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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.
In network science, reciprocity is a measure of the likelihood of vertices in a directed network to be mutually linked. [1] Like the clustering coefficient , scale-free degree distribution , or community structure , reciprocity is a quantitative measure used to study complex networks .
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.
Reciprocity (electromagnetism), theorems relating sources and the resulting fields in classical electromagnetism; Reciprocity (electrical networks), reciprocity theorem as it relates to current and voltage in electrical networks; Reciprocity (network science), measures the tendency of vertex pairs to form mutual connections between each other
Figure 1: Example two-port network with symbol definitions. Notice the port condition is satisfied: the same current flows into each port as leaves that port.. In electronics, a two-port network (a kind of four-terminal network or quadripole) is an electrical network (i.e. a circuit) or device with two pairs of terminals to connect to external circuits.
Networks which include non-reciprocal materials in the transmission medium such as those containing magnetically biased ferrite components will be non-reciprocal. An amplifier is another example of a non-reciprocal network. A property of 3-port networks, however, is that they cannot be simultaneously reciprocal, loss-free, and perfectly matched ...
Reciprocity in linear systems is the principle that a response Rab, measured at a location (and direction if applicable) a, when the system has an excitation signal applied at a location (and direction if applicable) b, is exactly equal to Rba which is the response at location b, when that same excitation is applied at a. This applies for all ...
Typically, it is intended that each external connection to the network is between the terminals of just one port, so that these limitations are appropriate. For a generic multi-port network definition, it is assumed that each of the ports is allocated an integer n ranging from 1 to N , where N is the total number of ports.