Comparison of the radiation properfies of a sinusoidal current filament and a PEC dipole of near-zero radius

Among the relatively few problems in electromagnetics the solutions of which can be developed in closed form are the near and far fields of a sinusoidal current filament (SCF). Before the inception of computational electromagnetics, this fact led to the sinusoidal current filament being widely used as an approximation for the radiation characteristics of a thin wire, such as a center-fed dipole. The reason that this approximation proves to be useful is that the current on a PEC (perfectly electrically conducting) wire of near-zero radius (NZR) becomes a close approximation to a sinusoid, and their radiation patterns become very similar. However, as is shown here, while the sinusoidal current filament and near-zero-radius dipole are very similar in some respects, they are quite different in others. These similarities and differences are explored below, and their implications for how these two sources actually produce a far radiation field are explained