Near and far field
Encyclopedia
The near field and far field (or far-field) and the transition zone are regions of the electromagnetic radiation
field that emanates from a transmitting antenna
, or as a result of radiation scattering off an object. Certain behavior characteristics of electromagnetic field
s dominate at a given distance from the antenna or scattering object, while different behavior can dominate at another distance. Defined boundary regions categorize these behavior characteristics. For antennas shorter than the wavelength of the radiation they emit, these regional boundaries are measured in terms of a ratio of the distance from the radiating source
to the wavelength
of the radiation. For antennas physically larger than the radiation they emit, this factor must be taken into account also, and this extends the near-field region.
The "far-field" extends outward beginning about two wavelengths distance from an electromagnetically "short" antenna, to infinity. A "short" antenna is defined in this context as one that is shorter than the wavelength of the radiation it emits (see rules for longer antennas, below). The far-field is the region in which the field acts as "normal" electromagnetic radiation. The power of this radiation decreases as the square of distance from the antenna, and absorption of the radiation has no effect on the transmitter. By contrast, the "near-field", which is inside about one wavelength distance from the antenna, is a region in which there are strong inductive and capacitative 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. Also, in the part of the near-field closest to the antenna (called the "reactive 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 that power has been absorbed from the closest near-field zone, but if this power is not absorbed by another antenna, the transmitter does not supply as much power to the antenna, nor does it draw as much from its own power supply. Finally, the "transition zone" between these near and far field regions, extending over the distance from one to two wavelengths from the antenna, 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. The image above-right shows these regions and boundaries.
Such regions categorize field behaviors that vary, 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.
For antennas that have a characteristic physical length longer than the wavelength of the radiation they emit, and for focused or "dish" antennas of diameter longer than the wavelength of the radiation, the near and far-field distances cannot be in terms of simple radiation wavelength, but must be qualified in terms of the factor
where R is the distance from the antenna, D is the antenna diameter or length, and λ is the wavelength of the radiation. When this distance R is smaller than two wavelengths of the radiation, the region inside this radius is considered near-field, but when R is longer than two wavelengths, this region is considered the antenna far-field. The behaviors in these regions are the same as described above for electromagnetically "short" antennas. This behavior of considerably extends the near-field effects of focused antennas, and antennas that emanate high-frequency radiation.
consists of an electric field
component E and a magnetic field
component H. In the far-field, the relationship between the electric field component E and the magnetic component H is that characteristic of any freely propagating wave, where (in units where c = 1) E is equal to H at any point in space. By contrast, in the near-field, the relationship between E and H becomes very complex. Also, unlike the far-field where electromagnetic waves are usually characterized by a single polarization type (horizontal, vertical, circular, or elliptical), all four polarization types can be present in the near-field.
The near-field itself is further divided into the reactive near-field and the radiative near-field. The "reactive" and "radiative" near-field designations are also a function of wavelength (or distance). However, these boundary regions are a fraction of one wavelength within the near-field. The outer boundary of the reactive near-field region is commonly considered to be a distance of 1/2π times the wavelength (λ/2π or 0.159 x λ) from the antenna surface. The radiative near-field (also called the "Fresnel region") covers the remainder of the near-field region, from λ/2π out to λ (one full wavelength).
in this region problematic. This is because to calculate power, not only E and H both have to be measured but the phase relationship
between E and H must also be known.
In this reactive region, not only is an electromagnetic wave being radiated outward into far-space but there is a "reactive" component to the electromagnetic field, meaning that the nature of the field around the antenna is sensitive to, and reacts to, EM absorption in this region (this is not true for absorption far from the antenna, which has no effect on the transmitter or antenna near-field).
Very close to the antenna, in the reactive region, energy
of a certain amount, if not absorbed by a receiver, is held back and is stored very near the antenna surface. This energy is carried back and forth from the antenna to the reactive near-field by electromagnetic radiation of the type that slowly changes electrostatic and magnetostatic effects. For example, current flowing in the antenna creates a purely magnetic component in the near-field, which then collapses as the antenna current begins to reverse, causing transfer of the field's magnetic energy back to electrons in the antenna as the changing magnetic field causes a self-inductive effect on the antenna that generated it. This returns energy to the antenna in a regenerative way, so that it is not lost. A similar process happens as electric charge builds up in one section of the antenna under the pressure of the signal voltage, and causes a local electric field around that section of antenna, due to the antenna's self-capacitance. When the signal reverses so that charge is allowed to flow away from this region again, the built-up electric field assists in pushing electrons back in the new direction of their flow, as with the discharge of any unipolar capacitor. This again transfers energy back to the antenna current.
