# Cascaded Frequency Selective Surfaces with Matryoshka Geometry for Ultra-Wideband Bandwidth
## 4 Results Analysis
### Comparisons of Experimental and Simulated Results  
It was expected that the experimental results would not be identical to the simulated ones due to many factors. There could be external factors in the experiment, such as the environment or the manufacturing process. There were also ideal factors in the simulation, such as the infinite plane and an exact source wave. Simulations do not consider that even a directive antenna, like the horn antenna used in setup, can suffer diffractions, reflections, and other effects when the signal wave interacts with the edges of objects like the measurement window or the surrounding environment. In the analysis of the measured and simulated results, Figure 25 presents the frequency results of the simulated and measured \(x\) and \(y\) polarizations of the band-reject FSS with matryoshka geometry, and Figure 26 shows the frequency results of the band-pass FSS with the inverse matryoshka geometry with the simulated and measured \(x\) and \(y\) polarizations. By analyzing Figure 25, it was possible to see the similarities and discrepancies between the measured and simulated results of the reject-band FSS. The first simulated resonance frequency is at 1.75 GHz for both polarizations, and the measurements are at 1.78 and 1.77 GHz for the \(x\) and \(y\) polarizations, respectively. Comparing these values, there is a displacement of 0.03 GHz from the simulations to the measurements. When the bandwidth of the first resonance was analyzed, the simulated frequency results presented a bandwidth from 1.60 GHz to 1.95 GHz, while the bandwidth in measured frequency results ranged from 1.64 GHz to 1.99 GHz. These bandwidths from simulated and measured results together presented an overlap of more than 77%. The highest discrepancy in Figure 25 was the bandwidth around the second resonance frequency. The simulation presented a resonance frequency at 3.8 GHz, and both \(x\) and \(y\) polarizations in the measured results showed the second resonance frequency at 3.6 GHz. Those frequencies presented a discrepancy of 0.2 GHz as well as an overlap of 60% between the bandwidths around them. Such discrepancies can occur due to expected differences between the simulations and measurements, such as the FSS not being infinite or the plane wave not being ideal. In Figure 26, we observe some discrepancies when comparing simulated and measured results. The first peak, around 1.75 GHz, remained the same for both the measured and simulated results, but the second resonance frequency was shifted by 0.05 GHz, with the simulation frequency being 3.8 GHz and the measurement frequency being 3.75 GHz. The bandwidth below \(-\)10 dB in the frequency results in Figure 26 showed an interesting behavior at both resonance frequencies. The measured bandwidths started before and  
Figure 26: Comparison of experimental and simulated frequency responses for single layer FSS with matryoshka geometry, band-pass mode, and incident wave polarizations \(x\) and \(y\). ended after the ones in the simulated result, thus presenting a larger range than expected from simulations. The bandwidth around the first resonance frequency in the measured results was from 2.0 GHz to 3.5 GHz, while in the simulation, it ranged from 2.3 GHz up to 3.5 GHz, a gain of 0.3 GHz. The bandwidth around the second resonance frequency in the simulation has a section from 4.1 GHz to 4.8 GHz, while the measurement goes from 3.9 GHz to higher than 5 GHz. The comparisons between the measured and simulated results of the band-pass FSS were more in agreement than those of the band-reject FSS, and the additional bandwidth was a distinct influence on the cascaded FSS. Analyzing the frequency responses of a single layer FSS, shown in Figures 25 and 26, it is possible to see that their resonance frequencies are present in the frequency response of the cascaded FSS, as shown in Figures 27-29 for different spacings between the layers, contributing to a wider bandwidth.