1. Lecture 01 - Node Voltage Analysis
EE 2415
Lecture 01 - Node Voltage Analysis

2. Introduction to the Node Voltage Method
More direct than branch equations
Fewer equations to solve
Choose one node as reference
Express all variables in terms of node voltages
Solution is set of node voltages w.r.t. chosen reference node
Solution completely defines the circuit

3. Node Voltage Example 1 (1/4)
Apply KCL at Node 1:
Use Ohm’s Law:

4. Node Voltage Example 1 (2/4)
Apply KCL at Node 2:
Use Ohm’s Law:

5. Node Voltage Example 1 (3/4)
KCL for Node 1:
KCL for Node 2:

6. Node Voltage Example 1 (4/4)

7. Node Voltage Example 1a (1/2)

8. Node Voltage Example 1a (2/2)

9. Node Voltage Example 2 (1/2)
KCL for Node 1:
KCL for Node 2:

10. Node Voltage Example 2 (2/2)
Substitute:
into KCL equations
Node 1:
Node 2:

11. Node Voltage Example 2a (1/2)
Substituting for ix:

12. Node Voltage Example 2a (2/2)

13. Node Voltage Example 3 (1/2)
KCL for Node 1:
KCL for Node 2:

14. Node Voltage Example 3 (2/2)
Substitute:
into KCL equations
Node 1:
Node 2:

15. Node Voltage Example 3a (1/2)
After Substitution:

16. Node Voltage Example 3a (2/2)
Substitute and solve:

17. Node Voltage Example 4 (1/3)
No KCL equation possible at node 1 or at node 2.
KCL can be applied at the supernode.

18. Node Voltage Example 4 (2/3)
Supernode:
Other relationships:
and

19. Node Voltage Example 4 (3/3)

20. Node Voltage Example 4a (1/2)

21. Node Voltage Example 4a (2/2)
Substitute and solve:

22. Alternative to Supernode (1/2)
Node 1:
Node 2:

23. Alternative to Supernode (2/2)
Use Ix to get same
info as Supernode: