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Near and far field
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==Definitions== The separation of the electric and magnetic fields into components is mathematical, rather than clearly physical, and is based on the relative rates at which the amplitude of different terms of the electric and magnetic field equations diminish as distance from the radiating element increases. The amplitudes of the far-field components fall off as <math>1/r</math>, the ''radiative'' near-field amplitudes fall off as <math>1/r^2</math>, and the ''reactive'' near-field amplitudes fall off as <math>1/r^3</math>.{{efn|name=power_vs_amplitude|Amplitude fall-off is not to be confused with the ''power'' fall-off; power falls off as the amplitude squared.}} Definitions of the ''regions'' attempt to characterize locations where the activity of the associated field ''components'' are the strongest. Mathematically, the distinction between ''field components'' is very clear, but the demarcation of the spatial ''field regions'' is subjective. All of the field components overlap everywhere, so for example, there are always substantial far-field and radiative near-field components in the closest-in near-field reactive region. The regions defined below categorize field behaviors that are variable, even within the region of interest. Thus, the boundaries for these regions are approximate [[rules of thumb]], as there are no precise cutoffs between them: All behavioral changes with distance are smooth changes. Even when precise boundaries can be defined in some cases, based primarily on antenna type and antenna size, experts may differ in their use of nomenclature to describe the regions. Because of these nuances, special care must be taken when interpreting technical literature that discusses far-field and near-field regions. The term ''near-field region'' (also known as the ''near field'' or ''near zone'') has the following meanings with respect to different [[telecommunications]] technologies: * The close-in region of an [[antenna (radio)|antenna]] where the angular [[field (physics)|field]] distribution is dependent upon the distance from the antenna. * In the study of diffraction and antenna design, the near field is that part of the radiated field that is below distances shorter than the [[Fraunhofer distance]],<ref>{{cite book |title=Antenna Theory: Analysis and Design |first=Constantine A. |last=Balanis |edition=3rd |year=2005 |at=Chapter 2, page 34}}</ref> which is given by <math>d_\text{F} = \frac{2 D^2}{\lambda}</math> from the source of the diffracting edge or antenna of longitude or diameter {{mvar|D}}. * In [[fiber-optic communication]], the region near a source or [[aperture]] that is closer than the [[Rayleigh length]]. (Presuming a Gaussian beam, which is appropriate for fiber optics.) ===Regions according to electromagnetic length=== The most convenient practice is to define the size of the regions or zones in terms of fixed numbers (fractions) of wavelengths distant from the center of the radiating part of the antenna, with the clear understanding that the values chosen are only approximate and will be somewhat inappropriate for different antennas in different surroundings. The choice of the cut-off numbers is based on the relative strengths of the field component amplitudes typically seen in ordinary practice. ====Electromagnetically short antennas==== [[File:Field regions for typical antennas vector.svg|thumb|left|500px|alt=Antenna field regions for antennas that are equal to, or shorter than, one-half wavelength of the radiation they emit, such as the whip antenna of a citizen's band radio, or the antenna in an AM radio broadcast tower.|Field regions for antennas equal to, or shorter than, one-half wavelength of the radiation they emit, such as the whip antenna of a citizen's band radio, or an AM radio broadcast tower.]] {{Clear}} For antennas shorter than half of the wavelength of the radiation they emit (i.e., electromagnetically "short" antennas), the far and near regional boundaries are measured in terms of a simple ratio of the distance {{mvar|r}} from the [[radio frequency|radiating source]] to the [[wavelength]] {{mvar|λ}} of the radiation. For such an antenna, the near field is the region within a radius {{math|''r'' ≪ ''λ''}}, while the far-field is the region for which {{math|''r'' ≫ 2 ''λ''}}. The transition zone is the region between {{math|''r'' {{=}} ''λ''}} and {{math|''r'' {{=}} 2 ''λ'' }}. The length of the antenna, {{mvar|''D''}}, is not important, and the approximation is the same for all shorter antennas (sometimes idealized as so-called ''point