Wave propagation in nonhomogeneous multiconductor systems using the concept of natural modes

The theory of natural modes is well established in the solution of homogeneous multiconductor-transmissionline equations. In this paper the concept is generalised to include the case of nonhomogeneoussy stems. The well known theory of image parameters is developed for the multiconductor case. This is done by transforming the phase voltages and currents and developing the equation for the image admittance matrix. In the process it is shown that natural modes do exist, but that their values are different at the two ends of the system. The modal parameters depend on the eigenvectors of a matrix which is formed from the basic admittance matrixes in the 2-port equation. The image propagation matrix is next defined. Since the admittance levels at the two ends of the system are not the same, the equations are developed in terms of the total voltage-current product at each end of the system. It is shown that the solution depends on the same eigenvalue matrix as for the image admittance. The relationship between the image propagation matrix and the short- and open-circuit admittance matrixes is developed. The theory is concluded by showing that the nonhomogeneous system is equivalent to a homogeneous one with an ideal polyphase transformer at one end, or half of an equivalent homogeneous network. At all points the equivalence between the equations of the multiconductor case and the well known two-conductor case is stressed. The paper concludes by considering a useful field of application for the theory, i.e. to the analysis of the power-line carrier characteristics of multiconductor transposed lines.