The total active reflection coefficient (TARC) within

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

scattering theory In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiat ...

, relates the total incident

power Power may refer to: Common meanings * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power, a type of energy * Power (social and political), the ability to influence people or events Math ...

to the total outgoing power in an N-port

microwave component Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequencies between 300 MHz and ...

. The TARC is mainly used for multiple-input multiple-output (

MIMO In radio, multiple-input and multiple-output (MIMO) () is a method for multiplying the capacity of a radio link using multiple transmission and receiving antennas to exploit multipath propagation. MIMO has become an essential element of wirel ...

) antenna systems and

array antennas An antenna array (or array antenna) is a set of multiple connected antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas (called ''elements'') are usually connected to a single receiver ...

, where the outgoing power is unwanted reflected power. The name shows the similarities with the

active reflection coefficient The active reflection coefficient (ARC) is the reflection coefficient for a single antenna element in an array antenna, in the presence of mutual coupling. The active reflection coefficient is a function of frequency in addition to the excitation of ...

, which is used for single elements. The TARC is the square root of the sum of all outgoing powers at the ports, divided by the sum of all incident powers at the ports of an N-port antenna. Similarly to the

, the TARC is a function of

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

, and it also depends on scan angle and tapering. With this definition we can characterize the multi-port

antenna Antenna (: antennas or antennae) most commonly refers to: * Antenna (zoology), one of a pair of appendages used for sensing in arthropods * Antenna (radio), or aerial, an electronic device that transmits, receives, or detects radio waves ** Anten ...

’s frequency

bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...

and

radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes: * ''electromagnetic radiation'' consisting of photons, such as radio waves, microwaves, infr ...

performance. When the antennas are made of lossless materials, TARC can be computed directly from the

scattering matrix In physics, the ''S''-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory ...

by :

\Gamma^t_a = \frac,

where

a].

/math> is the antenna's

/math> is the excitation

vector Vector most often refers to: * Euclidean vector, a quantity with a magnitude and a direction * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...

, and

/math> represents the scattered vector. The TARC is a

real number In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...

between zero and one, although it is typically presented in

decibel scale The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a p ...

. When the value of the TARC is equal to zero, all the delivered power is accepted by the antenna and when it is equal to one, all the delivered is coming back as outgoing power (thus the all power is reflected, but not necessarily in the same port). The normalized total accepted power is given by

(1-, \Gamma^t_a, ^2)

. Since antennas in general have radiation efficiency

0 \leq \epsilon \leq 1

, the normalized total radiated power is given by

\epsilon_l =  \epsilon (1-, \Gamma^t_a, ^2)

. If the

directivity 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 is the ratio of the radiation intensity in a given direction f ...

of the antenna array is known, the

realized gain Realization or realisation may refer to: * ''Realization'' (Eddie Henderson album), a 1973 album by Eddie Henderson * ''Realization'' (Johnny Rivers album), a 1968 album by Johnny Rivers * ''Realization'' (climb), a sport climbing route in Ceü ...

can therefore be computed by multiplication by

\epsilon_l

. As with all reflection coefficients, a small reflection coefficient does not guarantee a high radiation efficiency since the small reflected signal could also be due to losses.

References

* * * * * * * {{cite journal , author1=A. R. Mallahzadeh , author2=S. Es'haghi , author3=A. Alipour , name-list-style=amp , title=DESIGN OF AN E-SHAPED MIMO ANTENNA USING IWO ALGORITHM FOR WIRELESS APPLICATION AT 5.8 GHz , journal=Progress in Electromagnetics Research , volume=90, year=2009 , pages=187–203 , url=http://www.jpier.org/PIER/pier90/13.08122704.pdf, doi=10.2528/PIER08122704 , doi-access=free Scattering theory Matrices (mathematics) Antennas (radio)

See also

References