The input impedance of a thin dipole with sinusoidal surface current distribution by the Poynting vector method

The input impedance of a thin (a≪λ) center-fed dipole with an assumed sinusoidal surface current distribution is obtained by the Poynting vector method. It is shown that by retaining the surface current distribution rather than replacing it by the classical equivalent line current on the dipole axis, the Poynting vector method can be used in a straightforward way and the dipole impedance obtained as a series in powers of ka. The series is appropriately truncated to order (ka)² since it is assumed that the dipole is thin (ka≪1)