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Reverted edits by 86.140.146.236 (talk) to last revision by Qwfp (HG)

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Reverted edits by 97.83.128.130 (talk) to last version by 216.8.148.170

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	~~Grateful~~ to ~~meet you! My~~ current ~~name~~ is ~~Eusebio Ledbetter~~. ~~To drive~~ is a ~~brand new thing that~~ I'~~m completely addicted to~~. ~~South Carolina~~ is ~~where~~ [~~http~~:/~~/www~~.~~dailymail~~.co.uk/~~home~~/~~search~~.~~html?sel=site&searchPhrase=options options] home~~ is ~~and We all don~~'~~t plan on converting~~ to it. I used ~~to be unemployed but~~ at the ~~moment I am~~ a ~~cashier~~ but the ~~promotion for no reason comes~~. I'~~m not good at web development but you might choose~~ to to ~~check my website~~: ~~http~~://~~prometeu~~.~~net~~/<br><br>~~my web blog~~ :: ~~clash~~ of ~~clans hack android;~~ [http://~~prometeu~~.~~net~~/ ~~my website~~],		{{About\|the theorem in electrical circuits\|Norton's theorem for queueing networks\|flow-equivalent server method}}
			Known in Europe as the '''Mayer–Norton theorem''', '''Norton's theorem''' holds, to illustrate in DC [[circuit theory]] terms, that (see image):
			:*Any [[linearity\|linear]] [[electrical network]] with [[voltage source\|voltage]] and [[current source\|current]] sources and only [[resistance (electricity)\|resistance]]s can be replaced at terminals A-B by an equivalent current source I<sub>NO</sub> in [[series and parallel circuit\|parallel]] connection with an equivalent resistance R<sub>NO</sub>.
			:*This equivalent current I<sub>NO</sub> is the current obtained at terminals A-B of the network with terminals A-B [[short circuit]]ed.
			:*This equivalent resistance R<sub>NO</sub> is the resistance obtained at terminals A-B of the network with all its voltage sources [[short circuit]]ed and all its current sources [[open circuit]]ed.

			For AC systems the theorem can be applied to [[Reactive power\|reactive]] [[Electrical impedance\|impedance]]s as well as resistances.

			The '''Norton equivalent''' circuit is used to represent any network of linear sources and impedances at a given [[frequency]].
			[[File:Norton equivelant.png\|thumb\|alt=text\|Any [[Black box (systems)\|black box]] containing resistances only and voltage and current sources can be replaced by an [[equivalent circuit]] consisting of an equivalent current source in parallel connection with an equivalent resistance.]]

			Norton's theorem and its dual, [[Thévenin's theorem]], are widely used for circuit analysis simplification and to study circuit's initial-condition and steady-state response.

			Norton's theorem was independently derived in 1926 by [[Siemens\|Siemens & Halske]] researcher [[Hans Ferdinand Mayer]] (1895–1980) and [[Bell Labs]] engineer [[Edward Lawry Norton]] (1898–1983).<ref>Mayer</ref><ref>Norton</ref><ref>Johnson (2003b)</ref><ref>Brittain</ref><ref>Dorf</ref>

			To find the equivalent,

			# Find the Norton current ''I''<sub>No</sub>. Calculate the output current, ''I''<sub>AB</sub>, with a [[short circuit]] as the [[External electric load\|load]] (meaning 0 resistance between A and B). This is I<sub>No</sub>.
			# Find the Norton resistance ''R''<sub>No</sub>. When there are no [[dependent source]]s (all current and voltage sources are independent), there are two methods of determining the Norton impedance ''R''<sub>No</sub>.
			::* Calculate the output voltage, ''V''<sub>AB</sub>, when in [[Open-circuit voltage\|open circuit]] condition (i.e., no load resistor — meaning infinite load resistance). ''R''<sub>No</sub> equals this V<sub>AB</sub> divided by I<sub>No</sub>.
			::or
			::* Replace independent voltage sources with short circuits and independent current sources with open circuits. The total resistance across the output port is the Norton impedance ''R''<sub>No</sub>.

			This is equivalent to calculating the Thevenin resistance.
			:However, when there are dependent sources, the more general method must be used. This method is not shown below in the diagrams.
			::* Connect a constant current source at the output terminals of the circuit with a value of 1 Ampere and calculate the voltage at its terminals. This voltage divided by the 1 A current is the Norton impedance ''R''<sub>No</sub>. This method must be used if the circuit contains dependent sources, but it can be used in all cases even when there are no dependent sources.

			==Example of a Norton equivalent circuit==
			{\|
			\|-
			\|[[Image:Thevenin and norton step 1.png\|framed\|Step 0: The original circuit]] \|\| [[Image:Norton step 2.png\|framed\|Step 1: Calculating the equivalent output current]] \|\| [[Image:Thevenin and norton step 3.png\|framed\|Step 2: Calculating the equivalent resistance]]
			\|}
			[[Image:Norton step 4.png\|framed\|right\|Step 3: The equivalent circuit]]

			In the example, the total current ''I''<sub>total</sub> is given by:

			:<math>
			I_\mathrm{total} = {15 \mathrm{V} \over 2\,\mathrm{k}\Omega + (1\,\mathrm{k}\Omega \\| (1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega))} = 5.625 \mathrm{mA}.
			</math>

			The current through the load is then, using the [[current divider rule]]:

			:<math>
			I_\mathrm{No} = {1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega \over (1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega)} \cdot I_\mathrm{total}
			</math>
			:<math>
			= 2/3 \cdot 5.625 \mathrm{mA} = 3.75 \mathrm{mA}.
			</math>

			And the equivalent resistance looking back into the circuit is:

			:<math>
			R_\mathrm{eq} = 1\,\mathrm{k}\Omega + (2\,\mathrm{k}\Omega \\| (1\,\mathrm{k}\Omega + 1\,\mathrm{k}\Omega)) = 2\,\mathrm{k}\Omega.
			</math>

			So the equivalent circuit is a 3.70 mA current source in parallel with a 2 kΩ resistor.

