Characteristics of a transmission line with earth return: a conformal transformation approach

Wave propagation on a transmission line with earth return is analysed employing conformal mapping. This method is usually restricted to problems in two dimensions, but by allowing the medium to take on nonuniform characteristics, it can be extended to account for the presence of field vectors in the axial direction. Simple, closed-form expressions for propagation constant and impedances are found in contrast to previous results which required infinite integrals, except for very special and restrictive cases. The formulas agree asymptotically and numerically with those given by Carson and Wise, but can be applied to a wider range of situations.