Dispersion analysis of printed periodic structures by using a pole-zero network synthesis

A new method is presented, for the efficient derivation of the dispersion equation associated to periodic planar structures. In order to illustrate the basic concepts, the method is presented here for the case of a periodic dipole structure above a ground plane, but it is potential applicable to any kind of any kind of frequency selective surfaces (FSS) printed on or embedded in stratified dielectric media. This method appears powerful for determining bandgaps in artificial magnetic surfaces composed by FSS backed by ground planes, as well as for the dispersion analysis of leaky wave structures. The method is based on a pole-zero large bandwidth synthesis of the periodic structure, obtained starting from the reflection coefficient response of the FSS on a large frequency band. This synthesis provide an analytical expression of the equivalent network associated to the printed surface, and allows a simple determination of the dispersion equation. Preliminary results confirm the accuracy of the process and its efficiency with respect to conventional methodology.