A Systematic Transmission Line Model for the Analysis of Self-Resonant Structures Within Multi-Layer Dielectric Media

This paper introduces a transmission line model analysis for dielectric-loaded self-resonant structures (SRSs). Equivalent circuit models, besides their fast computational time, usually offer some insights into the underlying physics of the electromagnetic structures, hence simplifying and improving the design and optimization criteria of these structures. A systematic approach for deriving impedance expressions of SRS on and within multi-layer dielectric media is presented. The process of extracting equivalent circuit parameters from impedance expressions is explained. The trends of equivalent circuit parameters are studied with different dielectric medium properties and various angles of incidence for an SRS with multiple resonant states highlighting the effect of changing the physical and electrical dimensions on the equivalent circuit parameters. The transmission line model responses are compared to full-wave simulation results, and model accuracy is assessed using the mean absolute error criteria. Furthermore, a new simplified method for calculating the forward transmission coefficient of an SRS within multi-layer media is proposed. This expression offers fundamental insights into the factors contributing to the $S_{21}$ response. Finally, experimental measurements for SRS embedded in a multi-layer dielectric media inside a waveguide is conducted and compared to the equivalent model with very good agreement.