Download Equivalent isotropically radiated power

Equivalent isotropically radiated power
From Wikipedia, the free encyclopedia
(Redirected from EIRP)
Jump to: navigation, search
In radio communication systems, Equivalent isotropically radiated power (EIRP)
or, alternatively, Effective isotropic radiated power is the amount of power that
would have to be emitted by an isotropic antenna (that evenly distributes power in all
directions and is a theoretical construct) to produce the peak power density observed
in the direction of maximum antenna gain. EIRP can take into account the losses in
transmission line and connectors and includes the gain of the antenna. The EIRP is
often stated in terms of decibels over a reference power level, that would be the power
emitted by an isotropic radiator with an equivalent signal strength. The EIRP allows
making comparisons between different emitters regardless of type, size or form. From
the EIRP, and with knowledge of a real antenna's gain, it is possible to calculate real
power and field strength values.
EIRP(dBm) = (Power of Transmitter (dBm)) – (Losses in transmission line
(dB)) + (Antenna Gain(dBi))
where antenna gain is expressed relative to a (theoretical) isotropic reference antenna.
This example uses dBm, although it is also common to see dBW.
Decibels are a convenient way to express the ratio between two quantities. dBm uses
a reference of 1mW and dBw uses a reference of 1W.
dBm = 10 log(power out / 1mW)
and
dBW = 10 log(power out / 1W)
A transmitter with a 50W output can be expressed as a 17dBW output
16.9897 = 10 * log(50/1)
The EIRP is used to estimate the service area of the transmitter, and to co-ordinate
transmitters on the same frequency so that their coverage areas do not overlap.
In built-up areas, regulations may restrict the EIRP of a transmitter to prevent
exposure of personnel to high power electromagnetic fields however EIRP is
normally restricted to minimise interference to services on similar frequencies
-------------------------
Isotropic antenna
From Wikipedia, the free encyclopedia
Jump to: navigation, search
An isotropic antenna is an ideal antenna that radiates power with unit gain uniformly
in all directions and is often used as a reference for antenna gains in wireless systems.
There is no actual physical isotropic antenna; a close approximation is a stack of two
pairs of crossed dipole antennas driven in quadrature. The radiation pattern for the
isotropic antenna is a sphere with the antenna at its center.
Antenna gains are often specified in dBi, or decibels over isotropic. This is the power
in the strongest direction relative to the power that would be transmitted by an
isotropic antenna emitting the same total power.
------------------
A simple half-wave dipole antenna that a shortwave listener might build.
Elementary doublet
An elementary doublet is a small length of conductor
wavelength ) traversed by an alternating current:
(small compared to the
Here
is the pulsation (and the frequency). is, as usual
. This writing
using complex numbers is the same as the writing used with phasors or impedances.
Note that this dipole cannot be physically constructed. The circulating current needs
somewhere to come from and somewhere to go through. In reality, this small length
of conductor will be just one of the multiple bits in which we must divide a real
antenna in order to calculate its proprieties. The interest of this imaginary elementary
antenna is that we can easily calculate the far electrical field of the electromagnetic
wave radiated by each elementary doublet. We give just the result:
Where,





is the far electric field of the electromagnetic wave radiated in the θ
direction.
is the permittivity of vacuum.
is the speed of light in vacuum.
is the distance from the doublet to the point where the electrical field
evaluated.
is the wavenumber
is
The exponent of accounts for the phase dependence of the electrical field on time
and the distance to the dipole.
The far electric field
of the electromagnetic wave is coplanar with the conductor
and perpendicular with the line joining the dipole to the point where the field is
evaluated. If the dipole is placed in the center of a sphere in the axis south-north, the
electric field would be parallel to geographic meridians and the magnetic field of the
electromagnetic wave would be parallel to geographic parallels.
Short dipole
A short dipole is a physically feasible dipole formed by two conductors with a total
length very small compared to the wavelength . The two conducting wires are fed
at the center of the dipole. We assume the hypothesis that the current is maximal at
the center (where the dipole is fed) and that it decreases linearly to be zero at the ends
of the wires. Note that the direction of the current is the same in the both dipole
branches. To the right in both or to the left in both. The far field
of the
electromagnetic wave radiated by this dipole is:
Emission is maximal in the plane perpendicular to the dipole and zero in the direction
of wires, that is, the current direction. The emission diagram is circular section torus
shaped (left image) with zero inner diameter. In the right image doublet is vertical in
the torus center.
