# Triangular Sierpinski Microwave Band-Stop Resonators for K-Band Filtering
## 7 Experimental Results and Discussion
### Measurements  
The measurements were performed using an on-wafer characterization setup, composed of a Karl-Suss PM5 Probe Station mounting GSG (ground-signal-ground) \(|Z|\)-Probes, connected to an HP8510C vector network analyzer system working up to 50 GHz. The single resonators nominally working around 20 GHz and named C0 and C1 were measured, with the results shown in Figures 14 and 15, respectively. Figure 14: Theoretical and experimental response for the C0 resonator. A significant shift in the expected frequency of resonance and an enlarged bandwidth were obtained. Figure 15: Simulated and experimental response for the C1 Sierpinski resonator. The experimental responses for C0 and C1 were significantly shifted in comparison with the expected resonance frequencies. This agrees with the previous discussion about the difficulty of exactly calibrating the frequency of resonance owing to additional elements to be considered in the equivalent circuit. Further contributions should include the feeding network and the boundaries in order to properly model the resonator response. The measured enlargement of the bandwidth is not necessarily a negative characteristic, but it must be considered in some detail to understand how to control it. Resonators designed to work around 26 GHz have also been manufactured and characterized. As discussed in the design section, we expected well-pronounced resonances, especially for the configurations C2 and C3, with deeper notches compared to C0 and C1. To demonstrate the expected better performances at these frequencies of the devices C2 and C3, we first measured the pure configurations from C0 to C3, obtaining the results plotted in Figure 16.  
From the plot in Figure 16, it appears that the poor performances expected for C0 and C1 are confirmed, whereas a good electrical coupling is exhibited by the configurations C2 and C3, and by the mixed C2C3 resonator. A more detailed analysis of the C2C3 configuration is shown in Figure 17, where the simulated structure, the predicted response, and the experimental results are shown. Except for the usual frequency shift, to be calibrated for application purposes, the proposed resonator exhibits quite good performances, with a peak lower than \(-20\) dB, and in this case, low losses along the line. Figure 16: Experimental response for the transmission parameter S\({}_{21}\) (in dB scale) of the C0, C1, C2, and C3 resonators for the operation at approximately 26 GHz. In addition, the response of the mixed configuration C2C3 was also measured and was shown and compared with the performance of the other resonators. Following the simulations presented in the previous sections, 20 GHz and 26 GHz hexagonal structures have been manufactured and tested including the most promising C1 and C3 configurations. The example of the 26 GHz composition is shown in the photo in Figure 18, but the shape is the same as the structures for the 20 GHz operation, which, of course, are more extended than those in Figure 18.  
The response for the C3 structure is plotted in Figure 19, comparing the simulation and experimental measurement. Figure 17: (**a**) C2C3 structure, with the geometry C2 on the top and C3 on the bottom of the resonator, and (**b**) its simulated response for the S\({}_{21}\) parameter compared with the experimental measurement. Figure 18: C1 (**left** side) and C3 (**right** side) structures arranged in the hexagonal configuration. The photo is for the 26 GHz resonators, but the geometry is the same as the 20 GHz structure. From the analysis of the experimental data, it appears that the proposed Sierpinski configurations are promising for the K-band operation, and they generally fulfill the re  
Figure 21: Measured and simulated responses of the small hexagonal resonator based on the C3 Sierpinski configuration for operating frequencies around 26 GHz. In this case, the expected frequency of resonance is around 25 GHz, but the actual frequency is close to 26 GHz. Additional expected modes were not recorded in the experimental measurements.