How do I make a +12V and -12V power supply?

Note, these are limited in output current.

Maybe 2 of these
wired back to back like you mentioned (+12(-+)12- | where (-+) = GND

Yeah, those have a very limited output current. 20W is too low.

You won't get 40W unless those amplifiers have a bridged-output, or 2-Ohm speakers (or two 4-Ohm speakers in parallel). But most amplifiers aren't designed for 2-Ohm loads.

Power = Voltage squared/Resistance (There are other ways to calculate power but that's the easiest way for power amplifiers.)

12V Peak (24V peak-to-peak with dual power supplies) is about 8.5V RMS = about 20W into 4-Ohms. (Half that into 8-Ohms). That's the "ideal best case" assuming no voltage-loss across the amplifier.

A bridge amplifier doubles the voltage across the speaker for 4 times the power (assuming it can put-out the required current).

P.S.
High-power car amplifiers have a built-in voltage booster.

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If you get (genuine) decent brand (Meanwell is very commonly used as a reliable brand for instance), this shouldn't be an issue.

Firstly that only works if one or both of the supplies are isolated (the -ve output isn't connected to ground on the lower supply).

Secondly if you do this you need protection diodes across each supply to prevent one from back-feeding the other (some supplies may have this built in, but if not sure just connect a beefy diode across each supply, cathode to +ve, anode to -ve, to prevent that supply from being reverse driven by the other.

Otherwise switch-on transients may simply blow up one of the supplies instantly.

Whatever you do the common output rail should be connected to mains earth for safety and to reduce mains hum.

Is this really meaningful for a switchmode supply?

The output of such a supply is little more than a ("beefy" Schottky) diode in series with the output winding, in the same orientation you describe. Once the output is brought to zero, the switchmode drive will be shut off and that diode will simply harmlessly conduct any "back-fed" current. :thinking:

You underestimate the amount of damage that reverse driving can do - you need to prevent it from happening, both to protect the power supplies and the amplifier circuit itself.

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