Isotropic radiator

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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.

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[edit] 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. [1]

[edit] Antenna Theory

In antenna theory, the isotropic radiator is a theoretical radiator having a directivity of 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 coherent isotropic radiator cannot exist, as the isotropic radiator, with a radiation pattern (as expressed in spherical coordinates) of

{\vec E}\left(r,\theta,\phi\right)=\frac{e^{jkr}}{4\pi r}{\hat u}\left(\theta,\phi\right)
(note that the magnitude of this function is independent of the spherical angles \displaystyle\theta and Failed to parse (Cannot write to or create math output directory): \displaystyle\phi

, but it is permissible for the vector's direction, as represented by the unit vector {\hat u} to be a function of \displaystyle\theta and Failed to parse (Cannot write to or create math output directory): \displaystyle\phi ) would violate the Helmholtz Wave Equation, as derived from Maxwell's Equations.

Although the Sun and other stars radiate equally in all directions, their radiation pattern does not violate Maxwell's equations, because radiation from a star is 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.

[edit] 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 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.

[edit] 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.

[edit] Sound

An isotropic radiator is a theoretical perfect speaker exhibiting equal sound volume in all directions.

[edit] See also

[edit] References

  1. ^ Cosmic Microwave Background - Introduction

[edit] External links