Simple Analytical Dispersion Equations for the Shielded Sievenpiper Structure

Closed form expressions for the dispersion curves of the shielded Sievenpiper structure are derived in terms of the geometric and electromagnetic parameters of the structure. A compact form of the dispersion equation is presented in this paper, arrived at by using multiconductor transmission-line theory and assuming that the series loading capacitor and shunt loading inductor are added to the per-unit length impedance and admittance matrices in a continuous (homogeneous) manner. This approximate model is shown to yield excellent agreement with the full model (in which the loading parameters are not incorporated in a continuous manner), under suitable conditions. The dispersion curve provided by this model is analyzed and it is shown that there exists a frequency band (stopband) supporting complex modes. Analytical expressions for the edges of this complex-mode band are derived, and the variation of these expressions as functions of the geometry is explored