Laplacian transform analysis of circuits with linear lumped parameters

IN THE first article of this series¹ the direct operational method of Heaviside was discussed. In the second article² the theory of functions of a complex variable was considered. The results there obtained, in particular the theory of residues, are used in the present article to justify and extend Heaviside´s method. The Laplacian transform is introduced, and the method shown by which, with its aid, the general circuit with lumped linear parameters subject to any given impressed voltages and arbitrary initial conditions may be solved in a straight-forward systematic manner. The questions of the validity of many doubtful steps taken in the manipulation of Heaviside´s operators do not arise in this method, since the Laplacian transform analysis makes no use of operators. The connection between the transform and the operational schemes is given, and many of the Heaviside formulas used in the first article are derived.