On replacing the line current approximation by surface currents in the Poynting vector method for the impedance of thin dipoles

In the classic Poynting vector method for determining the impedance of a thin dipole, the current density on the surface of the circular cylindrical conductors of radius a /spl Lt//spl lambda/ is assumed to be a sinusoidal standing wave, vanishing at the ends of the dipole. To simplify the analysis the surface current is replaced by an "equivalent" filamentary line current flowing on the axis of the dipole. The electric field of this line current can be obtained in closed form, whereas much more difficult is the calculation of E due to the cylindrical current distribution. However, it is the dipole impedance that is of primary interest. In this paper we show that if the radius a is much less than the dipole\´s half-length l, then the retention of the surface current distribution in the Poynting vector method does not render the calculation of the dipole\´s impedance significantly more difficult.