Propagation Analysis of HF Currents and Voltages on Lossy Power Lines

Matrix analysis is described of voltage and current propagations along a resistive conductor system above an imperfectly conducting ground. Square matrices and their functions are considered as operators in a vector space. Conductor voltages and currents are represented as vectors and resolved into modes or eigenvectors of the propagation matrix. It is shown that although the modal transformation is hot power invariant the mode are independent but not orthogonal. General and modal reflection-free line terminations are developed. A brief review of some simplified modal analyses is described. A numerical solution is demonstrated. Mathematical background is appended.