An Effective Current Approach for Hallén’s Equation in Center-Fed Dipole Antennas With Finite Conductivity

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 2011 and 2013 papers, for a perfectly conducting (PC) linear cylindrical antenna of infinite length, with application to the finite-length antenna. We discuss our results in connection with the PC 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 the experimental results.