Surface Impedance Boundary Conditions in Time Domain for Guided Structures of Arbitrary Cross Section With Lossy Dielectric Walls

This paper presents a procedure to implement the concept of surface impedance boundary condition (SIBC) for lossy dielectrics in time domain. The SIBC formulation, validation, and results are obtained with a time domain numerical method, namely the transmission-line matrix (TLM). The formulation of surface impedance in frequency domain is converted to the time domain using a rational approximation followed by a bilinear transform with a canonical representation in the state-space. This surface impedance formulation has been implemented in TLM. Simulations show that the proposed model is valid for interfaces between air and a lossy dielectric, and arbitrary conductivity $sigma$. An application that concerns mode propagation in a rectangular tunnel with lossy dielectric walls is shown. A comparison with an approximate method proposed by Marcatilli is presented. It confirms that the propagation in electrically large guided structures, such as tunnels with lossy dielectric walls, can be efficiently modeled by this approach.