- Thévenin's theorem
In electrical circuit theory,

**Thévenin's theorem**for linearelectrical network s states that any combination ofvoltage source s,current source s andresistor s with two terminals is electrically equivalent to a single voltage source "V" and a single series resistor "R". For single frequency AC systems the theorem can also be applied to general impedances, not just resistors. The theorem was first discovered by German scientistHermann von Helmholtz in 1853, but was then rediscovered in 1883 by French telegraph engineer Léon Charles Thévenin (1857 -1926 ).This theorem states that a circuit of voltage sources and resistors can be converted into a

**Thévenin equivalent**, which is a simplification technique used in circuit analysis. The Thévenin equivalent can be used as a good model for a power supply or battery (with the resistor representing theinternal impedance and the source representing theelectromotive force ). The circuit consists of an idealvoltage source in series with an idealresistor .**Calculating the Thévenin equivalent**To calculate the equivalent circuit, one needs a resistance and some voltage - two unknowns. And so, one needs two equations. These two equations are usually obtained by using the following steps, but any conditions one places on the terminals of the circuit should also work:

# Calculate the output voltage, "V"

_{AB}, when inopen circuit condition (no load resistor - meaning infinite resistance). This is "V"_{Th}.

# Calculate the output current, "I"_{AB}, when those leads are short circuited (load resistance is 0). "R"_{Th}equals "V"_{Th}divided by this "I"_{AB}.

* The equivalent circuit is a voltage source with voltage "V"_{Th}in series with a resistance "R"_{Th}.Step 2 could also be thought of like this: :2a. Now replace voltage sources with short circuits and current sources with open circuits.:2b. Replace the load circuit with an imaginary ohm meter and measure the total resistance, "R", "looking back" into the circuit. This is "R"

_{Th}.The Thévenin-equivalent voltage is the voltage at the output terminals of the original circuit. When calculating a Thévenin-equivalent voltage, the

voltage divider principle is often useful, by declaring one terminal to be "V"_{out}and the other terminal to be at the ground point.The Thévenin-equivalent resistance is the resistance measured across points A and B "looking back" into the circuit. It is important to first replace all voltage- and current-sources with their internal resistances. For an ideal voltage source, this means replace the voltage source with a short circuit. For an ideal current source, this means replace the current source with an open circuit. Resistance can then be calculated across the terminals using the formulae for

series and parallel circuits .**Example**In the example, calculating equivalent voltage:

:$V\_mathrm\{AB\}=\; \{R\_2\; +\; R\_3\; over\; (R\_2\; +\; R\_3)\; +\; R\_4\}\; cdot\; V\_mathrm\{1\}$

::$=\; \{1,mathrm\{k\}Omega\; +\; 1,mathrm\{k\}Omega\; over\; (1,mathrm\{k\}Omega\; +\; 1,mathrm\{k\}Omega)\; +\; 2,mathrm\{k\}Omega\}\; cdot\; 15\; mathrm\{V\}$

::$=\; \{1\; over\; 2\}\; cdot\; 15\; mathrm\{V\}\; =\; 7.5\; mathrm\{V\}$(notice that "R"

_{1}is not taken into consideration, as above calculations are done in an open circuit condition between A and B, therefore no current flows through this part which means there is no current through R_{1}and therefore no voltage drop along this part)Calculating equivalent resistance:

: $R\_mathrm\{AB\}\; =\; R\_1\; +\; left\; (\; left\; (\; R\_2\; +\; R\_3\; ight\; )\; |\; R\_4\; ight\; )$:: $=\; 1,mathrm\{k\}Omega\; +\; left\; (\; left\; (\; 1,mathrm\{k\}Omega\; +\; 1,mathrm\{k\}Omega\; ight\; )\; |\; 2,mathrm\{k\}Omega\; ight\; )$:: $=\; 1,mathrm\{k\}Omega\; +\; left(\{1\; over\; (\; 1,mathrm\{k\}Omega\; +\; 1,mathrm\{k\}Omega\; )\}\; +\; \{1\; over\; (2,mathrm\{k\}Omega\; )\; \}\; ight)^\{-1\}\; =\; 2,mathrm\{k\}Omega$

**Conversion to a Norton equivalent**A Norton equivalent circuit is related to the Thévenin equivalent by the following equations::$R\_\{Th\}\; =\; R\_\{No\}\; !$:$V\_\{Th\}\; =\; I\_\{No\}\; R\_\{No\}\; !$:$V\_\{Th\}\; /\; R\_\{Th\}\; =\; I\_\{No\}!$

**Practical limitations***Many, if not most circuits are only linear over a certain load range, thus the Thévenin equivalent is valid only within this linear range and may not be valid outside the range.

*The Thévenin equivalent has an equivalent I-V characteristic only from the point of view of the load.

* Since power is not linearly dependent on voltage or current, the power dissipation of the Thévenin equivalent is not identical to the power dissipation of the real system.

**In popular culture**Both Thévenin's theorem and Norton's theorem were featured in the 4th and 10th of May 2006

Doonesbury comic strip panels.**See also***

Norton's theorem

* Impedance

*Superposition theorem

*Extra element theorem

*Nodal analysis

*Mesh analysis

*Y-Δ transform (a.k.a. "Star-Delta transformation")

*Source transformation

*Léon Charles Thévenin

*Edward Lawry Norton **External links*** [

*http://tcts.fpms.ac.be/cours/1005-01/equiv.pdf Origins of the equivalent circuit concept*]

* [*http://www.allaboutcircuits.com/vol_1/chpt_10/8.html Thevenin's theorem at allaboutcircuits.com*]

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