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I have two BA4558 ICs from an old home stereo. I tested them with simple negative feedback circuit for each channel and with power supply of +/- 6V. The speakers I used are most likely with 8 ohm impedance but that is just a a guess.

The idea is two put together a simple and loud battery powered boombox for a mp3 player. Some hiss or minor distortion is ok. No need for a volume control as mp3 has that.

I guess I could bring the supply voltage up to -/+ 18V as mentioned in the datasheet. A friend of mine suggested adding some capacitors around the opamp and also to add some push-pull transistors after the opamp.

Any other ideas?

http://www.datasheetcatalog.org/datasheets/70/233498_DS.pdf

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First, if you mention uncommon ICs in a post, provide a link to a datasheet, so that everybody knows exactly what you're talking about.

You're not supplying a schematic of what you've got so far, but here's one idea.
Since you have two BA4558s you could use them in a BTL (for Bridge Tied Load) configuration. Each IC would handle one channel. In BTL one amplifier connects to one end of the speaker, the other is fed with the inverted signal and connects to the other end of the speaker. Note that each amplifier sees only half of the speaker's impedance.

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https://www.audiolabga.com/pdf/BA4558.pdf I cannot imagine obtaining much more that 1/4 Watt per channel since the absolute maximum power dissipation is 900mW.

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