## 4 Result and Discussion
The substrate thickness is d, and the branch index is m.  
The metamaterial property of the structure helps to achieve miniaturization and improve the performance of a system. The different shapes of the metallic rings create the metamaterial property in the structure. The rings can be in the shape of circular, elliptical, triangular or rectangular shape. Metamaterial property is represented based on the impedance plot, shown in Figure 14. The resonating behavior of the real and imaginary values represents the impedance behavior of the presented design structure. The two-dimensional radiation pattern of the planned design structure is shown in Figure 11:0 The far-field measurement for the proposed design is carried out in the anechoic chamber. The normalized radiation pattern for the different resonating frequencies is considered. The analysis is carried out for the resonating frequencies of 5.22 GHz, 7.771 GHz, 8.881 GHz and 10.891 GHz. Overall broader directivity is observed for the different resonating frequencies. The behavior of any design structure is represented in a better way using the surface current distribution. The charge distribution varies according to the different resonating frequencies. Since the radiation intensity at each point in space matches the resultant radiation from the antenna's small parts, it leads to the result variations. The frequency-dependent radiation pattern is a sum of the vectorial, and the radiation intensity from the various elements has different path lengths in terms of wavelength. The path difference will affect the phase difference as the wavelength decreases, causing a rapid drop in the radiation intensity with a deviation angle from the peak radiation intensity. The number of side lobes may also change. Figure 11:1 The metamaterial behavior representation of the proposed design structure using the impedance plot. The aperture illumination also fluctuates due to the antenna's resonates at different frequencies. As the frequency varies, the current will flow in different directions, and peaks and nulls will be situated elsewhere. Moreover, according to the essential equation \(\mathrm{G}(\theta,\varphi)=(4\pi\mathrm{A}(\theta,\varphi))/\lambda^{2}\), the wavelength varies with frequency. Consequently, altering the frequency will alter the antenna's emission pattern [41]. The values of the surface charge distribution of the proposed structure are represented in Figure 11:2 The surface charge distribution for the resonating frequency of 5.55 GHz is 1.29 \(\times\) 10\({}^{4}\) V/m, 7.771 GHz is 8.94 \(\times\) 10\({}^{3}\) V/m, 8.881 GHz is 8.15 \(\times\) 10\({}^{3}\) V/m, 10.891 GHz is 8.15 \(\times\) 10\({}^{3}\) V/m. The comparative study of the presented work with other articles is represented in Figure 11:3 The comparison is given with five similar designs published before. The comparison shows that the proposed design performs better than the other designs in terms of bands, size, gain, etc. The size and number of bands are significant because they give the flexibility to be used simultaneously in different applications. Figure 11:4 Two dimensional normalized measured and simulated radiation pattern (**a**) 5.22 GHz, (**b**) 7.771 GHz, (**c**) 8.881 GHz, (**d**) 10.891 GHz.