## 2 Design of Proposed Frequency Selective Surface with Harmonic Suppression
### The Reflection Coefficient and Transmission Coefficient Results of the Proposed FSS  
The equivalent circuit model (EC model) of the proposed Frequency Selective Surface (FSS), which integrates both the grid and loop structures, is illustrated in Figure 3. This model provides a theoretical basis for understanding the behavior of the FSS in response to electromagnetic waves. The grid structure of the manufactured FSS is shown in Figure 4a, and the loop structure is depicted in Figure 4b. These structures were meticulously designed to achieve the desired band-pass and band-stop filter characteristics. To comprehensively compare the reflection and transmission coefficient characteristics of the designed FSS with measured values, two distinct simulation methods were utilized. First, the CST Studio Suite was employed for unit cell simulation, as shown in Figure 5a. In this setup, the unit cell of the designed FSS was placed inside a waveguide with periodic boundary condition (PBC) walls. This configuration allowed for the measurement of the reflection coefficient (\(S_{11}\)) and the transmission coefficient (\(S_{21}\)) by adjusting the angle of incidence. By varying the angle, we could examine the wide-angle beam steering characteristics of the FSS, thereby ensuring that the FSS performs effectively under different incident angles. In parallel, the Advanced Design System (ADS) simulation provided by Keysight was used to validate the results, as shown in Figure 5b. This method involved inserting the calculated values of inductance (L) and capacitance (C) into the final EC model to evaluate the reflection and transmission coefficients. The dual approach of using both CST and ADS simulations ensured a robust analysis and cross-validation of the results. The wide-angle beam steering characteristics were specifically examined by changing the incident angle (\(\theta\)). When (\(\theta\)) is 0\({}^{\circ}\), the component values were determined as follows: \(L_{grid+patch}\) = 68.4 pH, \(C_{grid+patch}\) = 7.37 fF, \(L_{loop}\) = 19.6 pF, and \(C_{total}\) = 33.3 pF. These values were critical in achieving the desired filtering characteristics. Table 2 provides a detailed summary of these parameter values. For the accurate measurement of the transmission coefficient of the FSS, an experimental setup was established, as depicted in Figure 6b. A standard horn antenna was positioned at the ports of a Vector Network Analyzer (VNA). The FSS was mounted on a centrally located rotating device placed between the horn antennas. This setup allowed for the precise measurement of the transmission coefficient (\(S_{21}\)). By rotating the device, the transmission coefficient was measured at various angles, and the results were calculated by subtracting the \(S_{21}\) values with the FSS from the \(S_{21}\) values without the FSS. This method ensured that any discrepancies due to external factors were minimized. Figure 7a presents the simulation results for the reflection coefficient (\(S_{11}\)). At the operational frequency of 3.0 GHz, both CST and ADS simulations demonstrated that the FSS met the criterion of \(-\)10 dB or less for \(S_{11}\), indicating effective reflection suppression. Even when the beam was steered at 30\({}^{\circ}\), the reflection coefficient remained stable at \(-\)10 dB, showcasing the FSS's capability to maintain performance across different angles. Figure 7b compares the simulation and measurement results for the transmission coefficient (\(S_{21}\)). In the operating band of 3.0 GHz, the FSS operated as a band-pass filter with a minimal transmission loss of \(-\)0.1 dB. At the harmonic frequency of 6.0 GHz, the FSS exhibited band-stop filter characteristics with a significant transmission attenuation of approximately \(-\)50 dB. This substantial reduction in transmission at the harmonic frequency confirmed the FSS's effectiveness in harmonic suppression, validating both the theoretical design and practical implementation of the FSS.