network topology, node, branch, grapg definitions

 

NETWORK TOPOLOGY

Network topology is arrangement of various elements  (links, nodes ,etc.) of a electrical network such that  there is no distinction between different types of physical  elements of network. Instead this study is based on a  geometric pattern of a network. When a circuit is non planar or complicated with large  number of nodes and closed paths, then conventional  methods like KCL , KVL , Nodal analysis, Mesh analysis  etc becomes highly difficult. Analysis of such networks  can be done conveniently using network topology. Network topology is used to analyze voltage and currents  across various branches of an electrical circuit (more  particularly complicated circuit)

• Node: A node is a point in a circuit where two or  more circuit elements join . The number of  branches incident to that node is the degree  of its node.

• Junction Node: A node that joins three or more elements.

• Branch: A Single path containing one circuit element that connects one node to other node and is represented by a solid line.
• Loop: A loop is a closed path  i.e, it starts at a selected node, traces a set of connected basic circuit elements and returns to the original starting node without passing through any intermediate node more than once.
• Mesh: A mesh is a special type of loop which does not contain any other loops with in it.

Graph: A graph corresponding to a given network is obtained by replacing all circuit elements with lines.

Graph

A graph corresponding to a given network is obtained by replacing all circuit elements with lines.

Rank of a Graph : If there are ‘n’ nodes in a graph then rank of

the of the graph is (n-1)

Steps for drawing oriented graph: 1. Replace all resistors , inductors and capacitors by line segments 2. Replace voltage source by short circuit and current sources by open circuit  3.Assume directions of branch currents 4. Name all the nodes and branches