XXII. The transient behaviour of four-terminal networks

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Abstract
Starting with the canonical differential equations of a general, linear, bilateral, lumped network, and by the application of the Laplacian transformation and matrix algebra, the general theory of the transient behaviour of four-terminal networks is deduced. By the use of simple matrix multiplication, the general constants of complicated structures are determined, and the exposition is concluded with a discussion of the general smooth transmission line and the general ladder structure. A brief discussion of the Laplacian transformation is given in an appendix. In order to apply the theory to special cases, two tables are included. The first table gives the basic theorems for the manipulation of Laplacian transforms and the second table is a list of transforms of great use in the discussion of special cases. Many of the transforms given are scattered widely over the mathematical literature, and a compilation of these in tabular form should greatly facilitate the solution of certain transient problems.

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