# Cascaded Frequency Selective Surfaces with Matryoshka Geometry for Ultra-Wideband Bandwidth
## 1 Introduction
### Review  
FSSs are two-dimensional periodic arrays of electric-metallic elements that present behavior similar to that of electromagnetic filters. One of their possible configurations is presented in Figure 1 for an example of matryoshka geometry. These structures are designed for the purpose of reflecting or transmitting electromagnetic waves in different frequency bands. Such characteristics can be observed according to the type of element used in the arrangement, whether it is a patch or opening type, which directly influences the frequency response of the FSS, which may have band-reject or band-pass characteristics, respectively. In addition to the type of element, the geometry, the periodicity of the arrangement, the number and thickness of layers, the angle of incidence of the plane wave, and the dielectric on which the FSS is printed are factors that affect the performance and frequency response of an FSS [13,14]. Although the simple single-layer FSS is easy to fabricate, it is difficult to improve the bandwidth. This kind of FSS has a limitation that, in recent years, with the development of antennas with larger bandwidth, is becoming more and more cumbersome [15]. One of the solutions for this limitation is the design of FSSs with multiple layers, creating an optimized filter and a multiband performance on the frequency response, as will be seen in the examples ahead. Research on microstrips includes the development of new and different geometries, as well as the addition of methods to produce different results that may optimize the application of antenna electromagnetic waves. According to some studies [1,2,5,14,15], FSS structures can be represented by an equivalent circuit, considering the transverse electric mode, TE, and transverse magnetic mode, TM, incidence on conductive strips. The equivalent circuits have a formula for the number of inductors and capacitors as well as their positions in series or parallel for each geometry and can be seen as a model of what kind of filter they represent in the frequency response. For example, a square ring geometry's equivalent circuit is one inductor and one capacitor in series. The design of geometries, from the basic solid squares and circle rings to the fractals, has been a topic of research in FSS in many papers over the last few years [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]. The design in [16] presents four different stages of two distinct fractal geometries: one is the traditional Sierpinski fractal, and the other is an improved version. There is also an analysis of the FSS frequency response implemented with each stage for both fractals, showing their resonance frequency and bandwidth. Additionally, [PERSON] et al. [16] present an analysis of the measured frequency response of the FSS with the improved fractal geometry for different angles of incidence to demonstrate the effect of the transverse electric (TE) polarization and transverse metallic (TM) polarization. The paper [16] also presents a comparison of both geometries in the fourth stage. The improved design of the Sierpinski fractal is a good example of a geometry with stability to the incidence angle of polarization and bandwidths of 910 MHz and 1630 MHz at resonant frequencies 2.4 GHz and 5.45 GHz. In the present paper, a cascaded FSS with matryoshka geometry presents the advantage of reaching a larger bandwidth, around 2.4 GHz. This bandwidth includes frequencies from 1.8 GHz to 3.8 GHz, with applications for the 2.0 GHz band, the 5G in 3.5 GHz, and the wireless local-area network (WLAN) frequency range, as proposed for shielding in [16]. Figure 1: Example of frequency selective surface. A single square ring geometry on multiple layers is proposed in [17], using a total of four layers in their cascaded FSS to provide an absorption on a bandwidth of more than 3 GHz, from 2.4 GHz to 6.13 GHz. The FSSs are designed with a simple square ring geometry and the same FR-4 in each layer.