Frequency and Time Domain Green Function Technique for Nonuniform LCRG Transmission Lines with Frequency-Dependent Parameters

The reflection and transmission of waves on a nonuniform LCRG transmission line of finite length with frequency-dependent parameters are considered. A Green function technique combined with wave splitting is used both in the frequency domain and the time domain. In the frequency domain ordinary differential equations (ODEs) for the time-harmonic Green functions are obtained. In the time domain the transmission line model is established through a set of dispersion kernels. Partial differential equations (PDEs) for the time-domain Green functions are derived. Numerical results for transient reflected, transmitted and internal currents are presented. Furthermore, it is noted that a special case of the present formalism can be used to determine the reflected, transmitted and internal fields for normal plane wave incidence on a stratified dispersive and dissipative slab.