1. METHODS OF ANALYSIS Mesh Analysis Nodal analysis

2. Nodal Analysis 2 Supernode Determine v 1, v 2 +v1+v1 +v2+v2 22 44 10   + 2V 2A 7A

3. Nodal Analysis 2 Supernode +v1+v1 +v2+v2 22 44 10   + 2V 2A 7A Step 1 Determine the reference node Step 2 Assign the rest of the nodes with node voltages v1v1 v2v2

4. Nodal Analysis 2 Supernode +v1+v1 +v2+v2 22 44 10   + 2V 2A 7A v1v1 v2v2 Step 3 Write down equations using KCL for every non-reference node in terms of node voltages We cannot write equation for current with branch containing 2V voltage source ! To avoid this, we will combine nodes 1 and 2 to form a SUPERNODE

5. Nodal Analysis 2 Supernode +v1+v1 +v2+v2 22 44 10   + 2V 2A 7A v1v1 v2v2 To avoid this, we will combine nodes 1 and 2 to form a SUPERNODE supernode We will use KCL to sum all current going out of supernode:

6. Nodal Analysis 2 Supernode +v1+v1 +v2+v2 22 44 10   + 2V 2A 7A v1v1 v2v2 supernode We need another equation in order to solve v 1 and v 2 Applying KVL for the loop,

7. Nodal Analysis 2 Supernode +v1+v1 +v2+v2 22 44 10   + 2V 2A 7A v1v1 v2v2 Step 4 Obtain the node voltages by solving the simultaneous equations in step 3 and

8. Nodal Analysis 2 Supernode To summarize …. We form a supernode when there is a voltage source in between 2 non-reference nodes For example: Supernode needed since V s in between non-reference node +  ++ VsVs

9. ++ vbvb vava Nodal Analysis 2 Supernode To summarize …. For example: v1v1 v2v2 v3v3 Supernode needed since v a in between non-reference node We don’t need to form supernode. Also note that v 1 = V b We form a supernode when there is a voltage source in between 2 non-reference nodes

10. Nodal Analysis 2 Supernode To summarize …. For example: We form a supernode when there is a voltage source in between 2 non-reference nodes +  3i o  +

11. Nodal Analysis 2 Supernode To summarize …. We form a supernode when there is a voltage source in between 2 non-reference nodes Since we have combined two nodes, we lost 1 equation to solve the circuit.  we need one more equation to solve the circuit We write an equation (using KVL) that defines the voltage relationship between the two non-reference nodes that forms the supernodes

12. Nodal Analysis 2 Verification with Pspice +v1+v1 +v2+v2 22 44 10   + 2V 2A 7A v1v1 v2v2

13. Nodal Analysis 2 +v1+v1 +v2+v2 22 44 10   + 2V 2A 7A Mark reference node with 0. Mark the rest of the nodes with other than 0 0 12 Write the NETLIST for the circuit ans save it with.cir extension, e.g. example1.cir EXAMPLE 1 I1 0 1 DC 2 I2 2 0 DC 7 V1 2 1 DC 2 R1 1 0 2 R2 1 2 10 R3 2 0 4.END Verification with Pspice

14. Nodal Analysis 2 Open “Pspice AD Student” and simulate the circuit +v1+v1 +v2+v2 22 44 10   + 2V 2A 7A 0 12 Display the “Output file” Verification with Pspice