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Forms of the reciprocity theorems are used in many electromagnetic applications, such as analyzing electrical networks and antenna systems. [1] For example, reciprocity implies that antennas work equally well as transmitters or receivers, and specifically that an antenna's radiation and receiving patterns are identical.
A necessary condition for the aforementioned reciprocity property is that the materials in the antenna and transmission medium are linear and reciprocal. Reciprocal (or bilateral ) means that the material has the same response to an electric current or magnetic field in one direction, as it has to the field or current in the opposite direction.
There are limits to reciprocity: It applies only to passive antenna elements – active antennas that incorporate amplifiers or other individually powered components are not reciprocal. And even when the antenna is made of exclusively of passive elements, reciprocity only applies to the waves emitted and intercepted by the antenna.
The antenna pattern is the response of the antenna to a plane wave incident from a given direction or the relative power density of the wave transmitted by the antenna in a given direction. For a reciprocal antenna, these two patterns are identical. A multitude of antenna pattern measurement techniques have been developed.
Patch antenna gain pattern. A directional antenna or beam antenna is an antenna which radiates or receives greater radio wave power in specific directions. Directional antennas can radiate radio waves in beams, when greater concentration of radiation in a certain direction is desired, or in receiving antennas receive radio waves from one specific direction only.
For a given frequency, the antenna's effective area is proportional to the gain. An antenna's effective length is proportional to the square root of the antenna's gain for a particular frequency and radiation resistance. Due to reciprocity, the gain of any antenna when receiving is equal to its gain when transmitting.
Due to electromagnetic reciprocity, an antenna has the same radiation resistance when receiving radio waves as when transmitting. If the antenna is connected to an electrical load such as a radio receiver , the power received from radio waves striking the antenna is divided proportionally between the radiation resistance and loss resistance of ...
Reciprocity of electrical networks is a special case of Lorentz reciprocity, but it can also be proven more directly from network theorems. This proof shows reciprocity for a two-node network in terms of its admittance matrix, and then shows reciprocity for a network with an arbitrary number of nodes by an induction argument.