## 5 Results Analysis
### Meta-Atom Array Configurations
#### 5.2.4 4 \(\times\) 4 Array Analysis  
In Figure 13, the effective medium parameters are depicted at 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\) and 270\({}^{\circ}\) rotations. From Figure 14a, the permeability is from 7.79-14 GHz, covering almost 6.21 GHz in bandwidth; the permittivity is from 4.46-7.58 GHz, covering approximately 3.12 GHz in bandwidth; and the refractive index is from 4.44-6.54 GHz and 7.73-9.86 GHz, covering almost 2.10 GHz and 2.13 GHz for zero-degree rotation. In Figure 14d, the permeability ranges from 7.74-14 GHz, covering almost 6.26 GHz in bandwidth; the permittivity ranges from 4-7.53 GHz and 7.90-10 GHz, covering bandwidths of approximately 3.53 GHz and 2.10 GHz; and the refractive index ranges from 5-7.20 GHz (2.20 GHz in bandwidth) and 7.71-9.63 GHz (1.92 GHz in bandwidth) for 270-degree rotation. Figure 12: Amplitude of the permittivity, permeability and refractive index at (**a**) 0\({}^{\circ}\), (**b**) 90\({}^{\circ}\), (**c**) 180\({}^{\circ}\), (**d**) 270\({}^{\circ}\) rotations of the 3 \(\times\) 3 array structure. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Structure** & **Rotation Angle** & \(\epsilon\) & \(\mu\) & \(n\) & **EMR (\(\lambda\)/a)** & **Meta-Atom Type** \\ \hline \multirow{4}{*}{\(3\times 3\) Array} & 0\({}^{\circ}\) & \(-4.6\) & \(-16.2\) & \(-8.7\) & 8.5 & \\  & 90\({}^{\circ}\) & \(-1.8\) & \(-18.6\) & \(-5.9\) & 4.0 & \\ \cline{1-1}  & 180\({}^{\circ}\) & \(-4.6\) & \(-16.1\) & \(-8.6\) & 8.5 & \\ \cline{1-1}  & 270\({}^{\circ}\) & \(-1.8\) & \(-18.6\) & \(-5.9\) & 4.0 & \\ \hline \end{tabular}
\end{table} 
Table 5: Real values of \(\epsilon\), \(\mu\) and \(n\) at 9.20 GHz. Therefore, it is notable that the bandwidth of the permeability is always more than 6 GHz for all of the rotation angles. The array structure also shows left-handed characteristics at 9.20 GHz, with an effective medium ratio of more than 8 for 0-degree and 180-degree and 4 for 90-degree and 270-degree rotation, as shown in Table 6.  
The sensitivity of the proposed meta-atom has been explained in terms of the \(Q\)-factor. The bandwidth of the meta-atom is inversely related to the quality factor (\(Q\)-factor). The calculation of the \(Q\) factor has been performed using the 3-dB bandwidth of resonant frequency (\(\Delta f\)) and the resonant frequency (\(f_{0}\)) that has a resonance peak under \(-10\) dB. \[Q=\frac{f_{0}}{\Delta f}, \tag{15}\]  
It can be observed that the \(Q\)-factor is high, and this means that the reported meta-atom has high sensibility. The value of the \(Q\)-factor depends on the sharpness of the transmission and the location of resonant frequency. The reported antenna has been designed to use for long distance \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Structure** & **Rotation Angle** & \(\epsilon\) & \(\mu\) & \(n\) & **EMR (\(\lambda/\mathbf{a}\))** & **Meta-Atom Type** \\ \hline \multirow{4}{*}{4 \(\times\) 4 Array} & 0\({}^{\circ}\) & \(-3.3\) & \(-17.3\) & \(-7.6\) & 8.5 & \\  & 90\({}^{\circ}\) & \(-2.1\) & \(-18.2\) & \(-6.1\) & 4.0 & \\  & 180\({}^{\circ}\) & \(-3.5\) & \(-17.1\) & \(-7.8\) & 8.4 & \\  & 270\({}^{\circ}\) & \(-1.7\) & \(-18.9\) & \(-5.7\) & 4.0 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Real values of \(\epsilon\), \(\mu\) and \(n\) at 9.20 GHz. Figure 13: Amplitude of the permittivity, permeability and refractive index at: (**a**) 0\({}^{\circ}\), (**b**) 90\({}^{\circ}\), (**c**) 180\({}^{\circ}\), (**d**) 270\({}^{\circ}\) rotations of the 4 \(\times\) 4 array structure. telecommunication (C-band). This antenna is made of three layers; they are radiating patch, antenna substrate and ground plane. The ground plane is printed on the lower part of the substrate, where on the upper portion of the substrate, the radiating patch is printed using a microstrip line feeding in Figure 14a,b. The width and length of the microstrip line are stable with a view to attaining the 50 \(\Omega\) input impedance. The port of the microstrip feed line is attached to a Sub-Miniature Version A (SMA) connector.