Knowing this electric field, we can compute the total emitted power and then compute
the resistive part of the series impedance of this dipole:
ohms (for
).
----------------
Antenna gain
Antenna gain is the ratio of surface power radiated by the antenna and the surface
power radiated by a hypothetical isotropic antenna:
The surface power carried by an electromagnetic wave is:
The surface power radiated by an isotropic antenna feed with the same power is:
Substituting values for the case of a short dipole, final result is:
= 1.5 = 1.76 dBi
dBi simply means decibels gain, relative to an isotropic antenna.
[edit] Half-wave dipole or
dipole (lambda over 2)
A is an antenna formed by two conductors whose total length is half the wave
length. Note that from the electric standpoint, this is not a noteworthy length. As we
will see, at this length the impedance of the dipole is neither maximal nor minimal.
Impedance is not real but it does becomes real for a length of about
. The only
outstanding property of this length is that mathematical formulas miraculously
simplifies for this value.
In the case of this dipole, current is assumed to have a sinusoidal distribution with a
maximum at the center (where the antenna is fed) and zero at the two ends:
It is easy to verify that for
current is equal to
and for
the current is zero.
Even with this simplifying length, the formula obtained for the far electrical field of
the radiated electromagnetic wave is rather displeasing:
But the fraction
is not very different from
The resulting emission diagram is a slightly flattened torus.
.
The image on the left shows the section of the emission pattern. We have drawn, in
dotted lines, the emission pattern of a short dipole. We can see that the two patterns
are very similar. The image at right shows the perspective view of the same emission
pattern.
This time it is not possible to compute analytically the total power emitted by the
antenna (the last formula does not allow). However, a simple numerical integration
leads to a series resistance of:
ohms
This is not enough to characterize the dipole impedance, which has also an imaginary
part. Best thing is to measure the impedance. In the image at right we have drawn the
real and imaginary parts of the impedance of a dipole for lengths going from
to
The gain of this antenna is:
= 1,64 = 2,14 dBi
Below are the gains of dipole antennas of other lengths (note that gains are not in
dBi):
Gain of dipole antennas
length in
Gain
L
1.50
l
0.5
1.64
1.0
1.80
1.5
2.00
2.00
2.30
3.0
2.80
4.0
3.50
8.0
7.10
[edit] Quarter-wave antenna
The antenna and its image form a dipole that radiates only upward.
The quarter wave antenna or quarter wave monopole is a whip antenna that behaves
as a dipole antenna. It is formed by a vertical wire in length. It is fed in the lower
end, which is near a conductive surface which works as a reflector (see Effect of
ground). The current in the reflected image has the same direction and phase that the
current in the real antenna. The set quarter-wave plus image forms a half-wave dipole
that radiates only in the upper half of space.
In this upper side of space the emitted field has the same amplitude of the field
radiated by a half-wave dipole fed with the same current. Therefore, the total emitted
power is one-half the emitted power of a half-wave dipole fed with the same current.
As the current is the same, the radiation resistance (real part of series impedance) will
be one-half of the series impedance of a half-wave dipole. As the reactive part is also
divided by 2, the impedance of a quarter wave antenna is
gain is the same as that for a half-wave dipole ( ) that is 2,14 dBi.
ohms. The
The earth can be used as ground plane. However, the earth is not a good conductor. It
is rather a dielectric. The reflected antenna image is good when seen at grazing
angles, that is, far from the antenna, but not when seen near the antenna. Far from the
antenna and near the ground, electromagnetic fields and radiation patterns are the
same as for a half-wave dipole.. The impedance is not the same a with a good
conductor ground plane. Conductivity of earth surface can be improved with an
expensive copper wire mesh.
When ground is not available, as in a vehicle, other metallic surfaces can serve a
ground plane, for example the roof of the vehicle. In other situations, radial wires
placed at the foot of the quarter-wave wire can simulate a ground plane.
