Thévenin's Theorem

Objective

The objective of the Thévenin theorem is to simplify a complex linear circuit into an equivalent circuit with a single voltage source and resistance in serie, making analysis between two terminals (A and B) easier.

Statement

Any linear circuit located between points A and B can be modeled by an equivalent generator $(E_{th}, R_{th})$, where:

• $E_{th}$ is the open-circuit voltage between A and B
• $R_{th}$ is the equivalent resistance seen between A and B when the sources are deactivated

Example

Calculate the Thévenin voltage (the equivalent voltage between the two terminals of the network for which you are finding the Thévenin generator).

$$E_{th} = \frac{R}{R+R} \cdot E$$ $$E_{th} = \frac{E}{2}$$

Replace voltage sources with short circuits and current sources with open circuits. Calculate the Thévenin resistance (the equivalent resistance of the circuit).

$$R_{th} = \frac{R \cdot R}{R+R}$$ $$R_{th} = \frac{R \cdot R}{2R}$$ $$R_{th} = \frac{R}{2}$$

Finally, you can replace the original circuit with the Thévenin equivalent generator, which consists of a voltage source $E_{th} = \frac{E}{2}$ in series with a resistance $R_{th} = \frac{R}{2}$.