Multiconductor Transmission Lines Sensitivity via Two-Dimensional Laplace Transform

The paper deals with a non-traditional method for determination of sensitivities of voltage and/or current waves propagating down multiconductor transmission lines (MTLs). The main idea is to use a two-dimensional Laplace transform (2D-LT) to replace the originally partial differential equations describing the uniform MTLs in the (x, t)-domain with those of algebraic type in the (q, s)-domain. The 2D Laplace transform can be much easily treated as for the sensitivity with respect to the MTLs' per-unit-length matrix parameters. After the (q, s)-domain sensitivity assessment the two-dimensional numerical inversion of Laplace transforms (2D-NILT) method is applied to get the sensitivities in the (x, t)-domain. Boundary conditions incorporation is performed by using modified nodal analysis (MNA) method in the s-domain when one-dimensional Laplace transform (1D-LT) is applied. All the computations have been programmed in the Matlab language.