Enhanced Modelling of Split-Ring Resonators Couplings in Printed Circuits

An enhanced equivalent circuit approach for the magnetic/electric interaction of single split-ring resonators (SRRs) with printed lines is presented in this paper. A very simple and efficient lumped-element network is proposed to model the behavior of metamaterial-based printed lines over a wide frequency band. The same circuit topology can be used for the single- and two-mirrored SRRs loaded microstrip line. The corresponding circuit parameters are obtained from the multiconductor transmission line theory as well as from closed-form expressions that make use of just the resonance frequency and minimum of the reflection coefficient (which should be previously extracted from experiments or full-wave simulations). The comparison of our equivalent circuit results with measurements and full-wave simulations has shown a very good agreement in a considerably wider frequency band than other previously proposed simple equivalent circuits.