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In electromagnetics, an antenna's power gain or simply gain is a key performance number which combines the antenna's directivity and electrical efficiency. In a transmitting antenna, the gain describes how well the antenna converts input power into radio waves headed in a specified direction. In a receiving antenna, the gain describes how well the antenna converts radio waves arriving from a specified direction into electrical power. When no direction is specified, "gain" is understood to refer to the peak value of the gain, the gain in the direction of the antenna's main lobe. A plot of the gain as a function of direction is called the gain pattern or radiation pattern.
Antenna gain is usually defined as the ratio of the power produced by the antenna from a far-field source on the antenna's beam axis to the power produced by a hypothetical lossless isotropic antenna , which is equally sensitive to signals from all directions. For a given frequency, the antenna's effective area is proportional to the power gain. An antenna's effective length is proportional to the square root of the antenna's gain for a particular frequency and radiation resistance. Due to reciprocity, the gain of any reciprocal antenna when receiving is equal to its gain when transmitting.Usually this ratio is expressed in decibels, and these units are referred to as "decibels-isotropic" (dBi). An alternative definition compares the received power to the power received by a lossless half-wave dipole antenna, in which case the units are written as dBd. Since a lossless dipole antenna has a gain of 2.15 dBi, the relation between these units is
Directive gain or directivity is a different measure which does not take an antenna's electrical efficiency into account. This term is sometimes more relevant in the case of a receiving antenna where one is concerned mainly with the ability of an antenna to receive signals from one direction while rejecting interfering signals coming from a different direction.
Power gain (or simply gain) is a unitless measure that combines an antenna's efficiency and directivity D:
The notions of efficiency and directivity depend on the following.
The efficiency of an antenna is the total radiated power divided by the input power at the feedpoint
A transmitting antenna is supplied power by a feedline, a transmission line connecting the antenna to a radio transmitter. The input power to the antenna is typically defined to be the power supplied to the antenna's terminals (the feedpoint), so antenna power losses do not include power lost due to joule heating in the feedline and reflections back down the feedline due to antenna/line impedance mismatches.
The electromagnetic reciprocity theorem guarantees that the electrical properties of an antenna, such as efficiency, directivity, and gain, are the same when the antenna is used for receiving as when it is transmitting.
An antenna's directivity is determined by its radiation pattern, how the radiated power is distributed with direction in three dimensions. All antennas are directional to a greater or lesser extent, meaning that they radiate more power in some directions than others. The direction is specified here in spherical coordinates , where is the altitude or angle above a specified reference plane (such as the ground), while is the azimuth as the angle between the projection of the given direction onto the reference plane and a specified reference direction (such as north or east) in that plane with specified sign (either clockwise or counterclockwise).
The distribution of output power as a function of the possible directions is given by its radiation intensity (in SI units: watts per steradian, W⋅sr−1). The output power is obtained from the radiation intensity by integrating the latter over all solid angles :
The mean radiation intensity is therefore given by
The directive gain or directivity of an antenna in a given direction is the ratio of its radiation intensity in that direction to its mean radiation intensity . That is,
An isotropic antenna, meaning one with the same radiation intensity in all directions, therefore has directivity, D = 1, in all directions independent of its efficiency. More generally the maximum, minimum, and mean directivities of any antenna are always at least 1, at most 1, and exactly 1. For the half-wave dipole the respective values are 1.64 (2.15 dB), 0, and 1.
When the directivity of an antenna is given independently of direction it refers to its maximum directivity in any direction, namely
The power gain or simply gain of an antenna in a given direction takes efficiency into account by being defined as the ratio of its radiation intensity in that direction to the mean radiation intensity of a perfectly efficient antenna. Since the latter equals , it is therefore given by
As with directivity, when the gain of an antenna is given independently of direction it refers to its maximum gain in any direction. Since the only difference between gain and directivity in any direction is a constant factor of independent of and , we obtain the fundamental formula of this section:
If only a certain portion of the electrical power received from the transmitter is actually radiated by the antenna (i.e. less than 100% efficiency), then the directive gain compares the power radiated in a given direction to that reduced power (instead of the total power received), ignoring the inefficiency. The directivity is therefore the maximum directive gain when taken over all directions, and is always at least 1. On the other hand, the power gain takes into account the poorer efficiency by comparing the radiated power in a given direction to the actual power that the antenna receives from the transmitter, which makes it a more useful figure of merit for the antenna's contribution to the ability of a transmitter in sending a radio wave toward a receiver. In every direction, the power gain of an isotropic antenna is equal to the efficiency, and hence is always at most 1, though it can and ideally should exceed 1 for a directional antenna.
