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3-Lesson_Notes_Lecture13_ee205

# 3-Lesson_Notes_Lecture13_ee205 - Lecture 13 General Rules...

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Lecture 13 General Rules for Writing Circuit State Equations This lecture contains the following material Concepts of graph, tree, cut-set, etc. in circuit analysis Concept on fundamental loop and fundamental cut-set General rules for writing state equations An example demonstrating the use of general rules for writing circuit equations At the end of this lecture you should be able to Draw a graph for a circuit Learn how to select tree and tree branches Learn how to identify independent loop equations for KVL Learn how to write independent KCL equations Learn how to write state equations for a general circuit. Before proceeding with the general rules for writing circuit equations, let us learn some definitions, like Graphs Spanning tree (or, tree) Cut-sets Fundamental cut-set Fundamental loop, etc. Consider the simple resistive circuit with the sources, Fig.13.1

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The following figure (Fig.2) is a graph of Fig.1 Fig. 13.2 Figure 13.2 is an example of a connected graph. We can see that a graph is a collection of points and lines. The points are called nodes The lines are the edges Graphs can be unconnected (or, disconnected) graph also. Fig. 13.3 is an example of a disconnected graph. Fig. 13.3 Tree or Spanning Tree: A graph with n nodes and n-1 edges is called a spanning tree Branch: Each edge of a spanning tree is called a branch.
Fig. 13.4 Fig.13-4 shows three possible spanning trees of the connected graph given in Fig 13.2. Show that there are also other possible spanning trees.

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