Antenna gain
Encyclopedia
In electromagnetics, an antenna's power gain or simply gain is a key performance figure which combines the antenna
's directivity
and electrical efficiency
. As a transmitting antenna, the figure describes how well the antenna converts input power into radio wave
s headed in a specified direction. As a receiving antenna, the figure 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. A plot of the gain as a function of direction is called the radiation pattern
.
Antenna gain can be specified in a few different ways, sometimes invoking confusion. Most often gain is expressed in decibels with the units denoted as dBi. However sometimes the gain is compared to the maximum gain of a lossless half-wave dipole antenna
(1.64) in which case the units are written as dBd. 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 specified gain for any antenna applies identically whether it is used for transmitting or receiving.
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.
Eantenna and directivity
D:
When considering the power gain for a particular direction given by an elevation
(or "altitude
")
and azimuth 
, then:
is known as the directive gain. The directive gain signifies the ratio of radiated power in a given direction relative to that of an isotropic radiator which is radiating the same total power as the antenna in question but uniformly in all directions. Note that a true isotropic radiator does not exist in practice.
The power gain, on the other hand, signifies the ratio of radiated power in a given direction relative to that of an isotropic radiator
which is radiating the total amount of electrical power received by the antenna in question. This is in contrast to the directive gain which ignores any reduction in efficiency. If only a certain portion of the electrical power received from the transmitter is actually radiated by the antenna (its efficiency) the directive gain compares the power radiated in a given direction to that reduced power, ignoring the inefficiency. By instead comparing the radiated power in a given direction to the actual power that the antenna receives from the transmitter, the power gain takes into account that poorer efficiency, making it a more useful figure of merit for the ability of a transmitter in sending a radio wave toward a receiver.
The radiation intensity
expresses the power radiated per solid angle. In terms of 
the power gain in a specified direction can be calculated:
where Pelec signifies the electrical power received by the antenna from the transmitter.
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.
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.
. 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.
Let us find the gain of such an antenna.
Solution:
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 dipole we would find:
.
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 open space.
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
's directivity
Directivity
In electromagnetics, directivity is a figure of merit for an antenna. 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.An antenna's directivity is a...
and electrical efficiency
Antenna efficiency
In electromagnetics, antenna efficiency or radiation efficiency is a figure of merit for an antenna. It measures the electrical losses that occur throughout the antenna while it is operating at a given frequency, or averaged over its operation across a frequency band...
. As a transmitting antenna, the figure describes how well the antenna converts input power into radio wave
Radio Wave
Radio Wave may refer to:*Radio frequency*Radio Wave 96.5, a radio station in Blackpool, UK...
s headed in a specified direction. As a receiving antenna, the figure 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. A plot of the gain as a function of direction is called the radiation pattern
Radiation pattern
In the field of antenna design the term radiation pattern most commonly refers to the directional dependence of the strength of the radio waves from the antenna or other source ....
.
Antenna gain can be specified in a few different ways, sometimes invoking confusion. Most often gain is expressed in decibels with the units denoted as dBi. However sometimes the gain is compared to the maximum gain of a lossless half-wave dipole antenna
Dipole antenna
A dipole antenna is a radio antenna that can be made of a simple wire, with a center-fed driven element. It consists of two metal conductors of rod or wire, oriented parallel and collinear with each other , with a small space between them. The radio frequency voltage is applied to the antenna at...
(1.64) in which case the units are written as dBd. 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
Radiation resistance
Radiation resistance is that part of an antenna's feedpoint resistance that is caused by the radiation of electromagnetic waves from the antenna. The radiation resistance is determined by the geometry of the antenna, not by the materials of which it is made...
. Due to reciprocity
Reciprocity (electromagnetism)
In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints...
, the specified gain for any antenna applies identically whether it is used for transmitting or receiving.
Directive gain or directivity
Directivity
In electromagnetics, directivity is a figure of merit for an antenna. 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.An antenna's directivity is a...