[edit] Dipole characteristics
[edit] Frequency versus length
Dipoles that are much smaller than the wavelength of the signal are called Hertzian,
short, or infinitesimal dipoles. These have a very low radiation resistance and a high
reactance, making them inefficient, but they are often the only available antennas at
very long wavelengths. Dipoles whose length is half the wavelength of the signal are
called half-wave dipoles, and are more efficient. In general radio engineering, the
term dipole usually means a half-wave dipole (center-fed).
A half-wave dipole is cut to length according to the formula
[ft], where l
is the length in feet and f is the center frequency in MHz [1]. The metric formula is
[m], where l is the length in meters. The length of the dipole antenna
is about 95% of half a wavelength at the speed of light in free space. This is because
the impedance of the dipole is resistive pure at about this length.
[edit] Radiation pattern and gain
Dipoles have a toroidal (doughnut-shaped) reception and radiation pattern where the
axis of the toroid centers about the dipole. The theoretical maximum gain of a
Hertzian dipole is 10 log 1.5 or 1.76 dBi. The maximum theoretical gain of a λ/2dipole is 10 log 1.64 or 2.15 dBi.
Radiation pattern of a half-wave dipole
antenna. The scale is linear.
[edit] Feeder line
Gain of a half-wave dipole (same as left).
The scale is in dBi (decibels over
isotropic).
Ideally, a half-wave (λ/2) dipole should be fed with a balanced line matching the
theoretical 73 ohm impedance of the antenna. A folded dipole uses a 300 ohm
balanced feeder line.
Many people have had success in feeding a dipole directly with a coaxial cable feed
rather than a ladder-line. However, coax is not symmetrical and thus not a balanced
feeder. It is unbalanced, because the outer shield is connected to earth potential at the
other end. [2] When a balanced antenna such as a dipole is fed with an unbalanced
feeder, common mode currents can cause the coax line to radiate in addition to the
antenna itself, and the radiation pattern may be asymmetrically distorted. [3] This can
be remedied with the use of a balun.
--------------
A decibel is defined in two common ways.
When referring to measurements of power or intensity it is:
But when referring to measurements of amplitude it is:
where X0 is a specified reference with the same units as X. In many cases, the
reference is 1 and so is ignored. Which one people use depends on convention and
context. When the impedance is held constant, the power is proportional to the square
of the amplitude of either voltage or current, and so the above two definitions become
consistent.
An intensity I or power P can be expressed in decibels with the standard equation
where I0 and P0 are a specified reference intensity and power.
[edit] Examples
As examples, if PdB is 10 dB greater than PdB0, then P is ten times P0. If PdB is 3 dB
greater, the power ratio is very close to a factor of two
.
For sound intensity, I0 is typically chosen to be 10−12 W/m2, which is roughly the
threshold of hearing. When this choice is made, the units are said to be "dB SPL". For
sound power, P0 is typically chosen to be 10−12 W, and the units are then "dB SWL".
[edit] Decibels in electrical circuits
In electrical circuits, the dissipated power is typically proportional to the square of the
voltage V, and for sound waves, the transmitted power is similarly proportional to the
square of the pressure amplitude p. Effective sound pressure is related to sound
intensity I, density ρ and speed of sound c by the following equation:
Substituting a measured voltage or pressure and a reference voltage or pressure and
rearranging terms leads to the following equations and accounts for the difference
between the multiplier of 10 for intensity or power and 20 for voltage or pressure:
where V0 and p0 are a specified reference voltage and pressure. This means a 20 dB
increase for every factor 10 increase in the voltage or pressure ratio, or approximately
6 dB increase for every factor 2. Note that in physics, decibels refer to power ratios
only; it is incorrect to use them if the electrical or acoustic impedances are not the
same at the two points where the voltage or pressure are measured, though this usage
is very common in engineering. For example, the power carried by a sound wave at
atmospheric pressure is only proportional to the squared pressure amplitude as long as
the latter is much smaller than 1 atmosphere.
