## 4 Result and Discussion
Their response is analyzed regarding directivity, gain response, electric field, and radiation pattern. Antenna directivity represents the intended intensity concerning the average power in all directions [36]. The higher directivity value also represents the higher gain value [26]. The efficiency of the structure directly relates to the gain and directivity. The peak directivity of 0.6 dB is attained in the planned design, shown in Figure 5.1 The normalized directivity response is shown in Figure 5.2 The normalized directivity is measured over the zero to \(-3\) dB range. The normalized directivity is observed in the \(-28\) to 64 degrees (92 degrees) range. Further analysis of gain, electric field and the radiation pattern is considered for the less than \(-15\) dB of the reflection coefficient response. Figure 5.3 The simulated and measured multibands of reflection coefficient response over the frequency range from 4 GHz to 12 GHz. Overall, six band responses are observed in the proposed work. The antenna gain represents the maximum radiation intensity concerning the average intensity in all directions [37]. The gain and directivity represent the efficiency of the proposed design structure. Therefore, achieving a positive gain for all resonating frequencies is necessary. Figure 13 represent the total gain of the proposed design structure for the different resonating frequency. The value of the total gain for the different frequencies 5.221 GHz, 7.771 GHz, 8.880 GHz and 10.891 GHz is, respectively, 0.53 dB, 2.39 dB, 2.61 dB and 5.77 dB. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Band** & **First** & **Second** & **Third** & **Fourth** \\ \hline Resonating Frequency (GHz) & 5.22 & 7.771 & 8.881 & 10.891 \\ Reflection coefficient Response (dB) & \(-\)24.08 & \(-\)18.84 & \(-\)30.43 & \(-\)49.00 \\ Range of Tuning (GHz) & 5.071–5.561 & 7.531–7.881 & 8.671–9.041 & 10.671–11.071 \\ Bandwidth (MHz) & 490 & 350 & 370 & 400 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The summary of all presented results. Figure 11: The measured and simulated directivity plot of the presented design. Figure 12: The presented design’s normalized measured and simulated directivity plot. The effective permeability \(\left(\mu_{eff}\right)\), permittivity \(\left(\varepsilon_{eff}\right)\) and impedance \(\left(Z_{eff}\right)\) are measured using the scattering (S) parameters, and by taking the help of these parameters, the refractive index \(\left(n_{eff}\right)\) can be calculated [38; 39]. The ting discrepancy in the Q factor between the theoretical calculations and the numerical estimates provides direct proof for the crucial coupling that permits exceptional total absorption. Yet, when complete absorption through critical coupling can be achieved, the perfect absorber's impedance should equal that of the space (Z0 = 1) at the resonant wavelength from the perspective of the macroscopic electromagnetics. Therefore, Equation (6) is used to determine the effective impedance of a proposed structure [40]. \[\varepsilon_{eff}=\frac{n_{eff}}{Z_{eff}} \tag{4}\]  
\[\mu_{eff}=n_{eff}\times Z_{eff} \tag{5}\]  
Figure 13: Total gain plot presented design. (**a**) The gain for resonating frequency of 5.221 GHz is 0.53 dB. (**b**) The gain for resonating frequency of 7.771 GHz is 2.39 dB. (**c**) The gain for resonating frequency of 8.880 GHz is 2.61 dB. (**d**) The gain for resonating frequency of 10.891 GHz is 5.77 dB. The notation used for gain plot: 5.3889e-001 = 0.53 \(\times\) 10\({}^{-1}\). The same notation used for all figures. \[Z_{eff}=\sqrt{\frac{\left(1+S_{11}\right)^{2}-S_{21}^{2}}{\left(1-S_{11}\right)^{ 2}-S_{21}^{2}}} \tag{6}\]  
\[n_{eff}=\frac{1}{k_{0}d}\Big{\{}\text{Im}\Big{[}\text{ln}\Big{(}e^{ink_{0}d} \Big{)}\Big{]}+2m\pi-i\text{Re}\Big{[}\text{ln}\Big{(}e^{ink_{0}d}\Big{)}\Big{]} \Big{\}} \tag{7}\]  
\[e^{ink_{0}d}=\frac{S_{21}}{1-S_{11}\Big{(}\frac{z-1}{z+1}\Big{)}},\ k_{0}= \frac{2\pi f}{c} \tag{8}\]  
The speed of light is represented by \(c\) (m/s), and resonating frequency is \(f\).