Causality Analyzing for Transmission Line with Surface Roughness

Surface roughness of the conductor in transmission lines will introduce extra losses. The recently proposed Huray model is quite accurate for modeling these additional losses by changing R terms in RLGC models. However, only focusing on the loss modeling of the transmission line may lead to causality issues in time domain simulations. In this paper, the causality requirements of the RLGC models are theoretically analyzed firstly. Then, two solutions of the causality problems in Huray model-based transmission line with rough conductors modeling were proposed and compared. One of them is based on the numerical Hilbert transform, and the other one is analytically based on a complex-valued roughness factor. The causalities of those two solutions are validated by a time domain pulse through a transmission line. The results comparisons of the received pulse responses after the transfer functions show that both methods can improve the causality of the wave propagation term significantly, whereas the analytical solution has better performances and the numerical method has some limitations.