An isotropic radiator is a theoretical point source of waves that radiates the same intensity of radiation in all directions. It may be based on sound waves or electromagnetic waves, in which case it is also known as an isotropic antenna. It has no preferred direction of radiation, i.e., 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, for example in determining the gain of antennas. A coherent isotropic radiator of electromagnetic waves is theoretically impossible, but incoherent radiators can be built. An isotropic sound radiator is possible because sound is a longitudinal wave. The term isotropic radiation means a radiation field which has the same intensity in all directions at each receiving point; thus an isotropic radiator does not produce isotropic radiation.
Physics In physics, an isotropic radiator is a point source of electromagnetic radiation or sound. At a distance, the Sun and other stars are isotropic radiators of electromagnetic radiation.
Radiation pattern The radiation field of an isotropic radiator in empty space can be found from conservation of energy. The waves travel in straight lines away from the source point, in the radial direction r ^ {\displaystyle {\hat {\mathbf {r} }}} . Since it has no preferred direction of radiation, the power density ⟨ S ⟩ {\displaystyle \left\langle S\right\rangle } of the waves at any point does not depend on the angular direction ( θ , ϕ ) {\displaystyle (\theta ,\phi )} , but only on the distance r {\displaystyle r} from the source. 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 r {\displaystyle r} , must be the total power ⟨ P ⟩ {\displaystyle \left\langle P\right\rangle } in watts emitted by the source. Since the power density ⟨ S ⟩ {\displaystyle \left\langle S\right\rangle } 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 4 π r 2 {\displaystyle 4\pi r^{2}} of the sphere
Thus the power density radiated by an isotropic radiator decreases with the inverse square of the distance from the source. The term isotropic radiation is not used for the radiation from an isotropic radiator because it has a different meaning in physics. In thermodynamics it refers to the electromagnetic radiation pattern which would be found in a region at thermodynamic equilibrium, as in a black thermal cavity at a constant temperature. 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. This radiation field is different from that of an isotropic radiator, in which the direction of power flow is everywhere away from the source point, and decreases with the inverse square of distance from it.
Antenna theory In antenna theory, an isotropic antenna is a hypothetical antenna radiating the same intensity of radio waves in all directions. It thus is said to have a directivity of 0 dBi (dB relative to isotropic) in all directions. 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 electromagnetic waves of linear polarization can be shown to be impossible. Its radiation field could not be consistent with the Helmholtz wave equation (derived from Maxwell's equations) in all directions simultaneously. 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. In the far field the electric (and magnetic) field of a plane wave in free space is always perpendicular to the direction of propagation of the wave. So the electric field would have to be tangent to the surface of the sphere everywhere, and continuous along that surface. 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. Even though an exactly isotropic antenna cannot exist in practice, it is used as a base of comparison to calculate the directivity of actual antennas. Antenna gain G , {\displaystyle \scriptstyle \ G\ ,} which is equal to the antenna's directivity multiplied by the antenna efficiency, is defined as the ratio of the intensity I {\displaystyle \scriptstyle \ I\ } (power per unit area) of the radio power received at a given distance from the antenna (in the direction of maximum radiation) to the intensity I iso {\displaystyle \scriptstyle \ I_{\text{iso}}\ } received from a perfect lossless isotropic antenna at the same distance. This is called isotropic gain
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