Lecture 9 Superposition

Superposition Theorem (1/2) In a linear system, the linear responses of linear independent sources can be combined in a linear manner. This allows us to solve circuits with one independent source at a time and then combine the solutions. If an independent voltage source is not present it is replaced by a short circuit. If an independent current source is not present it is replaced by an open circuit.

Superposition Theorem (2/2) If dependent sources exist, they must remain in the circuit for each solution. Nonlinear responses such as power cannot be found directly by superposition Only voltages and currents can be found by superposition

Superposition Example 1 (1/4) Find I1, I2 and Vab by superposition

Superposition Example 1 (2/4) Step 1: Omit current source. By Ohm’s law and the voltage divider rule:

Superposition Example 1 (3/4) Step 2: Omit voltage source. By the current divider rule and Ohm’s law :

Superposition Example 1 (4/4) Combining steps 1 & 2, we get:

Superposition Example 2 (1/5) Find Ix by superposition

Superposition Example 2 (2/5) Activate only the 16 A Current source at the left. Then use Current Divider Rule:

Superposition Example 2 (3/5) Activate only the 16 A Current source at the right. Then use Current Divider Rule:

Superposition Example 2 (4/5) Activate only the 64 V voltage source at the bottom. Then use Ohm’s Law:

Superposition Example 2 (5/5) Sum the partial currents due to each of the sources: