Source transformation is the process of simplifying a circuit solution, especially with mixed sources, by transforming
voltage sources into
current sources, and vice versa, using
Thévenin's theorem and
Norton's theorem respectively.
[CPP. https://www.cpp.edu/~elab/projects/project_08/index.html.]
Process
Performing a source transformation consists of using
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
to take an existing
voltage source in
series with a
resistance
Resistance may refer to:
Arts, entertainment, and media Comics
* Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm:
** ''Resistance'' (comics), based on the video game of the same title
** ''T ...
, and replacing it with a
current source in
parallel with the same resistance, or vice versa. The transformed sources are considered identical and can be substituted for one another in a circuit.
[Nilsson, James W., & Riedel, Susan A. (2002). ''Introductory Circuits for Electrical and Computer Engineering''. New Jersey: Prentice Hall.]
Source transformations are not limited to resistive circuits. They can be performed on a circuit involving
capacitors
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of a ...
and
inductors as well, by expressing circuit elements as impedances and sources in the
frequency domain. In general, the concept of source transformation is an application of
Thévenin's theorem to a
current source, or
Norton's theorem to a
voltage source. However, this means that source transformation is bound by the same conditions as Thevenin's theorem and Norton's theorem; namely that the load behaves linearly, and does not contain dependent voltage or current sources.
Source transformations are used to exploit the equivalence of a real current source and a real voltage source, such as a
battery. Application of Thévenin's theorem and Norton's theorem gives the quantities associated with the equivalence. Specifically, given a real current source, which is an ideal current source
in
parallel with an
impedance , applying a source transformation gives an equivalent real voltage source, which is an ideal voltage source in
series with the impedance. The impedance
retains its value and the new voltage source
has value equal to the ideal current source's value times the impedance, according to Ohm's Law
. In the same way, an ideal voltage source in series with an impedance can be transformed into an ideal current source in parallel with the same impedance, where the new ideal current source has value
.
Example calculation
Source transformations are easy to compute using
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
. If there is a voltage source in
series with an
impedance, it is possible to find the value of the equivalent
current source in
parallel with the impedance by dividing the value of the voltage source by the value of the impedance. The converse also holds: if a current source in parallel with an impedance is present, multiplying the value of the current source with the value of the impedance provides the equivalent voltage source in series with the impedance. A visual example of a source transformation can be seen in Figure 1.
::
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A brief proof of the theorem
The transformation can be derived from the
uniqueness theorem. In the present context, it implies that a black box with two terminals must have a unique well-defined relation between its voltage and current. It is readily to verify that the above transformation indeed gives the same V-I curve, and therefore the transformation is valid.
See also
*
Ohm's Law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
*
Thévenin's theorem
*
Current source
*
Voltage source
*
Electrical impedance
References
Electrical engineering
Electronic engineering
Electrical circuits
Electronic circuits
Electronic design
Circuit theorems