eeng2009lec4 - 5.1 Nodes and Node Voltages EENG 2009 Nodes...

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EENG 2009 FS 2006 Part 5: Nodal Analysis 146 EENG 2009 Part 5. Nodal Analysis 5.1 Nodes and Node Voltages 5.2 Nodal Analysis By Example 5.3 Supernodes 5.4 Dependent Sources EENG 2009 FS 2006 Part 5: Nodal Analysis 147 Recall that nodes are the connected segments of conductor that remain when we remove the circuit elements (which at present for us are either resistors or sources). 9 A 16 Ω 8 Ω 12 Ω 3 A Identify the nodes for the given circuit. Redraw the circuit with the circuit elements removed and note the connected segments of conductors. We see that there are 3 nodes for this circuit: 5.1 Nodes and Node Voltages Nodes Example 1 Solution: A single node!
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EENG 2009 FS 2006 Part 5: Nodal Analysis 148 A node voltage associated with a given node is defined to be the voltage difference between the given node and a reference node, which has been chosen from among the nodes. For a circuit with N essential nodes, there are N–1 node voltages. Once the set of node voltages is determined, all the other voltages and currents can be obtained in a straightforward manner. Identify a reference node and corresponding node voltages for the given circuit (whose nodes we found in the previous example). 9 A 16 Ω 8 Ω 12 Ω 3 A Node Voltages Example 2 EENG 2009 FS 2006 Part 5: Nodal Analysis 149 node 1 v 1 v 2 Reference node, ground, earth, “sea level” Using the results of Example 1, we draw the circuit with the nodes emphasized: 9 A 16 Ω 8 Ω 12 Ω 3 A Next choose the bottom node as the reference node, and designate the node voltages for the other two nodes as v 1 and v 2 : 9 A 16 Ω 8 Ω 12 Ω 3 A node 2 Example 2 Solution:
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EENG 2009 FS 2006 Part 5: Nodal Analysis 150 9 A 16 Ω 8 Ω 12 Ω 3 A 1 2 v 1 v 2 64 V 48 V 16 V The voltage across the 16- Ω branch is not a node voltage. It is a branch voltage, and is actually the difference between the two node voltages v 1 and v 2 . voltmeter voltmeter voltmeter + + + The voltage being measured is a branch voltage. Node Voltages! Measurement of Branch and Node Voltages EENG 2009 FS 2006 Part 5: Nodal Analysis 151 1 2 v 1 v 2 3 + v 12 + v 23 + v 13 Find the relationships among the branch voltages and the node voltages . There are three branch voltages , v 13 , v 12 , and v 23 , and two node voltages , v 1 and v 2 (not counting v 3 ). The branch voltages v 13 and v 23 are clearly equal to the node voltages v 1 and v 2 : v 13 = v 1 v 23 = v 2 The branch voltage v 12 is a combination of the node voltages v 1 and v 2 . Branch Voltages In Terms of Node Voltages Example 3 Solution:
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EENG 2009 FS 2006 Part 5: Nodal Analysis 152 v 12 = v 13 –v 23 = v 1 2 Note the correlation with the order of the subscripts: The subscripts of v 12 are 1 & 2 and the subscripts of the two node voltages being subtracted are 1 & 2. In general, We can write the branch voltage v 12 in terms of the node voltages v 13 and v 23 by applying KVL, as follows: 12 v 1 v 2 3 + v 12 + v 23 + v 13 node j node k v j v k Memorize me!
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This note was uploaded on 06/01/2008 for the course COMPUTER E 203 taught by Professor Uzengil during the Spring '08 term at Jefferson College of Health Sciences.

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eeng2009lec4 - 5.1 Nodes and Node Voltages EENG 2009 Nodes...

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