(crudely) approximating a loudness circuit

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I'm probably way off base here, but I got this harebrained idea.

Imagine a 4 way dsp'ed active bluetooth speaker, driven by two stereo amps modules (one for bass, one for mid/high), both with volume control, and some measure of variable gain (TDA7498E in my case). The volume on these modules gets set at a certain value, and then left alone, with main volume control being your bluetooth device.

What if we set the gain on the amp that drives the bass, at a lower level than the amp that drives the mid and high, but the volume on the bass amp higher.

Would the net effect be that the bass attenuates less than the mid/highs, if we use the bluetooth device to reduce the volume of the system? This of course assumes that amplification is steeper with a higher gain, which i don't know is true...

Idle minds are wondering about this stuff...
 
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I assume by gain you are referring to the feedback resistors at the TDA7498E chip and by volume you are referring to some kind of input signal attenuator before the amplifier.

Since both gain and volume controls are linear (they don't impart non-linear distortion), decreasing one and increasing the other proportionally will result in no net effect*. If you were hoping that adjusting them in some way would result in a more bassy tonal balance when the system volume control is set low or high this is not the case. To achieve that would require some kind of non-linear or dynamic compression circuit applied to the bass signal. Usually this would be accomplished in DSP to achieve an effect that is volume dependant. Alternatively you can add a static EQ filter which can be manually enabled or disabled by a 'loudness' button like classic amplifiers/receivers typically have.

*Typically you want to run the gain of your amplifier as low as possible and the 'volume' or signal level as high as possible while still achieving an acceptable in-room sound level with the volume control at max. This ensures the best signal to distortion/noise ratio.
 
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