EE40Lecture 7Venkat AnantharamNodal Analysis: general methodNodal Analysis: Example #3Nodal Analysis: Example #4Dependent SourcesPlanar GraphSlide 1EE40 Spring 08 Venkat AnantharamEE40Lecture 7Venkat Anantharam2/6/08Reading: Chap. 2Mesh AnalysisSlide 2EE40 Spring 08 Venkat AnantharamNodal Analysis: general method1. Choose a reference node (“ground”)2. Group the nodes that are connected by voltage sources into supernodes (the reference may also become a supernode)3. Define unknown node/supernode voltages (those at the nodes/supernodes that are not the reference. Relative voltages at the nodes within a supernode are determined by the voltage sources.)4. Write KCL at each unknown node/supernode, (expressing current in terms of the node voltages using the I-V relationships of the circuit elements)5. Solve the set of independent equations (n-1-(#voltage sources) equations for n-1-(#voltage sources) unknown node/supernodevoltages 6. Use the remaining KCL equations to find the currents through the voltage sources. (there will be (#voltage sources) such equations)Slide 3EE40 Spring 08 Venkat AnantharamNodal Analysis: Example #3supernodeOne equation : KCL at supernodeThere is one equation in one unknownThe relative voltages of the node within the supernodeare determined by the voltage source.R4R2I2VaVb+-VLLI1Slide 4EE40 Spring 08 Venkat AnantharamNodal Analysis: Example #4V2V1R2R1R4R5R3I1VaVbThere are two unknowns.There are two equations in these unknowns Here there is no floating voltage source.If you had instead chosen the reference at one of the current source terminals you would have a supernode of three nodesand another node, for again two equations in two unknowns.Slide 5EE40 Spring 08 Venkat AnantharamDependent SourcesTreat each dependent source (of any of the four kinds) as a new variable, associated to a ``known” source and proceed as before. At the end, you get an extra equation from the dependency that defines the source, for each dependent source.These extra equations will allow you to complete the solution.Slide 6EE40 Spring 08 Venkat AnantharamPlanar Graph• The graph of a circuit is called planar if it can be drawn on a page without being forced to have any branch cross over another branch. • An example of a graph that is not planar is the complete bipartite graph with 3 left nodes and three right nodes (6 nodes and 9 edges in total). Try drawing this on a page without branch
View Full Document
Unlocking...