Norton's Theorem

Objective

The objective of the Norton theorem is to simplify a complex linear circuit into an equivalent circuit consisting of a single current source in parallel with a resistance, 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 $(I_{N}, R_{N})$, where:

• $I_{N}$ is the short-circuit current between A and B
• $R_{N}$ is the equivalent resistance seen between A and B when the sources are deactivated

Example

Determination of $I_N$ with a short-circuit

$$I_{AB} = \frac{E}{R}$$

Determination of $R_N$ without the sources

$$R_N = \frac{R \cdot R}{R + R} = \frac{R \cdot R}{2R} = \frac{R}{2}$$

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