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| '''Source transformation''' is simplifying a circuit solution, especially with mixed sources, by transforming a voltage into a [[Electric current|current]] source, and vice versa.<ref name="Oppenheimer">Oppenheimer, Samuel L. (1984). ''Fundamentals of Electric Circuits''. New Jersey: Prentice Hall.</ref> Finding a solution to a circuit can be difficult without using methods such as this to make the circuit appear simpler. Source transformation is an application of [[Thévenin's theorem]] and [[Norton's theorem]].
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| == 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 replace it with a [[current source]] in [[parallel circuit|parallel]] with the same resistance. Remember that Ohm's law states that a voltage on a material is equal to the material's resistance times the amount of current through it (V=IR). Since source transformations are bilateral, one can be derived from the other. <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 however. They can be performed on a circuit involving [[capacitors]] and [[inductors]], as long as the circuit is first put into 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]].
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| Specifically, 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, suppose we have a real current source I, which is an ideal current source in [[Series and parallel circuits|parallel]] with an [[Electrical impedance|impedance]]. If the ideal current source is rated at I amperes, and the parallel resistor has an impedance Z, then applying a source transformation gives an equivalent real voltage source, which is ideal, and in [[Series and parallel circuits|series]] with the impedance. This new voltage source V, has a value equal to the ideal current source's value times the resistance contained in the real current source <math>V=I*Z</math>. The impedance component of the real voltage source retains its real current source value.
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| In general, source transformations can be summarized by keeping two things in mind:
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| * [[Ohm's Law]]
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| * Impedances remain the same
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| == Example calculation ==
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| Source transformations are easy to perform as long as there is a familiarity with [[Ohms Law]]. If there is a voltage source in [[series circuit|series]] with an [[Electrical impedance|impedance]], it is possible to find the value of the equivalent [[current source]] in [[parallel circuit|parallel]] with the impedance by dividing the value of the voltage source by the value of the impedance. The converse also applies here: if a current source in parallel with an impedance is present, multiplying the value of the current source with the value of the impedance will result in the equivalent voltage source in series with the impedance. A visual example of what is being done during a source transformation can be seen in Figure 1.
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| '''Remember:'''
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| <br style="clear:both;"/>
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| <br style="clear:both;"/>
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| <math>V=I*Z</math>
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| <br style="clear:both;"/>
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| <br style="clear:both;"/>
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| <math>I=\cfrac {V}{Z} </math>
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| [[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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| == See also ==
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| * [[Ohms Law]]
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| * [[Thévenin's theorem]]
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| * [[current source]]
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| * [[voltage source]]
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| * [[electrical impedance]]
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| ==References==
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| <references/>
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| [[Category:Electrical engineering]]
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| [[Category:Electronic engineering]]
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| [[Category:Electrical circuits]]
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| [[Category:Electronic circuits]]
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| [[Category:Electronic design]]
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| [[Category:Circuit theorems]]
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