Thevenin’s Theorem
Thevenin’s theorem states that ‘ Any linear circuit may be reduced to a
simplified two-terminal circuit consisting of a single voltage VTH in
series with a single resistor RTH ’ as shown in the diagram,
The above diagram is called Thevenin’s equivalent circuit which consists
of equivalent voltage source VTH and equivalent resistance RTH.
The values of equivalent voltage source VTH and equivalent resistance
RTH is depend on the values in the original circuit.
VTH and RTH
The equivalent voltage VTH is one part of the complete Thevenin
equivalent circuit and the other part is RTH
VTH is defined to be the open circuit voltage between two points in a
circuit.
RTH is the total resistance appearing between two terminals in a given
circuit with all voltage sources replaced by a short circuit and all
current sources replaced by open circuit.
Thevenin’s Theorem procedure
A summary of steps for applying Thevenin’s theorem is as follows :
1. Open the two terminals (remove any load) between which you want to
find the Thevenin equivalent circuit. Label the resulting two terminals.
2. Determine the Thevenin resistance RTH between the two terminals with
all voltage sources shorted and all current sources opened. It may be
necessary to redraw the circuit to simplify this step.(Setting all sources to
zero)
3. Determine the open-circuit voltage across the two open terminals. The
resulting open-circuit voltage will be the value of Thevenin’s voltage
VTH.(Returning all sources to their original position)
4. Connect VTH and RTH in series to produce the complete Thevenin
equivalent for the original circuit.
5. Place the load resistor removed in step 1 across the terminals of the
Thevenin equivalent circuit. The load current can now be calculated using
only Ohm’s law and it has the same value as the load current in the original
circuit.
Thevenin Equivalent Circuit - Example
To determine the Thevenin equivalent of any circuit, determine the
equivalent voltage VTH and the equivalent resistance RTH . For example,
in the diagram, the Thevenin equivalent circuit between point A and B is
found as follows.
1.Open the terminal A and B. Remove any load between these points.
2. Determine VTH between point A and B. In this circuit the voltage
across A and B is the Thevenin equivalent voltage.
In this circuit, the voltage from A to B is the same as the voltage across
R2 because there is no current through R3, therefore no voltage drop
across it. VTH is expressed as follow :
V
TH


R

2 
=
R + R 
2
 1
E
3.
Determine the RTH with all voltage sources shorted. In this
circuit, the resistance from A to B is R3 in series with the parallel
combination of R1 and R2. Therefore RTH is expressed as follows :
R
TH
=R
3
 R R



1
2
+

R + R 
2
 1
4. Connect VTH and RTH in series to produce the complete Thevenin
equivalent for the original circuit.
5. Place the load resistor RL across terminal A and B of the Thevenin
equivalent circuit.
Thevenin Equivalency depends on the Viewpoint
The Thevenin equivalent for any circuit depends on the location of the
two points from between which the circuit is viewed. For example if you
view the circuit in the diagram between points A and C, you obtain a
completely different result if you viewed it between point A and B or
between points B and C.
a) Viewed between points A and C
V
TH


R +R


3
2
=

R + R + R 
2
3
 1
R  R + R 
3
R
= 1 2
TH R + R + R
1
2
3
E
b) Viewed between points A and B
V
=
TH



R +
 1

R

2
E
R +R 
2
3
R  R + R 
3
R
= 2 1
TH R + R + R
1
2
3
c) Viewed between points B and C
V
=
TH



R +
 1

R

3
E
R +R 
2
3
R  R + R 
2
R
= 3 1
TH R + R + R
1
2
3
Norton’s Theorem
Norton’s theorem can be stated as ‘Any network may be reduced to a
simplified two-terminal circuit consisting of a single current source IN
and a single shunt resistor RN’ as shown in the diagram.
IN and RN
IN is one part of the complete Norton equivalent circuit and the other part
is RN .
IN is defined to be the short circuit current between two points in a
circuit.
RN is the total resistance appearing between two terminals in a given
circuit with all voltage sources replaced by a short circuit and all
current sources replaced by open circuit.
Norton’s Theorem Procedure
1. Short the terminals between which you want to find the Norton
equivalent circuit. Label the resulting two terminals.
2. Determine the resistance (RN) between the two terminals (opened)
with all voltage sources shorted and all current sources is opened (RN =
RTH). It may be necessary to redraw the circuit to simplify this step.
(Setting all sources to zero).
3. Determine the current (IN) through the shorted terminals.(Returning
all sources to their original position)
4. Connect IN and RN in parallel to produce the complete Norton
equivalent for the original circuit.
5. Place the load resistor removed in step 1 across the terminals of
the Norton equivalent circuit. The load current can now be calculated
using only Ohm’s law and it has the same value as the load current in the
original circuit.