Numerical simulation of nonuniform multiconductor transmission lines with HF losses in Matlab: Laplace-domain and time-domain approaches

The paper describes two approaches to a numerical simulation of waves propagation on multiconductor transmission lines (MTL) in case the additional losses at high frequencies (HF), like is a skin effect, are to be taken into account. Such numerical simulations can be required at solving signal integrity issues in current high-speed electronic systems where the interconnect structures, often modelled as general MTLs, play an important role. Both the Laplace-domain and time-domain approaches are discussed, corresponding to telegraph equations with a half-order derivative term. A simple example is simulated in Matlab, based on Laplace domain and a numerical inverse Laplace transform (NILT). Basic starting points for a direct time-domain solution are also briefly sketched, as well as utilization of a modified nodal analysis (MNA) method enabling to cover the MTL systems with more complex load circuits.