# Thevenin's and Norton's Theorem > [!NOTE] Thevenin's Theorem > *Thevenin's theorem* states that a [[Linear Circuit|linear]] *two-terminal* circuit can be replaced by an equivalent circuit consisting of a voltage source $\mathbf{V}_{\text{Th}}$ in *series* with an [[impedance]] $\mathbf{Z}_{\text{Th}}$. > > The value of the voltage source is the *Thevenin voltage* $\mathbf{V}_{\text{Th}}$ and is equal to the *open circuit voltage* at the terminals. The *Thevenin impedance* $\mathbf{Z}_{\text{Th}}$ is equal to the impedance of the circuit. > [!NOTE] Norton's Theorem > *Norton's theorem* states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source $\mathbf{I}_{\text{Th}}$ in *parallel* with an impedance $\mathbf{Z}_{\text{N}}$. > > The value of the current source is the *Norton current* $\mathbf{I}_{\text{N}}$ and is equal to the *short circuit current* when the terminals are connected together. The impedance $\mathbf{Z}_{\text{N}}$ is equivalent to the Thevenin impedance $\mathbf{Z}_{\text{Th}}$. Thevenin's and Norton's theorem are [[Duality#Electrical circuits|duals]] of each other. ## Thevenin impedance The *Thevenin impedance*, $\mathbf{Z}_{\text{Th}}$, can be found by the following methods. - The *input impedance* measured at the terminals when *all* independent sources are off. This *does not work* if there are *any* dependant sources. - Ratio of the Thevenin voltage to the Norton current, also the short circuit current. - Turning off *all* independent sources and attaching an *arbitrary* voltage or current source to the terminals and measuring the *resulting current* or *voltage* respectively. For simplicity, these sources are often set to $1\angle 0^{\circ}$. ![[TheveninResistance.svg]] ^fe1db9 ## Source transformation Thevenin's and Norton's theorem are also related by [[source transformation]], and thus $\mathbf{Z}_{\text{Th}}=\mathbf{Z}_{\text{N}}$ ![[TheveninNortonEquivalents.svg]]