Thevenins

Thevenin's theorem is a fundamental result in circuit analysis that states any linear, bilateral network of sources and impedances connected to two terminals can be replaced by an equivalent circuit consisting of a single voltage source in series with a single resistance. This Thevenin equivalent, denoted Vth in series with Rth, behaves identically to the original network from the perspective of the terminals for all external loads.

To determine the Thevenin equivalent, the open-circuit voltage Voc at the terminals is found with no load connected. If the network contains only independent sources, the Thevenin resistance Rth can be found from Voc and the short-circuit current Isc, using Rth = Voc / Isc. If dependent sources are present, Rth cannot be obtained by deactivating all sources alone. In such cases, independent sources are turned off, a test source is applied at the terminals, and the resulting current or voltage is used to compute Rth as Rth = Vtest / Itest.

Thevenin equivalents are particularly useful for simplifying the analysis of circuits when the load varies. By replacing the network with Vth and Rth, one can easily compute the load current and voltage for different loads without reanalyzing the entire network. The Thevenin and Norton equivalents are interchangeable representations of the same network: Vth = In Rth and Rth = Rn, with In being the Norton current.

The theorem is named after Léon Charles Thévenin, who published the concept in the late 19th century. It remains a core tool in electrical engineering for linear, time-invariant, bilateral networks.