Wave propagation in nonhomogeneous systems. Properties of the chain matrix

Nonhomogeneous multiconductor transmission systems occur in a number of instances in practice. Examples are crossbonded cable systems and regularly transported overhead-line systems. Recursive methods of analysis fail because of the amount of computation involved. In the paper the theoretical equations for the multiconductor chain matrix are developed. It is proved that the eigenvalues of the chain matrix occur in reciprocal pairs and that the eigenvectors of the reciprocals are simply related to those of the eigenvalues. This reduces computation and avoids numerical instability in evaluating widely separated eigenvalues. These properties have not previously been published and may have applications in a number of fields as well as transmission lines. It is then noted that, provided the system response is only needed at a comparatively small number of points, computation is much more efficient than would be the case for recursive methods. In conclusion it is noted that this paper is the last in a series in which the equivalence between the theorems of simple and multiconductor systems is established by means of matrix functions.