A Fresnel zone ( ), named after physicist
Augustin-Jean Fresnel, is one of a series of confocal
prolate ellipsoid
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.
An ellipsoid is a quadric surface; that is, a surface that may be defined as th ...
al regions of space between and around a transmitter and a receiver. The primary wave will travel in a relative straight line from the transmitter to the receiver. Aberrant transmitted radio, sound, or light waves which are transmitted at the same time
can follow slightly different paths before reaching a receiver, especially if there are obstructions or deflecting objects between the two. The two waves can arrive at the receiver at slightly different times and the aberrant wave may arrive out of phase with the primary wave due to the different path lengths. Depending on the magnitude of the phase difference between the two waves,
the waves can interfere constructively or destructively. The size of the calculated Fresnel zone at any particular distance from the transmitter and receiver can help to predict whether obstructions or discontinuities along the path will cause significant interference.
Significance
In any wave-propagated transmission between a transmitter and receiver, some amount of the radiated wave propagates off-axis (not on the line-of-sight path between transmitter and receiver). This can then
deflect off objects and then radiate to the receiver. However, the direct-path wave and the deflected-path wave may arrive out of
phase, leading to
destructive interference when the phase difference is half an odd integer (
) multiple of the
period. The n-th Fresnel zone is defined as the locus of points in 3D space such that a 2-segment path from the transmitter to the receiver that deflects off a point on that surface will be between n-1 and n half-wavelengths out of phase with the straight-line path. The boundaries of these zones will be ellipsoids with foci at the transmitter and receiver. In order to ensure limited interference, such transmission paths are designed with a certain clearance distance determined by a Fresnel-zone analysis.
The dependence on the interference on clearance is the cause of the picket-fencing effect when either the radio transmitter or receiver is moving, and the high and low signal strength zones are above and below the receiver's
cut-off threshold. The extreme variations of signal strength at the receiver can cause interruptions in the communications link, or even prevent a signal from being received at all.
Fresnel zones are seen in
optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
,
radio communications,
electrodynamics,
seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
,
acoustics,
gravitational radiation, and other situations involving the radiation of waves and
multipath propagation
In radio communication, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric reflection and refraction, and refle ...
. Fresnel zone computations are used to anticipate obstacle clearances required when designing highly directive systems such as
microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ra ...
parabolic antenna systems. Although intuitively, clear line-of-sight between transmitter and receiver may seem to be all that is required for a strong antenna system, but because of the complex nature of radio waves, obstructions within the first Fresnel zone can cause significant weakness, even if those obstructions are not blocking the apparent line-of-sight signal path. For this reason, it is valuable to do a calculation of the size of the 1st, or primary, Fresnel zone for a given antenna system. Doing this will enable the antenna installer to decide if an obstacle, such as a tree, is going to make a significant impact on signal strength. The rule of thumb is that the primary Fresnel zone would ideally be 80% clear of obstacles, but must be at least 60% clear.
Spatial structure
Fresnel zones are confocal
prolate ellipsoid
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.
An ellipsoid is a quadric surface; that is, a surface that may be defined as th ...
al shaped regions in space (e.g. 1, 2, 3), centered around the line of the direct transmission path (path AB on the diagram). The first region includes the ellipsoidal space which the direct line-of-sight signal passes through. If a stray component of the transmitted signal bounces off an object within this region and then arrives at the receiving antenna, the
phase shift will be something less than a quarter-length wave, or less than a 90º shift (path ACB on the diagram). The effect regarding phase-shift alone will be minimal. Therefore, this bounced signal can potentially result in having a positive impact on the receiver, as it is receiving a stronger signal than it would have without the deflection, and the additional signal will potentially be mostly in-phase. However, the positive attributes of this deflection also depends on the polarization of the signal relative to the object (see the section on polarization under the Talk tab).
The 2nd region surrounds the 1st region but excludes it. If a reflective object is located in the 2nd region, the stray sine-wave which has bounced from this object and has been captured by the receiver will be shifted more than 90º but less than 270º because of the increased path length, and will potentially be received out-of-phase. Generally this is unfavorable. But again, this depends on polarization (see the section on polarization under the Talk tab). Use of same
circular polarization (e.g. right) in both ends, will eliminate odd number of reflections (including one).
The 3rd region surrounds the 2nd region and deflected waves captured by the receiver will have the same effect as a wave in the 1st region. That is, the sine wave will have shifted more than 270º but less than 450º (ideally it would be a 360º shift) and will therefore arrive at the receiver with the same shift as a signal might arrive from the 1st region. A wave deflected from this region has the potential to be shifted precisely one wavelength so that it is exactly in sync with the line-of-sight wave when it arrives at the receiving antenna.
The 4th region surrounds the 3rd region and is similar to the 2nd region. And so on.
