Superposition Theorem

According to the superposition theorem, the response across each element in a linear, active, bilateral network with more than one source is the sum of the responses obtained from each source evaluated independently, and all other sources are replaced by their internal resistance. When two or more sources are present and connected, the superposition theorem is utilised to solve the network.

In other words, if a number of voltage or current sources act in a linear network, the total current in any branch is the algebraic sum of all the currents that would be produced if each source acted independently while all the other independent sources were replaced by their internal resistances.

It only applies to circuits that meet the ohm’s law requirements (i.e., for the linear circuit).

Linear circuit

A linear circuit is an electrical circuit that operates on the superposition principle. Any linear circuit can benefit from the superposition theorem. When numerous independent sources are present, the voltages and currents created by each can be calculated independently and then added algebraically. This eliminates the need to write a series of loop or node equations, making calculations easier.

When the voltage or current in the circuit is increased, the values of electronic parts (such as resistance, capacitance, inductance, gain, and so on) do not change. Linear circuits are advantageous because they can enhance and process electronic signals with minimal distortion. A sound system is an example of linear circuit-based electronic equipment.

Superposition theorem

The assumption of linearity between the response and excitation of an electrical circuit underpins the superposition theorem. It asserts that when numerous independent sources act at the same time in a linear circuit, the response in that branch is equal to the total of the responses owing to each independent source acting at a time.

Only one independent source will be considered at a time in this procedure. As a result, the remaining independent sources must be removed from the circuit. The voltage sources can be eliminated by shorting their two terminals, and the current sources can be eliminated by opening their two terminals.

Steps to apply Superposition theorem

i.The initial step is to choose one source among the many available in the bilateral network. Any one of the circuit’s multiple sources can be taken into consideration initially.

ii.All sources must be changed by their internal impedance, with the exception of the specified source.

iii.Evaluate the current flowing through or the voltage drop across a specific network node using a network simplification approach.

iv.The same applies to all other sources in the circuit when evaluating a single source.

v.After you’ve gotten the results for each individual source, add them all up to get the overall voltage drop or current across the circuit element.

Limitations of superposition theorem

·Non-linear circuits are not covered by the theorem. Because linearity is required, the Superposition Theorem can only be used to calculate voltage and current, but not power. When only one source is considered at a time, power dissipation is a nonlinear function that does not add up to an accurate total algebraically.

·The superposition theorem demands the presence of two or more sources in the circuit.

Conclusion

When adding up each source’s individual contributions, be careful when assigning signs to the quantities. Each unknown quantity should be assigned a reference direction. A positive sign in the total indicates that a contribution from a source is in the same direction as the reference direction; a negative sign indicates that it is in the opposite direction.

All of the components of a circuit must be linear to employ the superposition theorem with currents and voltages.

It’s worth noting that the superposition theorem doesn’t apply to power because it isn’t a linear quantity.