## 7 Results and Discussion  
The mathematical analyser CST was employed in this study to determine the S-parameters and different coefficients of the unit cell. Figure 13 represent the reflection coefficient (S11) and S21. The unit cell recorded resonance frequencies at 2.89 GHz, 9.42 GHz, and 15.16 GHz with \(-25\) dB, \(-22.24\) dB, and \(-28\) dB amplitude, respectively. As for S11, negative peaks were observed at 3.78 GHz and 10.20 GHz with \(-23.72\) dB and \(-8.98\) dB amplitude, respectively. Bandwidths of 0.39 GHz at S-band, 0.94 GHz at X-band, and 2.64 GHz at Ku-band are also depicted in Figure 13. Moreover, the numerical data were extracted for permittivity, permeability, and refractive index using MATLAB code (Figures 14-16). According to Figure 13, it is found that every resonance of S21 was tracked by an S11 minimum. Since every minimum frequency of S21 was lower than that of the corresponding S11 minimum frequency, every resonance was treated as an electrical resonance in the unit cell. Meanwhile, Figure 14; Figure 15 represent the results of permittivity and permeability. It is observed that the value permittivity goes through from maximum to minimum while resonance takes place in S21. The figures also denoted that minimum values of \(\mu\) were derived from minimum S11 points. The values of permittivity changed from positive to negative when \(\mu\) positively changed the quantity. Since the refractive index was related to the frequency, the near-null property at the negative permittivity region is depicted in Figure 16. Due to the negative permittivity of the projected unit cell in a certain frequency region, the proposed design was termed a negative-permittivity (ENG) metamaterial. Applying the Drude function [24].  
\[\varepsilon(\omega)=1-\frac{\omega_{p}^{2}}{\omega(\omega+i\Gamma)} \tag{11}\]  
where \(\Gamma\) is the attenuation function due to energy disintegration in the plasmons, and \(\omega_{p}\) is the plasmon frequency which is determined by \(\omega_{p}=\frac{dq^{2}}{\varepsilon_{0}m}\). Also, d represents effective density, q for electron charge, \(\in_{0}\) for permittivity of free space, and m for the mass of the electron. If \(\Gamma\approx 0\) then \(\omega<\omega_{\text{p}}\) and then permittivity (\(\varepsilon\)) will be negative. Thus, the EM wave will not propagate. This unique property (negative permittivity) of the metamaterial can widely be used in various types of communication systems, for instance, bandwidth improvement of the antenna [25] and microwave filter. Meanwhile, the negative refractive index property can be utilised for cloaking, sensing, and enhancing antennas. To validate the authentication of the result, the unit cell was simulated by CST and HFSS (S11 and S21) are illustrated in Figure 17. The extracted parameters and their respective frequencies values are listed in Table 3 and comparison of resonance frequencies between the unit cell and arrays are listed in Table 4.  
Figure 12: Comparison of CST and ADS transmission coefficient S21 results.  
Figure 14: Real and imaginary permittivity (\(\epsilon\)) of the unit cell.  
Figure 13: CST results of S11 and S21 of the unit cell.  
Figure 15: Real and imaginary permeability (\(\upu\)) of the unit cell.  
Figure 16: Real and imaginary refractive index (n) of the unit cell.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Types of** & **Unit Cell** & **2 \(\times\) 1 Array** & **2 \(\times\) 2 Array** &
\begin{tabular}{c} **Max. Shift of** \\ **Frequency (\%)** \\ \end{tabular} \\ \hline
1 st resonance & 2.89 & 2.87 & 2.87 & 0.69 \\ (GHz) & 9.42 & 9.32 & 9.29 & 1.3 \\
3 rd resonance & 15.16 & 15.12 & 15.14 & 0.26 \\ (GHz) & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of resonance frequencies among the unit cell and arrays.  
Figure 17: Validation of S11 and S21 of the unit cell based on CST and HFSS.