If unobstructed and in a perfect environment, radio waves will travel in a relatively straight line from the transmitter to the receiver. But if there are reflective surfaces that interact with a stray transmitted wave, such as bodies of water, smooth terrain, roof tops, sides of buildings, etc., the radio waves deflecting off those surfaces may arrive either out-of-phase or in-phase with the signals that travel directly to the receiver. Sometimes this results in the counter-intuitive finding that reducing the height of an antenna increases the
signal-to-noise ratio at the receiver.
Although radio waves generally travel in a relative straight line, fog and even humidity can cause some of the signal in certain frequencies to scatter or bend before reaching the receiver. This means objects which are clear of the line of sight path will still potentially block parts of the signal. To maximize signal strength, one needs to minimize the effect of obstruction loss by removing obstacles from both the direct radio frequency
line of sight (RF LoS) line and also the area around it within the primary Fresnel zone. The strongest signals are on the direct line between transmitter and receiver and always lie in the first Fresnel zone.
In the early 19th century, French scientist
Augustin-Jean Fresnel created a method to calculate where the zones are — that is, whether a given obstacle will cause mostly in-phase or mostly out-of-phase deflections between the transmitter and the receiver.
Clearance calculation
The concept of Fresnel zone clearance may be used to analyze
interference by obstacles near the path of a radio beam. The first zone must be kept largely free from obstructions to avoid interfering with the radio reception. However, some obstruction of the Fresnel zones can often be tolerated. As a
rule of thumb the maximum obstruction allowable is 40%, but the recommended obstruction is 20% or less.
For establishing Fresnel zones, first determine the RF line of sight (RF LoS), which in simple terms is a straight line between the transmitting and receiving antennas. Now the zone surrounding the RF LoS is said to be the Fresnel zone.
The cross sectional radius of each Fresnel zone is the longest at the midpoint of the RF LoS, shrinking to a point at each vertex, behind the antennas.
Formulation
Consider an arbitrary point ''P'' in the LoS, at a distance
and
with respect to each of the two antennas.
To obtain the radius
of zone
, note that the volume of the zone is delimited by all points for which the difference in distances, between the direct wave (
) and the reflected wave (
) is the constant
(multiples of half a
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
). This effectively defines an ellipsoid with the major axis along
and foci at the antennas (points A and B). So:
:
Re-writing the expression with the coordinates of point
and the distance between antennas
, it gives:
:
:
Assuming the distances between the antennas and the point
are much larger than the radius and applying the
binomial approximation for the square root,
(for ''x''≪1), the expression simplifies to:
:
which can be solved for
:
:
For a satellite-to-Earth link, it further simplifies to:
:
Note that when
or
, which implies that the foci seem to coincide with the
vertices of the ellipsoid. This is not correct and it's a consequence of the approximation made.
Setting the point
to one of the vertices (behind an antenna), it's possible to obtain the error
of this approximation:
:
Since the distance between antennas is generally tens of km and
of the order of cm, the error is negligible for a graphical representation.
On the other hand, considering the clearance at the left-hand antenna, with
, and applying the binomial approximation only at the right-hand antenna, we find:
:
:
The quadratic polynomial roots are:
:
Applying the binomial approximation one last time, we finally find:
:
So, there should be at least half a wavelength of clearance at the antenna in the direction perpendicular to the line of sight.
The vertical clearance at the antenna in a
slant direction
In radio electronics, especially radar terminology, slant range or slant distance is the distance along the relative direction between two points. If the two points are at the same level (relative to a specific datum), the slant distance equals t ...
inclined at an
altitude angle ''a'' would be:
:
Maximum clearance
For practical applications, it is often useful to know the maximum radius of the first Fresnel zone. Using
,
, and
in the above formula gives
:
where
:
is the distance between the two antennas,
:
is the
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of the transmitted signal,
:
≈ is the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
in the air.
Substitution of the numeric value for
followed by a
unit conversion results in an easy way to calculate the radius of the first Fresnel zone
, knowing the distance between the two antennas
and the frequency of the transmitted signal
:
*
*
See also
*
Beam diameter
The beam diameter or beam width of an electromagnetic beam is the diameter along any specified line that is perpendicular to the beam axis and intersects it. Since beams typically do not have sharp edges, the diameter can be defined in many differ ...
*
Diversity scheme
*
Ellipse#Elliptical reflectors and acoustics
*
Fresnel diffraction
*
Fresnel integral
*
Fresnel number
The Fresnel number (''F''), named after the physicist Augustin-Jean Fresnel, is a dimensionless number occurring in optics, in particular in scalar diffraction theory.
Definition
For an electromagnetic wave passing through an aperture and hitti ...
*
Fresnel zone plate
*
Fresnel zone antenna
*
Microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ra ...
*
Near field
*
Path loss
*
Rain fade
*
Weissberger's model
References
*
External links
Online Fresnel Zone Calculator: Support the global languageGenerate 3D Fresnel zone, as a Google Earth KML fileFresnel zone calculator and elevation chartFresnel zone calculatorFEN Fresnel zone calculatorMore Fresnel zone details
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Diffraction
Radio frequency propagation