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Field Regions

Overview

The fields surrounding an antenna are divided into 3 principle regions:

  1. Reactive Near Field
  2. Radiative Near Field (Fresnel Region)
  3. Far Field (Fraunhofer Region)

The 3 fields are categorized roughly based on the relative rates at which the amplitude of parts of the electric and magnetic fields diminish as distance from the radiating element increases:

  • Reactive Near Field: amplitude falls off as \(r^{-3}\)
  • Radiative Near Field: amplitude falls off as \(r^{-2}\)
  • Far Field: amplitude falls off as \(r^{-1}\)

The boundaries of the field regions are defined dependent on the length of the antenna, \(D\), and the wavelength of the radio wave, \(\lambda\).

Electromagnetically Short Antennas

For antennas shorter than half of the wavelength of the radiation they emit (\(D < \lambda / 2\)), the boundaries is defined as follows:

  • \(r < \frac{\lambda}{2 \pi}\): Reactive Near Field
  • \(\frac{\lambda}{2 \pi} < r < \lambda\): Radiative Near Field
  • \(\lambda < r < 2 \lambda\): "Transition zone"
  • \(r > 2 \lambda\): Far Field

Despite the definition of far-field distance above, the far-field generally starts at

\[ r > \frac{2D^2}{\lambda} \]

Electromagnetically Long Antennas

For antennas physically larger than a half-wavelength of the radiation they emit  (\(D > \lambda / 2\)), the near and far fields are defined in terms of the Fraunhofer distance \(d_F\):

  • \(r < 0.62 \sqrt{\frac{D^3}{\lambda}}\): Reactive Near Field
  • \(0.62 \sqrt{\frac{D^3}{\lambda}} < r < d_F\): Radiative Near Field
  • \(r > d_F\): Far Field

where

\[ d_F = \frac{2D^2}{\lambda} \]

with additional constraints that

\[ d_F \gg D \\ d_F \gg \lambda \]

Reference