## 2 Design of Proposed Frequency Selective Surface with Harmonic Suppression
### Design of Proposed Loop Structure with Band-Stop Filter Characteristics  
Using the EC approximation method developed by [PERSON] [15], the thin metal was periodically placed in a loop on the same plane as the dielectric. The loop exhibited both inductance and capacitance components. In particular, the square loop structure has a significant inductance component in TE mode and a capacitance component in TM mode. If the loop structure is expressed as an EC Model, it becomes a band-stop filter where the L and C components are in series, as shown in Figure 2a. The reactance component of the loop structure is represented by Equation (5), whereas the susceptance component is represented by Equation (6) [17]. Here, \(G\) in Equation (7) represents [PERSON]'s theorem as a second-order integral. To design an FSS that acts as a band-stop filter at 6.0 GHz, an FSS with the structure shown in Figure 2b is proposed. This is essentially a square loop shape, but the resonance frequency was lowered owing to the high value of C. Patches were attached to each corner to solve this. The capacitance (\(C_{patch}\)) between the patches within the loop was configured in a series. The \(C_{patch}\) value was obtained using Equation (2). The value of \(C_{total}\) was obtained from parallel calculations of \(C_{loop}\) and \(C_{patch}\), as shown in Equation (10) [18]. \[X_{TE}=\frac{w_{5}\cdot L_{loop}}{Z_{0}}=\frac{d\cos(\theta)}{\lambda}\cdot( \ln(\csc(\frac{\pi w_{5}}{2d}))+G(d,w_{5},\lambda,\theta)) \tag{5}\]  
Figure 1: Configuration of the proposed grid structure: (**a**) equivalent circuit model, (**b**) frequency selective surface grid design. \[B_{TE}=\frac{w_{5}\cdot C_{loop}}{Y_{0}}=\frac{4d\sec(\theta)}{\lambda}\cdot(\ln( \csc(\frac{\pi g}{2d}))+G(d,w_{5},\lambda,\theta)) \tag{6}\]  
\[G(d,w_{5},\lambda,\theta)=\frac{0.5(1-\beta^{2})^{2}[(1-\frac{\beta^{2}}{4})(A_ {+}+A_{-})+4\beta^{2}A_{+}A_{-}]}{(1-\frac{\beta^{2}}{4})+\beta^{2}(1+\frac{ \beta^{2}}{2}-\frac{\beta^{4}}{8})(A_{+}+A_{-})+2\beta^{6}A_{+}A_{-}} \tag{7}\]  
\[A_{\pm}=\frac{1}{\sqrt{(\frac{d\sin\theta}{\lambda}\pm 1)^{2}-\frac{\beta^{2}}{ \lambda^{2}}}}-1 \tag{8}\]  
\[\beta=\sin(\frac{\pi w_{5}}{2d}) \tag{9}\]  
\[C_{total}=C_{loop}||C_{patch} \tag{10}\]  
To implement wide-angle beam steering characteristics in both the azimuth and elevation directions, the radio waves entering the FSS must be less affected by polarization. The proposed loop structure was designed to minimize the impact of the TE and TM modes by rotating it by 45\({}^{\circ}\) in the direction of the radio waves. Parameter \(d\) represents the unit cell size, defining the overall dimension of one repeating unit in the periodic FSS structure. This parameter is crucial as it sets the basic scale for the entire design. Parameter \(w_{4}\) indicates the gap between the unit cell and the loop, representing the distance between the edge of the loop and the boundary of the unit cell. This gap influences the overall capacitive and inductive characteristics of the loop structure. Parameter \(w_{5}\) defines the loop thickness, which is the width of the metallic loop strip and is important for determining the inductive properties of the loop structure. Parameter \(w_{6}\) denotes the size of the parasitic patches attached to the loop. These patches are used to fine-tune the electrical characteristics of the loop, especially its capacitive properties. Lastly, parameter \(g\) represents the distance between the loops, indicating the gap between adjacent loop structures in the periodic array. This parameter affects the coupling between loops and the overall filtering characteristics of the FSS. These parameters are essential in designing the loop structure to achieve the desired band-stop filter characteristics. By carefully adjusting these parameters, the performance of the FSS can be optimized for specific frequency-selective properties, including effective harmonic suppression.