A New Time-Domain Solution to Transmission Through a Multilayer Low-Loss Dielectric Wall Structure for UWB Signals

In this work the time-domain solution for transmission through a multilayer wall structure has been presented. A time-domain transmission coefficient formulation for transmission through an interface between two low-loss dielectric mediums with different electrical properties is derived. Both hard and soft polarizations are considered. A novel ray tracing algorithm for multilayer wall structure has been presented with accuracy of ray-traced path as close as order of 10-5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-5}$$\end{document}. Further, in depth formulation for actual refracted angles for different layers of the wall has been presented and exact frequency-domain formulation for transmitted field at the receiver has been obtained. The exact formulation has been simplified under the condition of low loss assumption and this simplified formulation has been converted to time-domain formulation using inverse Laplace transform. The proposed time-domain solution has been validated with the inverse fast Fourier transform of the corresponding exact frequency-domain solution. Further the computational efficiency of both the methods has been compared.