An Efficient Method for Calculating the Dispersion and Characteristic Impedance of Silicon Substrate-Integrated Gap Waveguide in Terahertz Band

Terahertz (THz) technology is poised to revolutionize future wireless communications, and the silicon substrate-integrated gap waveguide (SSIGW) is emerging as a promising solution for THz circuit design. Despite its potential, there is a notable lack of comprehensive studies on the dispersion and characteristic impedance of SSIGW. This article aims to bridge that gap by investigating these critical parameters through an innovative combination of the transverse resonance method (TRM) and the mode-matching technology (MMT), obtaining efficient closed-form expressions. To tackle the dispersion issue, the article first calculates the plasma wavenumber of the electromagnetic bandgap (EBG) structure using an equivalent circuit method. The y-direction phase constant of SSIGW is then determined through TRM, and the dispersion equation is obtained using MMT. Characteristic impedance is calculated by integrating the field distribution with its defining equation. Finally, the analysis of the attenuation constant is provided along with the calculation formula. To validate the effectiveness and correctness of theoretical calculations, SSIGWs operating in extremely high-frequency (EHF) and tremendously high-frequency (THF) bands are designed. Theoretical calculations are consistent with simulation results, with maximum errors of 4.4% (1.6%) for the bandgap range, 5.9% (9.6%) for the phase constant within the bandgap, and 7.8% (13.5%) for the characteristic impedance in the EHF (THF) band, respectively. Moreover, the theoretical calculation time is less than 1/55 of the simulation time, which significantly improves the efficiency of SSIGW THz circuit design. To validate the accuracy of this method for calculating the structure, experimental measurements of the phase constant, characteristic impedance, and attenuation constant are conducted at a center frequency of 55 GHz using a printed circuit board (PCB) process, demonstrating excellent consistency.