Short notes

Norton Theorem Short Notes

After reducing a complex network of five resistors and two voltage sources to its Norton equivalent at a pair of output terminals, you replace the entire sub-circuit with a single current source IN in parallel with resistance RN — then any load connected across those terminals sees exactly the same voltage and current as it would in the original network. This is the dual of Thevenin's theorem: same utility, same restrictions (linear bilateral networks), different equivalent circuit form. Norton's theorem is particularly convenient when multiple load values must be analysed because changing RL affects only the current divider formed by IN, RN, and RL.

EEE, ECE, EI

How it works

Norton equivalent circuit: short the output terminals and find the short-circuit current IN (using superposition, mesh, or node analysis). Find RN by deactivating all independent sources (voltage sources → short, current sources → open) and calculating the resistance seen at the terminals — same procedure as finding Rth in Thevenin's theorem, so RN = Rth. Conversion: Vth = IN·RN. For circuits with dependent sources: do not deactivate them; instead, apply a test voltage Vt at the terminals and find the resulting current It; then RN = Vt/It. Load current IL = IN · RN/(RN+RL) by current divider.

Key points to remember

Norton's theorem is valid only for linear bilateral networks — non-linear devices like diodes or transistors cannot be included unless the theorem is applied to the linearised small-signal model. The relationship Vth = IN·RN holds exactly between the two equivalent forms of the same network, so once you have one form you can derive the other by simple multiplication. When all sources are deactivated in a network containing only dependent sources, the resistance seen at the terminals is not simply calculated by inspection — always use the test source method. A current source in the Norton equivalent facing a purely resistive load gives maximum power when RL = RN, confirming the link with the maximum power transfer theorem.

Exam tip

The examiner always asks you to find the Norton equivalent of a network at specified terminals when a dependent source is present — always state that you cannot deactivate the dependent source, then apply a 1 V test source at the terminals and find the resulting current to get RN = 1/Itest.

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