Extension of Finitely Conducting Earth-Image-Theory Results to Any Range

Abstract
Finitely conducting earth-image-theory techniques have been employed to determine new formulas for the electric and magnetic fields produced by the four elementary dipole antennas for the air-to-air, surface-to-air, air-to- surface, and surface-to-surface propagation cases. The only restriction on the use of these formulas is that the index of refraction be large (i.e., the absolute value of n squared or = 10). They are valid at any frequency and at any range for the flat-earth case. These formulas 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 an earth-skin depth. In terms of computer time, these new formulas can be evaluated in fractions of a minute compared with hours for the complete numerical evaluation of the exact Sommerfeld integrals. These formulas are intended to supplement the author's recently derived subsurface-to-surface and air-to-air propagation formulas.

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