# A Ka-Band Circular Polarized Waveguide Slot Antenna with a Cross Iris
## 3 Antenna Analysis
This result indicates that the resonance frequency is moved to the upper frequency side because the dimension of the aperture changes by the addition of the rectangular matching cavity. A similar observation can be made for the axial ratio characteristic. In the second reference antenna, although the \(-10\) dB reflection coefficient bandwidth of \(5690\) MHz is achieved, most of the bandwidth except for \(900\) MHz (\(31.79\) GHz-\(32.69\) GHz) does not satisfy the \(3\) dB axial ratio requirement. This challenge often occurs when designing CP antennas [17; 25]. Figure 6: Simulated electric field distributions of the first reference antenna with different phases at \(31\) GHz: (**a**) phase = \(0^{\circ}\); (**b**) phase = \(90^{\circ}\); (**c**) phase = \(180^{\circ}\); (**d**) phase = \(270^{\circ}\). In the proposed antenna, to resolve this problem, a metallic cross iris is mounted on the bottom of the rectangular feeding waveguide to enhance the axial ratio bandwidth which is an important factor for evaluating the CP performance. It can be calculated using the following equation [26]. Figure 7: Simulated (**a**) reflection coefficient and (**b**) axial ratio of the first reference antenna, the second reference antenna and proposed antenna. \[AR_{linear\ scale}\ =\ \frac{\left[r^{2}+1^{2}+\left[r^{4}+1^{4}+2r^{2}\cos(2 \Delta)\right]^{1/2}\right]^{1/2}}{\left[r^{2}+1^{2}-\left[r^{4}+1^{4}+2r^{2}\cos (2\Delta)\right]^{1/2}\right]^{1/2}} \tag{3}\]  
where \(r\) is the ratio of magnitudes of orthogonal electric fields, and \(\Delta\) is the phase difference between the two orthogonal electric fields at the far zone. In general, it can be said that CP operates well when the value of the axial ratio is less than 3 dB. Accordingly, when \(r=1\), the phase difference should range from 70\({}^{\circ}\) to 110\({}^{\circ}\) and when \(\Delta=90^{\circ}\), the ratio of magnitudes should satisfy the range of \(\frac{1}{\sqrt{2}}\leq r\leq\sqrt{2}\). Figure 8 shows the simulated phase differences between the two orthogonal modes (\(E_{1}\) and \(E_{2}\)) of the proposed antenna and the second reference antenna. The phases of the two orthogonal electric fields can be minutely controlled separately because the iris structure consists of two arms with asymmetrical lengths (\(L_{1}\) and \(L_{2}\)). By adjusting the lengths of the cross iris, the improved 90\({}^{\circ}\) phase difference range (70\({}^{\circ}\) to 110\({}^{\circ}\)) is achieved (31.70 GHz-39.25 GHz). However, the 3 dB axial ratio bandwidth is not the same as the 90\({}^{\circ}\) phase difference range because the ratio of the magnitude of the two orthogonal electric fields should be considered. To analyze how the cross iris affects the magnitude of the two electric fields, simulated amplitudes of the two orthogonal modes of the proposed antenna and the second reference antenna are presented in Figure 9. In the second reference antenna, the two points where the mode lines cross are located at 30.04 GHz and 31.80 GHz. At these two points, the magnitudes of the two modes are equal. However, as shown in Figure 8, because the 90\({}^{\circ}\) phase difference range of the second reference antenna is from 31.7 GHz, it cannot be said that CP is generated at less than 31.7 GHz. Moreover, the difference in amplitude between the two modes from the second point (31.8 GHz) is increasing, which indicates deteriorated CP performance. For the proposed antenna, the magnitudes of the two orthogonal modes are equal at three points (30.75 GHz, 32.32 GHz, and 38.44 GHz). In addition, the amplitudes of the two modes become close to each other over the whole frequency range from (32.32 GHz to 38.44 GHz). It can be said that the proposed antenna has a good equal magnitude characteristic. Figure 8: Simulated phase difference between two orthogonal electric fields of the proposed antenna and the second reference antenna. Figure 10 depicts the simulated amplitudes of \(E_{1}\) and \(E_{2}\) modes for various values of two different lengths (\(L_{1}\) and \(L_{2}\)) of the cross iris.