# A Wideband Reflectarray Antenna for Satellite Application with Low Cross-Polarization
## 2 Unit Cell Structure and Characterization  
Figure 1 illustrates the configuration of the proposed unit cell. A spider-shaped structure is printed on the top layer of substrate I (Taconic RF 35 of thickness = 0.76 mm, \(\epsilon_{r}\) = 3.5, tand = 0.0018), which is composed of a dipole and three iterations of the pairs of circular arcs, and the middle layer is printed on the bottom layer of substrate I that comprises a circular ring along with a pair of concave arms. The middle layer and ground are separated by substrate II (Taconic RF 35 of thickness = 1.52 mm, \(\epsilon_{r}\) = 3.5, tand = 0.0018). Both the substrates are combined through an adhesive layer of thickness 0.09 mm and permittivity 4.4. The unit cell has a periodicity of 8 mm (0.31\(\lambda_{0}\)) in both the x- and y-directions, where \(\lambda_{0}\) is the free space wavelength at 11.725 GHz. To extract the phase reflection characteristics of the unit cell, an infinite-array approach is performed in ANSYS HFSS. The periodic boundary conditions on the side walls are master-slave, and a Floquet port is used for excitation [23]. The magnitude and phase reflection of the unit cell is illustrated in Figure 2. Under normal incidence, the unit cell is simulated and optimized at 11.725 GHz to achieve linear phase variations with a sufficient phase range over 800\({}^{\circ}\). The magnitude of the maximum reflection coefficient in the bandwidth is \(-0.19\) dB. The step-by-step evaluation of the unit cell is given in Figure 3. It should be noted that the middle layer is the same for all cases, as given in Figure 1b. In the first case(i), the reflection phase variation of \(500^{\circ}\) is achieved, using the dipole on the top layer. In the second case (ii) (dipole with first iteration (Itr1)), a reflection phase variation of nearly \(800^{\circ}\) is obtained, but the slope is dramatically changing. The slope gets better until D = 7 mm in the third case (iii) (dipole with Itr1 and Itr2) covering almost \(800^{\circ}\). Figure 2: Floquet port simulation of the unit cell at 11.725 GHz: (**a**) Magnitude of the reflection coefficient. (**b**) Phase of the reflection coefficient. Furthermore, checking the unit cell performance over the bandwidth, the normalized reflection phase curves for different frequencies are depicted in Figure 4. The phase curves are linear and insensitive to the frequency variation when D varies from 4.2 mm to 7 mm, which anticipates the broadband behavior of the unit cell. The effect of the various incident wave angles on the reflected phase performance is given in Figure 5, which shows a negligible phase variation with the angle of incidence. It is important to show the current distribution on the unit cell as it accounts for the low x-pol level. Figure 6a,b shows the current distribution on the top and middle layer of the unit cell at 11.725 GHz for the case when the dipole and iterations are not shorted with each other. The top-layer currents on the first and third iterations are symmetrical, which results in a complete single polarized net current. However, the dipole and second iteration carry asymmetrical currents that cause an increase in the x-pol level. Similarly, the currents on the concave arms in the middle layer are mirror images of each other, whereas the circular ring has a net counterclockwise current. In the figure, \(I_{y}\) and \(I_{x}\) represent the desired co-pol and x-pol currents on the unit cell. To avoid the x-pol current, the dipoles and iterations are shorted with each other, as shown in the proposed design. The current distributions are shown in Figure 6c,d on the top and middle layer of the unit cell, respectively. The net current on the top and middle layers exist only along the length of the dipole, whereas the components of all the currents that are orthogonal to the length of the dipole cancel each other out. Therefore, good performance can be anticipated in terms of the x-pol level. Figure 4: Normalized reflection phase curves at different frequencies over the bandwidth.