2.7:
Superposition Theorem
The superposition theorem is used in circuits with multiple independent sources.
To apply this theorem, keep one independent source at a time while replacing the inactive voltage source with a short-circuit and the inactive current source with an open-circuit, respectively.
The theorem states that the voltage across or the current through an element in a linear circuit is the algebraic sum of the contributions from the independent sources.
Consider a circuit with a voltage and a current source, where the voltage drop across a resistor must be determined.
The voltage drop has contributions from both independent sources.
The contribution of the voltage source is obtained by setting the current source to zero.
By applying Kirchhoff's voltage law, the loop current is determined. Using Ohm's law, the voltage drop is calculated.
Similarly, the current source contribution is obtained by setting the voltage source to zero.
Combining the resistors, the equivalent resistance is obtained. Using the current division rule and Ohm's law, the voltage drop is determined.
Finally, by adding the contributions from independent sources, the total voltage drop across the resistor is obtained.
2.7:
Superposition Theorem
The superposition principle is a fundamental concept stating that in a linear circuit, the voltage across (or current through) an element can be determined by summing the individual contributions of each independent source acting in isolation. When dealing with linear circuits containing multiple independent sources, this principle serves as a valuable tool for analysis. To apply the superposition principle effectively, one should focus on a single independent source at a time while deactivating all others. This approach yields the output (voltage or current) resulting from the active source.
The cumulative effect of all active sources can then be determined by algebraically adding their individual contributions. This simplifies the circuit analysis process. Notably, dependent sources remain unaffected as they are governed by circuit variables. It is worth noting that utilizing the superposition principle can lead to increased analytical effort. For example, when dealing with a circuit featuring three independent sources, one must analyze three separate, simplified circuits, each representing the contribution of an individual source. Despite this potential drawback, the superposition principle remains a valuable technique for simplifying complex circuits by replacing voltage sources with short circuits and current sources with open circuits.