# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 3 Results
### Planar Rounded Bow-tie Antenna  
The characteristics of a planar rounded bow-tie antenna were also calculated using the developed Wire-Grid and Triangle-Grid codes. Here, the obtained results were also compared with the results of EMPro with FDTD. The geometrical parameters of the antenna structure were as follows: the arm length \(l=146.2\) mm, the feed gap width \(S=4.997\) mm, the feed line width \(w=4.997\) mm, and the flare angle \(f=87^{\circ}\) (Figure 22a). The antenna was modeled using Triangle-Grid and EMPro with \(\lambda/40\) cells per wave-length (Figure 22b), as well as using Wire-Grid (Figure 22c). Each triangle edge in the achieved wire-grid model at the maximum frequency using the import function was considered to be as a wire with a radius of 1 mm and one segment. 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 with a radius of 0.5 mm 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 0.5, 1, and 1.5 GHz in Figures 23-25, respectively. As it can be seen, Wire-Grid illustrates closer RPs to EMPro ones than Triangle-Grid. However, the Triangle-Grid results are  
Table 7 summarizes the maximum gain values of the planar bow-tie 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 achieved 8% in Wire-Grid while in Triangle-Grid it reached 15%. Table 8 summarizes the antenna input impedance calculated values, the required memory, the simulation time spent, as well as \(N\) and the cond of the SLAE matrix Z. Table 9 contains the percentage of the relative difference between the values considered in Table 8 using the Wire-Grid and Triangle-Grid codes and those obtained using EMPro. It can be seen that, comparing to EMPro, Wire-Grid gives more accurate impedance results than Triangle-Grid. Even though, Triangle-Grid results are also acceptable with a maximum difference of 7%. Both codes consumed less time than EMPro to calculate the antenna characteristics, however, they required more memory than EMPro to store the necessary matrixes, especially in Wire-Grid. These results confirm that using the developed import function in Wire-Grid is very helpful and timesaving when modeling complex structures, since it does not require manual code construction of the antenna structure, but at the expense of increasing the unnecessary grid wire number. These results also prove that the wire-grid model, as an approximated model of the original structure, can efficiently replace it in the modeling process with a relatively small number of basic functions.  
Figure 24: RPs of the planar bow-tie antenna at a frequency of 1 GHz in the \(E\) (**a**) and \(H\) (**b**) planes: Triangle-grid (**- - -**), Wire-grid (**- -** -**) and EMPro (**—**).  
Figure 25: RPs of the planar bow-tie antenna at a frequency of 1.5 GHz in the \(E\) (**a**) and \(H\) (**b**) planes: Triangle-grid (**- -** -**), Wire-grid (**- -** -**) and EMPro (**—**).