An isotropic radiator is a theoretical point source of electromagnetic or sound waves 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.

Whether a radiator is isotropic is independent of whether it obeys Lambert's law.[citation needed] 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.

## 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, an isotropic antenna is a hypothetical antenna radiating the same intensity of radio waves in all directions. It has a directivity of 0 dBi (dB relative to isotropic),

In reality, a coherent isotropic radiator cannot exist, as the isotropic radiator, with a radiation pattern (as expressed in spherical coordinates) of

$\boldsymbol{E}(r,\theta,\phi)=\frac{e^{-jkr}}{4\pi r}{\boldsymbol{\hat{u}}}(\theta,\phi)$
(note that the magnitude of this function is independent of the spherical angles $\displaystyle\theta$ and $\ \phi$, but it is permissible for the vector's direction, as represented by the unit vector $\boldsymbol{\hat{u}}$ to be a function of $\ \theta$ and $\ \phi$)

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 can 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[citation needed] 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 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.

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.

In practice a quasi-ideal isotropic receiver is obtained with three orthogonal sensing devices with a radiation diagram of the omnidirectional type $\sin (\theta)$, like that of short dipole and small loop antennas.

The parameter used to define accuracy in the measurements is called isotropic deviation.

### 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.