## 2 Proposed Interface Layer Using a CPW
### Analysis of the Transitions of the Proposed Interface Layer  
Figure 4 shows the normalized E-field distributions according to the configurations in transition part \(A\). The E-field distributions were investigated on the \(zx\)-plane (\(y=0\) mm) at an observation frequency of 9.5 GHz. To analyze the influence of the configurations, we investigated the normalized E-field to observe the leakage E-field in the ranges of \(1\) mm \(\leq z\leq 3\) mm and \(-3\) mm \(\leq z\leq-1\) mm, which correspond to the outside of the interface layer. The mean value in the case without ground was 0.1397, as shown in Figure 3(a), whereas that in the case with ground was 0.1018, as shown in Figure 3(b). On the other hand, when the dense vias were inserted with ground, as shown in Figure 3(c) (proposed design), the mean value was observed to be 0.0876. Thus, the transition part \(A\) of the proposed interface layer using the CPW should be designed to include ground and vias to minimize the leakage fields.  
Figure 4: _Cont._  
Figure 3: Reflection and transmission coefficients of the proposed interface layer in the back-to-back configuration.  
Figure 5 represents the reflection coefficients at 9.5 GHz according to the variations of \(d_{1}\) and \(d_{2}\) applied to examine the influence of transition part \(B\). In this analysis, \(d_{1}\) varied from 0.05 to 1 mm, and \(d_{2}\) varied from 0.9 to 1.85 mm. Herein, design parameters of \(d_{1}\) = 0.85 mm and \(d_{2}\) = 1.35 mm were chosen, taking into account the ease of fabrication and reflection coefficients of less than \(-\)30 dB. A reflection coefficient of \(-\)30.7 dB was observed when the design parameters of \(d_{1}\) and \(d_{2}\) were 0.85 mm and 1.35 mm, respectively. These results indicate that the transmission characteristics can be improved by adjusting transition part \(B\).  
Figure 4: The normalized E-field distributions of the interface layer: (**a**) without ground; (**b**) with ground but without via; (**c**) with ground and via (proposed interface layer).  
Figure 6 illustrates the parametric study of transition part \(C\), which consists of the feed-pin (radius of \(r_{\text{f}}\)) and the perforated ground (radius of \(r_{\text{d}}\)). The transmission characteristics can be improved by adjusting the ratios of \(r_{\text{f}}\) and \(r_{\text{d}}\). To find the minimum reflection coefficient at 9.5 GHz, the parameter \(r_{\text{f}}\) was varied from 0.1 to 0.3 mm in increments of 0.02 mm, and \(r_{\text{d}}\) was changed from 0.8 to 1.4 mm in increments of 0.05 mm. In Figure 6, the dashed line represents the minimum reflection coefficients according to \(r_{\text{f}}\), indicating a required ratio of \(r_{\text{f}}\) to \(r_{\text{d}}\). Since the proposed interface layer uses a feed-pin with a radius (\(r_{\text{f}}\)) of 0.22 mm, the optimal radius of the perforated ground (\(r_{\text{d}}\)) is 1.4 mm. However, in our design, we chose a slightly smaller radius (\(r_{\text{d}}\)) of 1.3 mm to avoid overlapping with the surrounding vias while maintaining the reflection coefficient below \(-30\) dB. The reflection coefficients were \(-31.4\) dB at 9 GHz and \(-29.2\) dB at 10 GHz, respectively.