# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 3 Results
### Planar Rectangle Spiral Antenna  
The characteristics of a traditional planar rectangular spiral antenna were calculated using the developed Wire-Grid and Triangle-Grid codes. Here, the obtained results were compared with the results of EMPro software system that uses FDTD method [346]. The geometrical parameters of the antenna structure were as follows: the turns number \(t=1\dots\) 4, the metalized part width \(W=3.19\) mm, the outer square side length \(L=104.9\) mm, and the inner gap length \(L_{i}=1.59\) mm (Figure 14a). The antenna was modeled using Triangle-Grid and EMPro with \(\lambda/40\) cells per wavelength (Figure 14b), as well as using Wire-Grid (Figure 14c) but with adaptive segmentation and wires with radius of \(W/2\). Every Wire-Grid model turn was divided into \(m\) parts, where \(m\):\(1\dots\) 4, and each part was segmented using \(m\times n\times t\) segments, where \(n=5\), 4, 3 at frequencies of \(1\), \(3\), \(5\) GHz, respectively (Figure 14d). 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 \(1\), \(3\), \(5\) GHz in Figures 15-17, respectively. As can be seen, Wire-Grid illustrates closer RPs (antenna gain) to EMPro ones than Triangle-Grid. However, both codes showed a good agreement. Figure 14: Top view of the planar rectangular spiral antenna (**a**), its constructed meshed model in Triangle-Grid (**b**), the model in Wire-Grid (the red wire is the excitation source) (**c**), and its adaptive segmentation model (**d**). Figure 16: RPs of the planar rectangle spiral antenna at a frequency of 3 GHz in the \(E\) (**a**) and \(H\) (**b**) planes: Triangle-grid (**-** -), Wire-grid (**-** -) and EMPro (**—**). Figure 17: RPs of the planar rectangle spiral antenna at a frequency of 5 GHz in the \(E\) (**a**)and \(H\) (**b**) planes: Triangle-grid (**-** -), Wire-grid (**-** -) and EMPro (**—**). Figure 15: RPs of the planar rectangle spiral antenna at a frequency of 1 GHz in the \(E\) (**a**) and \(H\) (**b**) planes: Triangle-grid (**-** -), Wire-grid (**-** -) and EMPro (**—**). Table 1 summarizes the maximum gain values for the planar rectangle spiral antenna calculated in Wire-Grid and Triangle-Grid and their relative difference (RD) percentage from EMPro. As can be seen, the maximum difference does not exceed 6%. Table 2 summarizes the antenna input impedance calculated values, the required memory, the simulation time spent, the total number of basic functions (\(N\)), and the conditioning number (cond) of the SLAE matrix \(\mathbf{Z}\). Table 3 contains the relative difference percentage of the considered values in Table 2. It can be seen that Triangle-Grid gives more accurate results than Wire-grid comparing to EMPro regarding to the calculations of input impedance with maximum difference of 24%. However, regarding to the resource consumption, Wire-Grid surpasses it  
with the results of EMPro with FDTD. The geometrical parameters of the antenna structure were as follows: the turns number \(t=3.5\), the metalized part width \(W_{a}=5.735\) mm, the distance between them \(Sa=5.745\) mm, the outer diameter \(D_{o}=214.7\) mm, and the inner diameter \(D_{i}=13.63\) mm (Figure 18a). The antenna was modeled using Triangle-Grid and EMPro with \(\lambda/40\) cells per wavelength (Figure 18b), as well as using Wire-Grid (Figure 18c) but with adaptive segmentation and wires with radius of \(W_{a}/2\).