Superposition Theorem Objective of Lecture Introduce the superposition
Superposition Theorem
Objective of Lecture Introduce the superposition principle. Provide step-by-step instructions to apply superposition when calculating voltages and currents in a circuit that contains two or more power sources.
Superposition The voltage across a component is the algebraic sum of the voltage across the component due to each independent source acting upon it. The current flowing through a component is the algebraic sum of the current flowing through component due to each independent source acting upon it.
Steps 1. 2. 3. 4. 5. Turn on all independent sources , one at a time. Redraw circuit according to source type turned off. Solve for the voltages and currents in the new circuit. Repeat Steps 1 to 3. To find the total voltage across each component and the total current flowing, add the contributions from each of the voltages and currents found.
Turning Off Sources Voltage sources should be replaced with short circuits. A short circuit will allow current to flow across it, but the voltage across a short circuit is equal to 0 V. Current sources should be replaced with open circuits. An open circuit can have a non-zero voltage across it, but the current is equal to 0 A.
A Requirement for Superposition Use the same direction for current to flow through a component and the direction of the polarity (+ /_ signs) for the voltage across a component, when calculating these values in all of the subsequent circuits.
Example #1
Example #1 (con’t) Replace Is 1 and Is 2 with open circuits
Example #1 (con’t) Since R 2 is not connected to the rest of the circuit on both ends of the resistor, it can be deleted from the new circuit. Redraw circuit without R 2 in it.
Example #1 (con’t) Vs
Example #1 (con’t) Replace VS with a Short Circuit and Is 2 with an Open Circuit Redraw circuit. IS 1
Example #1 (con’t) IS 1 Note: The polarity of the voltage and the direction of the current through R 1 has to follow what was used in the first solution.
Example #1 (con’t) IS 1
Example #1 (con’t) IS 1
Example #1 (con’t) Replace VS with a Short Circuit and Is 1 with an Open Circuit IS 2
Example #1 (con’t) IS 2 R 2 and I 2 are not in parallel with R 1 and R 3. Since loop of I 1 and I 3 are connected at the same point, V across the terminal is zero. therefore I 1 = I 3 = 0 A.
Example #1 (con’t) IS 2
Example #1 Currents and voltages in original circuit with all sources turned on. I 1 I 2 I 3 Vs on +42. 9 m. A 0 +42. 9 m. A Is 1 on +0. 286 A -1 A -0. 714 A Is 2 on 0 A 2 A 0 A Total +0. 329 A +1 A -0. 671 A V 1 V 2 V 3 +2. 14 V 0 V 0. 857 V +14. 3 V -30 V -14. 3 V 0 V + 60 V 0 V 16. 4 V +30. 0 V -13. 4 V
Pspice Simulation
Summary Superposition can be used to find the voltages and currents in the circuit. To turn off a voltage source, replace it with a short circuit. To turn off a current source, replace it with an open circuit. Polarity of voltage across components and direction of currents through the components must be the same during each iteration through the circuit. The total of the currents and voltages from each iteration is the solution when all power sources are active in the circuit.
QUESTIONS? ? ?
- Slides: 21