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I found a pair of stereo speakers that come with an amplifier inside them.

They do run on mains voltage as they plug into the wall but the actual amplifier runs on DC, 12V to be precise. There is even an unused port that says 12V DC, presumably for a wall adapter. The first component in the circuit of those speakers is a center-tapped transformer that steps down the mains voltage to 12V (still ac). The outputs of the transformer are two 12V AC wires that directly connect to the full wave rectifier on the amp board and one center tap for getting the ground potential (hence the two 12V wires). In the end, the main audio controller and amplifier chips run on 12V DC.

Can you run this amplifier from a DC source, like a battery, if we ignore the transformer and directly connect it to the board?

I am asking this because I am planning on building a portable speaker with the components of these speakers.

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Since you already have a port marked 12 V DC ...you have your answer, Yes you can use a DC battery supply. Simply use the wires to that port, or connect to the connector location on the PCB to use the amplifier battery powered.

Since the transformer output is 12 V AC, the amplifier is likely able to work up to 15 V DC or more, but this is where you need to be just a little careful. A fully charged auto battery is about 13.8 V, and a 3S LiIon will be about 13 V ...both well within range. Just be aware that some batteries if on a charger the terminal voltage may rise above what you expect.

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