# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 3 Results
### Biconical Antenna  
The characteristics of a biconical antenna from [347] were also calculated using the developed Wire-Grid and Triangle-Grid codes. Here, the obtained results were also compared with the results obtained analytically from [348; 349]. The geometrical parameters of the antenna structure were as follows: \(g=20\) mm, \(a=508\) mm, and \(\Theta 1=\Theta 2=53.1\) (Figure 26a). The antenna was modeled using Triangle-Grid with \(\lambda/20\) cells per wave-length (Figure 26b). In Wire-Grid, the segment length was considered to be as \(\lambda/20\) and then \(\lambda/40\) (Figure 26c). Only the radial grid elements were used in the wire-grid model. The concentric grid elements were not used here because the amplitudes of the distributed currents among them are very small and their contribution to the radiated electric field is negligible. The values of the segment length \(S_{l}\) and the radius of the structure wires \(a_{s}\) were determined as \(S_{l}=\lambda/20\) and \(a_{s}=S_{l}/10\), 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, we used the port presented in Figure 11. In Wire-Grid a piece of wire was used to fill in the gap with a radius of \(a_{\text{gap}}=S_{l}/5\). The normalized electric \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Code** & **Value** & **0.5 GHz** & **1 GHz** & \multicolumn{2}{c}{**1.5 GHz**} \\ \hline \multirow{2}{*}{Wire-Grid} & \multirow{2}{*}{Maximum gain} & \multirow{2}{*}{1.72} & \multirow{2}{*}{2.47} & \(E\) & \(H\) \\ \cline{3-5}  & & & & 1.56 & 1.5 \\ \hline Triangle-Grid & Maximum gain & 1.7 & 2.15 & 1.71 & 1.49 \\ \hline EMPro & Maximum gain & 1.76 & 2.53 & 1.65 & 1.39 \\ \hline Wire-Grid & RD & 2\% & 2\% & 5\% & \({}^{*}-8\%\) \\ \hline Triangle-Grid & RD & 3\% & 15\% & \(-4\%\) & \(-7\%\) \\ \hline \hline \end{tabular} \({}^{*}(-)\) indicates by what percent the value is bigger than the reference one (here EMPro).  
\end{table} 
Table 7: The maximum gain values of the planar bow-tie antenna and the percentage of their relative difference from EMPro. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Code** & **Frequency (GHz)** & **Impedance (Ohm)** & **Memory (GB)** & **Time (ms)** & \(N\) & **Cond (Z)** \\ \hline \multirow{3}{*}{Wire-Grid} & 0.5 & 127.4 + j120.1 & \({}^{*}\approx\)1.47 & 10,723 & 5427 & 1.21 \(\times\) 10\({}^{9}\) \\  & 1 & 228.5 \(-\) 52.5 & \(\approx\)1.47 & 10,824 & 5427 & 2.43 \(\times\) 10\({}^{8}\) \\  & 1.5 & 158.1 + j54.8 & \(\approx\)1.47 & 10,970 & 5427 & 8.37 \(\times\) 10\({}^{7}\) \\ \hline \multirow{3}{*}{Triangle-Grid} & 0.5 & 131.3 + j120.8 & \(\approx\)0.12 & 473 & 671 & 2.56 \(\times\) 10\({}^{5}\) \\  & 1 & 229.0 \(-\) 71.4 & \(\approx\)0.21 & 5699 & 2489 & 2.08 \(\times\) 10\({}^{5}\) \\  & 1.5 & 173.5 + j38.8 & \(\approx\)0.54 & 24,039 & 5197 & 3.97 \(\times\) 10\({}^{6}\) \\ \hline \multirow{3}{*}{EMPro} & 0.5 & 127.5 + j122.1 & \(\approx\)0.08 & 12,000 & 94,068 & -** \\  & 1 & 214.7 \(-\) 71.9 & \(\approx\)0.21 & 34,000 & 224,640 & - \\ \cline{1-1}  & 1.5 & 160.4 + j43.6 & \(\approx\)0.30 & 53,000 & 366,336 & - \\ \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 8: The input impedance values of the planar bow-tie antenna, obtained using different codes with the corresponding computational costs.