A Variational Integral for Propagation Constant of Lossy Transmission Lines

By assuming that the current on a lossy transmission line flows in the axial direction, only a variational integral for the propagation constant can be readily obtained. This variational integral shows that the usual power loss method of evaluating the attenuation constant is valid for general transmission lines. This variational integral also shows that the perturbation of the loss-free phase constant is due to the increase in magnetic field energy caused by penetration of the field into the conductors.