An approximate analytical expression is derived for the equivalent capacitance of three-dimensional (3D) singly split ring resonators (SRRs) with square cross section. The total capacitance is expressed as the sum of the usual gap capacitance and the surface capacitance associated with the charges on the ring's surfaces. The surface capacitance is determined from analytical expressions for the electric field of a split square cylinder which are derived by conformal mapping. The proposed model can be used for the preliminary assessment of the resonant properties of square SRRs at any frequency. The validity of the developed formulas is assessed by comparing the resonant frequency of sample SRR configurations found analytically with the corresponding values obtained by numerical simulations.
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