Because of this energy storage and return effect, if either of the inductive or electrostatic effects in the reactive near-field transfers energy to electrons in a different (nearby) conductor, this energy is lost to the primary antenna, and thus an extra drain is seen on the transmitter circuit, resulting from the reactive near-field energy that is not returned.
The reactive component of the near-field can give ambiguous or undetermined results when attempting measurements in this region. In other regions, the power density is inversely proportional to the square of the distance from the antenna. In the vicinity very close to the antenna, however, the energy level can rise dramatically with only a small decrease in distance toward the antenna. In the short term, and the long term, this energy can adversely affect both humans and measurement equipment because of the high powers involved.
For example, metal objects such as steel beams can act as antennas by inductively receiving and then "re-radiating" some of the energy in the radiative near-field, forming a new radiating surface to consider. Depending on antenna characteristics and frequencies, such coupling may be far more efficient than simple antenna reception in the yet-more-distant far-field, so far more power may be transferred to the secondary "antenna" in this region than would be the case with a more distant antenna. When a secondary radiating antenna surface is thus activated, it then creates its own near-field regions, but the same conditions apply to them.
are regions around the source. The boundary between the two regions is only vaguely defined, and depends on the dominant wavelength
(λ) emitted by the source. In broad terms, for an electromagnetically short antenna, the near-field is the region within a radius r << λ, while the far field is the region for which r >> λ. The two regions are defined simply for mathematical convenience, enabling certain simplifying approximations. These regions are sometimes also called the "near-zone" and "far-zone". The latter is also frequently referred to as the "radiation zone", or "free space".
A more precise definition is given by the propagation properties. If the distance separating the transmitting and receiving antennas is larger than 2D2/λ, where D is the largest dimension of the source of the radiation, then it is a far field measurement (Fraunhofer diffraction
) and if the measuring distance is less 2D2/λ, it is a near-field measurement (Fresnel diffraction
).
The radiation zone is important because far-fields in general fall off in amplitude by 1/r. This means that the total energy per unit area at a distance r is proportional to 1/r2. The area of the sphere is proportional to r2, so the total energy passing through the sphere is constant. This means that the far-field energy actually escapes to infinite distance (it radiates).
The amplitude of other components of the electromagnetic field close to the antenna may be quite powerful, but, because of more rapid fall-off with distance than 1/r behavior, they do not radiate energy to infinite distances. Instead, their energies remain trapped in the region near the antenna, not drawing power from the transmitter unless they excite a receiver in the area close to the antenna. Thus, the near-fields only transfer energy to very nearby receivers, and, when they do, the result is felt as an extra power-draw in the transmitter. As an example of such an effect, power is transferred across space in a common transformer
or metal detector
by means of near-field phenomena (in this case inductive coupling
), in a strictly "short-range" effect (i.e., the range within one wavelength of the signal).
If sinusoidal currents are applied to a structure of some type, electric and magnetic fields will appear in space about that structure. If those fields extend some distance into space the structure is often termed an antenna. Such an antenna can be an assemblage of conductor
s in space typical of radio
devices or it can be an aperture
with a given current distribution radiating into space as is typical of microwave
or optical devices. The actual values of the fields in space about the antenna are usually quite complex and can vary with distance from the antenna in various ways.
Since in many practical applications one is interested only in effects where the distance from the antenna to the observer is very much greater than the largest dimension of the transmitting antenna, the equations describing the fields created about the antenna can be simplified by assuming a large separation and dropping all terms that provide only minor contributions to the final field. These simplified distributions have been termed the "far-field" and usually have the property that the angular distribution of energy does not change with distance, however the energy levels still vary with distance and time. Such an angular energy distribution is usually termed an antenna pattern.
Note that, by the principle of reciprocity
, the pattern observed when a particular antenna is transmitting is identical to the pattern measured when the same antenna is used for reception. Typically one finds simple relations describing the antenna far field patterns, often involving trigonometric functions or at worst Fourier
or Hankel transform
relationships between the antenna current distributions and the observed far field patterns. While far-field simplifications are very useful in engineering calculations, this does not mean the near-field functions cannot be calculated, especially using modern computer techniques. An examination of how the near-fields form about an antenna structure can give great insight into the operations of such devices.
