Approximated closed form characteristic impedance for the bed of nails-based gap waveguide

The parallel-plate ridge gap waveguide has been introduced recently. It consists of a metal ridge in a metamaterial magnetic conductor surface, covered by a metallic plate at a small height above it. The metamaterial surface is designed to provide a frequency band where parallel-plate modes are in cut-off, thereby allowing for a conned gap wave to propagate along the ridge. In this paper, the investigation upgrades the analytical expression of the modal dispersion equation given previously, by including the first higher order mode. Furthermore, the characteristic impedance of the dominant mode is analytically calculated, by means of three different closed form expressions