# Dual-Band Shared-Aperture Antenna with Pattern and Polarization Diversity
## 2 Antenna Design and Analysis
### Vivaldi Antenna Design  
To enable the designed antenna to cover the high-frequency frequency band, a metal Vivaldi antenna is placed inside the antenna Design 1 to form Design 2. The structure of Design 2 is shown in Figure 5. The feeding structure of Design 2 uses the lateral coaxial cable. The inner conductor of this coaxial cable is connected to one ridge of the Vivaldi antenna, and the outer conductor is connected to the other ridge, which facilitates the integration and processing of the Vivaldi antenna and monopole antenna. The expression equation for the exponential opening curve of the Vivaldi antenna is expressed as follows (\(C_{1}\) and \(C_{2}\) are constants, and the \(\alpha\) is the curvature of the groove line of the Vivaldi antenna) [31]:  
\[x(z)=C_{1}e^{az}+C_{2} \tag{1}\]  
In order to obtain a wide IMBW, the study of the Vivaldi antenna's key parameters is investigated. The working bandwidth of the Vivaldi antenna is mainly determined by  
Figure 4: **(a)** Reflection coefficient comparison between solid and hollow cone structure, (**b**) simulated reflection coefficient at different parameter \(\alpha\). Figure 5: Structure of Design 2, (**a**) side view, and (**b**) top view. the \(S\) and \(w_{3}\), which are the opening width at both ends of the exponential groove. The \(S\) and \(w_{3}\) are about half the wavelength of the cut-off frequencies of 21.02 and 29.6 GHz. In addition, the impedance-matching performance of the antenna is related to the length \(L_{1}\) of the exponential conical groove and \(L_{3}\), which represents the position of the coaxial cable feeding structure. Combined with the theoretical basis, the parameter \(L_{1}\) is analyzed to obtain a wider IMBW. Figure 6 shows the reflection coefficients of Design 2 with different \(L_{1}\), \(L_{3}\), and \(w_{3}\), indicating that two deep resonances at 25 and 29 GHz are generated within the operating bandwidth. When \(w_{3}\) increases, it can be seen that the low cut-off frequency of IMBW shifts to a higher frequency. When \(L_{1}\) increases, the overall working bandwidth of the antenna moves to the low frequency. Finally, \(L_{1}=6\), \(L_{3}=5\), and \(w_{3}=1.3\) are selected, and the optimized IMBW of the Vivaldi antenna is 21.02-29.6 GHz (8.58 GHz, 33.8%). To better analyze the working mechanism of Design 2, the electric field distribution of the antenna at 25 GHz is analyzed, and the corresponding electric field distribution is exhibited in Figure 7. It can be observed that when only the Vivaldi antenna structure exists, the energy radiates from the exponential gap to the opening of the antenna. The radiation field radiates in a large angle range, resulting in a sphere wave. By adding the hollow bowl around the Vivaldi antenna, the energy is more concentrated, which can be seen in Figure 7b. The electric field of the antenna in the maximum radiation direction is nearly the same as a plane wave after loading the metal bowl structure. There is negligible electric field distribution outside the metal bowl structure, and the radiation energy of the antenna is relatively more concentrated along the \(z\)-axis direction. As Figure 8 shows, the realized gain of Design 2 in the operating band is obviously higher than the one without loading the hollow cone structure, which proves the cone structure's function of concentrating energy. Figure 6: Simulated reflection coefficients of the Vivaldi antenna at different parameters (**a**) \(L_{1}\), (**b**) \(L_{3}\), and (**c**) \(w_{3}\). The medium polarization converter can turn the linear polarization waves emitted by the Vivaldi antenna into circular polarization waves. The medium polarization converter is placed directly above the monopole cone antenna, and its slabs form an angle of 45\({}^{\circ}\) along with the Vivaldi antenna. In the _xoy_ plane shown in Figure 9a, the direction of \(-45\) degrees from the \(x\)-axis is defined as the \(u\) direction, and the direction of 45 degrees from the \(x\)-axis is defined as the \(v\) direction, as shown in the figure.