Node Voltage Method
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There are three methods for node voltage analysis when voltage sources are present in a circuit. The first method replaces the voltage source and series resistance with an equivalent current source and parallel resistance. The second method selects one node as the reference node (voltage of 0V) and writes equations for the remaining nodes. The third method combines the nodes connected to the voltage source into a supernode and writes equations for the remaining standard nodes and supernode. Examples are provided to demonstrate each method.
Node Voltage Method
- 2. Node Analysis with Voltage Sources 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 There are three methods to deal with a voltage source First method: replace the voltage source and series resistance with equivalent current source and parallel resistance
- 3. Node Analysis with Voltage Sources Second method: Node B is selected as the reference node therefore V B =0 V A =Vs and therefore he voltage of node A is known. No node-voltage equation at node A is needed 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
- 4. Node Analysis with Voltage Sources Third method: Neither node A nor node B is selected as reference Node A and B are combined into one supernode The node voltage equations in the remaining N-3 nodes plus the supernode are written The equation related to the voltage source inside the supernode will provide the last equation:
- 5. Example 1 Find the voltage Vo using node-voltage analysis
- 7. Example 2 Find the input resistance of the circuit.
- 8. Solution: Node A has the voltage of the source therefore two node voltage equations are required
- 9. Example 3 Find Vo when element E is 10k Ω resistance.
- 10. Example 3 Solution :