# Cascaded Frequency Selective Surfaces with Matryoshka Geometry for Ultra-Wideband Bandwidth
## 4 Results Analysis
### Cascaded FSS
By analyzing the frequency responses in terms of \(|S(2,1)|\) for the wavefront incidence angle \(\varphi\) equal to \(15^{\circ}\), corresponding to the blue trace in Figures 23 and 24, one can see that the higher deviation to the black trace, corresponding to the incidence angle equal to \(0^{\circ}\), occurs in the range from 2 GHz to 3.4 GHz. For both polarizations, the frequency responses present a similar bandwidth, below \(-10\) dB, for an incidence angle equal to \(0^{\circ}\). The same can be said for the incidence angle equal to \(30^{\circ}\), corresponding to blue curves in Figures 23 and 24, with a slightly larger deviation but still maintaining a similar bandwidth for the incidence angle equal to \(0^{\circ}\). For an incidence angle equal to \(45^{\circ}\), shown in red traces of Figures 23 and 24, there is a noticeable difference in the bandwidths observed in the frequency responses for polarizations \(x\) and \(y\), regarding the frequency response obtained for an incidence angle equal to \(0^{\circ}\). For \(x\) polarization, the bandwidth changes from the range 2\(\sim\)3.2 GHz, for an incidence angle equal to \(0^{\circ}\) and gap of 4 mm between the FSS layers, to the range 2\(\sim\)3.7 GHz and an incidence angle equal to \(45^{\circ}\). For \(y\) polarization, the bandwidth changes from the range 1.78-3.82 GHz for an incidence angle equal to \(0^{\circ}\) to the range 2\(\sim\)5 GHz for an incidence angle equal to \(45^{\circ}\). Figure 23: Experimental frequency response of a cascaded matryoshka FSS with spacing between the layers equal to 4 mm and different values of the angle of incidence \(\varphi\). Figure 22: Experimental frequency response of a cascaded matryoshka geometry for different values of spacing between the layers and \(y\) polarization for the incident wave. Plotting the samples of frequency response obtained by simulation and experimental measurement of each single layer of the FSS for an incidence angle equal to \(0^{\circ}\), one obtains the curves shown in Figures 25 and 26. As expected, the simulated results are not identical to the experimental ones due to external factors such as environmental characteristics and non-ideal conditions of FSS manufacturing on the experimental side. On the other hand, ideal considerations, like infinite plane on the simulation side, are also taken into account. It is possible to reduce the influence of such factors by considering a reference measurement campaign performed on the setup. The biggest difference was the patterned decay of the range on the border between 1.8 GHz to 2 GHz. Although the behavior in experimental frequency response was not as variable as the simulation, the measured results still had visible differences for each spacing and kept their similarities with what was expected in the simulation. Figure 24: Experimental frequency response of a cascaded matryoshka FSS, spacing between the layers equal to 12 mm, \(y\) polarization for incident wave, and different values of the incidence angle. Figure 19:0 Comparison of experimental and simulated frequency responses for single layer FSS with matryoshka geometry, band-reject mode, and incident wave polarizations \(x\) and \(y\).