The surface roughness of copper foils has a considerable impact on the signal integrity performance of transmission lines at high data rates and long propagation distances. Existing surface roughness models for low-loss transmission lines are inadequate for accurate characterization. A new behavioral model for analyzing the surface roughness effects has been developed. The model is applied in the design process by adding a dispersive term to the bulk dielectric to represent the loss due to the foil surface roughness. By adding a broadband dielectric model into the original transmission model, time- and frequency-domain performance improvements are achieved.