Typical abbreviations
[edit] Absolute measurements
[edit] Electric power
A schematic showing the relationship between dBu (the voltage source) and dBm (the
power dissipated as heat by the 600 Ω resistor)
dBm or dBmW
dB(1 mW) — power measurement relative to 1 milliwatt.
dBW
dB(1 W) — similar to dBm, except reference level of 1 Watt. 0dBW =
+30dBm.
[edit] Electric voltage
dBu or dBv
dB(0.775 V) — (usually RMS) voltage amplitude referenced to 0.775 volt.
Although dBu can be used with any impedance, dBu = dBm when the load is
600 Ω. dBu is preferable, since dBv is easily confused with dBV. The "u"
comes from "unloaded".
dBV
dB(1 V) — (usually RMS) voltage amplitude of a signal in a wire, relative to 1
volt, not related to any impedance.
[edit] Acoustics
dB(SPL)
dB(Sound Pressure Level) — relative to 20 micropascals (μPa) = 2×10−5 Pa,
the quietest sound a human can hear.[1] This is roughly the sound of a
mosquito flying 3 metres away. This is often abbreviated to just "dB", which
gives some the erroneous notion that "dB" is an absolute unit by itself.
[edit] Radio power
dBm
dB(mW) — power relative to 1 milliwatt.
dBμ or dBu
dB(μV/m) — electric field strength relative to 1 microvolt per metre.
dBf
dB(fW) — power relative to 1 femtowatt.
dBW
dB(W) — power relative to 1 watt.
dBk
dB(kW) — power relative to 1 kilowatt.
[edit] Note regarding absolute measurements
The term "measurement relative to" means so many dB greater than or less than the
quantity specified.
Some examples:



3 dBm means 3 dB greater than 1 mW.
−6 dBm means 6 dB less than 1 mW.
0 dBm means no change from 1 mW, in other words 0 dBm is 1 mW.
[edit] Relative measurements
dB(A), dB(B), and dB(C) weighting
These symbols are often used to denote the use of different frequency
weightings, used to approximate the human ear's response to sound, although
the measurement is still in dB (SPL). Other variations that may be seen are
dBA or dBA. According to ANSI standards, the preferred usage is to write LA
= x dB, as dBA implies a reference to an "A" unit, not an A-weighting. They
are still used commonly as a shorthand for A-weighted measurements,
however.
dBd
dB(dipole) — the forward gain of an antenna compared to a half-wave dipole
antenna.
dBi
dB(isotropic) — the forward gain of an antenna compared to an idealized
isotropic antenna.
dBFS or dBfs
dB(full scale) — the amplitude of a signal (usually audio) compared to the
maximum which a device can handle before clipping occurs. In digital
systems, 0 dBFS would equal the highest level (number) the processor is
capable of representing. This is an instantaneous (sample) value as compared
to the dBm/dBu/dBv which are typically RMS.(Measured values are usually
negative, since they should be less than the maximum.)
dBr
dB(relative) — simply a relative difference to something else, which is made
apparent in context. The difference of a filter's response to nominal levels, for
instance.
dBrn
dB above reference noise See also dBrnC.
dBc
dB relative to carrier — in telecommunications, this indicates the relative
levels of noise or sideband peak power, compared to the carrier power.
[edit] Reckoning
Decibels are handy for mental calculation, because adding them is easier than
multiplying ratios. First, however, one has to be able to convert easily between ratios
and decibels. The most obvious way is to memorize the logs of small primes, but
there are a few other tricks that can help.
[edit] Round numbers
The values of coins and banknotes are round numbers. The rules are:
1.
2.
3.
4.
5.
One is a round number
Twice a round number is a round number: 2, 4, 8, 16, 32, 64
Ten times a round number is a round number: 10, 100
Half a round number is a round number: 50, 25, 12.5, 6.25
The tenth of a round number is a round number: 5, 2.5, 1.25, 1.6, 3.2, 6.4
Now 6.25 and 6.4 are approximately equal to 6.3, so we don't care. Thus the round
numbers between 1 and 10 are these:
Ratio
dB
1
0
1.25 1.6
1
2
2
3
2.5
4
3.2
5
4
6
5
7
6.3
8
8
9
10
10
This useful approximate table of logarithms is easily reconstructed or memorized.
