# Triangular Sierpinski Microwave Band-Stop Resonators for K-Band Filtering
## 8 Conclusions  
This paper proposes triangular-shaped band-stop resonators using the Sierpinski geometry for narrow-band microwave tuning around 20 GHz and 26 GHz; i.e., for K-Band applications. The K-Band frequencies are particularly appealing for systems implementing RADAR and satellite communications. As a novelty, fractal Sierpinski geometry was chosen to design, manufacture, and test planar resonators in a coplanar waveguide configuration (CPW).  
Sierpinski triangular patch resonators were proposed as building blocks for individual or coupled structures, taking advantage of the possibility of obtaining: (i) different frequencies of resonance maintaining the same footprint but enhancing the internal complexity of the structure, and (ii) arrays of resonators with size reduction, improved electrical response, and better integration compared to square or circular geometries.  
Advantages and critical issues in using the CPW excitation for the Sierpinski triangles were widely discussed in our contribution, giving evidence for the difference between the novel CPW structures and those excited by a microstrip line. In particular, the formal approach available in the literature to predict the frequency of resonance for triangles was developed for antennas fed by microstrips or via holes. However, our devices differ from the classical ones due to the CPW embedding, including feeding and boundaries, and the resonance frequency cannot be straightforwardly predicted. At this stage, the prediction of the frequency of resonance can only be obtained by combining electromagnetic simulations with experimental findings. Further electromagnetic simulation efforts linked to experiments will be necessary to build up equivalent circuits and analytical formulations to predict the spectrum of a CPW-fed Sierpinski microwave resonator.  
The peculiar results of our research activity concern the necessity to respect symmetrical boundaries for the single resonators and their mutual coupling to obtain acceptable electrical performances for the developed devices. Moreover, coupled structures exhibit improved electrical matching. On the other hand, optimization is still necessary to improve the coupling for all the Sierpinski configurations, considering all the possible internal complexities, as only some of them are immediately suitable for integration.  
Bandwidth control can be obtained using mixed configurations designed with mirrored half-triangles characterized by different internal complexity within the same structure.  
In the end, promising results have been obtained using partially optimized configurations, but efforts are still needed to fully study the spectral response and coupling conditions.  
Contributions from the Authors were the following: Technology and Program Co-Management, F.G.; Layout Design and Participation to Technology: E.P., G.C., J.I. and G.T.; Design and Test: G.M.S.; Circuit Analysis and Funding Acquisition, Device Design and Measurement, R.M. All authors have read and agreed to the published version of the manuscript.  
**Funding:** Co-funded by the Italian Space Agency Project <<METAMEMS>>, Grant No. ASI n. 2019-12-U.0--bando di finanziamento di progetti di ricerca industriale e/o sperimentale 'Nuove Idee per la Componentistica Spaziale del Futuro (\"TRL\")', Codice Unico di Progetto (CUP) F84118000380005.  
**Data Availability Statement:** Raw data available upon requirement.  
**Conflicts of Interest:** The authors declare no conflict of interest.