 8705 & \(6.43\times 10^{5}\) \\ \hline Triangle-Grid & 0.1 & \(23.72+j22.09\) & \(\approx\)0.11 & 133 & 341 & \(5.26\times 10^{19}\) \\  & 0.5 & \(93.44-j1.58\) & \(\approx\)0.36 & 13,531 & 3897 & \(2.32\times 10^{21}\) \\  & 1 & \(91.50+j16.46\) & \(\approx\)2.77 & 171,449 & 13,199 & \(1.28\times 10^{18}\) \\ \hline Analytically & 0.1 & \(40.40+j28.32\) & - ** & - & - & - \\  & 0.5 & \(101.80-j9.38\) & - & - & - & - \\  & 1 & \(88.64+j16.68\) & - & - & - & - \\ \hline \hline \end{tabular}  
* (\(\approx\)) denotes that the value is approximately equal to these numbers. ** (-) denotes that the data are not available.  
\end{table} 
Table 10: The input impedance values of the biconical antenna, obtained using different codes with the corresponding computational costs and analytically. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Code** & **Frequency (GHz)** & **RD Impedance (\%)** \\ \hline Wire-Grid (\(\lambda/20\)) & 0.1 & * \(-308\) \\ Wire-Grid (\(\lambda/20\)) & 0.5 & * \(-5\) \\  & 1 & \(-16.4\) \\ \hline Wire-Grid (\(\lambda/40\)) & 0.1 & 23.10 \\ Wire-Grid (\(\lambda/40\)) & 0.5 & * \(-0.24\) \\  & 1 & \(-22.85\) \\ \hline \hline \end{tabular}  
* (\(-\)) indicates by what percent the value is bigger than the reference one (here analytical values).  
\end{table} 
Table 11: The percentage of the relative difference between the input impedance absolute values of the biconical antenna calculated numerically and those calculated analytically. When modeling using Wire-Grid, the wide walls of the regular part (the index \(r\) is used to denote it) were divided into SZr parts along the z axis and SX\(r\) parts along the x axis, the narrow sides were SZr and SY\(r\), and the shortened back wall was divided into SXr and SYr, respectively. Here, we used the values of SZ\(r\) = SX\(r\) = 16 and SY\(r\) = 8. To approximate the extended part of the horn (index \(e\) is used to denote it), its wide walls were divided into SZ\(e\) parts on the z axis and SX\(e\) parts along the x axis, and the narrow ones into SY\(e\), parts along the y axis. It is assumed that SY\(e\) = SXe/2 and the values SZe = SXe = 32 and SY\(e\) = 16 were used. The values of the segment length \(Sl\) and the radius of the structure wires \(as\) were determined as \(Sl=\lambda/40\) and \(as=Sl/10\), respectively [347]. The antenna was excited using different port types located in the antenna gap with a potential difference of 1 V. In Triangle-Grid, the port presented in Figure 11 was used. In Wire-Grid a piece of wire was installed at the junction of the regular and irregular parts of the horn between its wide walls with a length of \(b\) and a radius of \(aex=Sl/5\).