As to why impedance _matching_ (in the proper sense of the term) of amps
and speakers is usually NOT desirable: basically the reason is that the
efficiency is very poor.

Let's suppose you have a power amplifier with an output Z of 0.1 ohms,
and you want to get maximal power out of it. It might seem that this
would deliver the most power into a 0.1 ohm speaker... and you could
make a 0.1 ohm speaker by tying a bunch of regular speakers in
parallel. The problem is that for this to work, the amp would need to
be able to deliver enormous quantities of current at a very low
voltage, and it's not feasible to design one that could do that. 

Conversely, let's say you have a 8 ohm speaker. For a given source
voltage, maximal power would be delivered to the speaker when the
output also has a 8 ohm internal impedance, but the problem is that
under that condition you are burning an equal amount of power in the
source: a lot of work is getting done by the load, but the system as a
whole is only 50% efficient. In practice you are better off designing
for efficiency, and upping the voltage.

At first it is not really obvious why it works like that, but if you
imagine the two extremes of the situation it makes more sense. If you
put a short circuit (using a very large wire) across a battery, the
battery will heat up but the wire will not. No work has been done
outside the battery, so the system is 0% efficient. Now consider an
infinitesimally tiny load attached to the battery. Efficiency is now
100% - the battery will not get hot because it isn't strained, but not
much work is being done either, because the load is insignificant. It
should be more intuitive now that the maximal power transfer would
happen when the load is being driven "as hard as the source can push",
but this is not the same thing as maximal _efficiency_. Since solid
state amps naturally have a very low Z, it does not make sense to put
an additional resistance at the source - that would just waste power in
the amp. Instead we enjoy higher efficiency by using a 4 to 8 ohm load,
and use higher voltages to reach the output power levels desired.

So that is why if an amplifier says it has "4 ohm outputs" what they're
really saying is "this output can make voltage and current levels
suitable to power a 4-ohm load", not "this output has a 4ohm
impedance".


-- 
seanadams
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