Transient and steady state solution of N-dimensional coupled networks and development of equivalent Pi and T matrix networks with distributed parameters

Abstract

This paper proposes a new computer based method for transient and steady state solution of n-dimensional coupled transmission line networks or communication circuits with distributed parameters. In this method, a novel approach has been developed for formulating and computing the n-dimensional generalized ABCD parameter matrices, as well as for developing and solving the equivalent n-dimensional coupled T and Pi networks with distributed parameters. The proposed method uses Cayley-Hamilton's theorem to compute the hyperbolic N-dimensional generalized ABCD parameter matrices with finite terms which are fundamental to the solution and development of the equivalent N-dimensional T and Pi matrix networks. The square root function of the complex matrix [W] is also computed with finite terms. As a result, truncation of matrices is eliminated, and an improved closed from solution is achieved. The method is straight forward, computationally efficient, and neither it involves the use of eigenvector based modal transformations necessary for diagonalization of parameter matrices nor it requires the evaluation of infinite series of hyperbolic functions with n-dimensional matrices as their arguments, and is extremely useful in the steady state and transient analysis of n-dimensional, unbalanced, coupled systems with distributed parameters. The method is extremely useful in the fault analysis of n-dimensional unbalanced coupled systems with distributed parameters. To date no such method is reported in the literature.