Unified Dispersion Relation of Groove Gap Waveguide and Substrate Integrated Waveguide Based on Transverse Resonance Method

This letter introduces a unified analytical model for the dispersion relations of both the groove gap waveguide (GGWG) and substrate integrated waveguide. First, analogous to rectangular waveguides, the dominant propagation mode in GGWG can be interpreted as bouncing propagating plane waves; hence, the transverse resonance condition holds in its cross section. Furthermore, we extend the existing equivalent impedance model of periodic pins to account for the oblique incidence condition. Subsequently, by integrating these advancements, the GGWG dispersion relation is derived. Full-wave simulation results corroborate the validity of the proposed model. Specifically, when the height of pins aligns with the distance between two parallel plates, GGWG functions as an SIW and remains applicable to the proposed analytical model. Generally, this model provides a novel perspective on the electromagnetic mechanism underlying the dispersion relations in these waveguides.