Numerical Issues in Line Models Based on a Thin Wire Above a Lossy Ground

This paper investigates the causes of numerical instabilities that might occur in transmission line models if the so-called image approximations are used for the evaluation of the per-unit-length parameters when the ground is assumed lossy and a wide frequency range is considered. To assess whether these instabilities are inherent to the formulation of the line parameters, results were compared with two well-established models: a full-wave model and a quasi-transverse electromagnetic approximation. Both approaches provided stable models throughout the whole frequency range. Two different methodologies are used for the determination of the modal propagation constant in a full-wave model leading to similar results. Time-domain responses based on the numerical Laplace transform and the method of characteristics were used to verify the accuracy and stability of the tested models. The input voltage considered for the time-domain responses included a small perturbation to excite the passivity violations found in the modeling using image approximations. Some aspects related to a full-wave model based on the method of characteristics using rational fitting are also presented.