EE40 Lecture 7 Venkat Anantharam 2 6 08 Reading Chap 2 Mesh Analysis EE40 Spring 08 Slide 1 Venkat Anantharam Nodal Analysis general method 1 2 Choose a reference node ground 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 supernode voltages 6 Use the remaining KCL equations to find the currents through the voltage sources there will be voltage sources such equations EE40 Spring 08 Slide 2 Venkat Anantharam Nodal Analysis Example 3 supernode VLL Va I1 Vb R2 R4 I2 One equation KCL at supernode There is one equation in one unknown The relative voltages of the node within the supernode are determined by the voltage source EE40 Spring 08 Slide 3 Venkat Anantharam Nodal Analysis Example 4 R1 Vb V 1 R2 R3 Va I1 R5 R4 V2 There 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 nodes and another node for again two equations in two unknowns EE40 Spring 08 Slide 4 Venkat Anantharam Dependent Sources Treat 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 EE40 Spring 08 Slide 5 Venkat Anantharam Planar 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 crossings EE40 Spring 08 Slide 6 Venkat Anantharam
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