# Dual-Band Frequency Selective Surface-Backed Reflectarray for High-Speed Ka-Band Satellites
## 2 Proposed Unit Cell Configurations  
The majority of the Ka-band high-throughput satellites (HTS) operate typically in the frequency range of 27.5-31 GHz for the uplink, whereas the 17.7-21.2 GHz band is used as the downlink. In this work, 20 GHz and 30 GHz are chosen as the design frequencies of the reflectarray with dual-band operation. The periodicity of the unit cells is determined using Equation (1) to avoid grating lobes and to obtain the required phase range [28]. \[D<\lambda/(1+sin\ \theta) \tag{1}\]  
where \(\lambda\) is the wavelength at the operation frequency and \(\theta\) is the angle of the radiated beam. The periodicity of the unit cells for 20 and 30 GHz should be chosen equal. Thus, \(D\) of the unit cells is chosen as 6 mm, which renders orientation of the main beam direction up to \(\theta=42^{\circ}\). Proposed unit cells for the 20 GHz and 30 GHz reflectarray are shown in Figure 1. The star shape of the 30 GHz unit cell given in Figure 1a is constructed by the combination of a square with width \(a\) and its \(45^{\circ}\) rotated version. Rogers 5870 substrate material with a thickness of \(t_{1}=0.79\) mm and \(\varepsilon_{r}=2.33\) is chosen as the substrate material. The conductor of the FSS is etched to the reverse side of the Rogers 5870 printed circuit board. Thus, to create the pattern of the FSS and 30 GHz unit cells, two sides of the same substrate material are used. The unit cell proposed for the 20 GHz reflectarray is given in Figure 1b. It is designed as a derivative of the first iteration of the Minkowski fractal. It is composed of four circles with a diameter of half square width added to the four corners of the square. Rogers 3003 substrate (\(\varepsilon_{r}=3\)) with \(t_{2}=0.76\) mm thickness is chosen as the substrate material of the unit cell. A ring-shaped conductor is used in the unit cell structure of the FSS. The FSS structure consists of a ring with \(w=0.25\) mm width and \(r=2.02\) mm radius. A 1 mm-thick air layer between the two printed circuit boards serves as the substrate of the FSS. The FSS unit cell is designed to pass wave propagation at 20 GHz and stop the 30 GHz band. S-parameters of the FSS unit cell are shown in Figure 2. The top view of the FSS is given as an inset in figure. The scattering parameters show that the FSS unit cell works as a bandpass filter up to 24 GHz and shows bandstop filter characteristics afterwards (\(-3\) dB cutoff is considered). The dual-band reflectarray with FSS should be constructed by placing the higher frequency reflectarray to the top and lower frequency reflectarray to the bottom [29]. The FSS surface is positioned between two substrates. In our case, the reflective surface for 30 GHz will be at the top layer, while the reflective surface for 20 GHz will be at the bottom layer. The FSS structure between them will behave like a ground plane at 30 GHz and as a passband filter at 20 GHz. Figure 1: Proposed unit cells of the reflectarrays: (**a**) 30 GHz; (**b**) 20 GHz. Figure 2: Scattering parameters of the FSS unit cell. The distribution of the phases of the unit cells on the reflective surface determines the characteristic of the radiated beam. Thus, it is critical to obtain the required phase values accurately for reflectarray design. In order to obtain the phase range, \(a\) and \(b\) parameters of the unit cells are varied at the corresponding frequencies. Since FSS acts as the ground plane for the 30 GHz reflectarray, it is also included in the unit cell simulations. Similarly, FSS with air substrate and 30 GHz reflectarray unit cell are included to the unit cell simulations of the 20 GHz reflectarray. The phase variation in the multilayer structure is given in Figure 3 as the function of \(a\) parameter. An approximately 290\({}^{\circ}\) phase range is obtained at 30 GHz by the star shaped unit cell. This range reduces to 220\({}^{\circ}\) when the FSS unit cell is included.