[edit] The 4 → 6 energy rule
To one decimal place of precision, 4.x is 6.x in dB (energy).
Examples:



4.0 → 6.0 dB
4.3 → 6.3 dB
4.7 → 6.7 dB
[edit] The "789" rule
To one decimal place of precision, x → (½ x + 5.0 dB) for 7.0 ≤ x ≤ 10.
Examples:





7.0 → ½ 7.0 + 5.0 dB = 3.5 + 5.0 dB = 8.5 dB
7.5 → ½ 7.5 + 5.0 dB = 3.75 + 5.0 dB = 8.75 dB
8.2 → ½ 8.2 + 5.0 dB = 4.1 + 5.0 dB = 9.1 dB
9.9 → ½ 9.9 + 5.0 dB = 4.95 + 5.0 dB = 9.95 dB
10.0 → ½ 10.0 + 5.0 dB = 5.0 + 5.0 dB = 10 dB
[edit] −3 dB ≈ ½ power
A level difference of ±3 dB is roughly double/half power (equal to a ratio of 1.995).
That is why it is commonly used as a marking on sound equipment and the like.
Another common sequence is 1, 2, 5, 10, 20, 50 ... . These preferred numbers are very
close to being equally spaced in terms of their logarithms. The actual values would be
1, 2.15, 4.64, 10 ... .
The conversion for decibels is often simplified to: "+3 dB means two times the power
and 1.414 times the voltage", and "+6 dB means four times the power and two times
the voltage ".
While this is accurate for many situations, it is not exact. As stated above, decibels are
defined so that +10 dB means "ten times the power". From this, we calculate that +3
dB actually multiplies the power by 103/10. This is a power ratio of 1.9953 or about
0.25% different from the "times 2" power ratio that is sometimes assumed. A level
difference of +6 dB is 3.9811, about 0.5% different from 4.
To contrive a more serious example, consider converting a large decibel figure into its
linear ratio, for example 120 dB. The power ratio is correctly calculated as a ratio of
1012 or one trillion. But if we use the assumption that 3 dB means "times 2", we
would calculate a power ratio of 2120/3 = 240 = 1.0995 × 1012, giving a 10% error.
[edit] 6 dB per bit
In digital audio linear pulse-code modulation, the first bit (least significant bit, or
LSB) produces residual quantization noise (bearing little resemblance to the source
signal) and each subsequent bit offered by the system doubles the (voltage) resolution,
corresponding to a 6 dB ratio. So for instance, a 16-bit (linear) audio format offers 15
bits beyond the first, for a dynamic range (between quantization noise and clipping) of
(15 × 6) = 90 dB, meaning that the maximum signal (see 0 dBFS, above) is 90 dB
above the theoretical peak(s) of quantization noise. The negative impacts of
quantization noise can be reduced by implementing dither.
[edit] dB chart
As is clear from the above description, the dB level is a logarithmic way of expressing
not only power ratios, but also voltage ratios The following tables are cheat-sheets
that provide values for various dB power ratios and also "voltage" ratios.
[edit] Commonly used dB values
dB level
power
ratio
dB level
−30 dB 1/1000 = 0.001
−30 dB
−20 dB 1/100 = 0.01
−20 dB
−10 dB 1/10 = 0.1
−10 dB
−3 dB 1/2 = 0.5 (approx.)
3 dB 2 (approx.)
−3 dB
3 dB
voltage
ratio
= 0.03162
= 0.1
= 0.3162
= 0.7071
= 1.414
10 dB 10
10 dB
= 3.162
20 dB 100
20 dB
= 10
30 dB 1000
30 dB
= 31.62
Unit conversions
Zero dBm equals one milliwatt. A 3 dB increase represents roughly doubling the
power, which means that 3 dBm equals roughly 2 mW. For a 3 dB decrease, the
power is reduced by about one half, making −3 dBm equal to about 0.5 milliwatt. To
express an arbitrary power P as x dBm, or go in the other direction, the equations
and
,
respectively, should be used.
The Decibel watt or dBW is a unit for the measurement of the strength of a signal
expressed in decibels relative to one watt. It is used because of its capability to
express both very large and very small values of power in a short range of number, eg
10 watts = 10 dBW, and 1,000,000 W = 60 dBW.
where P is an arbitrary power.
