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Can I add a small application board together with the amplifier to the power supply?
Yes, depending on the SMPS you can add a small application, for maximum ratings please refer to the datasheet of the SMPS.
https://www.hypex.nl/FAQ-DIYClassD/FAQ-Hypex/Switch-Mode-Power-Supplies/Switch-Mode-Power-Supplies/Can-I-add-a-small-application-board-together-with-the-amplifier-to-the-power-supply