# A Ka-Band Circular Polarized Waveguide Slot Antenna with a Cross Iris
## 3 Antenna Analysis  
In the proposed antenna design, the hexagonal shaped cavity with a rectangular waveguide shown in Figure 3 is used as an initial model (first reference antenna) to realize the circular polarization. The hexagonal shape is similar to a corner truncated patch antenna, which can be theoretically analyzed using a cavity model with the magnetic walls resonating in TM (Transverse Magnetic) mode [21]. However, this hexagonal cavity resonates TE mode with electrical side walls [22]. The truncated corners make the hexagonal cavity generate E-fields as two orthogonal modes, which are written in this paper as the \(E_{1}\) mode and \(E_{2}\) mode. As shown in Figure 4, because the truncated part (\(C_{1}\)) acts as additional capacitive loading, the \(E_{1}\) mode has slower phase velocity and smaller guided wavelength than does the \(E_{2}\) mode. As a result, a CP mode is generated by the addition of a lagging (\(E_{1}\)) mode and leading (\(E_{2}\)) mode. In a waveguide antenna, the operating frequency and axial ratio performance are predominantly affected by the dimension and shape of the cavity [17; 22]. As the dimension of a hexagonal cavity increases, the operation frequency bandwidth is expected to increase. However, the dimension of the hexagonal cavity is limited to the size of a feeding rectangular waveguide. Under such restriction, the lengths of a set of diagonal edges (\(C_{1}\) and \(C_{2}\)) of the cavity are optimized to obtain the best performance. Figure 5 shows the simulated reflection coefficient and axial ratio of the first reference antenna with different values of \(C_{1}\) and \(C_{2}\). As shown in Figure 5, as the dimension of the hexagonal cavity becomes smaller the resonance frequency shifts to the higher side. The circular polarization performance of the first reference antenna is acceptable when \(C_{1}\) = 6.5 mm and \(C_{2}\) = 4.4 mm with the 3 dB axial ratio bandwidth ranging from 30.37 GHz to 31.2 GHz. The first reference antenna has a \(-6\) dB reflection coefficient bandwidth of 3250 MHz (from 30.23 GHz to 33.48 GHz). Figure 4: Definition of the two orthogonal modes: (**a**) \(E_{1}\) mode; (**b**) \(E_{2}\) mode. Figure 3: The geometry of the initial model antenna (first reference antenna). To investigate that the circular polarization characteristic is achieved by the hexagonal cavity, the variation of the electric field distributions of the first reference antenna with different phases at 31 GHz are illustrated in Figure 6. As shown in Figure 6, the electric field rotates clockwise as the phase changes from \(0^{\circ}\) to \(270^{\circ}\). Therefore, we conclude that the first reference antenna has a left-handed circular polarization (LHCP) characteristic. Figure 5: Simulated (**a**) reflection coefficient and (**b**) axial ratio of the first reference antenna for different values of \(C_{1}\) and \(C_{2}\). Although the first reference antenna presents a reasonably good \(-6\) dB reflection coefficient and \(3\) dB axial ratio bandwidth, additional impedance matching is required because satellite applications generally impose a \(-10\) dB reflection coefficient criteria for communication efficiency [23]. To improve the impedance matching characteristic, we added a rectangular matching cavity located on the hexagonal cavity (second reference antenna). In the equivalent circuit, the long side (\(S_{2}\)) of the matching cavity acts as a capacitance while the short side (\(S_{1}\)) has an inductive characteristic [24]. Therefore, the impedance matching from the feeding rectangular waveguide to free space is improved through choosing proper values of \(S_{1}\) and \(S_{2}\) for the height (\(H_{3}\)) of \(0.5\) mm. The optimized values of \(S_{1}\) and \(S_{2}\) are \(4.3\) mm and \(4.8\) mm, respectively. As shown in Figure 7, the simulated \(-10\) dB impedance bandwidth of the second reference antenna becomes \(5690\) MHz (\(30.81\)-\(36.50\) GHz). Meanwhile, the \(3\) dB axial ratio bandwidth obtained is \(900\) MHz (\(31.79\)-\(32.69\) GHz).