Norton Equivalent

Formula

Description

Norton's theorem is the dual of Thévenin's theorem: any linear two-terminal circuit can be replaced by a current source (Isc) in parallel with a resistance (Rn). The Norton current equals the short-circuit current, and the Norton resistance equals the Thévenin resistance. Converting between Thévenin and Norton equivalents is straightforward: Vth = In × Rn, and the resistance is the same in both representations. Norton equivalents are often more convenient when analyzing parallel circuits or current-mode systems.

Variables

• Rn — Norton equivalent resistance (Ω)
• Voc — Open-circuit voltage (V), equal to In × Rn
• Isc — Short-circuit (Norton) current (A)

Practical Notes

Current sources are less intuitive than voltage sources for many engineers, but Norton equivalents are natural for transistor modeling (the output of a BJT in active mode is well modeled as a current source). Current mirrors in analog ICs are described using Norton equivalent circuits. Source transformation between Thévenin and Norton is reversible and lossless.