Download 2. Norton`s theorem

2. Norton’s theorem
An American engineer, E.L. Norton at Bell Telephone Laboratories, proposed a theorem
similar to Thevenin’s theorem.
Norton’s theorem states that a linear two-terminal network can be replaced by an
equivalent circuit consisting of a current source IN in parallel with resistor RN, where iN is
the short-circuit current through the terminals and RN is the input or equivalent resistance
at the terminals when the independent sources are turned off. If one does not wish to turn
off the independent sources, then RN is the ratio of open circuit voltage to short–circuit
current at the terminal pair.
Figure (a) Original circuit
Figure (b) Norton’s equivalent circuit
Figure (b) shows Norton’s equivalent circuit as seen from the terminals a-b of the original
circuit shown in Fig. (a). Since this is the dual of the Thevenin circuit, it is clear that Rt = Rn
and IN =Voc / Rt. In fact, source transformation of Thevenin equivalent circuit leads to
Norton’s equivalent circuit.
Procedure for finding Norton’s equivalent circuit:
(1) If the network contains resistors and independent sources, follow the instructions below:
(a) Deactivate the sources and find RN by circuit reduction techniques.
(b) Find IN with sources activated.
(2) If the network contains resistors, independent and dependent sources, follow the steps
given below:
(a) Determine the short-circuit current IN with all sources activated.
(b) Find the open-circuit voltage Voc.
(c)
.
(3) If the network contains only resistors and dependent sources, follow the procedure
The open–circuit and short–circuit test are sufficient to find any Thevenin or Norton
equivalent.
2.1 PROOF OF THEVENIN’S AND NORTON’S THEOREMS
The principle of superposition is employed to provide the proof of Thevenin’s and Norton’s
theorems. Derivation of Thevenin’s theorem:
Let us consider a linear circuit having two accessible terminals x-y and
excited
by
an
external current source. The linear circuit is made up of resistors, dependent and independent
sources. For the sake of simplified analysis, let us assume that the linear circuit contains only
two independent voltage sources v1 andv2 and two independent current sources i1 and i2.
The terminal voltage v may be obtained, by applying the principle of superposition. That is, v
is made up of contributions due to the external source and independent sources within the
linear network.
Hence
Figure 2 Current-driven circuit
Figure 3 Thevenin’s equivalent circuit