# A Multi-Frequency Omnidirectional Antenna Based on a Ring-Shaped Structure
## 2 Theory and Design
Figure 2 shows the structural diagram of the evolution of a single-band antenna into a multi-band antenna. During the design process, we also discussed the influence of the shift of the antenna back structure on the antenna performance, among which, the simulation results of the back without a ring, three rings and three cross-shaped open rings have a similar trend, but the cross-shaped open ring structure makes the overall performance of the antenna optimal. Therefore, in this paper, we focus on the impact of the upper surface radiation patch structure on antenna performance. Figure 3 shows the simulation reflection coefficient (S\({}_{11}\)) curve corresponding to the antenna evolution process. As shown in Figure 3a, the radiant patch is an open resonator with a single ring, and the resonant frequency of the antenna is only 0.38 GHz. Figure 3b shows the double-rings radiant patch. Since multi-frequency resonances can be achieved between circular split ring resonators of different sizes, the resonant frequencies of the antennas are 0.25, 0.53, 1.06, 1.46, and 2.03 GHz, but only at 2.03 GHz, the return loss (S\({}_{11}\)) is less than \(-10\) dB. Figure 3c based on the two becomes a three-ring open resonator radiation patch, enhancing the effect of multi-frequency resonance. Not only does the return loss (S\({}_{11}\)) at the resonant points at 1.10, 1.32, and 2.07 GHz exceed 10 dB but new resonant points are added at 1.63, 1.97, and 2.9 GHz, indicating that the antenna has a multi-frequency capacity and can operate simultaneously in six bands from 0 to 3 GHz. To better understand the reason for the multi-frequency radiation properties of the antenna, the surface current distribution of the antenna was simulated and analyzed at the following six frequencies: 1.10, 1.33, 1.63, 1.97, 2.08, and 2.69 GHz. The results are shown in Figure 4.  
\[f_{0}=\left[\sqrt{\left(C_{SRRs}R_{SRRs}^{2}\right)/L_{SRRs}-1}\right](2\pi C_{SRRs }R_{SRRs}) \tag{1}\]0 Antenna design process: (**a**) Single ring patch; (**b**) Double rings patch; (**c**) Three rings patch. As shown in Figure 4, the structure of the three open-loop resonators on the antenna surface. At lower frequencies, 1.10, 1.33, and 1.63 GHz. This suggests that, at lower frequencies, the outermost ring structure plays a major role in the emission. In the three higher frequency bands of 1.97, 2.08, and 2.69 GHz, the surface currents of the three open ring structures are uniform and high in density, so the three open ring structures act as radiation in the higher frequency bands. Figure 5 shows the antenna radiation direction diagram in the E and H planes at six operating frequency points (1.10, 1.33, 1.63, 1.97, 2.08, and 2.69 GHz). As can be seen from Figure 5, when the antenna operates at 1.10, 1.33, and 1.63 GHz, surface E presents obvious \"8\" shaped half-wave dipole directional radiation characteristics, and the maximum radiation direction is near 0\({}^{\circ}\). The orientation map of the surface H is approximately a positive circle, indicating that the antenna has omnidirectional radiation properties at this time. As the operating frequency changes from low to high, the direction of  
\[f_{0}=\left[\sqrt{\left(C_{SRRs}R_{SRRs}^{2}\right)/L_{SRRs}-1}\right](2\pi C_{SRRs }R_{SRRs}) \tag{1}\]1 The surface current distribution of the antenna at (**a**) 1.10 GHz; (**b**) 1.33 GHz (**c**) 1.63 GHz; (**d**) 1.97 GHz; (**e**) 2.08 GHz; (**f**) 2.69 GHz. \[f_{0}=\left[\sqrt{\left(C_{SRRs}R_{SRRs}^{2}\right)/L_{SRRs}-1}\right](2\pi C_{SRRs }R_{SRRs}) \tag{1}\]2 Simulation results of the return loss of three antennas. (a) Single ring patch; (b) Double rings patch; (c) Three rings patch. antenna radiation changes to some extent. At 1.97 GHz, the antenna radiates approximately in the direction of the half-wave dipole radiation, and the radiation direction shift is negligible. However, in the two high-frequency operating bands of 2.08 and 2.69 GHz, the current distribution of the split-ring resonator ring structure on the antenna surface is more complex.