## 3 Results and Discussion
### Unit Cell Metamaterial Structure Analysis  
The numerical and experimental results have been analyzed accordingly. S-parameters such as reflection coefficient (S\({}_{11}\)) and transmission coefficient (S\({}_{21}\)) were retrieved from the CST Microwave Studio software and plotted as shown in Figure 6a. According to the simulation, the oval-square-shaped SRR structure displayed S\({}_{11}\) with magnitudes of \(-34.64\) and \(-24.66\) dB at resonance frequencies of 7.33 and 9.06 GHz. According to the S\({}_{21}\) result, the metamaterial design had a dual frequency band. The resonance frequencies were 5.52 GHz and 8.81 GHz, with magnitudes of \(-43.03\) dB and \(-17.19\) dB, respectively. The experimental results for S\({}_{21}\), as shown in Figure 6a, revealed that the proposed design had dual frequency bands at 5.53 GHz and 8.31 GHz, with magnitudes of \(-31.18\) and \(-17.90\) dB, respectively. Meanwhile, the S\({}_{11}\) result presented resonance frequencies at 7.51 GHz and 8.31 GHz with magnitudes of \(-17.76\) dB and \(-17.90\) dB, respectively. The C-band resonance frequency of S\({}_{21}\) has a percentage difference of 0.18%, whereas the X-band resonance frequency difference was 5.68%. It was discovered that the simulated and experimental findings were practically identical. This is because the results can be influenced by several factors, which allow the discrepancies to happen between both methods. The measurement method was utilized to validate the simulation data, and there might be a calibration error of the Agilent N5227A vector network analyzer by utilizing the Agilent N4694-60001 Ecal device. Moreover, there has always been some mutual resonance effect between the transmitting and receiving ends of the waveguide. The array prototype of the metamaterial was measured by the pyramidal horn antenna. Therefore, the possible reason for the discrepancies in results might be due to the management of two horn antennas for the metamaterial array cell measurement. On the other hand, there  
Figure 5: The comparison of S\({}_{21}\) results for simulation and equivalent circuit. might be errors that occurred during the fabrication process. Finally, the permittivity of the substrate is an important factor in the variation of simulated and measured results. The resonance frequency depends on the substrate material's permittivity. If the permittivity is increased, then the resonant peaks are shifted toward the lower frequency. When the dielectric constant is increased, each capacitance value between the ground and the radiating elements is also raised. Since each capacitance of the radiating elements is in series with others, the system's equivalent capacitance is reduced. The decrease in the equivalent capacitance is another reason for the variation in the results. On a side note, the metamaterial structure's numerical simulation can be extended to 18 GHz because it can accomplish Ku-band due to the design's employment of a number of SRR. However, due to limits in the software's functionality, we primarily concentrated on the frequency range up to 12 GHz in this study. The method of retrieval of the effective medium parameter was required to characterize the electromagnetic properties of artificial materials. The primary electromagnetic properties that needed to be studied in order to classify metamaterials were electric permittivity and magnetic permeability. The values of impedance and refractive index were extracted from the scattering parameter, S\({}_{11}\) and S\({}_{21}\) data, and subsequently, \(\varepsilon\) and \(\upmu\) were also retrieved. The results can be seen in Figure 6b, where the real part values of relative \(\varepsilon\) and \(\upmu\) are below zero at a specified frequency range. From 5.94 GHz to 12 GHz, the value of relative \(\varepsilon\) was negative, with the maximum value of \(-\)518.34 at the frequency of 8.44 GHz.