-----------
Summary of the equations
Symbols in bold represent vector quantities, whereas symbols in italics represent
scalar quantities.
[edit] General case
Name
Differential form
Integral form
Gauss's
law:
Gauss' law
for
magnetism
(absence
of
magnetic
monopoles
):
Faraday's
law of
induction:
Ampère's
law
(with
Maxwell's
extension):
where in the integral form of Faraday's law is the instantaneous velocity of the
contour element, and the whole left-hand-side is the electromotive force around the
(possibly moving) circuit. The following table provides the meaning of each symbol
and the SI unit of measure:
Symbol
Meaning
SI Unit of Measure
electric field
volt per meter or,
equivalently,
newton per coulomb
magnetic field
also called the auxiliary field
ampere per meter
electric displacement field
also called the electric flux density
coulomb per square
meter
magnetic flux density
also called the magnetic induction
also called the magnetic field
tesla, or equivalently,
weber per square
meter
free electric charge density,
not including dipole charges bound in a material
coulomb per cubic
meter
free current density,
not including polarization or magnetization currents
bound in a material
ampere per square
meter
differential vector element of surface area A, with
infinitesimally
square meters
small magnitude and direction normal to surface S
differential element of volume V enclosed by surface
cubic meters
S
differential vector element of path length tangential
to contour C enclosing surface S
meters
the divergence operator
per meter
the curl operator
per meter
Although SI units are given here for the various symbols, Maxwell's equations are
unchanged in many systems of units (and require only minor modifications in all
others). The most commonly used systems of units are SI, used for engineering,
electronics and most practical physics experiments, and Planck units (also known as
"natural units"), used in theoretical physics, quantum physics and cosmology. An
older system of units, the cgs system, is also used.
The second equation is equivalent to the statement that magnetic monopoles do not
exist. The force exerted upon a charged particle by the electric field and magnetic
field is given by the Lorentz force equation:
where is the charge on the particle and is the particle velocity. This is slightly
different when expressed in the cgs system of units below.
Maxwell's equations are generally applied to macroscopic averages of the fields,
which vary wildly on a microscopic scale in the vicinity of individual atoms (where
they undergo quantum mechanical effects as well). It is only in this averaged sense
that one can define quantities such as the permittivity and permeability of a material,
below (the microscopic Maxwell's equations, ignoring quantum effects, are simply
those of a vacuum — but one must include all atomic charges and so on, which is
generally an intractable problem).
[edit] In linear materials
In linear materials, the polarization density (in coulombs per square meter) and
magnetization density
(in amperes per meter) are given by:
and the
and
fields are related to
and
by:
where:
χe is the electrical susceptibility of the material,
χm is the magnetic susceptibility of the material,
is the electrical permittivity of the material, and
μ is the magnetic permeability of the material
(This can actually be extended to handle nonlinear materials as well, by making ε and
μ depend upon the field strength; see e.g. the Kerr and Pockels effects.)
In non-dispersive, isotropic media, ε and μ are time-independent scalars, and
Maxwell's equations reduce to
In a uniform (homogeneous) medium, ε and μ are constants independent of position,
and can thus be furthermore interchanged with the spatial derivatives.
More generally, ε and μ can be rank-2 tensors (3×3 matrices) describing birefringent
(anisotropic) materials. Also, although for many purposes the time/frequencydependence of these constants can be neglected, every real material exhibits some
material dispersion by which ε and/or μ depend upon frequency (and causality
constrains this dependence to obey the Kramers-Kronig relations).
[edit] In vacuum, without charges or currents
The vacuum is a linear, homogeneous, isotropic, dispersionless medium, and the
proportionality constants in the vacuum are denoted by ε0 and μ0 (neglecting very
slight nonlinearities due to quantum effects).
