First-order symmetric modes for a slightly lossy coaxial transmission line

A complete set of solutions for Maxwell´s equations to first order in the normalized surface impedance z_s of the coaxial conductors is found. The derivation of the fields outlined assumes a vacuum dielectric and an infinitely thick outer conductor. It starts from J.P. Stratton´s work (1941) with a derivation of the determinantal equation for finding the eigenvalues for both the principal and waveguide modes in a lossy line. The first-order determinantal equation is found, preceded by an equation for calculating the proportionality constant for the fields intermediate between the center and outer conductor. The equations for lossy waveguide modes are new, and the principal mode fields include a term missing from the expressions that are found elsewhere in the literature. The resulting characteristic admittance and distributed line parameters are calculated; the distributed line resistance is significantly different from other calculations found in the literature