The impedance of a center-fed strip dipole by the Poynting vector method

The impedance of a center-fed strip dipole of width w and thickness t, with t≪w, is obtained by the Poynting vector method. With w also taken to be small with respect to the operating wavelength (w≪λ) the surface current on the dipole is modeled by the classical sinusoidal standing wave along its length. There are, however, appropriate transverse singularities assumed at the edges of the strip. The Poynting vector method leads to a two-dimensional integral in the transverse coordinates involving the classical mutual impedance between filamentary dipoles located on the surface of the strip itself as well as the above mentioned transverse edge singularities. A Legendre series expansion of this mutual impedance (the coefficients obtained by numerical integration) leads to a rapidly convergent series solution (eight terms) for the overall impedance of the strip dipole. Numerical results are provided For a variety of strip widths, thicknesses and lengths. They are compared with the impedances of equivalent circular dipoles of radius a=(w+t)/4 and good agreement occurs except for quite wide strips (w=0.05λ)