Superposition theorem

Essentially, that it is permissible, if there are two or more sources of electromotive force in a linear electrical network, to compute at any element of the network the response of voltage or of current that results from one source alone, and then the response resulting from another source alone, and so on for all sources, and finally to compute the total response to all sources acting together by adding these individual responses.

Thus, if a load of constant resistance is supplied with electrical energy from a linear network containing two batteries, two generators, or one battery and one generator, it would be correct to find the current that would be supplied to the load by one source (the other being reduced to zero), then to find the current that would be supplied to the load by the second source (the first source now being reduced to zero), and finally to add the two currents so computed to find the total current that would be produced in the load by the two sources acting simultaneously.

By means of the principle of superposition, effects are added instead of causes. This principle seems so intuitively valid that there is far greater danger of applying superposition where it is incorrect than of failing to apply it where it is correct. It must be recognized that for superposition to be correct the relation between cause and effect must be linear.

This article is about the superposition theorem in electrical circuits. For other uses, see superposition.

The superposition theorem for electrical circuits states that the response (Voltage or Current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, while all other independent sources are replaced by their internal impedances.

To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:

1. Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential. i.e. V=0, internal impedance of ideal voltage source is ZERO (short circuit)).
2. Replacing all other independent current sources with an open circuit (thereby eliminating current. i.e. I=0, internal impedance of ideal current source is infinite (open circuit).

This procedure is followed for each source in turn, then the resultant responses are added to determine the true operation of the circuit. The resultant circuit operation is the superposition of the various voltage and current sources.

The superposition theorem is very important in circuit analysis. It is used in converting any circuit into its Norton equivalent or Thevenin equivalent.

Applicable to linear networks (time varying or time invariant) consisting of independent sources, linear dependent sources, linear passive elements Resistors, Inductors, Capacitors and linear transformers.

External links

• All About Circuits - gives its own explanation of the superposition theorem.
• On the Application of Superposition to Dependent Sources in Circuit Analysis - proves superposition of dependent sources is valid.

References

• Electronic Devices and Circuit Theory 9th ed. by Boylestad and Nashelsky

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