Miniaturization of Frequency Selective Surfaces Using 2.5-D Knitted Structures: Design and Synthesis

This paper explores the potential of using vias for the miniaturization of frequency selective surfaces (FSSs). A new concept of knitting the loop-type FSS elements in 2.5-D is proposed, where successive segments of the loop are placed alternately on the two surfaces of the substrate and then interconnected through vias. A 2.5-D square-loop FSS (2.5-D SL-FSS) based on the proposed method is designed with the inclusion of ten vias at each side and characterized by a full-wave simulator. The transmission curves indicate a significant size reduction with a figure-of-merit.0/p = 16, where.0 is the free-space wavelength of resonant frequency and p is the periodicity of unit element. In addition, the frequency response of this miniaturized FSS is also stable for various incident angles and polarizations. Furthermore, a general equivalent circuit model (ECM) is developed for 2.5-D SL-FSS by combining the prevailing electrical models of planar square loop and through-silicon vias. A wide set of parametric simulations for various element sizes, substrate thicknesses, and via counts are carried out with this ECM. Then, its performance is assessed on the basis of root-mean-square error (RMSE) criteria by comparing the results with appropriate electromagnetic simulations. The findings suggest that the ECM has sufficient accuracy for estimating the resonant frequency of 2.5-D SL-FSS with the RMSE values close to 3%. Moreover, the proposed concept of knitting is further validated by measuring two physical prototypes of the 2.5-D SL-FSS and the experimental results show a good consistency with full-wave simulations.