Causality Preserving Passivity Enforcement for Traveling-Wave-Type Transmission-Line Models

Transmission-line models must be passive in order to guarantee stable time-domain simulations. Enforcing the passivity by adding a conductance matrix to the line model has been proposed, which is established by a frequency sweep. This leads to instantaneous coupling between the two line ends, thus violating the causality of the line. This letter shows that the coupling terms can be removed with only a negligible change to the model's perturbation. The removal of coupling terms makes the approach more suitable for the application with existing transmission-line models.