## 3 Results and Discussion  
Before interpreting the results, the measurement device and its arrangement mentioned in the previous section are shown in Figure 7. The transient solver of the simulation program was used to obtain an accurate result, and the necessary number of network applications was provided. The return loss of the antenna was measured with the aid of a network analyzer. The reflection coefficients of Antenna-1, Antenna-2, and Antenna-3 are given in Figure 8a-c, respectively, to show both the advantage of the adjustable surface conductivity of graphene and to examine its usefulness in microwave antenna designs. Analyses were carried out by applying electrical fields of 0.1, 0.3, 0.5, and 0.7 eV, respectively, to the antenna created in the CST Microwave Studio software environment. These data presented in Figure 8 prove the advantages of highly variable graphene conductivity for tuning the antenna resonance frequency, which is also mentioned in the graphene material part. Accordingly, the relaxation time (\(\tau\)) is accepted as 0.1 ps. When the data in the figure are examined, there is an observed improvement in harmony of the chemical potential for Antenna-1 and the reflection coefficient, while inconsistency is observed for Antenna-2 and Antenna-3, especially at 0.7 eV. It has been shown that the polarization and permeability of the antennas can be achieved without making any changes in the antenna dimensions or physical structure only by changing the voltage applied to the graphene layer, which changed the Fermi energy level [94; 95; 96; 97]. Equation (1) shows that the conductivity of graphene can be adjusted dynamically by changing its chemical potential. Figure 9a-c represent the actual and simulated values of graphene surface permeability for Antenna-1, Antenna-2, and Antenna-3, respectively, when the chemical potential is changed between 0 and 1.0 eV. Figure 7: Measurement setup by using Keysight Technologies’ PNA-L Agilent vector network analyzer. Figure 8: Reflection coefficient of (**a**) Antenna-1, (**b**) Antenna-2, and (**c**) Antenna-3 for varying chemical potential. Figure 9: The real and imaginary parts of the graphene dielectric permittivity for (**a**) Antenna-1, (**b**) Antenna-2, and (**c**) Antenna-3 as the functions of the chemical potential. Figure 10 shows the bandwidth performance of the antennas in terms of return loss along with the lower (\(f_{L}\)) and upper (\(f_{H}\)) frequencies, where the return loss curve exceeds \(-10\) dB. While it is seen that Antenna-1 provides the best performance in terms of return loss bandwidth, other antennas perform quite well in wideband ranges. Although the results of the simulation and experimental studies are generally compatible, minor inconsistencies may occur. Simulation environments are ideal environments,  
Figure 10: Reflection coefficients of (**a**) Antenna-1, (**b**) Antenna-2, and (**c**) Antenna-3 for bandwidth performance. and the values of materials used in simulation environments are average values. There are slight differences between the values of PLA and graphene material used in the simulation environment and the materials used. In addition, minor faults caused by production, such as scratches or difficulties in soldering the SMA connector, can lead to different results. Another important situation is that this study used a graphene filament for antennas instead of the raw graphene material. The comparison for efficiency and performance of graphene-based bow-tie antennas with previous ultra-wideband antennas are given in Table 4. This table shows that the graphene-based bow-tie antennas designed in this study perform quite well compared to other studies in the literature. The results obtained from these three proposed antennas show that they can operate in a wide bandwidth of 2-20 GHz. It has been proven that the geometric changes made in the conductive parts of the antenna also affect their performance.