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
Power gain (or simply gain) is a unitless measure that combines an antenna's efficiencyAntenna efficiency
In electromagnetics, antenna efficiency or radiation efficiency is a figure of merit for an antenna. It measures the electrical losses that occur throughout the antenna while it is operating at a given frequency, or averaged over its operation across a frequency band...
Eantenna and directivity
Directivity
In electromagnetics, directivity is a figure of merit for an antenna. 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.An antenna's directivity is a...
D:
When considering the power gain for a particular direction given by an elevation
Horizontal coordinate system
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. This coordinate system divides the sky into the upper hemisphere where objects are visible, and the lower hemisphere where objects cannot be seen since the earth is in...
(or "altitude
Horizontal coordinate system
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. This coordinate system divides the sky into the upper hemisphere where objects are visible, and the lower hemisphere where objects cannot be seen since the earth is in...
")
and azimuth , then: is known as the directive gain. The directive gain signifies the ratio of radiated power in a given direction relative to that of an isotropic radiator which is radiating the same total power as the antenna in question but uniformly in all directions. Note that a true isotropic radiator does not exist in practice.The power gain, on the other hand, signifies the ratio of radiated power in a given direction relative to that of an isotropic radiator
Isotropic radiator
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...
which is radiating the total amount of electrical power received by the antenna in question. This is in contrast to the directive gain which ignores any reduction in efficiency. If only a certain portion of the electrical power received from the transmitter is actually radiated by the antenna (its efficiency) the directive gain compares the power radiated in a given direction to that reduced power, ignoring the inefficiency. By instead comparing the radiated power in a given direction to the actual power that the antenna receives from the transmitter, the power gain takes into account that poorer efficiency, making it a more useful figure of merit for the ability of a transmitter in sending a radio wave toward a receiver.
The radiation intensity
Radiation intensity
In electromagnetism, radiation intensity describes the power density that an antenna creates in a particular solid angle. A solid angle is a section of the surface of the imaginary sphere around the antenna....
expresses the power radiated per solid angle. In terms of the power gain in a specified direction can be calculated:where Pelec signifies the electrical power received by the antenna from the transmitter.
Figures used for antenna gain
Published figures 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.
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
Partial gain is calculated as power gain, but for a particular polarizationPolarization
Polarization is a property of certain types of waves that describes the orientation of their oscillations. Electromagnetic waves, such as light, and gravitational waves exhibit polarization; acoustic waves in a gas or liquid do not have polarization because the direction of vibration and...
. It is defined as the part of the radiation intensity
Radiation intensity
In electromagnetism, radiation intensity describes the power density that an antenna creates in a particular solid angle. A solid angle is a section of the surface of the imaginary sphere around the antenna....
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.
Example calculation
Suppose a lossless antenna has a radiation pattern given by:Let us find the gain of such an antenna.
Solution:
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 dipole we would find:
.Total radiated power
Total radiated power is a measurement of antenna gain with or without the power absorption effects (loss) that may be caused by objects in the proximity of the antenna. TRP is measured in the lab as radiated power compared to an Isotropic Antenna. TRP can also be measured while in the close proximity of power absorbing loses 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 open space.
See also
- Antenna efficiencyAntenna efficiencyIn electromagnetics, antenna efficiency or radiation efficiency is a figure of merit for an antenna. It measures the electrical losses that occur throughout the antenna while it is operating at a given frequency, or averaged over its operation across a frequency band...
- DirectivityDirectivityIn electromagnetics, directivity is a figure of merit for an antenna. 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.An antenna's directivity is a...
- Directional antennaDirectional antennaA directional antenna or beam antenna is an antenna which radiates greater power in one or more directions allowing for increased performance on transmit and receive and reduced interference from unwanted sources....
- Antenna effective areaAntenna effective areaIn telecommunications, antenna effective area or effective aperture expresses an antenna's ability to collect an incident radio wave and deliver it as an electrical current at the antenna's terminals...
- CardioidCardioidA cardioid is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type of limaçon and can also be defined as an epicycloid having a single cusp...