The near-field is remarkable for reproducing classical electromagnetic induction
and electric charge effects on the EM field, which effects "die-out" with increasing distance from the antenna (with magnetic field strength proportional to the inverse-cube of the distance and electric field strength proportional to inverse-square of distance), far more rapidly than do the classical radiated EM far-field (E and B fields proportional simply to inverse-distance). Typically near-field effects are not important farther away than a few wavelengths of the antenna.
Far near-field effects also involve energy transfer effects that couple directly to receivers near the antenna, affecting the power output of the transmitter if they do couple, but not otherwise. In a sense, the near-field offers energy that is available to a receiver only if the energy is tapped, and this is sensed by the transmitter by means of answering electromagnetic near-fields emanating from the receiver. Again, this is the same principle that applies in induction coupled
devices, such as a transformer
, which draws more power at the primary circuit, if power is drawn from the secondary circuit. This is different with the far-field, which constantly draws the same energy from the transmitter, whether it is immediately received, or not.
for the electric
and magnetic field
s for a localized oscillating source, such as an antenna, surrounded by a homogeneous material (typically vacuum
or air), yields fields that, far away, decay in proportion to 1/r where r is the distance from the source. These are the radiating fields, and the region where r is large enough for these fields to dominate is the far field.
In general, the fields of a source in a homogeneous
isotropic medium
can be written as a multipole expansion
. The terms in this expansion are spherical harmonic
s (which give the angular dependence) multiplied by spherical Bessel functions (which give the radial dependence). For large r, the spherical Bessel functions decay as 1/r, giving the radiated field above. As one gets closer and closer to the source (smaller r), approaching the near-field, other powers of r become significant.
The next term that becomes significant is proportional to 1/r2 and is sometimes called the induction term. It can be thought of as the primarily magnetic energy stored in the field, and returned to the antenna in every half-cycle, through self-induction. For even smaller r, terms proportional to 1/r3 become significant; this is sometimes called the electrostatic field term and can be thought of as stemming from the electrical charge in the antenna element.
Very close to the source, the multipole expansion is less useful (too many terms are required for an accurate description of the fields). Rather, in the near-field, it is sometimes useful to express the contributions as a sum of radiating fields combined with evanescent fields, where the latter are exponentially decaying with r. And in the source itself, or as soon as one enters a region of inhomogeneous materials, the multipole expansion is no longer valid and the full solution of Maxwell's equations is generally required.
The diffraction
pattern in the near-field typically differs significantly from that observed at infinity and varies with distance from the source.
distribution is in essence independent of distance from the source. In the far-field, the shape of the antenna pattern is independent of distance. If the source has a maximum overall dimension D (aperture width) that is large compared to the wavelength λ, the far-field region is commonly taken to exist at distances from the source, greater than Fresnel parameter S = D2/(4λ), S > 1.
For a 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".
Using the usual approximation for the speed of light in free space c0 = 3 × 108 m/s gives the frequently used expression:
The electromagnetic field in the near-field region of an electrically small coil antenna is predominantly magnetic. For small values of r/λ, the wave impedance of an inductor is low and inductive, at short range being asymptotic to:
The electromagnetic field in the near-field region of an electrically short rod antenna is predominantly electric. For small values of r/λ, the wave impedance is high and capacitive, at short range being asymptotic to:
In both cases, the wave impedance converges on that of free space as the range approaches the far field.
. Virtual photons composing near-field fluctuations and signals, have effects that are of far shorter range than those of real photons.
Other
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
field that emanates from a transmitting antenna
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
, or as a result of radiation scattering off an object. Certain behavior characteristics of electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
s dominate at a given distance from the antenna or scattering object, while different behavior can dominate at another distance. Defined boundary regions categorize these behavior characteristics. For antennas shorter than the wavelength of the radiation they emit, these regional boundaries are measured in terms of a ratio of the distance from the radiating source
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
to the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
of the radiation. For antennas physically larger than the radiation they emit, this factor must be taken into account also, and this extends the near-field region.
