Residue and Partial Fraction Evaluations of Distributed and Lumped System Functions with Multiple Order Poles

System functions for a linear system formed with lumped and distributed components can involve transcendental functions. Inversion from the Laplace domain to the time domain usually requires direct residue evaluation of the inversion integral. An algorithm for the evaluation of the residue involving a system function containing multiple order poles is given. The method is well suited for use on a digital computer since it does not require the use of differential calculus. It contains, as a side benefit, a means of expanding rational functions into their partial fraction form. Examples are given showing its application to residue calculations and partial fraction expansions.