# A Novel Magnetic Coupling for Miniaturized Bandpass Filters in Embedded Coaxial SIW
## 3 Results  
As previously mentioned, the DuPontTM Green TapeTM 9K7 substrate has been chosen as LTCC dielectric tape in these designs. This is a low-loss glass ceramic dielectric tape for high-frequency applications that includes compatible gold and silver conductors. The final filter stack-up consists of 10 dielectric tape layers with un-fired thickness of 0.254 mm. Then, an additional tape with un-fired thickness of 0.127 mm has been added on the top of the tenth layer to implement the input-output feeding lines and ground-signal-ground (GSG) probe pads for measuring purposes.  
Due to the high number of layers in the stack-up, standard LTCC design rules recommend staggering via holes vertically (i.e., zig-zag position of the holes between layers) to limit the via-posting problem. The latter is a protrusion of the via hole at the external layers to the different \(z\)-shrinkage of the via fill paste and the tape material, which can provoke metal layer deformations. This technique has been applied in this design as can be seen in Figure 8a.  
First, the CSIW resonator presented in Section 2.2 has been fabricated and measured. A photograph of a prototype of the CSIW resonator is shown in Figure 9, while the measured results are shown in Figure 10. The agreement between the simulations and measurements is excellent. The TEM resonant frequency is \(f_{r}=1.55\) GHz, which is just 0.7% more than the simulated value, while the spurious-free band is around \(7.5\times f_{r}\). In fact, the first high-order mode (i.e., the TE\({}_{101}\)) is centered at 11.6 GHz.  
Figure 8: (a) Three-pole BPF filter layout; (b) Simulated frequency response.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \(l\) & \(w\) & \(h\) & \(d_{v}\) & \(d_{h}\) & \(r_{p,1}\) & \(r_{p,2}\) & \(h_{p}\) & \(g_{p}\) & \(w_{e}\) & \(h_{e}\) & \(w_{k}\) & \(h_{k}\) & \(p_{d}\) \\ \hline
32 & 9.5 & 2.24 & 0.68 & 0.18 & 4.3 & 4.36 & 1.792 & 0.448 & 1.25 & 1.12 & 0.25 & 1.12 & 0.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Layout Dimensions of the Three-Pole CSIW Filter (Unit: mm).  
In addition, the extracted \(Q_{u}\) from measurements is very similar to the simulated one, both being around 150. This value is slightly lower than those represented in Figure 3. Indeed, the CSIW resonators are fabricated in the very same stack-up of the three-pole BPFs, thus they share the same coupling arrangement that results in a more coupled resonators (i.e., measured \(S_{21}=-0.6\) dB).  
On the other hand, Figure 11b shows a photograph of an embedded CSIW filter prototype, while the comparison between measured and simulated results are depicted in Figure 12. Again, the agreement between simulations in Ansys HFSS and measurements is excellent. Basically, there is no frequency shift between responses, thus validating the proposed topology and its LTCC manufacturing. The filter IL and RL are 1.2 dB and around 15 dB, respectively, while the filter FBW is 10% as expected. The extracted \(Q_{u}\) from measurements is close to 165, thus validating the study of Section 2.2.  
Figure 10: Measured and simulated results of the embedded coaxial SIW resonator: (**a**) wideband response up to 15 GHz and (**b**) passband of the resonance.  
Figure 9: Photo of the CSIW resonator prototype.  
The filter shows a stop-band bandwidth of more than 8 GHz, up to 10 GHz, with a rejection always better than 30 dB. This means that the spurious-free band is greater than \(7\times f_{0}\), which is very close to the performance of the designed CSIW resonator. Concerning the discrepancy between simulated and measured stop-band performance, this could be due to the probe station setup. Finally, the filter size is \(32\times 9.5\times 2.24\,\mathrm{mm^{3}}\), which corresponds to \(0.426\times 0.126\times 0.03\,\lambda_{g}^{3}\) and \(0.16\times 0.047\times 0.01\,\lambda_{0}^{2}\), where \(\lambda_{g}\) is the guided wavelength at 1.5 GHz.