Thevenin's theorem

(electricity) A theorem in network problems which allows calculation of the performance of a device from its terminal properties only: the theorem states that at any given frequency the current flowing in any impedance, connected to two terminals of a linear bilateral network containing generators of the same frequency, is equal to the current flowing in the same impedance when it is connected to a voltage generator whose generated voltage is the voltage at the terminals in question with the impedance removed, and whose series impedance is the impedance of the network looking back from the terminals into the network with all generators replaced by their internal impedances. Also known as Helmholtz's theorem.

This theorem, from electric circuit theory, is also known as the Helmholtz or Helmholtz-Thévenin theorem, since H. Helmholtz stated it in an earlier form prior to M. L. Thévenin. Closely related is the Norton theorem, which will also be discussed. Laplace transform notation will be used. See also Laplace transform.

Thévenin's theorem states that at a pair of terminals a network composed of lumped, linear circuit elements may, for purposes of analysis of external circuit or terminal behavior, be replaced by a voltage source V(s) in series with a single impedance Z(s). The source V(s) is the Laplace transform of the voltage across the pair of terminals when they are open-circuited; Z(s) is the transform impedance at the two terminals with all independent sources set to zero (Fig. 1).

Network and its Thévenin equivalent. (a) Original network. (b) Thévenin equivalent circuit.

Norton's theorem states that a second equivalent network consists of a current source I(s) in parallel with an impedance Z(s). The impedance Z(s) is identical with the Thévenin impedance, and I(s) is the Laplace transform of the current between the two terminals when they are short-circuited (Fig. 2).

Network and its Norton equivalent. (a) Original network. (b) Norton equivalent circuit.

Thévenin's and Norton's equivalent networks are related by the equation V(s) = Z(s) · I(s).

These theorems are useful for the study of the behavior of a load connected to a (possibly complex) system that is supplying electric power to that load. See also Superposition theorem (electric networks).

Theorem that replaces any complex network with a single voltage source in series with a single resistance.