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# Node Voltage Method

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### Node Voltage Method

1. 1. Node Voltage Method
2. 2. Node Analysis with Voltage Sources <ul><li>When voltage sources are added to the circuit the node voltage analysis will be slightly different as the current through a voltage source Is not directly related to the voltage across it </li></ul><ul><li>There are three methods to deal with a voltage source </li></ul><ul><li>First method: replace the voltage source and series resistance with equivalent current source and parallel resistance </li></ul>
3. 3. Node Analysis with Voltage Sources <ul><li>Second method: </li></ul><ul><li>Node B is selected as the reference node therefore V B =0 </li></ul><ul><li>V A =Vs and therefore he voltage of node A is known. No node-voltage equation at node A is needed </li></ul><ul><li>The node voltage equations at the remaining N-2 nodes are written and solved in the usual way to find the N-2 unknown node voltages </li></ul>
4. 4. Node Analysis with Voltage Sources <ul><li>Third method: </li></ul><ul><li>Neither node A nor node B is selected as reference </li></ul><ul><li>Node A and B are combined into one supernode </li></ul><ul><li>The node voltage equations in the remaining N-3 nodes plus the supernode are written </li></ul><ul><li>The equation related to the voltage source inside the supernode will provide the last equation: </li></ul>
5. 5. Example 1 <ul><li>Find the voltage Vo using node-voltage analysis </li></ul>
6. 6. Example 1 Solution:
7. 7. Example 2 <ul><li>Find the input resistance of the circuit. </li></ul>
8. 8. <ul><li>Solution: Node A has the voltage of the source therefore two node voltage equations are required </li></ul>
9. 9. Example 3 <ul><li>Find Vo when element E is 10k Ω resistance. </li></ul>
10. 10. Example 3 Solution :