as a base of comparison to calculate the directivity of actual antennas. Antenna gain , which is equal to the antenna's directivity multiplied by the antenna efficiency, is defined as the ratio of the intensity (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 received from a perfect lossless isotropic antenna at the same distance. This is called isotropic gain Gain is often expressed in logarithmic units called decibels (dB). When gain is calculated with respect to an isotropic antenna, these are called decibels isotropic (dBi) The gain of any perfectly efficient antenna averaged over all directions is unity, or 0 dBi. Isotropic receiver In EMF measurement applications, an isotropic receiver (also called isotropic antenna) is a calibrated radio receiver with an antenna which approximates an isotropic reception pattern; that is, it has close to equal sensitivity to radio waves from any direction. It is used as a field measurement instrument to measure electromagnetic sources and calibrate antennas. The isotropic receiving antenna is usually approximated by three orthogonal antennas or sensing devices with a radiation pattern of the omnidirectional type , such as short dipoles or small loop antennas. The parameter used to define accuracy in the measurements is called isotropic deviation. Optics In optics, an isotropic radiator is a point source of light. The sun approximates an 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. Sound An isotropic sound radiator is a theoretical loudspeaker radiating equal sound volume in all directions. 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. Derivation of aperture of an isotropic antenna The aperture of an isotropic antenna can be derived by a thermodynamic argument. 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