# A Gap Waveguide-Based Compact Rectangular Waveguide to a Packaged Microstrip Inline Transition
## 5 Simulation Results  
The procedure above has been applied to a microstrip to standard rectangular waveguide transition working at W-band. The dimensions obtained are compiled in Tables 2 and 3 for the first and second models, respectively. A perspective view of the Chebyshev transformer and a top view of the microstrip to ridge gap waveguide transition are shown in Figures 5 and 6. First, both parts of the transition were simulated separately using the 3D full-wave simulator Ansys High Frequency Structure Simulator (HFSS), based on the finite element method. The performance of the first transition is shown in Figure 7. Since a back-to-back configuration was used for experimental validation, a comparison between the performances of single and back-to-back configurations is presented in the same figure. In the case of the back-to-back configuration, both transitions were connected by a 5.18 mm long microstrip line. Figure 4: Cut-off frequency of the second mode of the GGW for channel heights. (Inset) Cut-off frequency expression, where \(c\) is the speed of light and \(m\) and \(n\) are the indexes of the \(TE_{mn}\) mode, (2,0) in this case. The red line represents the upper limit of the W-band. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Design Value** & **Fabricated Value** \\ \hline \(w\) & 2650 & 2590 \\ \(w_{r}\) & 1200 & 1130 \\ \(b_{1}\) & 115 & 116 \\ \(b_{2}\) & 130 & 116 \\ \(b_{3}\) & 377 & 361 \\ \(b_{4}\) & 852 & 909 \\ \(b_{5}\) & 1200 & 1212 \\ \(l_{1}\) & 400 & 470 \\ \(l_{2}\) & 550 & 470 \\ \(l_{3}\) & 673 & 685 \\ \(l_{4}\) & 705 & 683 \\ \(l_{5}\) & 726 & 697 \\ \(l_{t}\) & 1500 & 1467 \\ \(w_{t}\) & 1300 & 1256 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dimensions of the first transition model; see Figure 1a for reference. All dimensions in \(\upmu\)m.  
Figure 5: Microstrip to standard rectangular transition: (**a**) perspective view of the Chebyshev transformer split in half for the first model and (**b**) for the second model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Design** & **Fabricated** \\ \hline \(w_{t}\) & 300 & 317 \\ \(w_{r}\) & 325 & 256 \\ \(b_{0}\) & 115 & 158 \\ \(b_{1}\) & 325 & 378 \\ \(b_{2}\) & 700 & 758 \\ \(b_{3}\) & 975 & 957  
For the single transition the return loss is better than 20 dB for almost the whole bandwidth (77-107.9 GHz). The mean return loss is 23.9 dB, and in the whole W-band bandwidth, it is below 15.74 dB. For the back-to-back configuration the performance slightly degrades: the return loss is better than 19 dB within the 75-108.3 GHz bandwidth. This slight degradation of the return loss performance, compared to the single transition, is ascribed to the reflections due to the non-perfect matching at both ports. On the other hand, the single transition presents insertion loss below 0.6 dB, with mean value 0.3 dB. The back-to-back transition has a maximum insertion loss of 1.3 dB and a 0.6 dB mean value. This insertion loss increment is mainly caused by the losses associated with the 5.18 mm microstrip line in between both transitions. However, in both cases the insertion loss is below 1 dB and the return loss is better than 19 dB. For the second transition model, the comparison of the predicted response of single and back-to-back configurations is shown in Figure 8. The single transition performs return loss higher than 15 dB for the whole W-band and better than 20 dB from 80 GHz to 107.3 GHz. The mean value is 26.68 dB. The insertion losses are lower than 0.5 dB and its mean value is 0.27 dB. On the other hand, the back-to-back transition performs return loss higher than 10 dB for the whole band and better than 15 dB from 78 GHz to 107 GHz. Figure 8: Simulation of the scattering parameters for the microstrip to standard WR-10 single (solid line) and back-to-back transitions (dashed line), second prototype: (**left**) insertion loss and (**right**) return loss.