# Conceptual Design of a Semi-Dual Polarized Monopulse Antenna by Computer Simulation
## 2 Feed Design
The directivity patterns of the elevation difference channel are the same as those of the azimuth difference channel except they are rotated by 90\({}^{\circ}\) around the \(z\)-axis. The maximum directivity of the difference pattern in the \(\varphi\) = 0\({}^{\circ}\) cut ranges from 8.8 dBi to 10.4 dBi at 14.5-16.0 GHz. The directivity is decreased by about 6 dB when we move from the \(\varphi\) = 0\({}^{\circ}\) cut to \(\varphi\) = 45\({}^{\circ}\) cut. The taper in the difference channel directivity at \(\theta\) = \(\pm\)75\({}^{\circ}\) (the sum channel 10 dB half beamwidth) is 12-18 dB at 14.5-16.0 GHz. Figure 11 shows the phase patterns of the azimuth difference channel (Del AZ) in the \(\varphi\) = 0\({}^{\circ}\) cut and in \(\varphi\) = 45\({}^{\circ}\) cut with the far-field origin at the phase center (0.2 mm into the waveguide). Over the 10 dB beamwidth (approximately 150\({}^{\circ}\)) of the sum pattern, the maximum phase variation is \(\pm\)63\({}^{\circ}\) at 14.5-16.0 GHz. The optimum phase center for the difference pattern is 4.0 mm in front of the waveguide aperture. In this case, the maximum phase variation is \(\pm\)25\({}^{\circ}\) at 14.5-16.0 GHz. In this work, we use the phase center of the sum pattern as the phase center for the monopulse feed. Figure 12 shows the 3D directivity patterns at 14.5 GHz of the sum and azimuth difference channels. The sum  
Figure 8: RHCP phase patterns of the sum channel. Figure 9: RHCP axial ratio patterns of the sum channel. The diameter of the reflector has been selected for 36 dBc sum gain, while also maintaining good difference patterns. The reflector illumination angle given by Equation (1) is chosen for the optimum efficiency of the sum pattern. \[\theta=2\tan^{-1}\frac{1}{4F/D} \tag{1}\]  
In Equation (1), \(F\) is the focal length and \(D\) is the reflector diameter. The feed illumination angle \(\theta\) is chosen to be the 10 dB taper angle of the sum pattern directivity, which is 75.4\({}^{\circ}\). The feed's phase center is placed at the focal point of the reflector. Both the feed and the reflector are simulated together to factor in the effect of feed scattering in the far-field directivity patterns of the reflector. Table 3 shows the dimensions of the reflector designed in this work. The reflection and coupling coefficients of the feed illuminating the reflector are shown in Figure 14, which is only slightly changed from the values of the feed alone shown in Figure 6. At 14.5-16.0 GHz, the reflection coefficients of the sum and difference channels are less than \(-\)15 dB and \(-\)10 dB, respectively. The coupling coefficient between Port 1 and Port 2 of the sum channel is less than \(-\)12.5 dB. Comparing Figures 6 and 14, we note that the reflection coefficient of the rectangular waveguide radiator of the difference channel is increased. The sum channel reflection and isolation are changed only a little by the presence of the reflector. A hole and a vertex plate at the reflector center may help reduce the reflection coefficient of the difference channel. However, we did not try to reduce the reflection coefficient. Figure 15 shows the sum channel directivity patterns of the reflector in \(\varphi=0^{\circ}\) and \(\varphi=45^{\circ}\) cuts for \(-5^{\circ}\leq\theta\leq 5^{\circ}\). The maximum directivity ranges from 36.1 dBc to 36.7 dBc at 14.5-16.0 GHz. At 16.0 GHz, the aperture efficiency of the reflector is \(-\)1.76 dB or 67%. The maximum sidelobe level is about \(-\)21 dB. The 3 dB beamwidth ranges from 2.80\({}^{\circ}\) to 2.50\({}^{\circ}\) when the frequency changes from 14.5 GHz to 16.0 GHz. Figure 16 shows the sum channel axial ratio patterns of the reflector in \(\varphi=0^{\circ}\) and \(\varphi=45^{\circ}\) cuts. In the \(\varphi=0^{\circ}\) cut, the axial ratio is less than 2.5 dB, while it is less than 5.0 dB in the \(\varphi=45^{\circ}\) cut over \(-2^{\circ}\leq\theta\leq 2^{\circ}\) at 14.5-16.0 GHz. The boresight axial ratio is 0.65 dB.