Fast Method for the Assessment of SRR or ELC-Based Planar Filters: Numerical Analysis and Experiments

We present a general-purpose, fast and computationally efficient numerical method to predict the performance of filters based on electric-LC (ELC) resonators or split-ring resonators (SRR) in a very large frequency range (i.e., 8–40 GHz). In particular, we tackle the problem arising from the design of arrays of ELC/SRR-based resonators developed in a multi-layer dielectric stack under a coplanar waveguide excitation. The intrinsic complexity of the analyzed structure (open, multi-layer, and with resonators) makes it unpractical to rely exclusively on full-wave electromagnetic simulations. Furthermore, the presence of multiple modes in propagation can lead to a quite difficult assessment of the optimal simulation conditions. For all these reasons, we propose a method based on the cascade of scattering matrices for all the sub-modules of the considered filters. We demonstrate the efficacy of the proposed numerical technique for a good prediction of the high-frequency performance of the filters. The fabrication on silicon substrate of structures integrating electric-LC resonators (for X band applications) or split-ring resonators (for Ka band applications) serves the purpose of validating the presented method, with a very good agreement between simulations and measurements.