## 3 Very Compact Waveguide OMT with Folded Ports  
The design described in Section 2 is adapted here to include folded single-mode ports as proposed in [20]. Besides reducing the footprint of the component, this design variant has the advantage to be well adapted to additive manufacturing techniques, avoiding most overhanging parts in the original design when printing along the longitudinal direction of the feed assembly [16]. CAD views of the modified design are reported in Figure 5, introducing two additional design parameters: \(b_{f}\), corresponding to the narrow wall dimension of the folded waveguides, and \(c_{f}\), corresponding to the symmetric chamfer at the transition to the OMT. The optimized values for these parameters are \(b_{f}=2.8\) mm and \(c_{f}=2.9\) mm, which result in the folded waveguides being very close to each other. Implementing a mill radius of 1.1 mm, as also implemented in Section 2, the worst case distance between the waveguides is \(d_{f}=1.05\) mm (see Figure 5), which is well in line with typical constraints of CNC milling and additive manufacturing techniques. A full-wave model of this modified waveguide OMT was also implemented in Ansys HFSS, adding a milling radius of 1.1 mm to all outer edges, as carried out in the model of Section 2. Considering the good agreement between measured and simulated data demonstrated in the previous section, only numerical results are reported here. The change in the waveguide transition design slightly detunes the response of the component, specifically the XPD, with the resonance shifting to lower frequencies. A small adjustment of some design parameters is required. The updated design values for the folded case are reported in Table 2. The remaining parameters keep the same values as in Table 1.  
The simulated reflection and port-to-port coupling coefficients for this model are reported in Figure 6 in _solid lines_. For comparison, the simulation results of the reference case are also reported in _dashed lines_. Interestingly, this configuration was found to improve the scattering parameters, with worst case reflection and coupling coefficients of \(-24.9\) dB and \(-24.8\) dB, respectively, over the operating frequency band. For reference, the numerical results obtained for the standalone OMT with folded ports are also reported in Figure 6 in _dotted lines_, confirming the little impact of the horn antenna also in this case. Figure 4: XPD of the compact waveguide OMT assembled with a conical horn (on-axis value), comparing measured (_solid lines_) and simulated (_dashed lines_) results. The simulated standalone OMT results are overlaid in _dotted lines_. The specifications are marked with a _black thick line_. The simulated on-axis XPD of the OMT assembled with the horn is reported in Figure 7 in _solid lines_. The results of the reference design are provided for comparison in _dashed lines_. The OMT design with folded ports achieved an XPD better than 30.1 dB over the nominal bandwidth, comparable to that of the reference OMT design. The performance of the standalone OMT with folded ports is reported in Figure 7 in _dotted lines_, confirming that this parameter is also mostly unaffected by the horn antenna. Note that this design was still constrained with the width of the probing section being set equal to the width of the standard WR42 waveguide and the common port being constrained by the available \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Value (mm)** & **Parameter** & **Value (mm)** & **Parameter** & **Value (mm)** \\ \hline \(z\) & 4.15 & \(d_{1}\) & 5.73 & \(z_{1}\) & 2.50 \\ \(c\) & 1.16 & \(d_{2}\) & 2.63 & \(z_{2}\) & 2.49 \\ \(b_{f}\) & 2.80 & \(c_{f}\) & 2.90 & \(d_{f}\) & 1.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design parameters of the very compact waveguide OMT in the K-band with folded single-mode ports.