# The Uses of a Dual-Band Corrugated Circularly Polarized Horn Antenna for 5G Systems
## 2 Mode Converter and Circularly Polarized Converter Design
### Circularly Polarized Converter  
In the previous research results [4], it is found that the single ridge structure has a very good effect on narrow frequency applications. In the proposed design, double ridge structure is used since the single ridge structure cannot meet the design conditions at both the low-frequency band (26.5-30.0 GHz) and the high-frequency band (36.0-40.0 GHz). The ridge structure is designed to be tunable and this flexible design will benefit its use in a wide range of applications.  
The schematic layout of the mode converter and circularly polarization converter is shown in Figure 3a while the 3D structure and parameters of the circular polarization converter are shown in Figure 3b. The ridged polarizer is located at a \(\pm 45^{\circ}\) offset with respect to the E field axis, and an incident linearly polarized wave (TE\({}_{11}\) mode), with polarization orientation which lies at the center between the x axis and y axis, is assumed, as shown in Figure 3c.  
Figure 1: The cross-section view of the dual-band corrugated circularly polarized horn.  
Figure 2: E field pattern of mode converter at: (**a**) 28 GHz and (**b**) 39 GHz. (Normalized to max value for red areas and minimum value for blue areas).  
wave represented by the superposition of two equal-amplitude orthogonal TE\({}_{11}\) waves which have 90\({}^{\circ}\) differential phase shifting between them [12]. In the polarization converter region, the propagation constants \(\beta_{1}\) and \(\beta_{2}\) of the E\({}_{1}\) and E\({}_{2}\) field are not the same because the cross section of circular waveguide is slightly perturbed by the ridged polarizer. E\({}_{2}\) causes more phase delay than E\({}_{1}\). This will make the antenna act as a right-hand circularly polarization antenna. Consequently, if the rectangular waveguide is rotated by 90\({}^{\circ}\), a left-hand circularly polarization antenna will be created, as shown in Figure 3d.  
Ridged polarizer can be accomplished by choosing an appropriate height, width, and length for the ridged polarizer to attain a 90\({}^{\circ}\) phase difference at the circular waveguide output port. The theoretical phase difference can be estimated using the formula in Equation (1).  
\[\begin{array}{ll}\Delta\psi&=\psi_{1}-\psi_{2}=(-\beta_{1}\ell)-(-\beta_{2} \ell)=(\beta_{2}-\beta_{1})\ell=2\pi\ell\Big{(}\frac{1}{\lambda_{g2}}-\frac{1} {\lambda_{g1}}\Big{)}\\ &\hskip 142.26378 pt=\frac{2\pi\ell}{c}\Big{(}\sqrt{f^{2}-f_{2}^{2}}-\sqrt{f^{2} -f_{c1}^{2}}\Big{)}\end{array} \tag{1}\]  
where \(\Delta\psi\) is the phase difference of orthogonal TE\({}_{11}\) mode, \(\ell\) is the length of the ridged polarizer, \(f_{c1}\) and \(f_{c2}\) are the cutoff frequencies of E\({}_{1}\) and E\({}_{2}\), respectively.\(f_{c1}\) and \(f_{c2}\) can be determined by the transverse resonance technique [13].  
According to the formula, the phase of the electric field is affected by the length of A1. The amplitude of the electric field is compressed by the ridges that are controlled by the parameters H and D, while the return loss can be optimized by changing the angle \(\theta\) of the ridge. The optimized parameters of the circularly polarized converter are listed in Table 1. Figure 4 presents the electric field versus phase change graphs at an operating frequency of 28.5 GHz. The circularly polarized wave can be produced by this circularly polarized converter.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline A1 & 17 mm \\ \hline A2 & 9 mm \\ \hline H & 1.46 mm \\ \hline \(\theta\) & 8.5 degrees \\ \hline D & 1.50 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of circularly polarized converter.  
Figure 4: E field pattern of waveguide with different phases (at 28.5 GHz).