翻訳と辞書 Words near each other ・ Tellancourt ・ Tellanur ・ Tellapadu ・ Tellarite ・ Tellaro ・ Tellaste ・ Telle ・ Telle Whitney ・ Tellecey ・ Tellef Dahll ・ Tellef Dahll Schweigaard ・ Tellef Wagle ・ Tellef Øgrim ・ Tellefsen ・ Tellegen ・ Tellegen's theorem ・ Tellego ・ Tellem ・ Tellem (surname) ・ Tellement j'ai d'amour pour toi ・ Tellement j'ai d'amour... ・ Tellenburg Castle ・ Tellenlied ・ Tellepsen Builders ・ Teller ・ Teller (elections) ・ Teller (magician) ・ Teller (surname) ・ Teller Airport ・ Teller Amendment Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tellegen's theorem ： ウィキペディア英語版 Tellegen's theorem Tellegen's theorem is one of the most powerful theorems in network theory. Most of the energy distribution theorems and extremum principles in network theory can be derived from it. It was published in 1952 by Bernard Tellegen. Fundamentally, Tellegen's theorem gives a simple relation between magnitudes that satisfy Kirchhoff's laws of electrical circuit theory. The Tellegen theorem is applicable to a multitude of network systems. The basic assumptions for the systems are the conservation of flow of extensive quantities (Kirchhoff's current law, KCL) and the uniqueness of the potentials at the network nodes (Kirchhoff's voltage law, KVL). The Tellegen theorem provides a useful tool to analyze complex network systems including electrical circuits, biological and metabolic networks, pipeline transport networks, and chemical process networks. == The theorem == Consider an arbitrary lumped network whose graph $G$ has $b$ branches and $n\_$ nodes. In an electrical network, the branches are two-terminal components and the nodes are points of interconnection. Suppose that to each branch of the graph we assign arbitrarily a branch potential difference $W\_$ and a branch current $F\_$ for $k=1,2,\backslash dots,b$, and suppose that they are measured with respect to arbitrarily picked ''associated'' reference directions. If the branch potential differences $W\_,W\_,\backslash dots,W\_$ satisfy all the constraints imposed by KVL and if the branch currents $F\_,F\_,\backslash dots,F\_$ satisfy all the constraints imposed by KCL, then : $\backslash sum\_^\; W\_\; F\_\; =\; 0.$ Tellegen's theorem is extremely general; it is valid for any lumped network that contains any elements, ''linear or nonlinear'', ''passive or active'', ''time-varying or time-invariant''. The generality is extended when $W\_$ and $F\_$ are linear operations on the set of potential differences and on the set of branch currents (respectively) since linear operations don't affect KVL and KCL. For instance, the linear operation may be the average or the Laplace transform. The set of currents can also be sampled at a different time from the set of potential differences since KVL and KCL are true at all instants of time. Another extension is when the set of potential differences $W\_$ is from one network and the set of currents $F\_$ is from an entirely different network, so long as the two networks have the same topology (same incidence matrix) Tellegen's theorem remains true. This extension of Tellegen's Theorem leads to many theorems relating to two-port networks.〔''Tellegen's Theorem and Electrical Networks'' by Paul Penfield, Jr., Robert Spence, and Simon Duinker, The MIT Press, Cambridge, MA, 1970〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tellegen's theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.