An Effective-Current Approach for Hall\'{e}n's Equation in Center-Fed Dipole Antennas with Finite Conductivity

Abstract

We propose a remedy for the unphysical oscillations arising in the current distribution of carbon nanotube and imperfectly conducting antennas center-driven by a delta-function generator when the approximate kernel is used. We do so by formulating an effective current, which was studied in detail in a 2011 and a 2013 paper for a perfectly conducting linear cylindrical antenna of infinite length, with application to the finite-length antenna. We discuss our results in connection with the perfectly conducting antenna, providing perturbative corrections to the current distribution for a large conductance, as well as presenting a delta-sequence and the field of a Hertzian dipole for the effective current in the limit of vanishing conductance. To that end, we employ both analytical tools and numerical methods to compare with experimental results.