Accurate capacitance and inductance calculations for Koch fractal SRRs

In this paper, an efficient method is proposed for the characterization of the distributed capacitance and inductance of fractal Koch split ring resonators. The charge distribution and capacitance of the Kock-shape metallic strips were obtained using a simple electromagnetic (EM) approach combined to the method of moments. Another geometrical-based approach was also used to find the total inductance of the inclusion (self and mutual inductances). Through the above analysis, the resonant frequency can be accurately predicted for different Koch curve orders. Furthermore, the EM properties of the proposed structures were investigated and successfully compared to a conventional split ring resonator from the point of view of size reduction. The calculated theoretical lumped element values also agreed well with simulations.