			==Conversion to a Thévenin equivalent==
			[[Image:Thevenin to Norton2.PNG\|right]]

			A Norton equivalent circuit is related to the [[Thévenin theorem\|Thévenin equivalent]] by the following equations:
			:<math>R_{Th} = R_{No} \!</math>

			:<math>V_{Th} = I_{No} R_{No} \!</math>

			:<math>\frac{V_{Th}}{R_{Th}} = I_{No}\!</math>

			==Queueing theory==
			The passive circuit equivalent of "Norton's theorem" in [[queuing theory]] is called the Chandy Herzog Woo theorem.<ref>Johnson (2003a)</ref><ref>Gunther</ref> In a [[reversible queueing system]], it is often possible to replace an uninteresting subset of queues by a single ([[FCFS]] or [[Processor sharing\|PS]]) queue with an appropriately chosen service rate.<ref>Chandy et al.</ref>

			== See also ==
			*[[Millman's theorem]]
			*[[Source transformation]]
			*[[Superposition theorem]]
			*[[Thévenin's theorem]]
			*[[Maximum power transfer theorem]]
			*[[Extra element theorem]]
			==References==
			{{reflist}}
			==Bibliography==
			*{{cite journal\|last=Brittain\|first=J.E.\|title=Thevenin's theorem\|journal=IEEE Spectrum\|date=March 1990\|volume=27\|issue=3\|page=42\|doi=10.1109/6.48845\|url=http://ieeexplore.ieee.org/search/searchresult.jsp?newsearch=true&queryText=James+E.+Brittain+Thevenin%27s+theorem&.x=41&.y=17\|accessdate=1 February 2013}}
			*{{cite journal\|last=Chandy\|first=K. M.\|coauthors=Herzog, U.; Woo, L.\|title=Parametric Analysis of Queuing Networks\|journal=IBM Journal of Research and Development\|date=Jan 1975\|volume=19\|issue=1\|pages=36–42\|doi=10.1147/rd.191.0036\|url=http://scholar.google.ca/scholar_url?hl=en&q=http://citeseerx.ist.psu.edu/viewdoc/download%3Fdoi%3D10.1.1.93.9312%26rep%3Drep1%26type%3Dpdf&sa=X&scisig=AAGBfm1HEBU-rSFYLTIePQWPitczchOopA&oi=scholarr&ei=L3wQUfP9DOHWiwKYtICQAQ&ved=0CC4QgAMoADAA}}
			*{{cite conference\|last=Dorf\|first=Richard C.\|coauthors=Svoboda, James A.\|title=Chapter 5 – Circuit Theorems\|booktitle=Introduction to Electric Circuits\|year=2010\|publisher=John Wiley & Sons\|location=Hoboken, NJ\|isbn=978-0-470-52157-1\|url=http://ca.wiley.com/WileyCDA/WileyTitle/productCd-EHEP000347.html\|edition=8th\|pages=162-207}}
			*{{cite book\|last=Gunther\|first=N.J.\|title=Analyzing computer systems performance : with PERL::PDQ\|year=2004\|publisher=Springer\|location=Berlin\|isbn=3-540-20865-8\|page=281\|edition=Online-Ausg.\|url=http://books.google.com/?id=rp1EZKnr48kC&pg=PA83#v=onepage&q&f=false}}
			*{{cite journal\|last=Johnson\|first=D.H.\|title=Origins of the equivalent circuit concept: the voltage-source equivalent\|journal=Proceedings of the IEEE\|year=2003\|volume=91\|issue=4\|pages=636–640\|doi=10.1109/JPROC.2003.811716\|url=http://www.ece.rice.edu/~dhj/paper1.pdf}}
			*{{cite journal\|last=Johnson\|first=D.H.\|title=Origins of the equivalent circuit concept: the current-source equivalent\|journal=Proceedings of the IEEE\|year=2003\|volume=91\|issue=5\|pages=817–821\|doi=10.1109/JPROC.2003.811795\|url=http://www.ece.rice.edu/~dhj/paper2.pdf}}
			*{{cite journal\|last=Mayer\|first=H. F.\|title=Ueber das Ersatzschema der Verstärkerröhre (On equivalent circuits for electronic amplifiers]\|journal=Telegraphen- und Fernsprech-Technik\|year=1926\|volume=15\|pages=335–337}}
			*{{cite journal\|last=Norton\|first=E. L.\|title=Technical Report TM26–0–1860 – Design of finite networks for uniform frequency characteristic\|year=1926\|publisher=Bell Laboratories}}

			== External links ==
			* [http://www.allaboutcircuits.com/vol_1/chpt_10/9.html Norton's theorem at allaboutcircuits.com]

			[[Category:Circuit theorems]]

142.39.230.100: reverting vandalism

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Grateful to meet you! My current name is Eusebio Ledbetter. To drive is a brand new thing that I'm completely addicted to. South Carolina is where [http://www.dailymail.co.uk/home/search.html?sel=site&searchPhrase=options options] home is and We all don't plan on converting to it. I used to be unemployed but at the moment I am a cashier but the promotion for no reason comes. I'm not good at web development but you might choose to to check my website: http://prometeu.net/<br><br>my web blog :: clash of clans hack android; [http://prometeu.net/ my website],

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en>Smalljim: Reverted edits by 86.140.146.236 (talk) to last revision by Qwfp (HG)

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142.39.230.100: reverting vandalism