Input impedance of vertical dipoles near a lossy half space
Abstract
Exact solutions are derived for the input impedances of vertical magnetic and electric short dipoles over a lossy half space. The exact solution is expressed as a simple formula and a remainder, which takes the form of a rapidly converging series. Reduction to available approximate solutions in the literature under conditions of large dipole heights, large refractive index of the half space, or both is demonstrated. The derivation of new simple formulae that tend to the exact solutions when the refractive index of the half space approaches both limits of infinity or unity is of particular interest. Numerical examples are presented and compared with published results.
 Publication:

Radio Science
 Pub Date:
 April 1981
 DOI:
 10.1029/RS016i002p00179
 Bibcode:
 1981RaSc...16..179M
 Keywords:

 Dipole Antennas;
 Electric Dipoles;
 Electrical Impedance;
 Half Spaces;
 Magnetic Dipoles;
 Approximation;
 Diagrams;
 Numerical Integration;
 Electronics and Electrical Engineering