The discrete time domain Green's function or Johns matrix — A new powerful concept in transmission line modelling (TLM)

Abstract

Abstract A new TLM‐based concept analogous to the Green's function approach in classical electromagnetic theory is presented. It employs the procedure known as time domain diakoptics. The response of a TLM mesh to a unit impulse excitation at selected input points is interpreted as a discrete Green's function in the time domain, and the term ‘Johns matrix’ is proposed for this characteristic response. As in classical theory, the response of the mesh to an arbitrary excitation is found by convolving the excitation with its Johns matrix. This concept extends the generalized scattering parameter concept into the time dimension, opens unprecedented possibilities for partioning time domain problems at the field level, and permits large‐scale preprocessing of substructures for computer‐aided design. It also represents and elegant way of modelling broadband absorbing boundary conditions, imperfectly conducting walls and general frequency dispersive boundaries in the time domain.