Basic Electrical Engineering Series
Definition
Nortons Theorem
“The linear network behind a pair of terminals, may be replaced by a constant current generator, with a constant current equal to the short-circuit current at the terminals and an internal impedance equal to the impedance seen at the actual terminals, with all internal sources removed and replaced by their internal impedances...".
In any electric circuit we may easily calculate the current and voltages at any point using Kirchofs laws and ohms law. However as the complexity of the circuit increases the labour involved becomes tedious. Hence several electrical theorems have been developed in order to reduce the amount of work.
Nortons is one such theorem and it is applicable to both DC and AC circuit problems. It follows on naturally from Thevenins theorem.
First we look at the representation of linear souces.
Linear Sources
... there are two types - constant-voltage and constant-current sources.
Constant Voltage Scource - can be AC or DC, Z is the internal impedance of the generator
Constant Current Scource - can be AC or DC, Z is the internal impedance of the generator but may be represented as an admittance.
The Theorem
The above complicated circuit is equivalent to the following :
The generator current is the short circuit terminal current 'seen' at AB in the original circuit.
The generator internal impedance is equal to the impedance 'seen' looking into AB
ie in this case Zi = (((Z1+Z2)//Z3)+Z5 (// means in parrallel with)