Tellegen’s Theorem And Electrical Networks


Tellegen’s Theorem And Electrical Networks
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B. D. H. Tellegen was the first to point out (1952, 1953) the generality and wide-ranging usefulness of the theorem that bears his name. Nevertheless, the theorem is still not as widely known as its utility warrants. The authors of this monograph set out to correct this neglect, noting that "There is hardly a basic network theorem that cannot be proved by invoking Tellegen’s theorem. The simplicity and generality of the theorem make it attractive pedagogically, and its ability to generalize known results and lead to new results indicates its research value. This theorem definitely should be in every circuit designer’s kit of tools." Tellegen’s theorem is unusual in that it depends solely upon Kirchhoff’s laws and the topology of the network. The theorem thus applies to all electrical networks that obey Kirchhoff’s laws, whether linear or nonlinear, time-invariant or time-variant, reciprocal or nonreciprocal, passive or active, single-valued or multiple-valued, hysteretic or nonhysteretic. The excitation is arbitrary-it may be sinusoidal, exponential, periodic, transient, or random. Also, the initial conditions may be arbitrarily chosen. The modern interest in nonlinear and time-variant networks gives Tellegen’s theorem a special new importance, because it is one of the very few general theorems that apply to such networks.

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