# Cascaded Frequency Selective Surfaces with Matryoshka Geometry for Ultra-Wideband Bandwidth
## 4 Results Analysis
### Single-Layer FSS
The frequency response that presents the maximum resonance frequency displacement was obtained for an incidence angle of 45\({}^{\circ}\) for \(y\) polarization, in the green trace of Figure 12:2 Despite the first and second resonant frequencies being 1.74 GHz and 3.62 GHz, both close the frequency response with an inclination angle equal to 0\({}^{\circ}\) with 1.8 GHz and 3.6 GHz, the lower frequencies present different behavior regarding the other traces presented in Figure 16, showing a distortion in the bandwidth below \(-\)10 dB ranging from 1.2 GHz to 2.2 GHz. Comparing these results, we observe a difference smaller than 0.02 for both inclinations of 15\({}^{\circ}\) and 30\({}^{\circ}\) and a higher 0.06 GHz difference when the inclination is at 45\({}^{\circ}\). Also, except for the inclination of 45\({}^{\circ}\), all others have a range of 1.63 GHz to 2.0 GHz below \(-\)10 dB. Those resonance frequencies and bandwidths are considered influences on the FSS in cascade frequencies together with the other FSS resonance frequencies. The experimental frequency responses of the negative matryoshka geometry FSS, acting as a band-pass filter, are shown in Figures 17 and 18. Figure 12:3 Experimental frequency response of the FSS with band-reject matryoshka geometry for incident vertical polarization. Figure 12:4 Experimental frequency response of the FSS with band-reject matryoshka geometry for incident horizontal polarization. The frequency responses of the FSS with negative matryoshka geometry were more distinct in relation to the simulated results of the resonance frequencies for the \(y\) polarization of the transmitting signal, as shown in Figure 12:5 A resonance frequency around 1.2 GHz was present, similar to the \(x\) polarization at 45\({}^{\circ}\) of the matryoshka geometry, seen in the green trace of Figure 12:6 This disparity may be caused by the horn antenna's performance for signals with frequencies near the edge of its operating range. The resonance frequencies of the FSS with negative matryoshka geometry for \(x\) polarization on the incidence angle \(\varphi\) equal to 0\({}^{\circ}\), as shown in the black trace of Figure 18, were 2.6 GHz and 4.3 GHz, at which the transmission coefficient attained the lowest value. For \(y\) polarization on \(\varphi\) equal to 0\({}^{\circ}\), as shown in the black trace of Figure 18, these resonance frequencies were 2.8 GHz and 4.4 GHz. For both polarizations, the FSS behavior remained as a band-pass in the range from 3.35 GHz to 4.15 GHz around the 3.7 GHz frequency. When the incidence angle, \(\varphi\), of the measurement window was considered higher than 0\({}^{\circ}\), the first resonance frequency of the FSS remained stable for both horizontal and vertical polarizations, with the largest shifts of 0.06 GHz at 15\({}^{\circ}\) for \(x\) polarization, as shown in the red trace of Figure 12:7 When analyzing the second resonance frequency, the higher  
Figure 12:8 Experimental frequency response of the FSS with band-pass matryoshka geometry for incident horizontal \(x\) polarization. Figure 12:9 Experimental frequency response of the FSS with band-pass matryoshka geometry for incident wave with \(y\) polarization and different values for the incidence angle. shift for the \(x\) polarization was 0.2 GHz with the incidence angle \(\varphi\) equal to 45\({}^{\circ}\), as shown in the green trace of Figure 17, and 0.3 GHz for the \(y\) polarization, the same incidence angle, shown in the green trace of Figure 11.0 Comparing the range below \(-10\) dB, once again all the other inclinations except for 45\({}^{\circ}\) share a range of 2.0 GHz to 3.3 GHz