Since there is no current or electric charge present in the vacuum, we obtain the
Maxwell equations in free space:
These equations have a simple solution in terms of travelling sinusoidal plane waves,
with the electric and magnetic field directions orthogonal to one another and the
direction of travel, and with the two fields in phase, travelling at the speed
Maxwell discovered that this quantity c is simply the speed of light in vacuum, and
thus that light is a form of electromagnetic radiation. The currently accepted values
for the speed of light, the permittivity, and the permeability are summarized in the
following table:
Symbol
Name
Numerical Value
SI Unit of Measure Type
Speed of light
meters per second
defined
Permittivity
farads per meter
derived
Permeability
henries per meter
defined
-------------
For emitting and receiving antenna situated near the ground (in a building or a mast)
far from each other, distances traveled by direct and reflected rays are nearly the
same. There is no induced phase shift. If the emission is polarized vertically the two
fields (direct and reflected) add and there is maximum of received signal. If the
emission is polarized horizontally the two signals subtracts and the received signal is
minimum. This is depicted in the image at right. In the case of vertical polarization,
there is always a maximum at earth level (left pattern). For horizontal polarization,
there is always a minimum at earth level. Note that in these drawings the ground is
considered as a perfect mirror, even for low angles of incidence. In these drawings the
distance between the antenna and its image is just a few wavelengths. For greater
distances, the number of lobes increases.
Radiation patterns of antennas and their images reflected by the ground. At left the
polarization is vertical and there is always a maximum for
. If the polarization is
horizontal as at right, there is always a zero for
.
--------------
Path loss is usually expressed in dB. In its simplest form the path loss can be
calculated using the formula
, where P is the path loss in
decibels, n is the path loss exponent, d is the distance between the transmitter and the
receiver, usually measured in meters, and C is a constant which accounts for losses
occurring due to penetration through the walls of the building, due to absorption in the
human body, etc.
--------
Free space simply means that there is no material or other physical phenomenon
present except the phenomenon under consideration. Free space is considered the
baseline state of the electromagnetic field. Radiant energy propagates through free
space in the form of electromagnetic waves, such as radio waves and visible light
(among other electromagnetic spectrum frequencies). The constant value
is known
as the permeability of free space. The permittivity of free space, , is the ratio of the
electric displacement field to the electric field in free space. This permittivity is used
in the construction of the fine-structure constant. According to relativity, radiant
energy in free space propagates at the speed of light, independent of the speed of the
observer or of the source of the waves.
Ελεύθερου χώρου απλά σημαίνει ότι δεν υπάρχει κανένα υλικό ή άλλο φυσικό
φαινόμενο παρόν εκτός από το φαινόμενο υπό εξέταση. Ελεύθερου χώρου θεωρείται
κατάσταση βασικών γραμμών του ηλεκτρομαγνητικού τομέα. Η ακτινοβόλος
ενέργεια διαδίδει μέσω ελεύθερου χώρου υπό μορφή ηλεκτρομαγνητικών κυμάτων,
όπως τα ραδιο κύματα και το ορατό φως (μεταξύ άλλων ηλεκτρομαγνητικών
συχνοτήτων φάσματος). Η σταθερή αξία είναι γνωστή ως διαπερατότητα ελεύθερου
χώρου. Permittivity ελεύθερου χώρου, είναι η αναλογία του ηλεκτρικού τομέα
μετατοπίσεων στο ηλεκτρικό πεδίο σε ελεύθερου χώρου. Αυτό το permittivity
χρησιμοποιείται στην κατασκευή της σταθεράς λεπτός-δομών. Σύμφωνα με τη
σχετικότητα, η ακτινοβόλος ενέργεια σε ελεύθερου χώρου διαδίδει με την ταχύτητα
του φωτός, ανεξάρτητη από την ταχύτητα του παρατηρητή ή της πηγής των κυμάτων.
The permeability constant, magnetic constant or permeability of free space (μ0) is
the permeability of vacuum (or of free space). It is a mathematical factor relating
mechanical and electromagnetic units of measurement (so that the force of
electromagnetic interactions are measured in the same units as mechanical force).
Η σταθερή, μαγνητική σταθερά διαπερατότητας ή η διαπερατότητα ελεύθερου χώρου
(μ0) είναι η διαπερατότητα του κενού (ή ελεύθερου χώρου). Είναι ένας μαθηματικός
παράγοντας που αφορά τις μηχανικές και ηλεκτρομαγνητικές μονάδες της μέτρησης
(έτσι ώστε η δύναμη των ηλεκτρομαγνητικών αλληλεπιδράσεων μετριέται στις ίδιες
μονάδες με τη μηχανική δύναμη).
