Teorema de Tellegen

Tellegen's theorem is one of the most powerful theorems in network analysis. Many of the energy distribution theorems and the principles of network analysis can be derived from it. It was published in 1952 by Bernard Tellegen. Basically, the theorem gives a simple relation to the magnitudes that satisfy the laws of Kirchhoff in the electrical circuits.

Tellegen's theorem can be applied to a large multitude of network systems. The basic assumptions of the systems are the conservation of the flow of many quantities (Kirchhoff's Law of Law, LCK) and the set of potentials in the nodes of a network (Kirchhoff's Law of Voltages, LVK). The Tellegen theorem gives us a useful tool in the analysis of complex networks such as electrical circuits, metabolic and biological networks, pipeline networks and chemical process networks. The Theorem

It has a large number of applications, ranging from circuits with active and passive elements, linear and nonlinear, and sources that change over time. The great generality of the theorem derives from the fact that the only condition to be applied is that it complies with the two laws of kirchoff. If the passive sign convention is considered (the current is directed from the positive to the negative terminal), being v k ( t ) {\displaystyle v_{k}(t)} e i k ( t ) {\displaystyle i_{k}(t)} , the instantaneous stresses and currents, the Tellegen theorem states that:

∑ k = 1 r v k ( t ) . i k ( t ) = 0 {\displaystyle \sum _{k=1}^{r}v_{k}(t).i_{k}(t)=0}

Since the product of instantaneous voltage represents instantaneous power, Tellegen's theorem represents the conservation of power in a circuit, ie the sum of the powers supplied by the sources is equivalent to the powers absorbed by the resistances.

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