# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 3 Results
### Planar Rectangle Spiral Antenna
Each spiral arm was divided into \(B\) parts, where \(B=1\dots\ 360\times t-A\), where \(A\) is the smoothness factor which can affect the number of the wires in the structure and the length of each of them (here its values was assumed to be equal to 14.8), and each part was segmented using \(n\) segments, where \(n=1\dots\ B\) which corresponding its part (Figure 18d). The antenna was excited using different port types located in the antenna gap with a potential difference of 1 V. The discrete port was used in EMPro, while 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. The antenna gain was calculated in the \(E\) and \(H\) planes. The antenna RPs obtained using all codes were compared at the frequencies of 1, 1.5, and 2 GHz in Figures 19-21, respectively. As can be observed, the results for both codes illustrated a good agreement with EMPro ones. Figure 18: Top view of the spiral antenna (**a**), and its constructed grid in Triangle-Grid (**b**) and in Wire-Grid (the red wire is the excitation source) (**c**), and its adaptive segmentation model (**d**). Figure 21: RPs of the spiral antenna at a frequency of 2 GHz in the \(E\) (**a**) and \(H\) (**b**) planes: Triangle-grid (- - -), Wire-grid (- - -) and EMPro (-). Figure 19: RPs of the spiral antenna at a frequency of 1 GHz in the \(E\) (**a**) and \(H\) (**b**) planes: Triangle-grid (- - -), Wire-grid (- - -) and EMPro (-). Figure 14:0 RPs of the spiral antenna at a frequency of 1.5 GHz in the \(E\) (**a**) and \(H\) (**b**) planes: Triangle-grid (- - -), Wire-grid (- - -) and EMPro (-). Table 4 summarizes the maximum gain values of the planar spiral antenna calculated in Wire-Grid and Triangle-Grid, as well as the percentage of their relative difference from EMPro. As can be seen, the maximum difference also does not exceed 6%. Table 5 summarizes the antenna input impedance calculated values, the required memory, the simulation time spent, \(N\) and the cond of the SLAE matrix \(\mathbf{Z}\). Table 6 contains the percentage of the relative difference of the considered values in Figure 14:1 It can be seen that both Wire-Grid and Triangle-Grid give an acceptable antenna input impedance result comparing to EMPro with maximum differences of 16.5%. The basic functions used in this wire-grid model are increased on average by 55 times from the number used in the previous model This is due to the method of adaptive model segmentation applied here, which in turns leads to a remarkable increase in the consumed resources. Moreover, the conditioning number of the SLAE matrix \(\mathbf{Z}\) was increased indicating an inefficient adaptive method applied in segmentation. It is worth noting, however, that the authors could easily change the adaptive method and achieve more accurate results with less computational costs. However, they preferred to keep these results in order to demonstrate the sensitivity of the wire-grid model to segmentation, and to show its dynamic nature as well. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Code** & **Frequency (GHz)** & **RD Impedance (\%)** & **RD Memory (\%)** & **RD Time (\%)** \\ \hline \multirow{3}{*}{Wire-Grid} & 1 & 14.53 & \({}^{*}-160.33\) & 60.04 \\  & 1.5 & \(-5.70\) & \(-160.33\) & 71.90 \\  & 2 & \(-14.46\) & \(-160.33\) & 69.36 \\ \hline \multirow{3}{*}{Triangle-Grid} & 1 & \(-12.92\) & 87.60 & 97.30 \\  & 1.5 & \(-16.58\) & 77.69 & 89.06 \\ \cline{1-1}  & 2 & \(-8.41\) & 55.37 & 74.64 \\ \hline \hline \end{tabular} \({}^{*}\)(\(-\)) indicates by what percent the value is bigger than the reference one (here EMPro).  
\end{table} 
Table 6: The percentage of the relative difference between the considered input impedance values of the planar spiral antenna in Table 5 and EMPro.