Note that in the case of an impedance mismatch, Pin would be computed as the transmission line's incident power minus reflected power. Or equivalently, in terms of the rms voltage V at the antenna terminals:
where Zin is the feedpoint impedance.
Published numbers for antenna gain are almost always expressed in decibels (dB), a logarithmic scale. From the gain factor G, one finds the gain in decibels as:
Therefore, an antenna with a peak power gain of 5 would be said to have a gain of 7 dBi. "dBi" is used rather than just "dB" to emphasize that this is the gain according to the basic definition, in which the antenna is compared to an isotropic radiator.
When actual measurements of an antenna's gain are made by a laboratory, the field strength of the test antenna is measured when supplied with, say, 1 watt of transmitter power, at a certain distance. That field strength is compared to the field strength found using a so-called reference antenna at the same distance receiving the same power in order to determine the gain of the antenna under test. That ratio would be equal to G if the reference antenna were an isotropic radiator(irad).
However a true isotropic radiator cannot be built, so in practice a different antenna is used. This will often be a half-wave dipole, a very well understood and repeatable antenna that can be easily built for any frequency. The directive gain of a half-wave dipole is known to be 1.64 and it can be made nearly 100% efficient. Since the gain has been measured with respect to this reference antenna, the difference in the gain of the test antenna is often compared to that of the dipole. The "gain relative to a dipole" is thus often quoted and is denoted using "dBd" instead of "dBi" to avoid confusion. Therefore, in terms of the true gain (relative to an isotropic radiator) G, this figure for the gain is given by:
For instance, the above antenna with a gain G=5 would have a gain with respect to a dipole of 5/1.64 = 3.05, or in decibels one would call this 10 log(3.05) = 4.84 dBd. In general:
Both dBi and dBd are in common use. When an antenna's maximum gain is specified in decibels (for instance, by a manufacturer) one must be certain as to whether this means the gain relative to an isotropic radiator or with respect to a dipole. If it specifies "dBi" or "dBd" then there is no ambiguity, but if only "dB" is specified then the fine print must be consulted. Either figure can be easily converted into the other using the above relationship.
Note that when considering an antenna's directional pattern, "gain with respect to a dipole" does not imply a comparison of that antenna's gain in each direction to a dipole's gain in that direction. Rather, it is a comparison between the antenna's gain in each direction to the peak gain of the dipole (1.64). In any direction, therefore, such numbers are 2.15 dB smaller than the gain expressed in dBi.
Partial gain is calculated as power gain, but for a particular polarization. It is defined as the part of the radiation intensity corresponding to a given polarization, divided by the total radiation intensity of an isotropic antenna.
where and represent the radiation intensity in a given direction contained in their respective E field component.
As a result of this definition, we can conclude that the total gain of an antenna is the sum of partial gains for any two orthogonal polarizations.
Suppose a lossless antenna has a radiation pattern given by:
Let us find the gain of such an antenna.
First we find the peak radiation intensity of this antenna:
The total radiated power can be found by integrating over all directions:
Since the antenna is specified as being lossless the radiation efficiency is 1. The maximum gain is then equal to:
Expressed relative to the gain of a half-wave dipole we would find:
According to IEEE Standard 145–1993,realized gain differs from the above definitions of gain in that it is "reduced by the losses due to the mismatch of the antenna input impedance to a specified impedance." This mismatch induces losses above the dissipative losses described above; therefore, Realized Gain will always be less than Gain.
Gain may be expressed as absolute gain if further clarification is required to differentiate it from realized gain.
Total radiated power is the sum of all RF power radiated by the antenna when the source power is included in the measurement. TRP is expressed in Watts, or equivalent logarithmic expressions, often dBm or dBW.
TRP can be measured while in the close proximity of power-absorbing losses such as the body and hand of the Mobile Device Under Test User.
The TRP can be used to determine Body Loss (BoL). The Body Loss is considered as the ratio of TRP measured in the presence of losses and TRP measured while in free space.
