Rigorous Modeling and Optimization of Fractal SRRs

A new efficient method that characterizes the distributed capacitance and inductance within fractal-shape split-ring resonators is proposed. The electrical charge distribution along the inner fractal-shape inclusion was calculated using a simplified method that manipulates the method of moments' solution of the Green's functions for the equivalent circular ring resonator. Also, a systematic approach, that finds the inclusion's self and mutual inductances, was investigated. This new advanced analysis leads to an accurate estimation of the inclusion's resonant frequency. A Koch fractal-curve layout was used as a proof-of-concept to validate the proposed method. Moreover, the particle swarm optimization technique was applied to find the inclusions' dimensions from a search-space of solutions for a given resonant frequency. Extracted theoretical lumped-element values agreed well with both the simulated and measured values.