Class D amplifier transformer whining

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It is evidently the output from the speaker you are supposed to hear, not the amplifier and not the power supply.
Switch-mode implies a high-frequency carrier signal (which you can't hear) modulating an audible signal, which you are only supposed to hear from the speaker. But when currents pass coils, the electromagnetic field causes magnetic forces on other magnetic items and that may cause vibration. The whining you hear, does that follow the signal in the speakers?

A particular SMPS related problem is the low idle current drawn by amplifiers. This idle current for the amplifier may not be sufficient to take an SMPS to regular operation (typically PWM) but leaves the SMPS in some kind of low power/low performance mode where resonances are known to appear. Such whining does not follow the output signal.

Recently, in another power supply thread, whining of what I recall as a Meanwell power supply (high quality) was exactly due to this phenomenon. The supplier recommended a dummy load to bring the SMPS out of this low power operation.
The link is here:
Meanwell EPP-200-27 whining/hissing
 
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If it is the PSU that makes the whining, try to load it with power resistor (some 500mA current) in parallel with the amplifier. It is likely to go away with a stable, high loading. The power-resistor is not meant as a permanent solution, just for diagnosis.
 
You might also try to pot the whining inductor.

Dip it in molten wax (candle wax is fine and easy to get) , remember to leave it submerged a couple minutes to reach wax temperature because when cold, a "crust" of cold wax will form which won´t let it properly impregnate the winding, let excess drip back into the pot and reinstall.
You might even let it cool and do a double coat, faster this time so as not to remelt the first one.

I suggest wax because it´s cheap and available but mainly because it's "reversible" : worst case it does no good (I doubt it), you put the waxed inductor over some folded tissue or newspaper and hit it with a heat gun, wax will remelt and be absorbed by paper, leaving inductor as before.
 
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