The "far-field" extends outward beginning about two wavelengths distance from an electromagnetically "short" antenna, to infinity. A "short" antenna is defined in this context as one that is shorter than the wavelength of the radiation it emits (see rules for longer antennas, below). The far-field is the region in which the field acts as "normal" electromagnetic radiation. The power of this radiation decreases as the square of distance from the antenna, and absorption of the radiation has no effect on the transmitter. By contrast, the "near-field", which is inside about one wavelength distance from the antenna, is a region in which there are strong inductive and capacitative 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. Also, in the part of the near-field closest to the antenna (called the "reactive 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 that power has been absorbed from the closest near-field zone, but if this power is not absorbed by another antenna, the transmitter does not supply as much power to the antenna, nor does it draw as much from its own power supply. Finally, the "transition zone" between these near and far field regions, extending over the distance from one to two wavelengths from the antenna, 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. The image above-right shows these regions and boundaries.
Such regions categorize field behaviors that vary, 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.
For antennas that have a characteristic physical length longer than the wavelength of the radiation they emit, and for focused or "dish" antennas of diameter longer than the wavelength of the radiation, the near and far-field distances cannot be in terms of simple radiation wavelength, but must be qualified in terms of the factor
where R is the distance from the antenna, D is the antenna diameter or length, and λ is the wavelength of the radiation. When this distance R is smaller than two wavelengths of the radiation, the region inside this radius is considered near-field, but when R is longer than two wavelengths, this region is considered the antenna far-field. The behaviors in these regions are the same as described above for electromagnetically "short" antennas. This behavior of considerably extends the near-field effects of focused antennas, and antennas that emanate high-frequency radiation.Propagation characteristics
Any electromagnetic radiationElectromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
consists of an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
component E and a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
component H. In the far-field, the relationship between the electric field component E and the magnetic component H is that characteristic of any freely propagating wave, where (in units where c = 1) E is equal to H at any point in space. By contrast, in the near-field, the relationship between E and H becomes very complex. Also, unlike the far-field where electromagnetic waves are usually characterized by a single polarization type (horizontal, vertical, circular, or elliptical), all four polarization types can be present in the near-field.
The near-field itself is further divided into the reactive near-field and the radiative near-field. The "reactive" and "radiative" near-field designations are also a function of wavelength (or distance). However, these boundary regions are a fraction of one wavelength within the near-field. The outer boundary of the reactive near-field region is commonly considered to be a distance of 1/2π times the wavelength (λ/2π or 0.159 x λ) from the antenna surface. The radiative near-field (also called the "Fresnel region") covers the remainder of the near-field region, from λ/2π out to λ (one full wavelength).
Reactive near-field, or the nearest part of the near-field
In the reactive near-field (very close to the antenna), the relationship between the strengths of the E and H fields is often too complex to predict. Either field component (E or H) may dominate at one point, and the opposite relationship dominate at a point only a short distance away. This makes finding the true power densityPower density
Power density is the amount of power per unit volume....
in this region problematic. This is because to calculate power, not only E and H both have to be measured but the phase relationship
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
between E and H must also be known.
In this reactive region, not only is an electromagnetic wave being radiated outward into far-space but there is a "reactive" component to the electromagnetic field, meaning that the nature of the field around the antenna is sensitive to, and reacts to, EM absorption in this region (this is not true for absorption far from the antenna, which has no effect on the transmitter or antenna near-field).
Very close to the antenna, in the reactive region, energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
of a certain amount, if not absorbed by a receiver, is held back and is stored very near the antenna surface. This energy is carried back and forth from the antenna to the reactive near-field by electromagnetic radiation of the type that slowly changes electrostatic and magnetostatic effects. For example, current flowing in the antenna creates a purely magnetic component in the near-field, which then collapses as the antenna current begins to reverse, causing transfer of the field's magnetic energy back to electrons in the antenna as the changing magnetic field causes a self-inductive effect on the antenna that generated it. This returns energy to the antenna in a regenerative way, so that it is not lost. A similar process happens as electric charge builds up in one section of the antenna under the pressure of the signal voltage, and causes a local electric field around that section of antenna, due to the antenna's self-capacitance. When the signal reverses so that charge is allowed to flow away from this region again, the built-up electric field assists in pushing electrons back in the new direction of their flow, as with the discharge of any unipolar capacitor. This again transfers energy back to the antenna current.
Because of this energy storage and return effect, if either of the inductive or electrostatic effects in the reactive near-field transfers energy to electrons in a different (nearby) conductor, this energy is lost to the primary antenna, and thus an extra drain is seen on the transmitter circuit, resulting from the reactive near-field energy that is not returned.
The reactive component of the near-field can give ambiguous or undetermined results when attempting measurements in this region. In other regions, the power density is inversely proportional to the square of the distance from the antenna. In the vicinity very close to the antenna, however, the energy level can rise dramatically with only a small decrease in distance toward the antenna. In the short term, and the long term, this energy can adversely affect both humans and measurement equipment because of the high powers involved.
