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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.

In radio engineering, an **antenna** is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies an electric current to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves. In reception, an antenna intercepts some of the power of a radio wave in order to produce an electric current at its terminals, that is applied to a receiver to be amplified. Antennas are essential components of all radio equipment.

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.

In antenna theory, antenna efficiency is most often used to mean **radiation efficiency**. In the context of antennas, one often just speaks of "efficiency." It is a measure of the electrical efficiency with which a radio antenna converts the radio-frequency power accepted at its terminals into radiated power. Likewise, in a receiving antenna it describes the proportion of the radio wave's power intercepted by the antenna which is actually delivered as an electrical signal. It is not to be confused with aperture efficiency which applies to aperture antennas such as the parabolic reflector.

- Power gain
- Efficiency
- Directivity
- Gain
- Summary
- Gain in decibels
- Partial gain
- Example calculation
- Realized gain
- Total radiated power (TRP)
- See also
- References
- Bibliography

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.^{ [1] } 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 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.

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.

**Radiation resistance** is that part of an antenna's feedpoint resistance that is caused by the radiation of electromagnetic waves from the antenna, as opposed to *loss resistance* which is caused by ordinary electrical resistance in the antenna, or energy lost to nearby objects, such as the earth, which dissipate RF energy as heat.

In classical electromagnetism, **reciprocity** refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources) and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints. Reciprocity is closely related to the concept of Hermitian operators from linear algebra, applied to electromagnetism.

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.

A transmitting antenna accepts **input power** at some point along the feedline. The point is typically taken to be at the antenna (the *feedpoint*), thereby not counting power lost due to joule heating in the feedline and reflections back down the feedline. The **efficiency** of an antenna is the ** total radiated power ** divided by the input power at the feedpoint

**Joule heating**, also known as **Ohmic heating** and **resistive heating**, is the process by which the passage of an electric current through a conductor produces heat.

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.

Antennas are invariably directional to a greater or lesser extent, according to how the output power is distributed in any given direction in three dimensions. We shall specify direction 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

- since there are 4π steradians in a sphere
- using the first formula for .

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 1 in all directions independently 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

- using the second equation for
- using the equation for

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, *P _{in}* would be computed as the transmission line's incident power minus reflected power. Or equivalently, in terms of the rms voltage

where *Z _{in}* 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.

**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 half-wave dipole we would find:

- .

According to IEEE Standard 145-1993,^{ [1] }**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.^{ [1] }

**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.^{ [2] }

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.^{ [3] }

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 antenna theory, a **phased array** usually means an **electronically scanned array**, a computer-controlled array of antennas which creates a beam of radio waves that can be electronically steered to point in different directions without moving the antennas. In an array antenna, the radio frequency current from the transmitter is fed to the individual antennas with the correct phase relationship so that the radio waves from the separate antennas add together to increase the radiation in a desired direction, while cancelling to suppress radiation in undesired directions. In a phased array, the power from the transmitter is fed to the antennas through devices called *phase shifters*, controlled by a computer system, which can alter the phase electronically, thus steering the beam of radio waves to a different direction. Since the array must consist of many small antennas to achieve high gain, phased arrays are mainly practical at the high frequency end of the radio spectrum, in the UHF and microwave bands, in which the antenna elements are conveniently small.

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 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 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.

The **method of image charges** is a basic problem-solving tool in electrostatics. The name originates from the replacement of certain elements in the original layout with imaginary charges, which replicates the boundary conditions of the problem.

**Spherical multipole moments** are the coefficients in a series expansion of a potential that varies inversely with the distance R to a source, *i.e.*, as 1/*R*. Examples of such potentials are the electric potential, the magnetic potential and the gravitational potential.

**Cylindrical multipole moments** are the coefficients in a series expansion of a potential that varies logarithmically with the distance to a source, i.e., as . Such potentials arise in the electric potential of long line charges, and the analogous sources for the magnetic potential and gravitational potential.

The **Newman–Penrose** (**NP**) **formalism** is a set of notation developed by Ezra T. Newman and Roger Penrose for general relativity (GR). Their notation is an effort to treat general relativity in terms of spinor notation, which introduces complex forms of the usual variables used in GR. The NP formalism is itself a special case of the tetrad formalism, where the tensors of the theory are projected onto a complete vector basis at each point in spacetime. Usually this vector basis is chosen to reflect some symmetry of the spacetime, leading to simplified expressions for physical observables. In the case of the NP formalism, the vector basis chosen is a null tetrad: a set of four null vectors—two real, and a complex-conjugate pair. The two real members asymptotically point radially inward and radially outward, and the formalism is well adapted to treatment of the propagation of radiation in curved spacetime. The Weyl scalars, derived from the Weyl tensor, are often used. In particular, it can be shown that one of these scalars— in the appropriate frame—encodes the outgoing gravitational radiation of an asymptotically flat system.

The main **trigonometric identities** between trigonometric functions are proved, using mainly the geometry of the right triangle. For greater and negative angles, see Trigonometric functions.

Photon transport in biological tissue can be equivalently modeled numerically with Monte Carlo simulations or analytically by the radiative transfer equation (RTE). However, the RTE is difficult to solve without introducing approximations. A common approximation summarized here is the diffusion approximation. Overall, solutions to the diffusion equation for photon transport are more computationally efficient, but less accurate than Monte Carlo simulations.

Dual-Band Blade Antenna, a type of commercial RF "Blade antenna" that uses a "plane and slot design" to get efficient omni-directional coverage at two distinctly different RF bands. It has additive properties similar to a monopole antenna.

**Multipole radiation** is a theoretical framework for the description of electromagnetic or gravitational radiation from time-dependent distributions of distant sources. These tools are applied to physical phenomena which occur at a variety of length scales - from gravitational waves due to galaxy collisions to gamma radiation resulting from nuclear decay. Multipole radiation is analyzed using similar multipole expansion techniques that describe fields from static sources, however there are important differences in the details of the analysis because multipole radiation fields behave quite differently from static fields. This article is primarily concerned with electromagnetic multipole radiation, although the treatment of gravitational waves is similar.

The Two-Rays Ground Reflected Model is a radio propagation model which predicts the path losses between a transmitting antenna and a receiving antenna when they are in LOS. Generally, the two antenna each have different height. The received signal having two components, the LOS component and the multipath component formed predominantly by a single ground reflected wave.

In physics and engineering, the radiative heat transfer from one surface to another is the equal to the difference of incoming and outgoing radiation from the first surface. In general, the heat transfer between surfaces is governed by temperature, surface emissivity properties and the geometry of the surfaces. The relation for heat transfer can be written as an integral equation with boundary conditions based upon surface conditions. Kernel functions can be useful in approximating and solving this integral equation.

- 1 2 3 "IEEE Standard Definitions of Terms for Antennas".
*IEEE STD 145-1993*: 1–32. 1993-07-01. doi:10.1109/IEEESTD.1993.119664. ISBN 978-0-7381-0555-0. - ↑ "CTIA Test Plan for Wireless Device Over-the-Air Performance Rev. 3.4.2" (PDF).
*Certification Test Plans*. CTIA. May 2015. Archived (PDF) from the original on 2016-02-16. - ↑ Mobile Broadband Multimedia Networks: Techniques, Models and Tools for 4G by Luís M. Correia

*Antenna Theory*(3rd edition), by C. Balanis, Wiley, 2005, ISBN 0-471-66782-X*Antenna for all applications*(3rd edition), by John D. Kraus, Ronald J. Marhefka, 2002, ISBN 0-07-232103-2

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