Theoretical approach to verify the resonance frequency of a square split ring resonator

An analytical model for a square split ring resonator (S-SRR) having a single split-gap is considered here to reliably estimate the fundamental resonance frequency of the ring. An S-SRR is assumed to be equivalent to a series-resonant LC loop. The approximate formulas for equivalent self-inductance and total capacitance of the ring are derived separately. The total capacitance of the ring is expressed as a sum of a gap capacitance and a surface capacitance (which is associated with charges on the SRR walls). Both the capacitances are influenced by not only the medium in split-gap but also the dielectric constant of substrate. These are taken care of by including appropriate weight factors in the expressions for the capacitances. Again, using the software CST Microwave Studio, the resonance frequencies are calculated for several values of split-gap and SRR side length. Then the results of simulation are compared with the results obtained from our formula. It is found that simulation results agree quite well with the analytical results. Also, the analytical result for resonance frequency of SRR shows good agreement with a previously published experimental result. This model can be used for studies of the resonant properties of split rings in the microwave and terahertz regions.