maximum Power Transfer Theorem

Although applicable to all branches of electrical engineering, this theorem is particularly useful
for analysing communication networks. The overall efficiency of a network supplying maximum
power to any branch is 50 per cent. For this reason, the application of this theorem to power transmission
and distribution networks 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 (through at reduced efficiency) specially when 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, this 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 sources removed
leavin g behind their internal resistances. , , A
W'
 a load resistanceof RLis connectedacross I I R
the terminals A and B of a network which consists of a generator
of e.m.f. E and internal resistance Rg and a series resistance R
which, in fact, represents the lumped resistance of the connecting
wires. Let Rj =Rg + R =internalresistanceof the networkas
viewed from A and B.
According to this theorem, RL will abstract maximum power
from the network when RL=Rj'
Let us consider an a.c. source of internal impedance (R) + j X) supplying power to a load
impedance (RL + jXJ. It can be proved that maximum power transfer will take place when the
modulesof the loadimpedanceis equalto the modulusof the sourceimpedancei.e. I ZLI = I Z) I
Where there is a completely free choice about the load, the maximum power transfer is obtained
when load impedance is the complex conjugate of the source impedance. For example, if source
impedance is (R) +jX), then maximum transfer power occurs, when load impedance is (R) - jX). It
can be shown that under this condition, the load power is = E-/4R).The variation of 11with RL is shown in . The maximum value of 11is unity when
RL = 00and has a value of 0.5 when RL =Rj' It means that under maximum power transfer conditions,
the power transfer efficiency is only 50%. As mentioned above, maximum power tr-ansfer condition
is important in communication applications but in most power systems applications, a 50% efficiency
is undesirable because of the wasted energy. Often, a compromise has to be made between
the load power and the power transfer efficiency. For example, if we make RL = 2 Rj' then