## 2 Characteristic Theory-Based Antenna Methodology
In this case, a parallel response of Modes 1 to 4 was noted in response to an incident electric field from 23 to 30 GHz. Similar characteristics continued from 30 to 44 GHz. The characteristic angle showed a linear phase change of modes through Figure 4c. Modes 1 and 4 had an inductance effect, and Modes 2 and 3 had a capacitance effect from 23 to 30 GHz, with a maximum equal-phase difference of 40\({}^{\circ}\). From 30 GHz onwards, all modes converged at a CA \(\approx\) 180\({}^{\circ}\). This response showed that the summation of modes \(J_{1}+J_{2}+J_{3}+J_{4(partial)}\) contributed to resonance from 23 to 30 GHz. From 30 to 44 GHz, the summation of \(J_{1}+J_{2}+J_{3}+J_{4}+J_{5}\) led to resonance. Overall, the structure was estimated to have good impedance matching from 23 to 44 GHz, resulting in a broadband antenna. Furthermore, the radiation patterns were analyzed by considering the surface current distributions of these modes in Figure 5.  
Figure 2: (**a**) The antenna structure of two concentric rings (Ant2) and their results: (**b**) MS difference and (**c**) CA difference. The proposed antenna was estimated to generate broadband characteristics with resonance at 28 GHz. The shape of the antenna has a circular ring, so it was expected that the current from the feed line would flow in both directions. The right and left equilateral triangles provide the return path for the current, thereby making the current flow in a clockwise and anti-clockwise direction, generating circular polarization. Therefore, the analysis of CP behavior was also carried out through surface currents of CMA. Due to the antenna's broadband characteristics, the current behavior was studied at 25, 28, 35, and 38 GHz, as shown in Figure 5. To achieve circular polarization, the surface current of sets of resonant modes should have had equal magnitude with the orthogonal phase. From the MS and CA, it was clear that the sum of \(J_{1}\) to \(J_{4}\) contributed to resonance from 23 to 30 GHz. Therefore, the surface current \(J_{1}\) to \(J_{4}\) at 25 and 28 GHz is shown in Figure 5a,b. At 25 GHz, \(J_{1}\) and \(J_{2}\) had vertical polarization, and \(J_{3}\) and \(J_{4}\), horizontal polarization. However, the magnitude of \(J_{1}\) and \(J_{2}\) was poor, resulting in a smaller minor axis compared to the major axis of \(J_{3}\) and \(J_{4}\). As a result, the polarization was linear on the y-axis. A similar behavior was studied at 28 GHz; \(J_{2}\) and \(J_{4}\) had higher magnitudes, leading to linear polarization in the y-axis. However, at 35 and 38 GHz, a pair of modes achieved CP. Looking closely at 35 GHz, \(J_{1}+J_{2}+J_{5}\) had y-axis polarization, and \(J_{3}+J_{4}\) had x-axis polarization in Figure 5c. A combination of these orthogonal modes achieved circular polarization. A similar pattern continued at 38 GHz, \(J_{1}+J_{4}\) had y-axis polarization and \(J_{2}+J_{3}+J_{5}\) had x-axis polarization, as observed in Figure 5d. Figure 3: (**a**) Concentric ring antenna added with another circular patch at the center of the radiator (Ant3). The corresponding (**b**) MS and (**c**) CA difference results. Further, an understanding of the resultant radiations from these surface currents is presented in Figure 6. The variations in current distribution with respect to different axes led to different radiation patterns. Here, only the consistent patterns generated by various modes with increasing frequency were considered. The CMA indicated that the proposed structure generated omnidirectional and bidirectional radiation in the XZ and YZ planes, with an approximated gain of 3.5 dBi. \[MS_{n}=\left|\frac{1}{1+j\lambda_{n}}\right| \tag{2}\]0 (**a**) Proposed antenna structure (Ant4) with its (**b**) MS and (**c**) CA responses. \[MS_{n}=\left|\frac{1}{1+j\lambda_{n}}\right| \tag{2}\]1 Surface current \(J_{n}\) at (**a**) 25 GHz, (**b**) 28 GHz, (**c**) 35 GHz, and (**d**) 38 GHz.