HOME

TheInfoList



OR:

Source transformation is the process of simplifying a circuit solution, especially with mixed sources, by transforming
voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
sources into current sources, and vice versa, using
Thévenin's theorem As originally stated in terms of direct-current resistance (electricity), resistive circuits only, Thévenin's theorem states that ''"Any linear circuit, linear electrical network containing only voltage source, voltage sources, current source, c ...
and
Norton's theorem In Direct current, direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to Electrical network, networks made of Linear time-invariant system, linear time-invariant Resi ...
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 electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...
to take an existing
voltage source A voltage source is a two-terminal (electronics), terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output Electric current, current. However, a r ...
in
series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used i ...
with a resistance, and replacing it with a
current source A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the dual of a voltage source. The term ''current sink'' is sometimes used for sources fed ...
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 In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...
and inductors as well, by expressing circuit elements as impedances and sources in the
frequency domain In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time ser ...
. In general, the concept of source transformation is an application of
Thévenin's theorem As originally stated in terms of direct-current resistance (electricity), resistive circuits only, Thévenin's theorem states that ''"Any linear circuit, linear electrical network containing only voltage source, voltage sources, current source, c ...
to a
current source A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the dual of a voltage source. The term ''current sink'' is sometimes used for sources fed ...
, or
Norton's theorem In Direct current, direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to Electrical network, networks made of Linear time-invariant system, linear time-invariant Resi ...
to a
voltage source A voltage source is a two-terminal (electronics), terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output Electric current, current. However, a r ...
. 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 I in parallel with an impedance Z, applying a source transformation gives an equivalent real voltage source, which is an ideal voltage source in
series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used i ...
with the impedance. The impedance Z retains its value and the new voltage source V has value equal to the ideal current source's value times the impedance, according to Ohm's Law V=I \, Z. 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 I = V/Z .


Example calculation

Source transformations are easy to compute using
Ohm's law Ohm's law states that the electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...
. If there is a voltage source in
series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used i ...
with an impedance, it is possible to find the value of the equivalent
current source A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the dual of a voltage source. The term ''current sink'' is sometimes used for sources fed ...
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. :: V = I\cdot Z, \qquad I = \cfrac VZ {{clear


A brief proof of the theorem

The transformation can be derived from the
uniqueness theorem In mathematics, a uniqueness theorem, also called a unicity theorem, is a theorem asserting the uniqueness of an object satisfying certain conditions, or the equivalence of all objects satisfying the said conditions. Examples of uniqueness theorems ...
. 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 electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...
*
Thévenin's theorem As originally stated in terms of direct-current resistance (electricity), resistive circuits only, Thévenin's theorem states that ''"Any linear circuit, linear electrical network containing only voltage source, voltage sources, current source, c ...
*
Current source A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the dual of a voltage source. The term ''current sink'' is sometimes used for sources fed ...
*
Voltage source A voltage source is a two-terminal (electronics), terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output Electric current, current. However, a r ...
*
Electrical impedance In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of Electrical_resistance, resistance and Electrical_reactance, reactance in a electrical circuit, circuit. Quantitatively, the impedan ...


References

Electrical engineering Electronic engineering Electrical circuits Electronic circuits Electronic design Circuit theorems