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Nodal and Mesh Analysis

Nodal and Mesh Analysis. Nodal Analysis KCL Consider Node current Node voltage. Example 1. Given => node current Determine => node voltage =>Find voltage at node 1,2 and 3. Steps of Nodal Analysis.

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Nodal and Mesh Analysis

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  1. Nodal and Mesh Analysis Nodal Analysis • KCL • Consider • Node current • Node voltage

  2. Example 1 Given => node current Determine => node voltage =>Find voltage at node 1,2 and 3

  3. Steps of Nodal Analysis • Assign a reference node => a node having the most electric elements connecting to it or a ground node if it is given • Apply KCL to each node except the reference node. • Solving the simultaneous equations.

  4. KCL@Node 1

  5. KCL@Node 2

  6. KCL@Node 3 From (2), (3) and (4) we get v1 = 5.412 V , v2 = 7.736 V , v3 = 46.32 V

  7. Example 2 From (1), (2) and (3) we get v1 = 4.8 V , v2 = 2.4 V , v3 = -2.4 V Determine v1, v2 and v3

  8. Example 3 From (1), (2) and (3) we get v1 , v2 , and v3 Determine v1, v2 and v3

  9. Example 4 (1) We know that KCL @ node 1  Because it connects to reference node, the node equation has not to determine. KCL @ node 2 Determine the voltage of the unknown node to reference voltages.

  10. Example 4 (2) KCL @ supernode (3,4) From (1) - (6) we get v1 = -12 V, v2 = -4 V, v3 = 0 V and v4 = -2 V Determine the voltage of the unknown node to reference voltages.

  11. Summarize of Nodal Analysis • Select the node to which the highest number of branches is connected as the referenced node. • Set up KCL equations for other nodes by expressing the unknown currents as a function of the node voltages measured with respect to the referenced node. • If the given circuit contains voltage sources, KCL equations of those two nodes connected by a voltage source are combined to eliminate the redundancy of KCL equations since the additional information is available through the node voltage. • Solve KCL equations to determine the node voltages.

  12. Mesh Analysis Mesh = a smallest loop (a loop does not contain other loops inside) Mesh analysis can be used only with planar-network.

  13. Mesh Analysis Procedure • Assign all mesh currents in the same direction. • Set up KVL equation for each mesh. Use Ohm’s law to express the voltages in term of the mesh currents • If the given circuit contains current sources on the perimeter of any meshes. That is, two meshes share current sources in common. Such meshes form a supermesh to eliminate the redundancy of KVL equations. • Solve KVL equations to determine the mesh currents

  14. Example 5 KVL @ mesh 1 KVL @ mesh 2 From (1) + (2), current flowing through 3 Ω = 6 – 4 = 2 A. from top to bottom. Determine the current flowing through 3 Ω resistor using mesh analysis.

  15. Example 6 KVL @ mesh 1 KVL @ mesh 2 KVL @ mesh 3 Find i1, i2 and i3

  16. Example 6 Because 5A source is at perimeter, The value i2 is already know Find ix using mesh analysis

  17. Example 7 Find i1 , i2 Supermesh

  18. Example 8 (1) Mesh analysis Find current flowing through 4.7 k Ω and 2.2 k Ω.

  19. Example 8 (2) Find current flowing through 4.7 k Ω and 2.2 k Ω. Node analysis

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