Solution of Maxwell's equations for log-periodic dipole antennas

A theory of the log-periodic dipole antenna, which is a solution of the antenna boundary-value problem, is presented here. The theory is derived from Maxwell's equations by solving the wave equation in cylindrical coordinates and satisfying all boundary conditions. The theory is not limited to the log-periodic dipole antenna, but can be easily modified and applied to other antenna configurations using parallel linear elements. The radiation coupling between all antenna elements is taken into account; the calculated results show good agreement with the measurements. Current distributions, radiation patterns, and antenna input impedances are considered, and the application of this theory to the problem of optimal log-periodic dipole antennas is presented as well. Such an antenna obtained by numerical computation is discussed in detail.