# Design of a Ku-Band Monopulse Antenna with a Truncated Reflector and an Open-Ended Waveguide Feed
## 3 Reflector Design  
Based on the foregoing design of the monopulse feed, a prime-focus parabolic reflector was designed. The reflector diameter was chosen for a sum gain of about 30 dB with good difference pattern characteristics. Figure 8a,b show the structure and dimensional parameters of the truncated reflector presented in this paper. The half illumination angles of the reflector in the \(E\)- and \(H\)-planes are denoted by \(\theta_{1}\) and \(\theta_{2}\) in Figure 8b. The equation for the reflector diameter \(D\), focal length \(F\), and \(E\)-plane illumination angle \(\theta_{1}\) is given by Equation (1):  
\[\theta_{1}=2\tan^{-1}\frac{1}{4F/D} \tag{1}\]  
Figure 6: (a) \(E\)-plane phase patterns of the sum channel. (b) \(H\)-plane phase patterns of the sum channel. Figure 7: (a) Phase patterns of the elevation difference channel. (b) Phase patterns of the azimuth difference channel. Since the \(H\)-plane beamwidth \(\theta_{2}\) is smaller than \(\theta_{1}\), the reflector is truncated, as shown in Figure 8a. Illumination angles \(\theta_{1}\) and \(\theta_{2}\) are adjusted for optimum performance in both the sum and difference patterns. When these angles are chosen for the best performance in the sum channel, the difference in the channel patterns is not good, so a compromise is required. The \(\theta_{1}\) and \(\theta_{2}\) parameters are obtained through an iterative calculation for the directivity pattern of the reflector. An optimum choice of \(\theta_{1}\) and \(\theta_{2}\) is made so that the gain requirement is met for the sum channel and a good monopulse slope performance can be obtained for the difference channels. The optimum values of \(\theta_{1}\) and \(\theta_{2}\) were found to be \(51^{\circ}\) and \(23^{\circ}\), respectively. The feed's phase center, at 1.0 mm inside the aperture, is placed at the focal point of the reflector. The waveguide is excited with the TE\({}_{10}\) mode using a wave port in the CST Studio Suite. As before, the sum and difference patterns are obtained by the proper combinations of four apertures of the feed. The reflector and the feed are simulated together so that the effect of the feed scattering is included in the far-field directivity patterns. Table 2 shows the dimensions of the designed reflector. Figure 9a shows the reflection coefficient of the TE\({}_{10}\)-mode-feed illuminating the reflector. The reflection coefficient is less than \(-10\) dB at 14-17 GHz, albeit with a slight increase in the periodic interference effects due to the presence of the reflector. The transmission coefficient or the coupling between apertures has also been increased again with period interferences. The \(E\)-plane coupling is still less than \(-15\) dB at 14-17 GHz, as seen in the \(S_{41}\) graph. The \(H\)-plane coupling (\(S_{21}\)) and diagonal-plane coupling (\(S_{31}\)) are less than \(-18\) dB at 14-17 GHz. Figure 9b shows the reflection and transmission coefficients of the probe-excited feed illuminating the reflector. The reflection coefficient is slightly larger than that of the TE\({}_{10}\)-mode excited feed and is still less than \(-10\) dB at 14-17 GHz. The coupling between the apertures is similar to that of the TE\({}_{10}\)-mode feed. The directivity patterns of the sum and difference channels are calculated by full-wave analysis using CST Studio Suite, including the feed. The sum-channel directivity patterns at smaller angles are shown in Figure 10a,b for the \(E\) plane and Figure 11a,b for the \(H\) plane. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & \(F\) (mm) & \(D\) (mm) & \(\theta_{1}\) (deg.) & \(\theta_{2}\) (deg.) & \(L_{t}\) (mm) & \(W_{t}\) (mm) \\ \hline
**Value** & 259 & 500 & 51 & 23 & 452.20 & 213.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dimensions of the truncated parabolic reflector. Figure 8: (a) Front view. (b) A 3D view of the proposed truncated parabolic reflector with a feed. 1.5\({}^{\circ}\) at 16 GHz; and 2.8\({}^{\circ}\), 1.4\({}^{\circ}\) at 17 GHz, respectively.