1. METHODS OF ANALYSIS Mesh Analysis Nodal analysis

2. Nodal Analysis An analysis technique to solve electrical circuit where the node voltages are used as the circuit variables It involves systematic steps with an objective to solve the node voltages With node voltages known, current in every branch can be calculated 66 22 77 1A 4A v1v1 v2v2 Reference node v 1, v 2 : node voltages If v 1 and v 2 are known, current in all branches can be calculated

3. Nodal Analysis 66 22 77 1A 4A Example 1

4. Nodal Analysis 66 22 77 1A 4A v1v1 v2v2 Step 1 Determine the reference node: typically the one with the most branches  bottom node Step 2 Assign the rest of the nodes with node voltages (referred to the reference node) Example 1

5. Nodal Analysis 66 22 77 1A 4A v1v1 v2v2 Step 3 Write down equations using KCL for every non-reference node in terms of node voltages  if there are N nodes, there should be (N-1) equations Step 4 Obtain the node voltages by solving the simultaneous equations in step 3 Example 1

6. Nodal Analysis Example 2 9k  3k  4k  6k  ++ 12 V Step 1 Determine the reference node : bottom node Step 2 Assign the rest of the nodes with nodal voltages Note: only nodes with 3 or more branches are assigned v1v1 v2v2 Determine the current in every branch

7. Nodal Analysis Example 2 Determine the current in every branch 9k  3k  4k  6k  ++ 12 V v1v1 v2v2 Step 3 Write down equations using KCL for every non-reference node in terms of node voltages Step 4 Obtain the node voltages by solving the simultaneous equations in step 3

8. Nodal Analysis Example 3 6k  12k  3k   2i o 2mA ioio Circuit containing dependent current source Step 1 Determine the reference node Step 2 Assign the rest of the nodes with node voltages v1v1 v2v2

9. Nodal Analysis Example 3 6k  12k  3k   2i o 2mA ioio Circuit containing dependent current source v1v1 v2v2 Step 3 Write down equations using KCL for every non-reference node in terms of node voltages Step 4 Obtain the node voltages by solving the simultaneous equations in step 3