## 4 Parametric Analysis  
Parametric analysis is conducted to evaluate the performance of the dual-band-reject FSS based on the geometrical parameters, including permittivity, the loss tangent, the substrate thickness, and the inter-element spacing. Figure 7a reveals the shielding characteristics of the presented FSS structure as a function of the dielectric constant of the substrate. It is observed from the figure that the rejection bands are shifted downwards with increments in the dielectric constant. These variations can be predicted by the relationship between the electrical length of the resonating element and the permittivity of the employed dielectric given by Equation (10). \[l\ \propto\ \frac{1}{\sqrt{\varepsilon_{eff}}}, \tag{10}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & & & & \\ \hline L\({}_{1}\) & 1.31 nH & L\({}_{2}\) & 0.52 nH & L\({}_{3}\) & 0.40 nH & - & - \\ C\({}_{1}\) & 1.13 pF & C\({}_{2}\) & 0.16 pF & C\({}_{3}\) & 0.18 pF & C\({}_{4}\) & 0.16 pF \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimized lumped parameters. Figure 6: (**a**) Lumped element formation. (**b**) Equivalent lumped circuit model (ECM) of the FSS shield. (**c**) ADS simulations performed to obtain an optimized response. (**d**) Comparison of the ECM and full-wave simulations. It is noticed that the attenuation level remains almost the same for both the rejection bands for various values of the dielectric constant. However, the bandwidth varies within the acceptable limits for the FSS design with respect to permittivity variations. Figure 7b shows the behavior of the FSS as a function of the loss tangent of the substrate used to design the FSS structure. The shielding effectiveness of 48 dB and 45 dB at the X- and Ku-bands is observed for the proposed design when tan\(\delta\) = 0.0009. It is noticed from the figure that the SE decays nearly exponentially as the tan\(\delta\) varies from 0 to 1. Figure 7c shows the impact of the thickness of employed dielectric on the performance of the FSS structure. Minor variations in the resonance frequency and bandwidth of the upper band of the FSS are observed with the increase in the thickness of the laminate. However, thickness variations do not affect the lower band performance. Furthermore, the physical footprint of the FSS unit cell is the most significant parameter to determine the resonance frequency. Separation among the resonating elements in an FSS array is generally referred to as interelement spacing, or the period. The overall size of a unit cell increases with an increase in the period. Inter-element spacing has a profound effect on the FSS performance. The shielding effectiveness of the unit cell is analyzed by keeping all the other parameters unchanged. When interelement spacing (\(d_{x}=d_{y}\)) is varied from 0.25 to 1.0 mm with a step size of 0.25 mm, the size of the dielectric slab increases, increasing the capacitance. An increase in the capacitance value reduces the resonance frequency; therefore, both the rejection bands are shifted upwards, as expected. Figure 7d signifies the effect of inter-element spacing variations on the EM shielding of the unit cell for the TE polarized wave mode at a normal incidence. A minor reduction in the bandwidth and the notch selectivity of the lower band can be observed, whereas the upper band remains intact. Thus, the overall results specified  
Figure 7: Parametric analysis of the FSS based on its geometrical parameters: (**a**) Impact of dielectric permittivity variations on the performance of the shield. (**b**) SE of the FSS as a function of loss-tangent of the employed substrate. (**c**) Variation in stopbands with respect to the thickness of the substrate of the FSS unit cell at normal incidence. (**d**) Resonant frequency variations with respect to the inter-element spacing of elements at the normal wave incidence TE\({}_{Z}\)-\(\theta^{\circ}\).