## 4 Parametric Study of the Oval-Square-Shaped SRR Structure
### The Design of Metamaterial Structure  
The metamaterial structure was altered until the desired simulated results were achieved. In this study, the metamaterial structure was designed for C- and X-band applications. Thus, the design was tweaked in a series of steps, as shown in Figure 11. Firstly, the structure just included three rings of oval-shaped SRR. The simulated result, on the other hand, revealed that the metamaterial structure obtained a resonance frequency of 13.34 GHz (Ku-band). Then, a square-shaped resonator was added. The transmission coefficient result improved to dual resonance frequencies of 7.52 GHz (C-band) and 15.08 GHz (Ku-band). Since this study was focused on the C- and X-bands, the design 3 structure was created by adding another square-shaped split ring resonator. The resonance frequency was gained at 7.02 GHz (C-band), 10.30 GHz (X-band), and 15.10 GHz (Ku-band). The metamaterial structure must have a compact size; therefore, a lower resonance frequency  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Substrate** & **Thickness** & **Dielectric Constant** & **Tangent Loss** \\ \hline FR-4 & 1.6 & 4.3 & 0.025 \\ \hline Rogers RO4003C & 0.508 & 3.55 & 0.027 \\ \hline Rogers RT5870 & 1.575 & 2.33 & 0.0012 \\ \hline Rogers RT5880 & 1.575 & 2.2 & 0.0009 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The properties of the substrate materials.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Substrate** & **Frequency Band** & **Resonance Frequency of S\({}_{21}\), GHz** & **Frequency Range, GHz** & **Magnitude, dB** \\ \hline FR-4 & C-band & 4.72 & 4.09–5.12 & \(-\)29.38 \\ \hline Rogers RO4003C & C- and X-band & 5.52, 8.81 & 4.98–5.92, & \(-\)43.03, \\  & & & 8.76–8.86 & \(-\)17.19 \\ \hline Rogers RT5870 & C- and X-band & 5.84, 9.77 & 5.27–6.28, & \(-\)42.76, \\  &  
needs to be achieved by the design. Having said that, another metamaterial structure was designed by connecting each of the rings with a split horizontal bar. However, the resonance frequency manifested by design 3 shifted to only a single frequency at 14.56 GHz (Ku-band). Finally, the metamaterial structure was designed with a gap between the oval and square-shaped rings to split the ring. The resonance frequency was improved to 5.52 GHz (C-band) and 8.81 GHz (X-band). The result of the S\({}_{21}\) for the performance of the steps taken was assembled in Figure 12.  
From the simulated result, it can be identified that the design of the metamaterial structure affected the resonance frequency. In further observations, the oval-square-shaped SRR was rotated 90\({}^{\circ}\) to the right, as shown in Figure 13. It can be seen that, from the figure, the S-parameter result of design A was different from that of design B. Based on the simulated result, design A exhibited dual band resonance frequencies at 7.21 GHz (C-band) and 10.72 GHz (X-band) with magnitudes of \(-\)42.05 and \(-\)40.24 dB, respectively. Meanwhile, design B also manifested dual bands at the resonance frequency of 5.52 GHz (C-band) with a magnitude of \(-\)43.03 dB, and 8.81 GHz (X-band) with a magnitude of \(-\)17.19 dB. Based on the result, although the design is identical, by changing the position of the metal gap, it will affect the resonance frequency. The difference in the resonance frequencies happened due to the electric and magnetic field polarization directions. Hence, when designing the metamaterial structure, researchers can consider rotating the position of the metal to identify the best structure for the desired properties for the applications.  
Figure 10: The comparison of S\({}_{11}\) and S\({}_{21}\) for the different type of substrate materials.  
Figure 11: The steps of developing the new oval-square-shaped metamaterial structure.  
Figure 12: The comparison for the S-parameters of the different design of metamaterials.