Solution of the transmission-line equations for lossy conductors and imperfect earth

A numerically stable and efficient method of diagonalising the product of the per-unit-length impedance and admittance matrices for multiconductor transmission lines with lossy conductors or lossy earth return is presented. Cases are discussed where, by an approximation, the product of these matrices, which is complex and frequency-dependent, can be diagonalised using a real, frequency-independent modal-decomposition matrix. Frequency dependence is included in the calculation of the modal-propagation constants.