# Flexible Rectenna on an Eco-Friendly Substrate for Application in Next-Generation IoT Devices
## 3 Results and Discussion  
### Flexible Antenna Design, Fabrication, and Testing  
According to the flowchart in Figure 1, we initially designed a fractal antenna on an eco-friendly substrate from natural rubber and RHA, aside from the rectifier. Figure 2 illustrates the configuration of the proposed compact and flexible antenna, which comprises a fractal monopole fed with a coplanar waveguide (CPW). In the first step of the design process, we developed a numerical model of the CPW transmission line on the eco-friendly substrate (Figure 3a). Then, we carefully optimized it to provide an optimal balance between compact size and a characteristic impedance of approximately 50 \(\Omega\) (\(\pm\)5%) within the targeted frequency bands. In the next step, we designed and optimized a monopole antenna (Figure 3b) chosen for its simple structure and wide operational bandwidth. Then, we used the symmetric binary fractal tree to enhance the antenna bandwidth, minimize the antenna dimensions [34], and achieve a more esthetic and unobtrusive design. Figure 3c shows the stages of forming the final fractal binary tree antenna with three branches. In the first stage, we used a vertical segment representing a monopole (parent branch). Next, we created two child branches at a 30\({}^{\circ}\) elevation angle from the parent, each with a length scaled to 75% of the parent branch. We repeated this branching pattern two more times, with each new branch separated by a 30\({}^{\circ}\) angle and scaled to 75% of the length of the previous branch. After that, via FDTD-based numerical simulations, as outlined in Section 2.3, we optimize the geometric dimensions of the fractal tree and the coplanar waveguide to achieve optimal bandwidth and radiation efficiency in target frequency bands. Figure 4 presents the antenna reflection coefficient magnitude, radiation efficiency, and gain obtained from the FDTD simulations. The results demonstrate that the optimized antenna design achieves excellent impedance matching with \(|\)S\({}_{11}\)\(|\)\(<-10\) dB across a wide  
Figure 2: Configuration of the proposed antenna. All dimensions are in millimeters. bandwidth from 2 GHz to 2.92 GHz, encompassing the targeted 5G and ISM frequency bands. Moreover, from numerically estimated results for efficiency and gain shown in Figure 4b, we can see that the antenna maintains a high radiation efficiency of 95% and stable gain (of about 2.2 dBi) across the operating-frequency range. Figure 5 illustrates the antenna 3D radiation patterns at 2.1 GHz, 2.5 GHz, and 2.9 GHz. From the results, we can observe that the antenna maintains an omnidirectional radiation pattern in the azimuth plane, enabling it to effectively receive signals from almost all directions. Moreover, due to the fractal geometry, the proposed antenna also supports dual linear polarization, which enhances its ability to harvest ambient RF energy regardless of electromagnetic waves' polarization. Dual linear polarization is particularly beneficial in real-world environments where polarization mismatch can significantly degrade performance. Figure 4: Simulated: (**a**) reflection coefficient magnitudes versus frequency; (**b**) radiation efficiency and maximum gain versus frequency. Figure 3: Antenna design process: (**a**) Input impedance and the numerical model of CPW; (**b**) reflection coefficient magnitude versus frequency and the numerical model of the optimized monopole antenna; (**c**) stages of forming the final fractal binary tree antenna. We fabricated a prototype, employing the methodology detailed in [35] to evaluate the antenna performance and validate the simulation results. The fractal tree and CPW were realized with 0.05 mm brass foil, while the flexible, eco-friendly substrate consisted of a 1.5 mm-thick natural rubber composite reinforced with RHA.