Thevenin

Thevenin's theorem is a fundamental result in circuit theory stating that any linear, bilateral electrical network with sources and resistive elements can be replaced at two terminals by a single voltage source in series with a resistor. The resulting equivalent circuit is known as the Thevenin or Thevenin equivalent.

The theorem is named after Léon Charles Thévenin, who published it in 1883. It provides a means to simplify the analysis of how a network drives a load by removing internal complexity and focusing on two key parameters: the Thevenin voltage and the Thevenin resistance.

To obtain the Thevenin equivalent, first determine the open-circuit voltage Voc across the two output terminals; this is the Thevenin voltage Vth. Next, determine the resistance seen from the terminals with all independent sources deactivated (voltage sources shorted, current sources opened). This resistance is Rth. If the network contains dependent sources, they must remain active when finding Rth, and a test source may be applied to the terminals to calculate the resulting voltage or current.

The Thevenin and Norton theorems are duals. Any Thevenin circuit (voltage source in series with Rth) has a Norton equivalent (current source in parallel with Rth) with In = Vth / Rth and In × Rth = Vth.

Applications of Thevenin’s theorem include simplifying the analysis of how a load draws power, determining voltage and current in the load for varying loads, and facilitating small-signal or AC analysis by using impedances. Limitations arise with nonlinear elements or time-varying behavior where linearization or alternate methods are required.