## 4 Simulation and Measurement Results  
The proposed design was fabricated to validate the simulated results, as shown in Figure 10. A 2.9 mm end launch connector (145-0701-851) was used to feed the signal from a vector network analyzer (Anritsu, Atsugi, Kanagawa, Japan). The VNA was calibrated with short, open, and precision 50 \(\Omega\) loads before measurement. With this process, the SMA and VNA port impedance would be matched to 50 \(\Omega\), causing negligible error in the measured results. The study of antenna structure through CMA indicated that Modes 1 to 4 and Modes 1 to 5 contributed to the resonance from 23 to 30 and 30 to 44 GHz. It was also found that the summation of orthogonal modes from 35 to 38 GHz generated circular polarization. These characteristics were further analyzed through antenna excitation in simulation HFSS (High Frequency Simulation Software) v.21.0 software and from the measurement results. As proof of validation, Figure 11 illustrates the simulated and measured reflection coefficient \(|\)S11\(|\). The achieved simulation and measurement bandwidths were 19.2 GHz (22-41.2 GHz) and 19 GHz (23-42 GHz), as depicted in Figure 11.  
Figure 9: Illustration of circular polarization at 38 GHz. (**a**) LHCP on the left portion of the antenna. (**b**) RHCP on the right portion of the antenna.  
The circular antenna structure splits the input current in both directions. Further, the four equilateral triangles, which connect the outer ring to the center circular patch, provide the return path to the current. Thus, the current flowing in the left and right of the radiator undergoes a \(\pm 90^{\circ}\) phase shift, resulting in RHCP and LHCP. These behaviors were studied in Section 3 with the E-field locus in the far-field region. This same behavior is also illustrated through the surface current in Figure 12 at 38 GHz. In the left portion of the antenna, the surface current changed its direction clockwise, and the left portion of the antenna was counterclockwise. The direction of the current on the conductor and the radiated E-field have opposite polarities, which can be understood from Equation (5):  
\[E=\int_{Surface}\frac{-j\omega\mu e^{-jkR}}{4\pi R}Jsds \tag{5}\]  
where \(\omega\) is the angular frequency, \(\mu\) is free space permittivity, \(k\) is the wavenumber, and \(R\) is the far-field distance.  
Figure 11: Simulated and measured reflection coefficients of the proposed antenna.  
Figure 10: (**a**) Top and (**b**) bottom views of the illustrating prototypical antenna.  
The antenna's \(-3\) dB axial ratio bandwidth was 3.5 GHz (36.5-40 GHz) from the simulation. The measured axial ratio bandwidth was 3.7 GHz (36.5-40.2 GHz), as displayed in Figure 13. The antenna resulted in a maximum gain of 6.2 dBi with an average gain of 4.75 dBi throughout its bandwidth. The proposed design has partial ground, due to which its radiation resulted in omnidirectional XZ and YZ planes, as displayed in Figure 14. Cross-polarization was minimal in the order of \(-45\) dB in the XZ plane. However, in the YZ plane, the cross-polarization was \(-17\) dB and \(-2\) dB due to the circular polarization characteristics of the antenna at 28 and 38 GHz, respectively.  
Figure 12: Surface current \(J_{n}\) for port excitation. The flow current depicts the RHCP and LHCP characteristics on the left and right portions of the antenna, respectively.  
Figure 13: Simulated and measured axial ratio and maximum gain.