Thévenin's theorem

In the theory of linear electrical networks the Thévenin 's theorem, named after Léon Charles Thévenin and also as a Helmholtz - Thévenin 's theorem, or Helmholtz theorem states indicates that any combination of voltage sources, current sources and resistors with respect to two terminals of electrically equivalent to a series circuit a voltage source and a resistor. This equivalent circuit is called or Thévenin equivalent in the German language equivalent voltage source. This theorem is used for example, for simplification of the circuit analysis.

Calculating the Thévenin equivalent

The Thévenin equivalent consisting of a resistor and a voltage source. To determine the two unknowns and two equations are required. These equations can be created in various ways. Most often one uses, however, the following:

• The output voltage at open terminals AB, ie without load resistor, determine. This open-circuit voltage is the Thevenin equivalent voltage.

To determine the Thevenin equivalent resistance, we mostly used one of the three following methods:

• Just replace all independent voltage sources by short circuits ( but maintains the internal resistance ) to delete all independent current sources ( ie replacing it by open circuits or interruptions ). Controlled (dependent) current or voltage sources, however, are to be left in the circuit! Then we can calculate the equivalent resistance. This is equal to the Thevenin equivalent resistance.
• If you know the short-circuit current, you use Ohm's Law to determine:

• It includes a resistor of known value to AB. Using the voltage divider law one can then determine the Thevenin equivalent resistance.

A common variant of this method is the half of the voltage: It includes a variable resistor ( potentiometer ) of AB and measures the tension. Then varying the value of the variable resistor, and measuring the half of the open circuit voltage across AB. The variable resistor is then equal to the Thevenin equivalent resistance.

The proof of Thévenin 's theorem is based on the principle of superposition.

Conversion between Norton and Thevenin equivalent

A Norton equivalent can be converted to a Thévenin equivalent using the following equations:

Note: the diagram is a notation and English equivalent to the German.

Extension for AC

The Norton 's theorem can be generalized to harmonic alternating current systems by impedances instead of ohmic resistors are used.

History

The Thévenin 's theorem was first discovered by the German scientist Hermann von Helmholtz in 1853. It was then in 1883 by the French engineer Léon Charles Thévenin ( 1857-1926 ) rediscovered.