Superposition theorem
This article is about the superposition theorem in electrical circuits. For other
uses, see Superposition (disambiguation).
The superposition theorem is a derived result of the superposition
principle suited to the network analysis of electrical circuits. The
superposition theorem states that for a linear system (notably including the
subcategory of time-invariant linear systems) 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, where all the 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:
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)).
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.
The theorem is 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.
Superposition works for voltage and current but not power. In other words, the
sum of the powers of each source with the other sources turned off is not the
real consumed power. To calculate power we first use superposition to find
both current and voltage of each linear element and then calculate the sum of
the multiplied voltages and currents.
However, if the linear network is operating in steady-state and each external
independent source has a different frequency, then superposition can be
applied to compute the average power or active power. If at least two
[1]
independent sources have the same frequency (for example in power systems,
where many generators operate at 50 Hz or 60 Hz), then superposition can't be
used to determine average power.
This article is about the superposition theorem in electrical circuits. For other
uses, see Superposition (disambiguation).
The superposition theorem is a derived result of the superposition
principle suited to the network analysis of electrical circuits. The
superposition theorem states that for a linear system (notably including the
subcategory of time-invariant linear systems) 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, where all the 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:
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)).
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.
The theorem is 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.
Superposition works for voltage and current but not power. In other words, the
sum of the powers of each source with the other sources turned off is not the
real consumed power. To calculate power we first use superposition to find
both current and voltage of each linear element and then calculate the sum of
the multiplied voltages and currents.
However, if the linear network is operating in steady-state and each external
independent source has a different frequency, then superposition can be
applied to compute the average power or active power. If at least two
[1]
independent sources have the same frequency (for example in power systems,
where many generators operate at 50 Hz or 60 Hz), then superposition can't be
used to determine average power.
