Editing Near and far field (section)

====Electromagnetically long antennas====
For antennas physically larger than a half-wavelength of the radiation they emit, the near and far fields are defined in terms of the '''[[Fraunhofer distance]]'''. Named after [[Joseph von Fraunhofer]], the following formula gives the [[Fraunhofer distance]]:
:<math display=block>d_\text{F} \; = \; \frac{2 D^2}{\lambda} \, ,</math>

where {{mvar|D}} is the largest dimension of the radiator (or the [[diameter]] of the [[Antenna (radio)|antenna]]) and {{mvar|λ}} is the [[wavelength]] of the radio [[wave]]. Either of the following two relations are equivalent, emphasizing the size of the region in terms of wavelengths {{math|λ}} or diameters {{math|D}}:
:<math display=block>d_\text{F} \; = \; 2 { \left( { D \over \lambda } \right) }^2 \lambda \; = \; 2 { \left( { D \over \lambda } \right) } D</math>

This distance provides the limit between the near and far field. The parameter {{mvar|D}} corresponds to the physical length of an antenna, or the diameter of a reflector ("dish") antenna.

Having an antenna electromagnetically longer than one-half the dominated wavelength emitted considerably extends the near-field effects, especially that of focused antennas. Conversely, when a given antenna emits high frequency radiation, it will have a near-field region larger than what would be implied by a lower frequency (i.e. longer wavelength).

Additionally, a far-field region distance {{math|''d''<sub>F</sub>}} must satisfy these two conditions.<ref>{{cite book |author=Rappaport, Theodore S. |title=Wireless Communications Principles and Practice |edition=19th printing, 2nd |publisher=Prentice-Hall |year=2010 |page=108}}</ref>{{Clarify|reason=These are imprecise, dumbed-down versions of what has been said more clearly above.|date=May 2015}}
:<math display=block>d_\text{F} \gg D\,</math>
:<math display=block>d_\text{F} \gg \lambda\,</math>

where {{mvar|D}} is the largest physical linear dimension of the antenna and {{math|''d''<sub>F</sub>}} is the far-field distance. The far-field distance is the distance from the transmitting antenna to the beginning of the Fraunhofer region, or far field.