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This theorem was initially discovered by the German scientist Hermann von Helmholtz in 1853, then in 1883 by the engineer French telegraph Leon Charles Thévenin.

Statement

The theorem of Thévenin is an electronic property, which establishes that a linear electrical communication seen of two points is equivalent to a perfect generator whose tension is equal to the potential difference to vacuum between these two points, in series with a resistance equal to that which one measures between the points when the independent generators are made passive.

Determination of the model of Thévenin

Commonly:

the tension of Thévenin is the tension between the terminals of the load when this one is disconnected (no-load voltage).
the resistance of Thévenin is that measured between the terminals of the load when this one is disconnected with the independent sources of tension replaced by a Court-circuit and the independent power sources by an open circuit.

From a mathematical point of view:

E_ {HT} = R_ {HT} \ times I_n

R_ {HT} = R_n

With I_n and R_n (power source and equivalent resistance for a model of Norton).

To determine the tension of Thévenin, one measures the no-load voltage with a voltmeter at the boundaries of the load.

To determine the resistance of Thévenin, we have 3 methods:

One extinguishes the independent sources and one calculates resistance equivalent
If one knows the tension of Thévenin $E_ {HT} ^ {}$ , to vacuum, and the current of Norton $I_n^ {}$ , in Court-circuit, one uses the preceding formula
One places a resistance which one knows the value on the terminals of the load, one takes the terminal voltage of this resistance and one uses the theorem of the Tension divider .
a current alternative of this method is that known as of the half-tension: One places a variable resistor (precise and calibrated) on the terminals of the load and one measures the tension. One then makes vary the value of resistance until having $\ frac {E_ {HT}} {2}$ , two resistances are then equal.

Demonstration

The demonstration of this theorem rests on the Principe of superposition, which makes it possible to extend the general information of its application to all electronic devices which function linearly.

One can imagine the situation where one connects two linear dipoles indicated respectively by the letters has and B, the goal of the step is then to find a diagram equivalent to the dipole has so that its behavior with respect to the dipole B remains identical.

Before connecting the dipoles has and B, one notes that the no-load voltages between their terminals are respectively $u_A (T) =u_ {A0} (T) \,$ and $u_B (T) \, =0$ because one considers first of all to simplify the demonstration that the dipole B does not contain electric sources and that all electric quantities, in open circuit, are initially null there (figure a).

One can then connect the two dipoles using a court-cicuit which one replaces, however in an equivalent way, by two sources of tension in series $u_1 \,$ and $u_2 \,$ which has the same amplitude equal to $u_ {A0} (T) \,$ but of the opposite orientations (figure b). In this new assembly, the currents and tensions are seen then, by application of the Principe of superposition, like the result of the cumulated action of two influences: that of $u_1 \,$ and of the electric sources located in has on the one hand (figure c) and that of $u_2 \,$ on the other hand (figure d). However, it clearly appears that the first of these influences is equivalent to the situation where the two dipoles were in open circuit and which it thus does not modify the electric quantities of B. the source of tension $u_2 \,$ of amplitude $u_ {A0} (T) \,$ put in series with the dipole has in which the influence of all independent electric sources was cancelled can thus seem as at the origin of the currents and tensions of the dipole B.

When the dipole B also contains independent electric sources, one still can using the Principe of superposition of returning to the preceding situation and of using the same reasoning. It is enough to find this situation to cancel the electric sources, in turn in each dipole, that making it possible to determine successively the dipoles of Thévenin equivalent to has and to B.

Example

In the example, calculation of the equivalent tension:

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}

(Note that R ₁ is not taken into account, because calculations above are made in open circuit between has and B, consequently, it not of current which passes through R₁ and thus any tension does not leave this part there)

Calculation of equivalent resistance:

R_ \ mathrm {AB} = R_1 + \ left (\ left (R_2 + R_3 \ right) \| R_4 \ right)

1 \, \ mathrm {K} \ Omega + \ left (\ left (1 \, \ mathrm {K} \ Omega + 1 \, \ mathrm {K} \ Omega \ right) \| 2 \, \ mathrm {K} \ Omega \ right)

1 \, \ mathrm {K} \ Omega + \ left ({1 \ over (1 \, \ mathrm {K} \ Omega + 1 \, \ mathrm {K} \ Omega)} + {1 \ over (2 \, \ mathrm {K} \ Omega)} \ right) ^ {- 1} 2 \, \ mathrm {K} \ Omega

External bonds

{{in}} Historique of the concept of circuit is equivalent.
Other evidence of the theorem: .

References

Leon C. Thévenin, Extension of the law of Ohm to the complex electromotive circuits (Yearly Telegraphic, 1883) volume 10, p222~224.
Leon C. Thévenin, On a new theorem of dynamic electricity (C.R. of the Meetings of the Academy of Science, 1883) p159~161.

See too

Theorem of Norton
Electricity
Laws of Kirchhoff (law of the meshs and law of the nodes)
Law of Ohm
Principle of superposition
Theorem of Millman
Theorem of reciprocity
Theorem of Tellegen
Open circuit

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