Isotropic radiator 2421481 221748724 2008-06-25T22:34:26Z Gmaxwell 156674 /* External links */ rm spam An '''isotropic radiator''' is a theoretical [[point source]] of waves which exhibits the same magnitude or properties when measured in all directions. It has no preferred direction of radiation. It radiates uniformly in all directions over a sphere centred on the source. It is a reference radiator with which other sources are compared. Isotropic radiators obey [[Lambert's law]]. == Physics == 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> ===Antenna Theory=== In antenna theory, the '''isotropic radiator''' is a theoretical radiator having a [[directivity]] of [[Decibel#Relative measurements|0 dBi (dB relative to isotropic)]], which means that the radiator equally transmits (or receives) electromagnetic radiation to/from any arbitrary direction. In reality, a '''[[Coherence (physics)|coherent]]''' isotropic radiator cannot exist, as the isotropic radiator, with a [[radiation pattern]] (as expressed in [[spherical coordinates]]) of :<math>{\vec E}\left(r,\theta,\phi\right)=\frac{e^{jkr}}{4\pi r}{\hat u}\left(\theta,\phi\right)</math> :(note that the magnitude of this function is independent of the spherical angles <math>\displaystyle\theta</math> and <math>\displaystyle\phi</math>, but it is permissible for the vector's direction, as represented by the unit vector <math>{\hat u}</math> to be a function of <math>\displaystyle\theta</math> and <math>\displaystyle\phi</math>) would violate the [[Helmholtz equation|Helmholtz Wave Equation]], as derived from [[Maxwell's Equations]]. 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 also expand uniformly in all directions, but sound waves are [[longitudinal waves]] and not [[transverse waves]]. 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 relative to an isotropic radiator, is a [[Hertzian Dipole]], which has 1.76 dBi. ====Hairy ball theorem==== 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 at least one point on the sphere. This means that there is some direction for which the electric field must be zero, and hence, non-uniform. ===Optics=== A point source of light. The sun approximates an isotropic radiator of light. Certain munitions such as flares and chaff have isotropic radiator properties. ===Sound=== An isotropic radiator is a theoretical perfect speaker exhibiting equal sound volume in all directions. == See also == *[[radiation pattern]] *[[E-plane and H-plane]] == References == <references/> == External links == *[http://arxiv.org/abs/physics/0312023v1 ''Isotropic Radiators'', Matzner and McDonald, arXiv] Antennas *[http://www.ee.surrey.ac.uk/Personal/D.Jefferies/antennas.html Antennas] D.Jefferies *[http://amsglossary.allenpress.com/glossary/search?id=isotropic-radiator1 isotropic radiator] AMS Glossary *[http://audioannals.com/04130023-Henricksen-txt.htm U.S. Patent 4,130,023 - Method and apparatus for testing and evaluating loudspeaker performance] *[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 *[https://ewhdbks.mugu.navy.mil/Glossary.htm Glossary] *[http://www.astro.ubc.ca/people/scott/cmb_intro.html Cosmic Microwave Background - Introduction] [[Category:Force]] [[Category:Radio frequency antenna types]] [[da:Isotropantenne]] [[de:Isotropstrahler]] [[fr:Antenne isotrope]] [[nl:Isotrope antenne]] [[pl:Antena izotropowa]] [[fi:Isotrooppinen antenni]]