Superposition theorem

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

The superposition theorem for electric circuits states that the total current in any branch of a bilateral linear circuit equals the algebraic sum of the currents produced by each source acting separately throughout the circuit.

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

replacing all other voltage sources with a short circuit (thereby eliminating difference of potential. i.e. V=0)
replacing all other current sources with an open circuit (thereby eliminating flow of current. i.e. I=0)

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

[edit] Bipolar Junction Transistor (BJT) networks

The superposition theorem also is applicable for the analysis and design of the dc and ac components of a BJT network, permitting the separation of the analysis of the dc and ac responses of the system.

Circuits utilizing voltage controlled devices such as the JFET and IGFET are treated differently because transconductance functions are involved. This means that the currents flowing in different branches do not "superpose" in the usual manner (because some currents are voltage-controlled from other branches of the circuit), so superposition cannot be used directly on the complete circuit. This same limitation applies to vacuum tube circuits. Superposition Theorem The total current in any part of a linear circuit equals the algebraic sum of the currents produced by each source separately. To evaluate the separate currents to be combined, replace all other voltage sources by short circuits and all other current sources by open circuits