New Formulas That Extend Norton's Farfield Elementary Dipole Equations to the Quasi-Nearfield Range

摘要

New formulas for the electric and magnetic fields produced by the four elementary dipole antennas have been derived for the air-to-air, subsurface-to-air, air-to-subsurface, and surface-to-surface propagation cases. These formulas are of rather simple form and reduce to previously derived results when either (1) the measurement distance is much less than a free-space wavelength, (2) the Sommerfeld numerical distance is small, or (3) the measurement distance is much greater than a free-space wavelength. These are valid at any frequency and at any range beyond a certain minimum distance for the flat-earth case.