Matrix analysis of transient voltage distributions in alternating ladder networks

The paper describes a procedure for calculating the transient voltage distribution following the impact of a voltage impulse of arbitrary shape at the input terminals of an alternating ladder network built up of two different sections recurring in alternating succession along the given network. A general type of alternating ladder network is considered, and thus a unified treatment is possible for a variety of circuits occurring in both light and heavy electrical engineering. The governing differential equations of the general alternating network are combined into a single matrix differential equation of the second order with constant coefficient matrices. The general closed-form solution of the matrix differential equation by the method of diagonalizing the coefficient matrices simultaneously is developed. Some particular applications of the derived formulae are discussed and the possibility of automation of the numerical procedure is indicated.