## 6 Results and Discussion
### Effective Medium Ratio (EMR) Analysis and Comparison  
The effective medium ratio represents the compactness of the unit cell. In Table 4, the proposed unit cell is compared with a few of the recent existing works, including references, year of development, shape, dimension, resonance frequencies, EMR, and frequency bands. The presented comparison shows that the proposed design has the highest effective medium ratio. The wavelength at the lowest resonance frequency is divided by the unit cell maximal size to achieve the EMR. A metamaterial unit cell can be either single negative or double negative once the EMR should be larger than 4 in order to establish its efficiency. The EMR is calculated from Equation (17) [29]. The wavelength and dimension are denoted by \(\lambda\) and L.  
\[EMR=\frac{\lambda}{L} \tag{17}\]Figure 12: Metamaterial (**a**) 1 \(\times\) 2 sized arrays without mirror positioning; (**b**) 1 \(\times\) 2 sized array with mirror positioning; (**c**) 2 \(\times\) 1 sized array with normal positioning; (**d**) 2 \(\times\) 1 sized array with transform positioning; (**e**) 2 \(\times\) 2 sized array with mirror positioning; (**f**) 4 \(\times\) 4 sized array with mirror positioning.  
According to Table 4, it is observed that the lower dimension of the unit cell with lower resonance frequencies can achieve a higher EMR. Though the material from Reference [26] represents a much smaller size unit cell of \(6\times 6\) mm\({}^{2}\) in dimension, it also has a high resonance frequency at a lower band among the compared metamaterial structures. We also obtained two frequency bands, where the double L-shaped unit cell with the dimension of \(10\times 10\) mm\({}^{2}\) has three frequency bands, although the EMR is very low. The developed structure competes with the square circle shape structure [30], where the number of bands (S, C, and X bands) are the same, but the following semi-circle shape structure [31] has the same number of resonance frequencies of four. From Reference [29], the unit cell provided only one resonance frequency under the S band. Because of its narrow band, the metamaterial unit cell also provided a high EMR at that point. The proposed unit cell obtains the miniaturization and higher EMR with quad-band resonance frequencies, indicating the metamaterial design was the most effective when compared to all other studies presented in Table 4. The compactness and quad-band properties indicate this metamaterial unit cell can be used for a variety of small-sized devices and could be useful in a wide array of applications.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**References** & **Year** & **Shape** & **Dimensions (mm)** &
\begin{tabular}{c} **Resonance** \\ **Frequencies (GHz)** \\ \end{tabular} & **EMR** & **Frequency Bands** \\ \hline
[25] & 2017 & Double C & 12 \(\times\) 12 & 3.36, 8.57, 11.57 & 7.42 & S, C, and X \\
[26] & 2017 & Delta loop & 6 \(\times\) 6 & 4.3, 7.6, 9.8 & 11.5 & C and X \\
[27] & 2019 & Double L & 10 \(\times\) 10 & 7.69, 8.47, 12.04, 13.14 & 3.9 & C, X and Ku \\
[28] & 2020 & Inverse-epsilon & 10 \(\times\) 10 & 2.38, 4.55, 9.42 & 12.61 & S, C and X \\
[29] & 2020 & Hook-C shape & 8 \(\times\) 8 & 2.93 & 12.78 & S-band \\
[30] & 2020 & Square-Circle & 8 \(\times\) 8 & 2.6, 6.3, 9.3 & 14.3 & S, C, and X \\
[31] & 2021 & Semi-Circle & 8 \(\times\) 8 & 2.48, 4.28, 9.36, 13.7 & 15.1 & C, S, X and Ku \\ Proposed & 2022 & Double C shaped & 8 \(\times\) 8 & 2.4, 5.64, 8.93, 11.5 & 15.6 & S, C, and X \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison between proposed metamaterial and recently developed metamaterials based on resonance frequencies, dimension, and EMR.  
Figure 13: Transmission coefficient (S21) of differently sized metamaterial arrays with positioning.