It is defined as the ratio of magnetic field density to magnetic field strength in
vacuum:
In SI units, the value is exactly expressed by:
μ0 = 4π×10−7 N/A2 = 4π×10−7 H/m
Permittivity is a physical quantity that describes how an electric field affects and is
affected by a dielectric medium, and is determined by the ability of a material to
polarize in response to the field, and thereby reduce the field inside the material.
Thus, permittivity relates to a material's ability to transmit (or "permit") an electric
field.
It is directly related to electric susceptibility. For example, in a capacitor, an increased
permittivity allows the same charge to be stored with a smaller electric field (and thus
a smaller voltage), leading to an increased capacitance.
In electromagnetism, electric displacement field D represents how an electric field E
influences the organization of electrical charges in a given medium, including charge
migration and electric dipole reorientation. Its relation to permittivity is
where the permittivity ε is a scalar if the medium is isotropic or a 3-by-3 matrix
otherwise.
In general, permittivity is not a constant, as it can vary with the position in the
medium, the frequency of the field applied, humidity, temperature, and other
parameters. In a nonlinear medium, the permittivity can depend on the strength of the
electric field. Permittivity as a function of frequency can take on real or complex
values.
In SI units, permittivity is measured in farads per metre (F/m). The displacement field
D is measured in units of coulombs per square metre (C/m2), while the electric field E
is measured in volts per metre (V/m). D and E represent the same phenomenon,
namely, the interaction between charged objects. D is related to the charge densities
associated with this interaction, while E is related to the forces and potential
differences.
[edit] Vacuum permittivity
Main article: electric susceptibility
Vacuum permittivity
vacuum.
(also called permittivity of free space) is the ratio D/E in
8.8541878176 × 10−12 F/m (C2/Jm),
where
c is the speed of light
μ0 is the permeability of vacuum.
All three of these constants are exactly defined in SI units.
Vacuum permittivity also appears in Coulomb's law as a part of the Coulomb force
constant,
, which expresses the attraction between two unit charges in vacuum.
The permittivity of a material is usually given relative to that of vacuum, as a relative
permittivity (also called dielectric constant). The actual permittivity is then
calculated by multiplying the relative permittivity by :
where
is the electric susceptibility of the material.
In physics, the electric displacement field or electric flux density is a vector-valued
field that appears in Maxwell's equations. It accounts for the effects of bound
charges within materials. "D" stands for "displacement," as in the related concept of
displacement current in dielectrics.
[edit] Definition
In general, D is defined by the relation
where E is the electric field,
density of the material.
is the vacuum permittivity, and P is the polarization
In most ordinary materials, however, D may be calculated with the simpler formula
where is the permittivity of the material; in linear isotropic media this will be a
constant, and in linear anisotropic media it will be a rank 2 tensor (a matrix)
[edit] Displacement field in a capacitor
Consider an infinite parallel plate capacitor placed in space (or in a medium) with no
free charges present except on the capacitor. In SI units, the charge density on the
plates is equal to the value of the D field between the plates. This follows directly
from Gauss's law, by integrating over a small rectangular box straddling the plate of
the capacitor:
The part of the box inside the capacitor plate has no field, so that part of the integral is
zero. On the sides of the box,
is perpendicular to the field, so that part of the
integral is also zero, leaving:
which is the charge density on the plate.
[edit] Units
In the standard SI system of units D is measured in coulombs per square meter
(C/m2).
This choice of units results in one of the simplest forms of the Ampère-Maxwell
equation:
If one chooses both B and H to be measured in teslas, and E and D to be measured in
newtons per coulomb, then the formula is modified to be:
Therefore it is seen as being preferential to express B & H, and D & E in different
sets of units.
Choice of units has differed in history, for instance in the electromagnetic system of
scientific units, in which the unit of charge is defined such that
(dimensionless), D and E are expressed in the same units.
Retrieved from "http://en.wikipedia.org/wiki/Electric_displacement_field"
----------------