Smallest possible simplest possible 7W amp for 2.2 ohm load?

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Power mosfet driver is the way to go. Don’t just stick the speaker in the collector of a single transistor - you will put DC into the speaker. At this level it probably won’t hurt it, but it won’t play as loud as it otherwise would - and more importantly, wastes battery power. Requires a complementary pair and an output capacitor. Mosfet driver chip can get you much closer to the rail as LV said, since it’s designed for switching. Don’t forget the output capacitor. You probably don’t need much bass response, so a small one will do. 100 uF 16 volt is pretty small physically.
 
I'm really thankful for everybody's really interesting suggestions and will be reviewing all of the ideas over the next week or so.

I have ordered TPA3118 and TPA3110 PBTL boards which will arrive soon, for me to use as eval boards. I also found that TI have another, lower power option - the TPA3138, which has 18.5W mono with a minimum load of 3.2 ohms. It also can operate on a power supply down to 3.5V which will help in my battery powered project. These chips also have a power limit configurable with resistors which will protect my speaker.

There's a chance that these chips may be overcomplicating the solution as I see lots of mentions of things like MOSFET / FET driver based circuits.
 
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I see you have edited the first post of this thread and moved the goalposts in now wanting it to be able to handle audio as well.

That negates a good percentage of the suggestions we have made as these were based on just pulse handling as per the original design brief...
 
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