Electrical Engineering ⇒ Topic : Nortons Theorem with sinusoidal excitation

Norton's Theorem

Another method of analysing a complex impedance circuit is given by Norton's theorem. The Norton equivalent form of any complex impedance circuit consists of an equivalent current source I_N and an equivalent impedance Z_N, arranged as shown in Fig. (a). The values of equivalent current and impedance depend on the values in the original circuit.

                                       figure (a)

Though Norton's equivalent circuit is not the same as its original circuit, the output voltage and current are the same in both cases; Norton's current is equal to the current passing through the short circuited output terminals and the value of impedance is equal to the impedance seen into the network across the output terminals

                                  figure (b)

Consider the circuit shown in Fig. (b).Norton's equivalent for the circuit shown in Fig.(b) between points A and B is found as follows. The current passing 3 through points A and B when it is short-circuited is the Norton's equivalent current, as shown in Fig. (c).

Norton's current I_N = V/Z₁

                            figure (c)

The impedance between points A and B, with the source replaced by a short circuit, is Norton's equivalent impedance. In Fig.(B), the impedance from A to B,Z₂ is in parallel with Z₁

Norton's equivalent circuit is shown in Fig. (d)

                                            figure (d)

The advantages seen with Thevenin's theorem apply to Norton's theorem. If we wish to analyze load resistor voltage and current over several different values of load resistance, we can use the Norton's 3 equivalent circuit again and again, applying nothing more complex than simple parallel circuit analysis to determine what's happening with each trial load.This theorem is not applicable to circuits consisting of nonlinear elements and not valid to unilateral circuits. This theorem is not valid where the magnetic coupling 3 exists between load and the circuit