# An In-Line Coaxial-to-Waveguide Transition for Q-Band Single-Feed-Per-Beam Antenna Systems
## 3 Results
### Tolerance Analysis
The proposed solution, shown in Figure 11, is to create a groove in the ridge, with a width equal to the pin diameter, and to short-circuit via the application of a two-component glue (like  
Figure 10: Return loss of the transition step shown in Figure 9. The g parameter modifies the impedance in the WG\({}_{\text{r}}\) step and introduces a mismatch with the coaxial cable which affects the RL. Figure 9: Section of the device involved in the second gap test: it is evaluated the performance by considering the device step from S section (upstream the air gap) to S’ (in the WG\({}_{\text{r}}\) step) and by varying the g parameter, which is related to the position of the pin insertion and to first ridge height. The RL is evaluated in input to the S section. a silver-filled epoxy paste, as EPO-TEK H20E). The significant size of the groove was small compared to the operative wavelength, so it would not affect the performance in a relevant way and the ridged step impedance kepteps almost the same. Figure 12 shows the deviation in the return loss for a 1 mm long groove compared with the base case, and confirmed a negligible deviation in the performance. However, our refined analysis considered several possible scenarios where the pin position was not perfectly centred along the WG but it presented an offset in the H-plane. A wider groove was considered, modelled as EPO-TEK H20E filled, and several potential errors due to the non perfect alignment of the end-launcher were considered (the cases are shown in a wide panel displayed in Figure 13):  
1. the original RL presented in Figure 7 (reference case);
2. a simple lateral shift of 0.4 mm (which covered a 0.8 mm range over a 1.1 mm ridge width) of the groove along the ridge width (Figure 13a,b);
3. a groove (wide twice the pin diameter, equal to the 40% off the ridge width) whose glue thickness was 20 \(\upmu\)m higher than the metallic ridge, with a lateral shift of 0.1 mm of the pin (the maximum available in the groove) (Figure 13c,d);
4. a groove (wide twice the pin diameter, equal to the 40% off the ridge width) whose glue thickness was 20 \(\upmu\)m higher than the metallic ridge and the direct contact was missing between the pin and the ridge, with a lateral shift of 0.1 mm of the pin (the maximum available in the groove) (Figure 13e,f). The graph in the Figure 14 reports the RLs over this study: all the cases considered keep the RL higher than 20 dB over the whole Q band, this assured a good tolerance on the pin shorting to the ridge. It is worth noting, by considering cases 3 and 4, that a non-direct contact of the pin was well compensated by the silver-filled glue, since the RL retained a value higher than 20 dB, thus implying that, in this unfortunate manufacturing error, the glue acted as a conductive pathway from the pin, still ensuring a good signal integrity. Further analysis showed that a groove width three times the pin diameters (with the relative pin misalignment) kept the RL over 18 dB over the whole Q-band. In Figure 15 is shown the field distribution on the cross-section at center of the \(\rm l_{p}\) long step where the coaxial pin penetrated in the WG: the misalignment of the pin and the grooved shorting did not affect the TE\({}_{10}\) mode in the WG. Therefore, from our simulations, a relevant insight and useful feedback to the future manufacturing step was found. Figure 12: Return loss comparison: the grooved short displayed in Figure 11 (blue line) does not introduce a relevant variation with respect to the return loss of the initial design shown in Figure 7.  
Figure 13: Geometry of the cases tested for the non perfect alignment of the end-launcher (gray) on the ridge (light gray), displayed in top and frontal view: (**a,b**) case 2, (**c,d**) case 3, (**e,f**) case 4. The glue which fills the groove is displayed in green.