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My class-D amplifier gets very hot with no load, or no input signal

Most times, this problem occurs due to problems with the output filter.

YBQ has written some guidelines about LC filter design at: http://focus.ti.com/general/docs/techdocsabstract.tsp?abstractName=sloa119a

The easiest way to check if it's a problem with your output filter for BTL amps is to connect the speaker directly to the IC (most of our BTL amps use BD modulation and can be tied directly to the speaker -- the filtering is used for EMC reasons). if the excess heating goes away, the filter is your problem.

Check the inductor - is it saturating? Be careful, the ratings are sometimes thermal ratings, and you care about loss of inductance versus current. We recommend inductors that maintain 80% of their inductance across the current range.

Trying to run the amplifier with an open load can cause problems -- RL is part of the filter equation. If the resonance of the filter lines up with the switching frequency,  you have excessive current flow in the filter. See the attached file.

Capacitors in the output filter should be metal film, or ceramic with X5R or better dieletric material. Capacitors made from Y5V have poor capacitance vs applied voltage characteristics, and your filter cut-off and resonance will shift all over the place. An excellent reference on output filter design for the device you are using is the EVM Users Guide. You can find it in the Product Folder for the amplifier you are using.