Radiative near-field (Fresnel region), or farthest part of the near-field
The radiative near-field (sometimes called the Fresnel region) does not contain reactive field components from the source antenna, since it is so far from the antenna that back-coupling of the fields becomes out-of-phase with the antenna signal, and thus cannot efficiently store and replace inductive or capacitative energy from antenna currents or charges. The energy in the radiative near-field is thus all radiant energy, although its mixture of magnetic and electric components are still different from the far-field. Further out into the radiative near-field (one half wavelength to 1 wavelength from the source), the E and H field relationship is more predictable, but the E to H relationship is still complex. However, since the radiative near-field is still part of the near-field, there is potential for unanticipated (or adverse) conditions.For example, metal objects such as steel beams can act as antennas by inductively receiving and then "re-radiating" some of the energy in the radiative near-field, forming a new radiating surface to consider. Depending on antenna characteristics and frequencies, such coupling may be far more efficient than simple antenna reception in the yet-more-distant far-field, so far more power may be transferred to the secondary "antenna" in this region than would be the case with a more distant antenna. When a secondary radiating antenna surface is thus activated, it then creates its own near-field regions, but the same conditions apply to them.
Radiation zone, including radiating far-field
The near-field and far-field of an antenna or other isolated source of electromagnetic radiationElectromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
are regions around the source. The boundary between the two regions is only vaguely defined, and depends on the dominant wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
(λ) emitted by the source. In broad terms, for an electromagnetically short antenna, the near-field is the region within a radius r << λ, while the far field is the region for which r >> λ. The two regions are defined simply for mathematical convenience, enabling certain simplifying approximations. These regions are sometimes also called the "near-zone" and "far-zone". The latter is also frequently referred to as the "radiation zone", or "free space".
A more precise definition is given by the propagation properties. If the distance separating the transmitting and receiving antennas is larger than 2D2/λ, where D is the largest dimension of the source of the radiation, then it is a far field measurement (Fraunhofer diffraction
Fraunhofer diffraction
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens....
) and if the measuring distance is less 2D2/λ, it is a near-field measurement (Fresnel diffraction
Fresnel diffraction
In optics, the Fresnel diffraction equation for near-field diffraction, is an approximation of Kirchhoff-Fresnel diffraction that can be applied to the propagation of waves in the near field....
).
The radiation zone is important because far-fields in general fall off in amplitude by 1/r. This means that the total energy per unit area at a distance r is proportional to 1/r2. The area of the sphere is proportional to r2, so the total energy passing through the sphere is constant. This means that the far-field energy actually escapes to infinite distance (it radiates).
The amplitude of other components of the electromagnetic field close to the antenna may be quite powerful, but, because of more rapid fall-off with distance than 1/r behavior, they do not radiate energy to infinite distances. Instead, their energies remain trapped in the region near the antenna, not drawing power from the transmitter unless they excite a receiver in the area close to the antenna. Thus, the near-fields only transfer energy to very nearby receivers, and, when they do, the result is felt as an extra power-draw in the transmitter. As an example of such an effect, power is transferred across space in a common transformer
Transformer
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field...
or metal detector
Metal detector
A metal detector is a device which responds to metal that may not be readily apparent.The simplest form of a metal detector consists of an oscillator producing an alternating current that passes through a coil producing an alternating magnetic field...
by means of near-field phenomena (in this case inductive coupling
Inductive coupling
In electrical engineering, two conductors are referred to as mutual-inductively coupled or magnetically coupled when they are configured such that change in current flow through one wire induces a voltage across the ends of the other wire through electromagnetic induction...
), in a strictly "short-range" effect (i.e., the range within one wavelength of the signal).
Summary
Electrical conductor
In physics and electrical engineering, a conductor is a material which contains movable electric charges. In metallic conductors such as copper or aluminum, the movable charged particles are electrons...
s in space typical of radio
Radio
Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...
devices or it can be an aperture
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...
with a given current distribution radiating into space as is typical of microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
or optical devices. The actual values of the fields in space about the antenna are usually quite complex and can vary with distance from the antenna in various ways.
