# Design of a Ku-Band Monopulse Antenna with a Truncated Reflector and an Open-Ended Waveguide Feed
## 2 Feed Design  
Figure 1 shows the structure and dimensional parameters of the monopulse feed presented in this paper. The feed consists of four rectangular-waveguide open-end radiators on a circular ground plane or flange. The beauty of the proposed feed is its simplicity. The waveguide is excited by a coaxial probe. Four waveguide radiators are combined to form a sum pattern, an elevation difference pattern, and an azimuthal difference pattern that are suitable for illuminating a parabolic reflector. The waveguide aperture dimensions \(a\) and \(b\) are chosen so that the feed will give suitable sum and difference patterns at 14-17 GHz. The gap between the rectangular apertures is chosen so that the grating lobe is suppressed in the visible region of the radiation angle while the coupling between the waveguide apertures is low enough (e.g., less than \(-20\) dB). A circular flange is employed to reduce backward radiation from the feed. Figure 1: Dimensional parameters of the designed feed. (**a**) Front view. (**b**) Side view. (**c**) Probe dimensions. Once the feed dimensions are determined, the waveguide is fed by a coaxial probe whose diameter and position are found by iterative parametric analysis. Critical to obtaining a good impedance matching of the probe-excited rectangular monopulse feed is the probe length (\(L\)), the probe diameter (\(E\)), and the probe's position away from the waveguide end wall (\(C\)). The length \(L\) of the probe is less than a quarter waveguide wavelength (\(<\)\(\lambda_{g}\)/4), and that makes it behave similar to a capacitor, thereby introducing capacitive susceptance to match the source to the load. All the parameters are optimized for frequencies of 14-17 GHz. The cutoff frequency of the fundamental TE\({}_{10}\) mode in the rectangular waveguide is 9.375 GHz, which is determined by the waveguide's broadwall dimensions \(a\). The dimensions in millimeters of the designed feed are shown in Table 1.  
Figure 2 shows four open-ended waveguide apertures, where \(A_{1}\), \(A_{2}\), \(A_{3}\), and \(A_{4}\) are apertures in quadrants one, two, three, and four, respectively. A sum pattern is obtained by adding all the apertures in the phase (\(A_{1}+A_{2}+A_{3}+A_{4}\)). An elevation difference pattern is obtained by deducting the two upper apertures from the two lower quadrants (\(A_{1}+A_{2}-A_{3}-A_{4}\)). Apertures \(A_{1}\) and \(A_{2}\) are excited with a phase of 0\({}^{\circ}\) while apertures \(A_{3}\) and \(A_{4}\) are fed with a phase of 180\({}^{\circ}\). This elevation difference pattern is used to compute the target's location in the elevation plane. The azimuthal difference pattern is realized by subtracting the right vertical apertures from the left vertical ones (\(A_{2}+A_{3}-A_{1}-A_{4}\)). Aperture \(A_{2}\) and \(A_{3}\) have a phase of 0\({}^{\circ}\), while apertures \(A_{1}\) and \(A_{4}\) are in a 180\({}^{\circ}\) phase. The azimuthal difference pattern is used to obtain the target's location in the azimuth plane. Figure 3a,b depict the reflection coefficient and transmission coefficients between apertures. In Figure 3a, the waveguides are excited with the TE\({}_{10}\) mode (wave port in CST Studio Suite), while they are excited with a coaxial probe in Figure 3b. Good results were obtained in the reflection and transmission coefficients in both cases at 14-17 GHz. Particularly, the reflection coefficient (\(S_{11}\)) of Figure 3a shows a good return loss below 14.29 dB from 14 GHz to 17 GHz, and in Figure 3b, the reflection coefficient is less than 12 dB at 14-17 GHz. The \(E\)-plane coupling is still less than 15 dB at 14-17 GHz, as can be seen in the \(S_{41}\) graph; the \(H\)-plane coupling (\(S_{21}\)) and diagonal-plane coupling (\(S_{31}\)) are less than 31 dB at 14-17 GHz in both cases. Figure 4a,b show the \(E\)- and \(H\)-plane directivity patterns of the sum channel. The maximum directivity of the sum channel is 13.4, 13.7, 14.3, and 14.8 dB at 14, 15, 16, and 17 GHz, respectively.