Transient analysis of unequal length multiconductor transmission lines via Haar wavelets-based numerical inversion of Laplace transform

The numerical inversion of the Laplace transform (NILT) with Pade approximation has been used as an important tool for time domain analysis of conducted EMI coupling paths modeled by transmission line (MTL) networks. In this paper a new NILT based on Haar wavelets theory is presented for the analysis of coupled unequal length transmission line with arbitrary linear terminals and interconnecting networks. The method, which uses an operational matrix derived from the Haar wavelets theory to evaluate the image of the Laplace transform, is more accurate than previous techniques based on the Pade approximation. Two numerical examples of unequal length MTL networks are demonstrated to verify the method validity.