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| {{refimprove|date=February 2013}}
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| An '''isotropic radiator''' is a theoretical [[point source]] of [[electromagnetic wave|electromagnetic]] or [[sound wave]]s 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.
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| Whether a radiator is isotropic is independent of whether it obeys [[Lambert's law]].{{citation needed|date=November 2011}} As radiators, a spherical black body is both, a flat black body is Lambertian but not isotropic, a flat chrome sheet is neither, and by symmetry the Sun is isotropic, but not Lambertian on account of [[limb darkening]].
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| == Physics ==
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| A point radiation or sound source. At a distance, the sun is an isotropic radiator of electromagnetic radiation. The [[Big Bang]] is another example of an isotropic radiator - the [[Cosmic Microwave Background]].<ref>[http://www.astro.ubc.ca/people/scott/cmb_intro.html Cosmic Microwave Background - Introduction<!-- Bot generated title -->]</ref>
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| ===Antenna theory===
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| In antenna theory, an '''isotropic antenna''' is a hypothetical antenna radiating the same intensity of [[radio wave]]s in all directions. It has a [[directivity]] of [[Decibel#Antenna measurements|0 dBi (dB relative to isotropic)]],
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| In reality, a '''[[Coherence (physics)|coherent]]''' isotropic radiator cannot exist, as the isotropic radiator, with a [[radiation pattern]] (as expressed in [[spherical coordinates]]) of
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| : <math>\boldsymbol{E}(r,\theta,\phi)=\frac{e^{-jkr}}{4\pi r}{\boldsymbol{\hat{u}}}(\theta,\phi)</math>
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| : (note that the magnitude of this function is independent of the spherical angles <math>\displaystyle\theta</math> and <math>\ \phi</math>, but it is permissible for the vector's direction, as represented by the unit vector <math>\boldsymbol{\hat{u}}</math> to be a function of <math>\ \theta</math> and <math>\ \phi</math>)
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| would violate the [[Helmholtz equation|Helmholtz Wave Equation]], as derived from [[Maxwell's Equations]].
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| Although the [[Sun]] and other [[star]]s radiate equally in all directions, their radiation pattern does not violate Maxwell's equations, because radiation from a star is '''[[Coherence (physics)|incoherent]]'''. Sound waves can also expand uniformly in all directions, but sound waves are [[longitudinal waves]] and not [[transverse waves]].
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| Even though an isotropic radiator cannot exist in practice, antenna directivity is usually compared to the directivity of an isotropic radiator, because the gain (which is closely related to directivity) relative to an isotropic radiator is useful in the [[Friis transmission equation]]. The smallest directivity a radiator can have{{Citation needed|date=March 2011}} relative to an isotropic radiator, is a [[Hertzian Dipole]], which has 1.76 dBi.
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| ====Hairy ball theorem====
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| Another way to explain why an isotropic radiator cannot exist is by using the [[hairy ball theorem]], which asserts that a [[continuous function|continuous]] [[vector field]] [[tangent]] to the surface of the sphere must fall to zero at one or more points on the sphere. This means that there is some direction for which the electric field must be zero, and hence, non-uniform.
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| ====Isotropic receiver====
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| In [[EMF measurements]] applications, an isotropic receiver (also called isotropic antenna), is a field measurement instrument which allows to obtain the total field independently of the tri-axial orthogonal arrangement chosen for orientation of the device itself.
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| In practice a quasi-ideal isotropic receiver is obtained with three orthogonal sensing devices
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| with a radiation diagram of the omnidirectional type <math> \sin (\theta)</math>, like that of [[Hertzian dipole|short dipole]] and small loop antennas.
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| The parameter used to define accuracy in the measurements is called [[EMF measurements#isotropic deviation|isotropic deviation]].
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| ===Optics===
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| A point source of light. The sun approximates an isotropic radiator of light. Certain munitions such as flares and chaff have isotropic radiator properties.
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| ===Sound===
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| An isotropic radiator is a theoretical perfect speaker exhibiting equal sound volume in all directions.
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| == See also ==
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| *[[radiation pattern]]
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| *[[E-plane and H-plane]]
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| == References ==
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| <references />
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| == External links ==
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| *[http://arxiv.org/abs/physics/0312023v1 ''Isotropic Radiators'', Matzner and McDonald, arXiv] Antennas
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| *[http://www.ee.surrey.ac.uk/Personal/D.Jefferies/antennas.html Antennas] D.Jefferies
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| *[http://amsglossary.allenpress.com/glossary/search?id=isotropic-radiator1 isotropic radiator] AMS Glossary
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| *[http://audioannals.com/04130023-Henricksen-txt.htm U.S. Patent 4,130,023 - Method and apparatus for testing and evaluating loudspeaker performance]
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| *[http://www.airpower.maxwell.af.mil/airchronicles/apj/apj94/dil.html Non Lethal Concepts - Implications for Air Force Intelligence] Published Aerospace Power Journal, Winter 1994
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| *[https://ewhdbks.mugu.navy.mil/Glossary.htm Glossary]
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| *[http://www.astro.ubc.ca/people/scott/cmb_intro.html Cosmic Microwave Background - Introduction]
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| {{Antenna_Types}}
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| [[Category:Force]]
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| [[Category:Radio frequency antenna types]]
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