antennas''). In all such antennas, the short length means that charges and currents in each sub-section of the antenna are the same at any given time, since the antenna is too short for the RF transmitter voltage to reverse before its effects on charges and currents are felt over the entire antenna length. ====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. ====Transition zone==== The ''transition zone'' between these near and far field regions, extending over the distance from one to two wavelengths from the antenna,{{citation needed|date=December 2011}} is the intermediate region in which both near-field and far-field effects are important. In this region, near-field behavior dies out and ceases to be important, leaving far-field effects as dominant interactions. (See the "Far Field" image above.) ===Regions according to diffraction behavior=== [[File:FarNearFields-USP-4998112.svg|thumb|left|500px |alt=Near- and far-field regions for an antenna larger (diameter or length {{mvar|D}}) than the wavelength of the radiation it emits, so that {{math|{{frac|''D''|λ}} ≫ 1}}. Examples are radar dishes and other highly directional antennas. |Near- and far-field regions for an antenna larger (diameter or length {{mvar|D}}) than the wavelength of the radiation it emits, so that {{math|{{frac|''D''|λ}} ≫ 1}}. Examples are radar dishes, satellite dish antennas, radio telescopes, and other highly directional antennas.]] {{clear}} ====Far-field diffraction==== {{Main|Fraunhofer diffraction}} As far as acoustic wave sources are concerned, if the source has a maximum overall dimension or aperture width ({{mvar|D}}) that is large compared to the wavelength {{mvar|λ}}, the far-field region is commonly taken to exist at distances, when the Fresnel parameter <math>S</math> is larger than 1:<ref>{{cite book |title=Acoustic Waves: Devices, imaging, and analog signal processing |editor=Kino, G. |publisher=Prentice Hall |year=2000 |at=Chapter 3, page 165}}</ref> :<math display=block>S = {4\lambda \over D^2} r > 1, \text{ for } r > r_\text{F} = {D^2 \over 4\lambda}.</math> For a [[light beam|beam]] focused at infinity, the far-field region is sometimes referred to as the ''Fraunhofer region''. Other synonyms are ''far field'', ''far zone'', and ''radiation field''. Any [[electromagnetic radiation]] consists of an [[electric field]] component {{math|'''E'''}} and a [[magnetic field]] component {{math|'''H'''}}. In the far field, the relationship between the electric field component {{math|'''E'''}} and the magnetic component {{math|'''H'''}} is that characteristic of any freely propagating wave, where {{math|'''E'''}} and {{math|'''H'''}} have equal [[Euclidean vector#Length|magnitudes]] at any point in space (where measured in units where [[speed of light|{{math|''c'']] {{=}} 1}}). ====Near-field diffraction==== {{Main|Fresnel diffraction}} In contrast to the far field, the [[diffraction]] pattern in the near field typically differs significantly from that observed at infinity and varies with distance from the source. In the near field, the relationship between {{math|'''E'''}} and {{math|'''H'''}} becomes very complex. Also, unlike the far field where [[electromagnetic wave]]s are usually characterized by a single [[polarization (waves)|polarization]] type (horizontal, vertical, circular, or elliptical), all four polarization types can be present in the near field.<ref name=OSHA-EM-rad/> The near field is a region in which there are strong inductive and capacitive effects from the currents and charges in the antenna that cause electromagnetic components that do not behave like far-field radiation. These effects decrease in power far more quickly with distance than do the far-field radiation effects. Non-propagating (or evanescent) fields extinguish very rapidly with distance, which makes their effects almost exclusively felt in the near-field region. Also, in the part of the near field closest to the antenna (called the ''reactive near field'', [[#Reactive near field, or the nearest part of the near field|see below]]), absorption of electromagnetic power in the region by a second device has effects that feed back to the transmitter, increasing the load on the transmitter that feeds the antenna by decreasing the antenna impedance that the transmitter "sees". Thus, the transmitter can sense when power is being absorbed in the closest near-field zone (by a second antenna or some other object) and is forced to supply extra power to its antenna, and to draw extra power from its own power supply, whereas if no power is being absorbed there, the transmitter does not have to supply extra power.
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