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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" ----------------