Source transformation: Difference between revisions

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{{Short description|Process of simplifying circuit solutions}}

{{about|electronic circuits|transformation of source code|Program transformation}}

'''Source transformation''' is the process of simplifying a circuit solution, especially with mixed sources, by transforming [[voltage]] sources into [[Electric current|current]] sources, and vice versa.<ref name="Oppenheimer">Oppenheimer, Samuel L. (1984). ''Fundamentals of Electric Circuits''. New Jersey: Prentice Hall.</ref> This method is used to simplify complex circuits, which may be otherwise difficult to solve by hand. Source transformation is an application ofusing [[Thévenin's theorem]] and [[Norton's theorem]] respectively.<ref name="CPP">CPP. https://www.cpp.edu/~elab/projects/project_08/index.html.</ref>

== Process ==

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Performing a source transformation consists of using [[Ohm's law]] to take an existing [[voltage source]] in [[series circuit|series]] with a [[resistor|resistance]], and replacing it with a [[current source]] in [[parallel circuit|parallel]] with the same resistance, or vice versa. The transformed sources are considered identical and can be substituted for one another in a circuit.<ref name="Nilsson">Nilsson, James W., & Riedel, Susan A. (2002). ''Introductory Circuits for Electrical and Computer Engineering''. New Jersey: Prentice Hall.</ref>

Source transformations are not limited to resistive circuits. They can be performed on a circuit involving [[capacitors]] 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.<ref>{{Cite book |last1=Ulaby |first1=Fawwaz T. |title=CIRCUITS-W/ACCESS |last2=Maharbiz |first2=Michel |last3=Furse |first3=Cynthia |author3-link=Cynthia Furse|date=2015-01-01 |publisher=National Technology & Science Press |isbn=978-1-934891-22-3 |edition=3rd |language=English}}</ref>

Source transformations are used to exploit the equivalence of a real current source and a real voltage source, such as a [[battery (electricity)|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 <math>I</math> in [[Series and parallel circuits|parallel]] with an [[Electrical impedance|impedance]] <math>Z</math>, applying a source transformation gives an equivalent real voltage source, which is an ideal voltage source in [[Series and parallel circuits|series]] with the impedance. The impedance <math>Z</math> retains its value and the new voltage source <math>V</math> has value equal to the ideal current source's value times the impedance, according to Ohm's Law <math>V=I* \, Z</math>. 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 <math> I = V/Z </math>.

== Example calculation ==

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:: <math> V = I\cdot Z, \qquad I = \cfrac VZ</math>

[[Image:Sourcetrans.jpg||frame|left|Figure 1. An example of a DC source transformation. Notice that the impedance Z is the same in both configurations.]]

[[Image:Sourcetrans.jpg||frame|left|Figure 1. An example of a DC source transformation. Notice that the impedance Z is the same in both configurations.]]

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