A computer based method for computing the N-dimensional generalized ABCD parameter matrices of N-dimensional systems with distributed parameters

The author presents a method for developing and solving, both in transient and steady state, the N-dimensional matrix networks of N-dimensional transmission line networks or communication circuits with distributed parameters. The method uses the Cayley-Hamilton theorem to compute the hyperbolic N-dimensional generalized ABCD parameter matrices with finite terms, which are fundamental to the solution of N-dimensional matrix networks. The square root function of a complex matrix is also computed with finite terms. As a result, truncation of matrices is eliminated. The method is extremely useful in the fault analysis of N-dimensional unbalanced coupled systems with distributed parameters