Superposition theorem

# Superposition theorem

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The superposition theorem for electrical circuits
Electrical network
An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current...

states that the response (Voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points â€” or the difference in electric potential energy per unit charge between two points...

or Current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

) 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
Electrical impedance
Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

.

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 source
Voltage source
In electric circuit theory, an ideal voltage source is a circuit element where the voltage across it is independent of the current through it. A voltage source is the dual of a current source. In analysis, a voltage source supplies a constant DC or AC potential between its terminals for any current...

s with a short circuit
Short circuit
A short circuit in an electrical circuit that allows a current to travel along an unintended path, often where essentially no electrical impedance is encountered....

(thereby eliminating difference of potential. i.e. V=0, internal impedance of ideal voltage source
Voltage source
In electric circuit theory, an ideal voltage source is a circuit element where the voltage across it is independent of the current through it. A voltage source is the dual of a current source. In analysis, a voltage source supplies a constant DC or AC potential between its terminals for any current...

is ZERO (short circuit
Short circuit
A short circuit in an electrical circuit that allows a current to travel along an unintended path, often where essentially no electrical impedance is encountered....

)).
2. Replacing all other independent current source
Current source
A current source is an electrical or electronic device that delivers or absorbs electric current. A current source is the dual of a voltage source. The term constant-current sink is sometimes used for sources fed from a negative voltage supply...

s with an open circuit
Open circuit
The term Open circuit may refer to:*Open-circuit scuba, a type of SCUBA-diving equipment where the user breathes from the set and then exhales to the surroundings without recycling the exhaled air...

(thereby eliminating current. i.e. I=0, internal impedance of ideal current source
Current source
A current source is an electrical or electronic device that delivers or absorbs electric current. A current source is the dual of a voltage source. The term constant-current sink is sometimes used for sources fed from a negative voltage supply...

is infinite (open circuit
Open circuit
The term Open circuit may refer to:*Open-circuit scuba, a type of SCUBA-diving equipment where the user breathes from the set and then exhales to the surroundings without recycling the exhaled air...

).

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 Resistor
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...

s, Inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...

s, Capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

s and linear transformer
Transformer
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductorsâ€”the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field...

s.