126 Practical MATLAB® Applications for Engineers
R.2.84 The maximum power transfer theorem states that maximum power is delivered to
a load RL connected to an ideal voltage source Vs connected to a series resistor Rs
when the load resistance RL is equal to the resistance Rs as illustrated in the circuit
diagram of Figure 2.25.
(Maximum power is delivered to RL when RL = Rs.)
R.2.85 For a load RL connected to an arbitrary network, maximum power is delivered to
the load RL, where RL is calculated in the following way:
a. The load is removed and replaced by an open circuit (with terminals aa’).
b. Calculate the Thevenin’s equivalent resistance RTH by looking into the open ter-
minals (aa’).
c. Maximum power is delivered to the load by adjusting RL to be equal to RTH.
R.2.86 Note that the maximum power transfer theorem holds for the case where RTH
is fi xed and RL is allowed to vary. If RL is fi xed but RTH is allowed to vary, then
maximum power delivered to RL will not occur when RL is equal to RTH, but rather
when RTH = 0.
R.2.87 For the example presented in R.2.83 referred to as Figure 2.15, maximum power is
delivered to the load RL (5 Ω) by changing (increasing) RL to 15 Ω. The resulting
Thevenin’s equivalent circuit of the given network as well as the new load RL is
shown in Figure 2.26.
The maximum power delivered to RL is then given by
PRL-maxV
60 W
()30
15
2(^)
R.2.88 If a circuit is purely resistive with no energy-storing elements (L or G) and switch-
ing occurring, then there will be no transient behavior, and current and voltages
FIGURE 2.24
The Norton’s equivalent circuit of the network of R.2.83.
RL = 5 Ω
RTH = 15 Ω
IN = 16 A
a′
a
FIGURE 2.25
Maximum power delivered to RL when RL = Rs.
RL
Rs
Vs