In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation. An elliptically polarized wave may be resolved into two linearly polarized waves in phase quadrature, with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, elliptically polarized waves exhibit chirality.
In the field of antenna design the term radiation pattern refers to the directional (angular) dependence of the strength of the radio waves from the antenna or other source.
Synchrotron radiation is the electromagnetic radiation emitted when charged particles are accelerated radially, e.g., when they are subject to an acceleration perpendicular to their velocity. It is produced, for example, in synchrotrons using bending magnets, undulators and/or wigglers. If the particle is non-relativistic, then the emission is called cyclotron emission. If, on the other hand, the particles are relativistic, sometimes referred to as ultrarelativistic, the emission is called synchrotron emission. Synchrotron radiation may be achieved artificially in synchrotrons or storage rings, or naturally by fast electrons moving through magnetic fields. The radiation produced in this way has a characteristic polarization and the frequencies generated can range over the entire electromagnetic spectrum which is also called continuum radiation.
Effective radiated power (ERP), synonymous with equivalent radiated power, is an IEEE standardized definition of directional radio frequency (RF) power, such as that emitted by a radio transmitter. It is the total power in watts that would have to be radiated by a half-wave dipole antenna to give the same radiation intensity as the actual source antenna at a distant receiver located in the direction of the antenna's strongest beam. ERP measures the combination of the power emitted by the transmitter and the ability of the antenna to direct that power in a given direction. It is equal to the input power to the antenna multiplied by the gain of the antenna. It is used in electronics and telecommunications, particularly in broadcasting to quantify the apparent power of a broadcasting station experienced by listeners in its reception area.
In radio and telecommunications a dipole antenna or doublet is the simplest and most widely used class of antenna. The dipole is any one of a class of antennas producing a radiation pattern approximating that of an elementary electric dipole with a radiating structure supporting a line current so energized that the current has only one node at each end. A dipole antenna commonly consists of two identical conductive elements such as metal wires or rods. The driving current from the transmitter is applied, or for receiving antennas the output signal to the receiver is taken, between the two halves of the antenna. Each side of the feedline to the transmitter or receiver is connected to one of the conductors. This contrasts with a monopole antenna, which consists of a single rod or conductor with one side of the feedline connected to it, and the other side connected to some type of ground. A common example of a dipole is the "rabbit ears" television antenna found on broadcast television sets.
In telecommunications, particularly in radio frequency, signal strength refers to the transmitter power output as received by a reference antenna at a distance from the transmitting antenna. High-powered transmissions, such as those used in broadcasting, are expressed in dB-millivolts per metre (dBmV/m). For very low-power systems, such as mobile phones, signal strength is usually expressed in dB-microvolts per metre (dBμV/m) or in decibels above a reference level of one milliwatt (dBm). In broadcasting terminology, 1 mV/m is 1000 μV/m or 60 dBμ.
In electromagnetics and antenna theory, antenna aperture, effective area, or receiving cross section, is a measure of how effective an antenna is at receiving the power of electromagnetic radiation. The aperture is defined as the area, oriented perpendicular to the direction of an incoming electromagnetic wave, which would intercept the same amount of power from that wave as is produced by the antenna receiving it. At any point , a beam of electromagnetic radiation has an irradiance or power flux density which is the amount of power passing through a unit area of one square meter. If an antenna delivers watts to the load connected to its output terminals when irradiated by a uniform field of power density watts per square meter, the antenna's aperture in square meters is given by:
An isotropic radiator is a theoretical point source of electromagnetic or sound waves which radiates the same intensity of radiation in all directions. It has no preferred direction of radiation. It radiates uniformly in all directions over a sphere centred on the source. Isotropic radiators are used as reference radiators with which other sources are compared, for example in determining the gain of antennas. A coherent isotropic radiator of electromagnetic waves is theoretically impossible, but incoherent radiators can be built. An isotropic sound radiator is possible because sound is a longitudinal wave.
Antenna 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.
In electromagnetics, directivity is a parameter of an antenna or optical system which measures the degree to which the radiation emitted is concentrated in a single direction. It measures the power density the antenna radiates in the direction of its strongest emission, versus the power density radiated by an ideal isotropic radiator radiating the same total power.
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