Abstract: Based on the transmission line approximation, three different equivalent coupling formulations (by Taylor et al., by Agrawal et al. and by Rachidi, resoectively) are been proposed for evaluating the interaction between an external electromagnetic field and a transmission line. An analytic method is used to discuss the load voltage and current response with the Taylor and Agrawal coupling models for a planewave excitation. The analytic solutions of the load response are obtained for the two models. It is proved that these solutions are equal indeed. In other words, the two coupling formulations are different expressions of the same equations, cast in terms of different combinations of various electromagnetic field components. By analytical frequency-domain solution and the Fourier trans