Thevenin’s
theorem was named after a French engineer M.L. Thevenin (1857-1926) who while
working in the Telegraphic Department published a statement of the theorem in
1893. The theorem provides a mathematical technique for replacing a given
network as viewed from two output terminals, by a single voltage source with a
series resistance. It makes the solution of complicated networks (particularly,
electronic networks) quite quick and easy. The application of this powerful
theorem will be explained with the help of the following simple example.
theorem was named after a French engineer M.L. Thevenin (1857-1926) who while
working in the Telegraphic Department published a statement of the theorem in
1893. The theorem provides a mathematical technique for replacing a given
network as viewed from two output terminals, by a single voltage source with a
series resistance. It makes the solution of complicated networks (particularly,
electronic networks) quite quick and easy. The application of this powerful
theorem will be explained with the help of the following simple example.
Suppose
we are required to find the current flowing through the load resistance RL
in figure 1a above, we can use Thevenin’s theorem and proceed as;
we are required to find the current flowing through the load resistance RL
in figure 1a above, we can use Thevenin’s theorem and proceed as;
1.)
Disconnect
RL from the circuit terminals A and B and redraw the circuit as
shown in figure 1b. Obviously, the terminals have become open circuited.
Disconnect
RL from the circuit terminals A and B and redraw the circuit as
shown in figure 1b. Obviously, the terminals have become open circuited.
2.)
Calculate
the open circuit voltage (Voc) which appears across terminals A and
B when they are open i.e. when RL is disconnected. As seen, Voc
= drop across R2 = IR2 where I is circuit current when A
and B are open.
Calculate
the open circuit voltage (Voc) which appears across terminals A and
B when they are open i.e. when RL is disconnected. As seen, Voc
= drop across R2 = IR2 where I is circuit current when A
and B are open.
This open circuit voltage (Voc)
is called Thevenin’s Voltage (Vth).
is called Thevenin’s Voltage (Vth).
1.)
Now,
imagine the battery to be removed from the circuit leaving its internal
resistance (r) behind and redraw the circuit as shown in figure 1c above. When
viewed inwards from terminals A and B, the circuit consist two parallel paths:
one containing R2 and the other containing (R1+r). The
equivalent resistance of the network as viewed from these terminals is given as
Now,
imagine the battery to be removed from the circuit leaving its internal
resistance (r) behind and redraw the circuit as shown in figure 1c above. When
viewed inwards from terminals A and B, the circuit consist two parallel paths:
one containing R2 and the other containing (R1+r). The
equivalent resistance of the network as viewed from these terminals is given as
R = R2|| (R1+r)
This
resistance is also called Thevenin’s resistance (Rth) (though, it is
also sometimes written as R0).
resistance is also called Thevenin’s resistance (Rth) (though, it is
also sometimes written as R0).
Consequently,
as viewed from terminals A and B, the whole network (excluding RL)
can be reduced to a single source (called Thevenin’s source) whose emf equals Voc
( or Vth) and whose internal resistance equals Rth
(or R0) as shown in figure 2 below.
as viewed from terminals A and B, the whole network (excluding RL)
can be reduced to a single source (called Thevenin’s source) whose emf equals Voc
( or Vth) and whose internal resistance equals Rth
(or R0) as shown in figure 2 below.
1.)
RL
is now reconnected across terminals A and B from where it was temporarily
removed earlier. Current flowing through RL can now be determined
as;
RL
is now reconnected across terminals A and B from where it was temporarily
removed earlier. Current flowing through RL can now be determined
as;
From
the above expressions, it is clear that any network of resistors and voltage
sources (and current sources as well) when viewed from any two points A and B
in the network, can be replaced by a single voltage source and a single
resistance (or impedance in the case of a.c. circuits) in series with the
voltage source.
the above expressions, it is clear that any network of resistors and voltage
sources (and current sources as well) when viewed from any two points A and B
in the network, can be replaced by a single voltage source and a single
resistance (or impedance in the case of a.c. circuits) in series with the
voltage source.
After
this replacement of the network by a single voltage source with a series
resistance has been accomplished, it is easy to find current in any load
resistance joined across the terminals A and B. This theorem is valid even for
those linear networks which have non-linear load.
this replacement of the network by a single voltage source with a series
resistance has been accomplished, it is easy to find current in any load
resistance joined across the terminals A and B. This theorem is valid even for
those linear networks which have non-linear load.
Therefore, Thevenin’s theorem as
applied to d.c. circuits can be stated as;
applied to d.c. circuits can be stated as;
The current flowing through a load
resistance (RL) connected across any two terminals A and B of a linear,
active bilateral network is given by Voc/(Rth + RL),
where Voc is the open-cercuit voltage (i.e. voltage across the two
terminals when RL is removed) and Rth is the internal
resistance of the network as viewed back into the open-circuited network from
terminals A and B with all voltage sources replaced by their internal
resistances (if any) and all current sources by infinite resistances
