Isotropic radiator

The waves travel in straight lines away from the source point, in the radial direction

Assuming it is located in empty space where there is nothing to absorb the waves, the power striking a spherical surface enclosing the radiator, with the radiator at center, regardless of the radius

in watts per square meter striking each point of the sphere is the same, it must equal the radiated power divided by the surface area

[5] In a cavity at equilibrium the power density of radiation is the same in every direction and every point in the cavity, meaning that the amount of power passing through a unit surface is constant at any location, and with the surface oriented in any direction.

Since it is entirely non-directional, it serves as a hypothetical worst-case against which directional antennas may be compared.

In reality, a coherent isotropic radiator of linear polarization can be shown to be impossible.

Consider a large sphere surrounding the hypothetical point source, in the far field of the radiation pattern so that at that radius the wave over a reasonable area is essentially planar.

However the hairy ball theorem shows that a continuous vector field tangent to the surface of a sphere must fall to zero at one or more points on the sphere, which is inconsistent with the assumption of an isotropic radiator with linear polarization.

Incoherent isotropic antennas are possible and do not violate Maxwell's equations.

received from a perfect lossless isotropic antenna at the same distance.

Gain is often expressed in logarithmic units called decibels (dB).

The gain of any perfectly efficient antenna averaged over all directions is unity, or 0 dBi.

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

The Sun approximates an (incoherent) isotropic radiator of light.

Certain munitions such as flares and chaff have isotropic radiator properties.

Whether a radiator is isotropic is independent of whether it obeys Lambert's law.

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.

Since sound waves are longitudinal waves, a coherent isotropic sound radiator is feasible; an example is a pulsing spherical membrane or diaphragm, whose surface expands and contracts radially with time, pushing on the air.

[10] The aperture of an isotropic antenna can be derived by a thermodynamic argument, which follows.

[11][12][13] Suppose an ideal (lossless) isotropic antenna A located within a thermal cavity CA is connected via a lossless transmission line through a band-pass filter Fν to a matched resistor R in another thermal cavity CR (the characteristic impedance of the antenna, line and filter are all matched).

Both cavities are filled with blackbody radiation in equilibrium with the antenna and resistor.

passes through the transmission line and filter Fν and is dissipated as heat in the resistor.

The rest is reflected by the filter back to the antenna and is reradiated into the cavity.

The resistor also produces Johnson–Nyquist noise current due to the random motion of its molecules at the temperature

Since the entire system is at the same temperature it is in thermodynamic equilibrium; there can be no net transfer of power between the cavities, otherwise one cavity would heat up and the other would cool down in violation of the second law of thermodynamics.

The radio noise in the cavity is unpolarized, containing an equal mixture of polarization states.

For example, a linearly polarized antenna cannot receive components of radio waves with electric field perpendicular to the antenna's linear elements; similarly a right circularly polarized antenna cannot receive left circularly polarized waves.

is the antenna's aperture, the amount of power in the frequency range

the antenna receives, this is integrated over all directions (a solid angle of

Radio waves are low enough in frequency so the Rayleigh–Jeans formula gives a very close approximation of the blackbody spectral radiance[b]