# Highly Compact Through-Wire Microstrip to Empty Substrate Integrated Coaxial Line Transition
## 3 Results  
As losses in this transition are mainly due to the presence of the dielectric, they could be reduced if substrates with an adequate loss behavior were used. Two ESICL back-to-back prototypes in the band 0-20 GHz were designed to validate this through-wire transition and its design procedure. For the first transition, a Taconic RF-10 substrate of permitivity \(\epsilon_{r}\) = 10.2, 0.25 mm height and copper metallization of 17.5 \(\upmu\)m with an additional copper electrodeposition of 9 \(\upmu\)m has been used to manufacture the microstrips, and it has been used a Rogers 4003C substrate of permitivity \(\epsilon_{r}\) = 3.55, 0.813 mm height and copper metallization of 17.5 \(\upmu\)m (plus 9 \(\upmu\)m of electrodeposition) for the rest of the layers. Table 1 shows the final dimensions for the first transition after the optimization process, whereas simulated results can be seen in Figure 3.  
For the second version of the transition, the same Rogers 4003C (0.813 mm height and 26.5 \(\upmu\)m of total metallization) substrate was used for all the layers. Table 2 shows the final dimensions for the second transition (all the layers manufactured with Rogers 4003C) after the optimization process. The device was measured with an Anritsu vector network analyzer and a de-embed on the initial microstrip was made using the custom TRL calibration kit shown in Figure 6. As it is revealed in Figure 7 there is good agreement between simulation and measurements: return loss is above 15 dB in the whole band of interest (as can be seen in Figure 7 left), whereas insertion loss is below 1 dB for \(f<14.5\) GHz, below 1.5 dB for \(14.5<f<17\) GHz and below 2.5 dB for \(17<f<20\) GHz (see Figure 7 right). To confirm the independence of the feeding line angle, a parametric simulation was made (considering only one transition, not the whole back-to-back). The angle was swept from \(0^{\circ}\) to \(180^{\circ}\) in intervals of \(30^{\circ}\). Results shown in Figure 8 demonstrate the small  
Figure 5: Composition of the final device: top view of the final device with scale reference. Figure 6: Custom TRL calibration kit. Figure 7: Results of the simulated and measured scattering parameters for the back-to-back prototype. variation of the reflection coefficient with changes in the angle. As the frequency increases, the evanescent modes that may be excited in the transition have a wider range and are able to store more energy, or in other words, the parasitics related to the feeding angle become more relevant; therefore, slight differences in \(S_{11}\) can be appreciated around 18 GHz, but they are so small that they are completely negligible and have no effect on the behavior of the prototype. This fact is reinforced in the trend shown for \(S_{21}\) depending on the angle, which is totally independent of it. This transition is also extremely robust and tolerant to the variability of the most critical dimensions (those with influence in the gap, the pads and the position of the filament) during the manufacturing process. A yield analysis was carried out considering that those dimensions could present a randomized and independent variation given by manufacturing tolerances; for those variations, it has been assumed a normal distribution with zero mean and standard deviation of 2 (the laser micromachining process tolerance), 25, 50 and 100 microns. Under those constraints, an acceptable performance quality rule has been adopted as having \(S_{11}<-15\) dB in the passband. The results shown in Table 3 reveal that this transition is extremely insensitive to small (2 microns) and medium (25 and 50 microns) manufacturing errors and quite acceptable for very high tolerance errors (100 microns). \begin{table}
\begin{tabular}{c c} \hline \hline
**Tolerance** & **\% of Transitions with \(S_{11}<-15\) dB** \\ \hline
2 microns & 100\% \\
25 microns & 99.83\% \\
50 microns & 92.84\% \\
100 microns & 76.80\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the yield analysis.