Maximum Power
Transfer Theorem
The Maximum Power Transfer Theorem is not so
much a means of analysis as it is an aid to system design.
Simply stated, the maximum amount of power will be
dissipated by a load resistance when that load resistance is
equal to the Thevenin/Norton resistance of the network
supplying the power. If the load resistance is lower or
higher than the Thevenin/Norton resistance of the source
network, its dissipated power will be less than maximum.
This is essentially what is aimed for in
stereo system design, where speaker "impedance" is matched
to amplifier "impedance" for maximum sound power output.
Impedance, the overall opposition to AC and DC current, is
very similar to resistance, and must be equal between source
and load for the greatest amount of power to be transferred
to the load. A load impedance that is too high will result
in low power output. A load impedance that is too low will
not only result in low power output, but possibly
overheating of the amplifier due to the power dissipated in
its internal (Thevenin or Norton) impedance.
Taking our Thevenin equivalent example
circuit, the Maximum Power Transfer Theorem tells us that
the load resistance resulting in greatest power dissipation
is equal in value to the Thevenin resistance (in this case,
0.8 Ω):
With this value of load resistance, the
dissipated power will be 39.2 watts:
If we were to try a lower value for the load
resistance (0.5 Ω instead of 0.8 Ω, for example), our power
dissipated by the load resistance would decrease:
Power dissipation increased for both the
Thevenin resistance and the total circuit, but it decreased
for the load resistor. Likewise, if we increase the load
resistance (1.1 Ω instead of 0.8 Ω, for example), power
dissipation will also be less than it was at 0.8 Ω exactly:
If you were designing a circuit for maximum
power dissipation at the load resistance, this theorem would
be very useful. Having reduced a network down to a Thevenin
voltage and resistance (or Norton current and resistance),
you simply set the load resistance equal to that Thevenin or
Norton equivalent (or visa-versa) to ensure maximum power
dissipation at the load. Practical applications of this
might include stereo amplifier design (seeking to maximize
power delivered to speakers) or electric vehicle design
(seeking to maximize power delivered to drive motor).
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