# A Gap Waveguide-Based Compact Rectangular Waveguide to a Packaged Microstrip Inline Transition
## 3 Groove Gap Waveguide Characteristics  
The cores of both transitions are groove gap waveguide (GGW) sections. The propagation characteristics of this type of gap waveguide have been studied, and its performance has been found to be similar to that of an equivalent rectangular waveguide, whose width is narrower than the width of the GGW channel [29; 30]. However, in the first proposed transition we are dealing with partially filled GGW. Therefore, the propagation characteristics of this dielectric-filled GGW have been analyzed.  
In addition, in order to facilitate the use of this transition with wide microstrip substrates, the gap between the pins and the lid was partially filled with a dielectric substrate, specifically, a 100 \(\upmu\)m thick slab of Rogers CuClad 233 (\(\epsilon_{r}=2.34\) and \(\tan\delta=0.009\)) with 17 \(\upmu\)m copper cladding. The structure of the pins can be seen in Figure 2a and the optimized dimensions are compiled in Table 1. These dimensions provide a bandgap between 25 and 125 GHz.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Description** & **Value (\(\upmu\)m) Transition (a)** & **Value (\(\upmu\)m) Transition (b)** \\ \hline a & pin size & 500 & 600 \\ d & pin height & 1120 & 1190 \\ h & air gap & 34 & 80 \\ p & period & 1050 & 1240 \\ \(h_{\text{subs}}\) & substrate thickness & 100 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dimensions of the bed of nails used in the two proposed transitions.  
Figure 1: 3D view of the proposed microstrip to rectangular waveguide transitions. (**a**) Dielectric-filled ridge and groove gap waveguide-based transition (RW-RGW-GGW-\(\upmu\)strip). (**b**) Groove gap waveguide-based transition (RW-GGW-\(\upmu\)strip).  
Figure 2: Perspective view of unit cells of: (**a**) metallic pin and (**b**) groove gap waveguide partially filled with Rogers CuClad substrate.  
For this analysis, the height of the GGW, including the dielectric substrate thickness, was the same as that of the equivalent rectangular waveguide. Since the design was done in the W-band (75-110 GHz), it corresponds to the height of the WR10 waveguide, i.e., 1.27 mm.  
Using this bed of nails, waveguides with different width, \(w\) in Figure 2b, have been analyzed, and their propagation constant, \(\beta\), has been obtained. These results are shown in Figure 3, where they are compared with the propagation constant of a WR10 rectangular waveguide.  
It can be observed that the propagation constant for all widths is similar at high frequencies. However, the behavior at low frequencies turns out to be quite different. The cut-off frequency of the GGW is higher than the cut-off frequency of the standard rectangular waveguide for the same propagation channel width. This effect is ascribed to the smaller electrical dimensions of the GGW when compared with the rectangular waveguide. In addition, larger dispersion was present in the GGW [30]. In this case, the most similar behavior in terms of propagation constant with the WR10 waveguide corresponds to GGW width \(w\) = 2.65 mm.  
In the second transition type, shown in Figure 1b, the GGW was not filled with the dielectric substrate and the pin dimensions were those used in [28]. These dimensions are also gathered in Table 1.