Since in many practical applications one is interested only in effects where the distance from the antenna to the observer is very much greater than the largest dimension of the transmitting antenna, the equations describing the fields created about the antenna can be simplified by assuming a large separation and dropping all terms that provide only minor contributions to the final field. These simplified distributions have been termed the "far-field" and usually have the property that the angular distribution of energy does not change with distance, however the energy levels still vary with distance and time. Such an angular energy distribution is usually termed an antenna pattern.
Note that, by the principle of reciprocity
Reciprocity (electromagnetism)
In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints...
, the pattern observed when a particular antenna is transmitting is identical to the pattern measured when the same antenna is used for reception. Typically one finds simple relations describing the antenna far field patterns, often involving trigonometric functions or at worst Fourier
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
or Hankel transform
Hankel transform
In mathematics, the Hankel transform expresses any given function f as the weighted sum of an infinite number of Bessel functions of the first kind Jν. The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor k along the r-axis...
relationships between the antenna current distributions and the observed far field patterns. While far-field simplifications are very useful in engineering calculations, this does not mean the near-field functions cannot be calculated, especially using modern computer techniques. An examination of how the near-fields form about an antenna structure can give great insight into the operations of such devices.
The near-field is remarkable for reproducing classical electromagnetic induction
Electromagnetic induction
Electromagnetic induction is the production of an electric current across a conductor moving through a magnetic field. It underlies the operation of generators, transformers, induction motors, electric motors, synchronous motors, and solenoids....
and electric charge effects on the EM field, which effects "die-out" with increasing distance from the antenna (with magnetic field strength proportional to the inverse-cube of the distance and electric field strength proportional to inverse-square of distance), far more rapidly than do the classical radiated EM far-field (E and B fields proportional simply to inverse-distance). Typically near-field effects are not important farther away than a few wavelengths of the antenna.
Far near-field effects also involve energy transfer effects that couple directly to receivers near the antenna, affecting the power output of the transmitter if they do couple, but not otherwise. In a sense, the near-field offers energy that is available to a receiver only if the energy is tapped, and this is sensed by the transmitter by means of answering electromagnetic near-fields emanating from the receiver. Again, this is the same principle that applies in induction coupled
Electromagnetic induction
Electromagnetic induction is the production of an electric current across a conductor moving through a magnetic field. It underlies the operation of generators, transformers, induction motors, electric motors, synchronous motors, and solenoids....
devices, such as a transformer
Transformer
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field...
, which draws more power at the primary circuit, if power is drawn from the secondary circuit. This is different with the far-field, which constantly draws the same energy from the transmitter, whether it is immediately received, or not.
Analysis
Solving Maxwell's equationsMaxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
for the electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s for a localized oscillating source, such as an antenna, surrounded by a homogeneous material (typically vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
or air), yields fields that, far away, decay in proportion to 1/r where r is the distance from the source. These are the radiating fields, and the region where r is large enough for these fields to dominate is the far field.
In general, the fields of a source in a homogeneous
Homogeneity (physics)
In general, homogeneity is defined as the quality or state of being homogeneous . For instance, a uniform electric field would be compatible with homogeneity...
isotropic medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
can be written as a multipole expansion
Multipole expansion
A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original...
. The terms in this expansion are spherical harmonic
Spherical Harmonic
Spherical Harmonic is a science fiction novel from the Saga of the Skolian Empire by Catherine Asaro. It tells the story of Dyhianna Selei , the Ruby Pharaoh of the Skolian Imperialate, as she strives to reform her government and reunite her family in the aftermath of a devastating interstellar...
s (which give the angular dependence) multiplied by spherical Bessel functions (which give the radial dependence). For large r, the spherical Bessel functions decay as 1/r, giving the radiated field above. As one gets closer and closer to the source (smaller r), approaching the near-field, other powers of r become significant.
The next term that becomes significant is proportional to 1/r2 and is sometimes called the induction term. It can be thought of as the primarily magnetic energy stored in the field, and returned to the antenna in every half-cycle, through self-induction. For even smaller r, terms proportional to 1/r3 become significant; this is sometimes called the electrostatic field term and can be thought of as stemming from the electrical charge in the antenna element.
Very close to the source, the multipole expansion is less useful (too many terms are required for an accurate description of the fields). Rather, in the near-field, it is sometimes useful to express the contributions as a sum of radiating fields combined with evanescent fields, where the latter are exponentially decaying with r. And in the source itself, or as soon as one enters a region of inhomogeneous materials, the multipole expansion is no longer valid and the full solution of Maxwell's equations is generally required.
