# An In-Line Coaxial-to-Waveguide Transition for Q-Band Single-Feed-Per-Beam Antenna Systems
## 3 Results
### Tolerance Analysis  
Since, as aforementioned in the introduction, the required accuracy and tight mechanical tolerances is one of the main issues at such frequencies [1], it is relevant to investigate some of the most critical parts in the design in order to estimate the tolerances in the manufacturing process. By performing accurate numerical experiments, as usually done when designing this type of RF devices, we expect to minimize post-realization tuning procedures and technological contingencies, while gaining relevant insights into the performance of the proposed in-line coaxial-to-waveguide transition at Q-band. The main issue is surely the connection between the pin and the waveguide. More precisely, the vertical offset with respect to the WG center is the most sensitive parameter: the gap g determines the characteristic impedance of the R-WG step immediately downstream the end launcher, so that it is matched to the latter, and in the same time it sets the impedance to be matched to the full waveguide through the Chebyshev impedance transformer. Therefore, we have evaluated the transition RL response over an interval of values of g around the optimal value. As shown in Figure 8, the RL was better than 20 dB over the whole Q band for a values range of g equal to 0.195-0.215 mm (about 10% around the design value). In this range the ridge kept higher than the first Chebyshev transformer ridge (h\({}_{\text{c1}}\) high), further increase \begin{table}
\begin{tabular}{l c c} \hline \hline
**Step** & **h [mm]** & **1 [mm]** \\ \hline
1 & 2.58 & 1.81 \\
2 & 2.37 & 1.9 \\
3 & 1.91 & 1.92 \\
4 & 1.22 & 1.9 \\
5 & 0.55 & 1.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometrical size of the Chebyshev impedance transformer. in g degraded the performance due to the impedance mismatch between the two ridge heights \(\text{h}_{\text{r}}\), \(\text{h}_{\text{c1}}\). As a matter of fact, by considering only the transition stadiums between the air gap and the first ridge as in Figure 9 (in the following, the WG step with the \(\text{h}_{\text{r}}\) high ridge was named \(\text{WG}_{\text{r}}\)), the matching showed a higher tolerance, as displayed in Figure 10. As reported in the graph, the RL was evaluated by varying g in the range 0.18-0.22 mm, which was a variation of 20% around 0.2 mm. The RL kept higher than 20 dB in all the variation range, by assuring a good tolerance for such a parameter and a suitable matching between the end launcher and the R-WG. It follows that, in the previous test, a significant contribution to the performance degradation was due to the different impedance value in the \(\text{WG}_{\text{r}}\) with respect to the theoretical value the Chebyshev transformer was matched to. Figure 8: Tolerance analysis for the vertical offset of the pin insertion. The return loss is evaluated by varying the gap g between the pin and the upper WG wall. Figure 7: Return loss and insertion loss evaluated in the section between the transverse section of the coaxial cable upstream the air gap and the transverse section of the hollow waveguide. This section is far enough from the Chebyshev transformer to avoid issues due to higher modes in the ridges’ edges. Therefore, in order to reduce the performance degradation of the manufactured device, it is worthwhile to split the design and manufacturing process in two steps (feasible, for instance, with milling or 3D printing technologies [43]). The first consists in the realization of the block from the coaxial end launcher to the aforementioned WG\({}_{\text{r}}\) step, once the real h\({}_{\text{r}}^{*}\) value is measured (and, the input impedance in WG\({}_{\text{r}}\) towards the launcher is known), the ridge-stepped Chebyshev transformer is designed and optimized with respect to h\({}_{\text{r}}^{*}\). In this way, a partial compensation of the inaccuracies given by unavoidable errors in the the construction process is obtained. Another significant matter is the short between the coaxial pin and the ridge.