System topology, cut-set and circle comparison

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Definitions. Associated Graph : A lumped system diagram is said to be joined if there exists no less than one way among the branches (neglecting their introduction ) between any pair of nodes.Sub Graph : A sub chart is a subset of the first arrangement of diagram branches alongside their comparing hubs..

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Slide 1

Arrange topology, cut-set and circle condition 20050300 HYUN KYU SHIM

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Definitions Connected Graph : A lumped organize diagram is said to be associated if there exists no less than one way among the branches (slighting their introduction ) between any match of hubs. Sub Graph : A sub diagram is a subset of the first arrangement of chart branches alongside their relating hubs.

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(A) Connected Graph (B) Disconnected Graph

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Cut – Set Given an associated lumped organize diagram, an arrangement of its branches is said to constitute a cut-set if its evacuation isolates the rest of the segment of the system into two sections.

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Tree Given a lumped arrange chart, a related tree is any associated subgraph which is included the greater part of the hubs of the first associated diagram, however has no circles.

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Loop Given a lumped organize diagram, a circle is any shut associated way among the chart branches for which each branch included is crossed just once and every hub experienced interfaces precisely two included branches.

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Theorems (an) A diagram is a tree if and just if there exists precisely one way between a sets of its hubs. (b) Every associated chart contains a tree. (c) If a tree has n hubs, it must have n-1 branches.

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Fundamental cut-sets Given a n - hub associated organize chart and a related tree, each of the n - 1 major slice sets regarding that tree is framed of one tree limb together with the negligible arrangement of connections to such an extent that the evacuation of this whole cut-arrangement of branches would isolate the rest of the bit of the diagram into two sections.

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Fundamental cutset lattice

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Nodal rate framework The major cutset conditions might be gotten as the suitably marked entirety of the Kirchhoff `s current law hub conditions for the hubs in the tree on either side of the comparing tree limb, we may dependably compose (An is nodal occurrence grid)

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Loop rate framework Loop rate lattice characterized by

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Loop frequency grid & KVL We characterize branch voltage vector We may compose the KVL circle conditions advantageously in vector – network shape as

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General Case

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To get the cut set conditions for a n-hub , b-branch associated lumped arrange, we first compose Kirchhoff `s law The nearby connection of these expressions with

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And current vector is determined as takes after

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Hence, We get cutset conditions

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Example

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subsequently the key cutset grid yields the cutset conditions

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For this situation we require fathom for the voltage capacity to acquire each branch variable.

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