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Isotropic radiator

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This is an old revision of this page, as edited by Jrthorpe (talk | contribs) at 16:23, 28 July 2006 (Add a small detail, you can make an isotropic antenna, it just must have a strange polarization pattern). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

An isotropic radiator is a theoretical point source 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 [1]

Antenna Theory

In antenna theory, the isotropic radiator is a theoretical ideal - a perfect omni-directional antenna displaying isotropy. An isotropic radiator has a directivity of 1. Normally it is taken to emit a plane polarization such as horizontal or vertical polarization.

If the P watts is supplied to the isotropic radiator, the energy density (watts per square metre) at a distance R metres from the centre of the radiator is P/(4 pi R^2). This is because power P spreads uniformly across the area (4 pi R^2) of a sphere of radius R.

An antenna emits an electromagnetic wave that has two components - the electric and magnetic fields. These are at right angles to each other and also at right angles to the direction of travel of the wave. This presents a problem for a theoretical isotropic radiator since there will be places on the unit sphere where we cannot specify a unique "polarization direction" for the direction of the electric field. Everything else is called anisotropic radiation.

True isotropic radiators do not exist in reality. This is because the electromagnetic wave is made up of two perpendicular components - the electric field E and the magnetic field H. The emitted electromagnetic wave moves perpendicular to the E-plane and H-plane. The wave cannot be lined up so that there is radiation in all directions and that neither the E or H planes cancel each other out. There must be a discontinuity.

This is best described as a topological theorem, the hairy ball theorem - one cannot comb the hair on a ball in a smooth manner so that there is no part or bald spot. In the same way, it is not possible to cover a sphere with square magnets so that they don't repel each other somewhere.

It is possible, theoretically, to build an antenna that transmits power isotropically. Though such an antenna cannot transmit plane polarization in every direction. Equal power over the sphere can be achieved by transmitting in two orthogonal polarizations. These polarization must vary across the sphere to accomodate the hairy ball theorem. Though, for most purposes of antenna theory such an antenna is not useful.

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

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