Lecture 7 Node Voltage Method ECE 205 Prof

Lecture 7 Node Voltage Method ECE 205 Prof. Ali Keyhani

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

Node Analysis with Voltage Sources Second method: • Node B is selected as the reference node therefore VB=0 • VA=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

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:

Example 1 Find the voltage Vo using node-voltage analysis

Example 1 Solution:

Example 2 Find the input resistance of the circuit.

Solution: Node A has the voltage of the source therefore two node voltage equations are required

Example 3 Find Vo when element E is 10 kΩ resistance.

Example 3 Solution: