Although applicable to all branches of electrical
engineering, maximum power transfer theorem is particularly useful for
analysing communication networks. The overall efficiency of a network supplying
maximum power to any branch is 50 percent. For this reason, the application of
this theorem to power transmission and distribution network is limited because,
in their case, the goal is high efficiency and not maximum power transfer.
engineering, maximum power transfer theorem is particularly useful for
analysing communication networks. The overall efficiency of a network supplying
maximum power to any branch is 50 percent. For this reason, the application of
this theorem to power transmission and distribution network is limited because,
in their case, the goal is high efficiency and not maximum power transfer.
However, in the case of electronic and
communication networks, very often, the goal is either to receive or transmit
maximum power involved is only a few milliwatts or microwatts. Frequently, the
problem of maximum power transfer is of crucial significance in the operation
of transmission lines and antennas.
communication networks, very often, the goal is either to receive or transmit
maximum power involved is only a few milliwatts or microwatts. Frequently, the
problem of maximum power transfer is of crucial significance in the operation
of transmission lines and antennas.
As applied to d.c. networks, maximum power transfer
theorem may be stated as follows:
theorem may be stated as follows:
A resistive load will abstract maximum power from a
network when the load resistance is equal to the resistance of the network as
viewed from the output terminals, with all energy source removed leaving their
internal resistances.
network when the load resistance is equal to the resistance of the network as
viewed from the output terminals, with all energy source removed leaving their
internal resistances.
Proof of maximum
power transfer theorem
power transfer theorem
So the voltage drop over the 20Ω resistance =20 x 2
= 40V.
= 40V.
Hence, VOC= VTH
= 40V (or VTH = 120 x 20/60
= 40V).
= 40V).
The resistance of the circuit as looked into the
network from point A and B (when battery has been removed) is
network from point A and B (when battery has been removed) is
Ri = RTH
= 60 + [40 || 20]
= 60 + 13.33
= 73.33Ω
The whole circuit up to AB can now be replaced by a
single source of e.m.f and a single resistance as shown in the figure below
single source of e.m.f and a single resistance as shown in the figure below
Example 2
Calculate the value of R which will absorb maximum
power from the circuit of the figure shown below. Also, compute the value of
maximum power
power from the circuit of the figure shown below. Also, compute the value of
maximum power
According to maximum power
transfer theorem, R will absorb maximum power when it equals 3.33Ω. In that case
transfer theorem, R will absorb maximum power when it equals 3.33Ω. In that case
I = 60/2RTH
I = 60/6.66 = 9A
PMAX = I2R
=
92 x 3.33
92 x 3.33
=
270W
270W