Near-field
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 antennaAntenna (radio)An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
where the angular fieldField (physics)In physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...
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 Fresnel parameter S = D2/(4λ) from the source of the diffracting edge or antenna of longitude or diameter D.
- In optical fiberOptical fiberAn optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...
communicationsTelecommunicationTelecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...
, the region close to a source or apertureApertureIn optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...
.
The diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
pattern in the near-field typically differs significantly from that observed at infinity and varies with distance from the source.
Far-field
The "far-field region" is the region outside the near-field region, where the angular fieldField (physics)
In physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...
distribution is in essence independent of distance from the source. In the far-field, the shape of the antenna pattern is independent of distance. If the source has a maximum overall dimension D (aperture width) that is large compared to the wavelength λ, the far-field region is commonly taken to exist at distances from the source, greater than Fresnel parameter S = D2/(4λ), S > 1.
For a beam
Light beam
A light beam or beam of light is a narrow projection of light energy radiating from a source into a beam. Sunlight is a natural example of a light beam when filtered through various mediums...
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".
Impedance
The electromagnetic field in the far-field region of an antenna is independent of the type of field radiated by the antenna. The wave impedance is the ratio of the strength of the electric and magnetic fields, which in the far-field are in phase with each other. Thus, the far-field "impedance of free space" is resistive and is given by:Using the usual approximation for the speed of light in free space c0 = 3 × 108 m/s gives the frequently used expression:
The electromagnetic field in the near-field region of an electrically small coil antenna is predominantly magnetic. For small values of r/λ, the wave impedance of an inductor is low and inductive, at short range being asymptotic to:
The electromagnetic field in the near-field region of an electrically short rod antenna is predominantly electric. For small values of r/λ, the wave impedance is high and capacitive, at short range being asymptotic to:
In both cases, the wave impedance converges on that of free space as the range approaches the far field.
Quantum field theory view
In the quantum view of electromagnetic interactions, far-field effects are manifestations of real photons, whereas near-field effects are due to a mixture of real and virtual photonsVirtual particle
In physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...
. Virtual photons composing near-field fluctuations and signals, have effects that are of far shorter range than those of real photons.
See also
Local effects- Fresnel diffractionFresnel diffractionIn optics, the Fresnel diffraction equation for near-field diffraction, is an approximation of Kirchhoff-Fresnel diffraction that can be applied to the propagation of waves in the near field....
for more on the near-field - Fraunhofer diffractionFraunhofer diffractionIn optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens....
for more on the far field - Near field communicationNear Field CommunicationNear field communication, or NFC, allows for simplified transactions, data exchange, and wireless connections between two devices in proximity to each other, usually by no more than a few centimeters. It is expected to become a widely used system for making payments by smartphone in the United States...
for more on near field communication technology - Resonant inductive couplingResonant inductive couplingResonant inductive coupling or electrodynamic induction is the near field wireless transmission of electrical energy between two coils that are highly resonant at the same frequency. The equipment to do this is sometimes called a resonant or resonance transformer. While many...
for magnetic device applications - Wireless energy transferWireless energy transferWireless energy transfer or wireless power is the transmission of electrical energy from a power source to an electrical load without artificial interconnecting conductors. Wireless transmission is useful in cases where interconnecting wires are inconvenient, hazardous, or impossible...
for some power transfer applications - MRI scanner A machine that transfers signals to and from the patient by near field magnetic effects at RF frequencies
Other
- Antenna measurementAntenna measurementAntenna measurement techniques refers to the testing of antennas to ensure that the antenna meets specifications or simply to characterize it. Typical parameters of antennas are gain, radiation pattern, beamwidth, polarization, and impedance....
covers Far-Field Ranges (FF) and Near-Field Ranges (NF), separated by the Fraunhofer distance. - Ground waves is a mode of propagation.
- Sky waves is a mode of propagation.
- Inverse-square lawInverse-square lawIn physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....
Patents
- George F. Leydorf, , Antenna near field coupling system. 1966.
- Grossi et al., , Trapped Electromagnetic Radiation Communication System. 1969., Reducing-Noise With Dual-Mode Antenna. 1969.
- Coffin et al., , Determination of Far Field Antenna Patterns Using Fresnel Probe Measurements. 1972.
- Hansen et al., , Method and Apparatus for Determining Near-Field Antenna Patterns. 1975
- Wolff et al.,, Method and apparatus for sensing proximity of an object using near-field effects