Superposition Theorem

It is an academic presentation slide about superposition theorem.

1. Submitted By: Imran Hossain Chowdhury ID:191-141-002 EEE,44 th Batch Superposition Theorem

2. Overview Definition Conditions to Apply Steps to Apply Example Usage

3. Definition Superposition Theorem states that voltage or current through an element of a linear, bilateral network having multiple sources is equivalent to the summation of generated voltage or current across that element, independently by each source present in the network. While at the time of considering a single source all other sources are replaced by their respective internal impedances. ‘ ‘ ‘ ‘

4. Conditions to Apply SPT   is applicable to both, AC and DC circuits. The elements in the circuit can be resistors(DC), capacitors or inductors(AC). Semiconductor devices like diodes are usually nonlinear, so cannot be applied SPT. SPT works for current and voltage, but not power.

5. Steps to Apply Turn off all independent sources except one. Redraw circuit. Solve for the voltages and currents in the new circuit. Turn off the active independent source and turn on one of the other independent sources. Repeat Steps 2 and 3. Continue until you have turned on each of the independent sources in the original circuit. To find the total voltage across each component and the total current flowing, add the contributions from each of the voltages and currents found in Step 3.

6. Steps to Apply

7. Example Find the current I using Superposition Theorem. I

8. Example Case-1: Only with Voltage Source I 1 = 20∠0/ (4 + j4) = 20∠0 / (5.65∠45) = 3.53∠- 45 or 2.49 –j2.49 A

9. Example Case-2 : Only with Current Source I 2 = 4∠90 × 4j/ (4 + j4) = 4∠90 × 4∠90 (5.65∠45) = 4∠90 × 0.707∠45 = 2.828∠135 or -1.99 + j1.99 A

10. Example Resultant Current: I = I 1 + I 2 = 3.53∠- 45 + 2.828∠135 = 0.785∠45 or 0.56 + j0.56 A

11. Usage Separating the contributions of the DC and AC independent sources. Example: To determine the performance of an amplifier, we calculate the DC voltages and currents to establish the bias point. The AC signal is usually what will be amplified. A generic amplifier has a constant DC operating point, but the AC signal’s amplitude and frequency will vary depending on the application.

12. Thank You