# Cascaded Frequency Selective Surfaces with Matryoshka Geometry for Ultra-Wideband Bandwidth
## 5 Conclusions  
The purpose of this paper is to present a cascaded FSS with two layers, one with matryoshka geometry and the other with its inverse matryoshka geometry, to extend the operational bandwidth to 2 GHz, in the range from 1.8 GHz to 3.8 GHz with a gap of 12 mm between layers and 1.2 GHz in the range from 2 GHz to 3.2 GHz with a gap of 4 mm  
Figure 29: Comparison of experimental and simulated frequency responses for cascaded FSS with matryoshka geometry, gap of 12 mm between layers, and incident wave polarizations \(x\) and \(y\). between the layers, making an ultra-wideband possible. This allows for a bandwidth that includes both 2.4 GHz and 3.65 GHz WLAN frequencies, as well as part of the 2 GHz band. The proposed cascaded FSSs were evaluated by simulated and measured results. It was shown that matryoshka geometry has advantages in comparison with other designs. The resonance frequencies were analyzed, revealing that the matryoshka geometry FSS behaved as a band-pass filter while its negative behaved as a band-reject one. Their different frequency responses and how complementary they were allowed for a larger bandwidth with the cascaded FSS layers. Cascaded FSSs with different spacing between the layers were characterized. The simulated frequency responses for each gap followed a pattern that reached a bandwidth of 2 GHz when the spacing was 12 mm or higher. Two square FSSs with an area of 24 mm\({}^{2}\) and 8 \(\times\) 8 unit cells were characterized, and their numerical results were analyzed according to the theoretical equations of the geometries. The cascaded matryoshka geometry showed to have a good coupling between the two layers, with the resonance frequencies complementing each other, making it possible to obtain a bandwidth greater than that of single layers. The results were analyzed for different polarizations as well as different incidence angles regarding the transmitting antenna opening plane. The proposed design showed the stability of the matryoshka geometry and how it was maintained even in a cascaded configuration. By maintaining the bandwidth for an incidence angle exceeding 30\({}^{\circ}\), the geometry proved its potential for applications that require insensibility to different incident angles and polarizations. The design and fabrication of cascaded FSSs allow the analysis of possible advantages and difficulties faced in the fabrication and measurement process of a two-layer FSS. Among these, there is the advantage of being easy to fabricate with the printed pattern applied to copper plates on an FR-4 substrate. To reproduce the spacing between layers in the measurements, simple acrylic frames were used. The use of acrylic is restricted only to the edges where the layers are fixed, while the substrate between the FSS layers is air. The biggest challenge of the experimental measurements is the alignment between the FSS layers. It needs to be as perfect as possible so that the geometries work in a complementary way. When there is an overlap of the metallic surfaces due to misalignment, the experimental results showed discrepancies from the simulated results. Even with these problems, the desired bandwidth was reached. The experimental characterization showed the similarities and differences of individual layers of FSSs and their influence on the offsets and peaks on the cascaded FSS. The performed analysis confirmed that the proposed design allowed the different geometries to complement each other and increase the bandwidth. The matryoshka geometry not only had resonance frequencies below 2 GHz but also a shorter distance between these frequencies. They were also stable across different incidence angles. This allowed the bandwidths of both layers to combine without generating additional peaks in the resulting bandwidth.