Transient and sensitivity analysis at semi-discrete multiconductor transmission line models

The paper deals with methods for the solution of transient phenomena and sensitivities at semi-discrete models of multiconductor transmission lines (MTL). The models are formed by a cascade connection of generalized lumped-parameter Π networks, they can be fed in arbitrary nodes, nonzero initial conditions can also be taken into account. The solutions shown here are formulated following the state-variable method. First the equations enabling to solve voltage and current distributions along the MTL wires are derived, both in the time domain and in the operational domain. Second the formulae for sensitivities of voltage and current distributions are derived, based on the s-domain solution. The sensitivities can be stated with respect to parameters of per-unit-length matrices, the MTL length and lumped parameters of the external circuits as well. In this case the time-domain solutions are obtained by using a numerical inversion of Laplace transforms. The matrices occuring in all the formulae are sparse which enables to take into account large numbers of Π sections in the models while using common PC for the computation. The Matlab language environment is used with advantages for this purpose