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In bridge mode your using both half's of the amp to make 1 more powerfull amplifier instead of a less powerfull 2 channel amp.If you look at the top circuit the input and outputs are marked as + and - not left and right.
I see, then how should I connect my source with a left and right channel?AFAICT In BTL mode you only have 1 power channel and have to use the +/- (L/R) inputs as 1 differential input channel, = one has to be inverted phase.
In bridge tied mode one would need a second amplifier chip for the other channel. Otherwise add both signals together to create a good old mono signal and use the inverted signal für the - input.In bridge mode the amplifiers see effectively half the speaker impedance. So with 4 ohms speakers the amplifiers see only an effective 2 Ohms load and would thus need more current and less voltage.So with 4 Ohms speakers better use non bridge tied mode.
I'm not sure what you're expecting, BTL gives 2X the voltage and 2X the current through the speaker so 4X the power, but you have to make one of the +/- (L/R) inputs inverted yourself.I'm no expert in audio, I've used simple 1 transistor to get 2 out of phase signals in the past.https://www.electronics-tutorials.ws/amplifier/phase-splitter.html
I agree that the datasheet does not show BTL driving a 4 ohms speaker because with the much higher power then the IC will melt.It can drive a 4 ohm speaker is the supply voltage is reduced enough (try 14V) for the maximum low distortion output to be a little less than 25W.