## 2 Design of Proposed Frequency Selective Surface with Harmonic Suppression  
### Design of Proposed Grid Structure with Band-Pass Filter Characteristics  
When metal is arranged periodically in a grid shape on a thin dielectric substrate, thin metals resembling wires generate magnetic fields around them in response to changes in the applied current [15]. This effect is similar to that of inductance, which is one of the characteristics of an electric circuit in the direction of the electric field. Additionally, in the H-field direction, it produces an effect similar to capacitance, which is one of the characteristics of an electric circuit. Therefore, depending on the incident direction of the electromagnetic wave, the direction parallel to the E-field is expressed in TE mode, and the direction parallel to the H-field is expressed in TM mode. Equation (1) represents the inductance component of the grid-wire structure. When patches are periodically placed on the same surface plane of a thin dielectric substrate, a capacitance occurs between the patches. The mathematical expression of this is shown in Equation (2). Figure 1a shows the band-pass filter, which consists of a parallel LC circuit, represented as an equivalent circuit model (EC model). In this study, we propose an FSS with the structure shown in Figure 1b to design a band-pass filter operating at 3.0 GHz. This is a Grid+Patch structure in which the patches are attached to all sides of the symmetrical square wire, allowing for both a grid and a patch to coexist simultaneously. The L and C values of Grid + Patch are the same as those for Equations (3) and (4) [16]. When a patch is added to the grid form, the total inductance in this structure is obtained by multiplying the L value of the grid by the wire length, as shown in Equation (3). The total capacitance of the structure can be expressed as the product of the existing capacitance and the length of the patch, as shown in Equation (4). The parameter \(d\) represents the unit cell size, defining the size of the repeating unit in the periodic grid structure. The parameter \(l\) indicates the thickness of the grid wire, which is the width of the metallic strip and plays a crucial role in determining the inductive component of the grid structure. The parameter \(w_{1}\) denotes the distance between the patches, defining the gap between adjacent patches in the grid structure, and influences the total capacitive component of the grid. Parameter \(w_{2}\) represents the size of each patch, specifically the width of the patches, which affects the electrical properties between the patches and the grid structure. Lastly, the parameter \(w_{3}\) indicates the distance from the end of the grid wire to the patch, defining the gap between the grid structure and the patch, which is essential for adjusting the overall electrical characteristics. \(\mu_{0}\) is the permeability of the vacuum state and \(\mu_{eff}\) is the relative permeability. \(\epsilon_{0}\) is the permittivity of the vacuum state and \(\epsilon_{eff}\) is the relative permittivity.  
\[L_{grid}=\mu_{0}u_{eff}\frac{1}{2\pi}\ln(\frac{1}{\sin(\pi l/2d)}) \tag{1}\]  
\[C_{grid}=\epsilon_{0}e_{eff}\frac{2}{\pi}\ln(\frac{1}{\sin(\pi w_{1}/2d)}) \tag{2}\]  
\[L_{grid+patch}=d\cdot L_{grid} \tag{3}\]  
\[C_{grid+patch}=(d-w_{1})\cdot C_{grid} \tag{4}\]