Superposition theorem:
The superposition theorem states that the response (voltage or current) across any element in a linear circuit can be determined by considering the individual effects of each independent source, one at a time, while setting all other independent sources to zero.
The superposition is a fundamental principle in electrical circuit analysis.
Representation of source:
We consider voltage source as a short circuit and current source as a open circuit.
Superposition theorem only applicable linear bilateral network.
It is important to note that the superposition theorem is only applicable to linear circuits, where the response is directly proportional to the applied stimuli (sources) and follows the principles of superposition. Nonlinear elements, such as diodes or transistors, cannot be analyzed using the superposition theorem.
Mathematically, the superposition theorem can be expressed as follows:
Consider a linear circuit with multiple independent sources (voltage or current sources) and resistors. Let's assume there are 'n' independent sources in the circuit.
1. For each independent source, assume all other independent sources are turned off (replaced by their internal resistances if applicable). This means setting the voltage sources to zero or the current sources to open circuit.
2. Calculate the response (voltage or current) across the desired element in the circuit using the reduced circuit obtained from step 1. This can be done using standard circuit analysis techniques such as Ohm's law, Kirchhoff's laws, or any other appropriate method.
3. Repeat steps 1 and 2 for each independent source, considering them one at a time.
4. Finally, the total response across the desired element is obtained by summing up the individual responses calculated in step 2, taking into account their polarities.
Mathematically, the superposition theorem can be represented as:
V_total = Σ(V_i)
where V_total is the total response across the desired element, V_i is the response due to the ith independent source, and the summation is performed over all independent sources in the circuit.
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