Analysis of Transmission Line Model with Uncertain Parameter Using the PC-FDTD Method

Abstract

Voltage and current wave propagation on transmission lines is commonly described by the telegrapher’s equations. However, in practical applications, the parameters of the telegrapher’s equations – such as inductance and capacitance – often exhibit uncertainty due to manufacturing tolerances, material inhomogeneities, and environmental variations. This study presents a numerical framework for solving the telegrapher’s equations with uncertain parameters using a combination of Polynomial Chaos Expansion and the Finite Difference Time Domain (FDTD) method. The proposed approach enables efficient uncertainty quantification while maintaining computational tractability. In addition to the numerical formulation, the conditional stability of our method is analyzed, and the discrete dispersion relation is derived and compared with the continuous dispersion relation. The results demonstrate that the PC–FDTD method is a robust and accurate tool for modeling wave behavior in transmission lines under parameter uncertainty.