## 5 Parametric Study  
The performance of the metamaterial unit cell depends on several factors such as the split gap of the ring, the width of the metamaterial resonator, substrate and its thickness, and boundary condition of the simulation environment. These factors directly hit the variation of inductance and capacitance property, which results in a change in resonance frequency of the metamaterial. Numerous parametric studies have been executed to investigate the effects of the split gap of the SRR and Coptic cross resonator, the width of the Coptic cross resonator, effect of different conductor on metamaterial resonator, effect of substrate material, and boundary condition of the simulation geometry. **Effect of split gap of SRR on \(\boldsymbol{S_{21}}\) results**:  
The \(S_{21}\) plot for the various split gap of SRR is introduced in Figure 5a. The split gap of the SRR initiates a capacitance variation that influences the resonance frequency of the metamaterial. The capacitance value decreases with the increasing split gap of the ring, which affects the resonance frequency to a higher value. The initial step introduces a split gap of 0.2 mm, exhibiting quadruple resonances with excellent magnitude. Then, the split gap was changed to 0.4 mm and 0.6 mm, showing the same response as the result of 0.2 mm split gap of SRR, but the resonance frequency moves to higher value. Finally, the no split gap is inserted inside the ring, which affects the resonance frequency, where the first resonance is moved to 4.14 GHz, and the second resonance frequency is almost diminished. It can be seen from Figure 5a that the resonance frequency for 0.2 mm split gap is better than other specified values. Finally, a 0.2 mm split gap is selected for the proposed design. **Effect of Coptic shape resonator width on \(\boldsymbol{S_{21}}\) results:**  
The \(S_{21}\) plot for the different widths of the Coptic shape resonator is outlined in Figure 5c. As the Coptic shape resonator's width increases, the overall inductance property decreases and the resonance frequency increases, because the resonance frequency is inversely proportional to the inductance. The width of the Coptic shape resonator was taken in four sizes, such as 0.4, 0.6, 0.8, and 1 mm. The effect of width analysis found that the first and second resonance frequencies were almost the same for different widths, but the third and fourth resonance frequencies increased slightly. In this analysis, the width was set to 0.6 mm for the proposed design. Figure 4: (a) The \(S_{21}\) plot on different design approaches. (b) The \(S_{11}\) plot on different design approaches. **Effect of split gap of Coptic shape resonator on \(S_{21}\) results:**  
The \(S_{21}\) plot for the various split gaps of the Coptic shape resonator is shown in Figure 5b. The capacitance property depends on the split size of the resonator. The first design starts with a 0.2 mm split gap of the Coptic shape resonator showing quadruple resonance frequency with excellent magnitude. The split gap was uniformly increased by 0.2 mm. An increase in the value of the resonance frequency was also observed. Lastly, no split gap was inserted into the Coptic shape resonator that affects the resonance frequency, where the third resonance frequency was shifted from 10.3 to 12.895 GHz and the fourth resonance disappeared. As shown in Figure 5b, it can be realized that the resonance frequency with magnitude is better than the other specified values for a Coptic shape resonator split gap of 0.4 mm. Finally, a split gap of 0.4 mm was chosen for the proposed design. **Effect of different resonating conductor on \(S_{21}\) results:**  
The effect of different resonating conductors on the resonance frequency of \(S_{21}\) is described in Figure 5d. The different metals such as gold, nickel, platinum, tantalum, and copper are used to test the performance of the metamaterial. First, copper is used as a patch to indicate the quadruple resonance frequency with excellent bandwidth.