Originally Posted by Kach22
an active crossover and passive crossover would introduce identical amounts of distortion if they were built using the same components
But they aren't. Actives don't use coils, and the cap values are some 1/100 of that for passive, so the highest quality caps can be used at minimal cost. And that's analog, digital crossovers can be even lower in distortion.
The only part of the signal being attenuated (and distorted) when it goes through a filter is the part of the signal that is not being used by the driver at the output of the filter. The portion of the signal being used goes through the filter untouched as if the filter was not even there.
That's not the case. In a low pass all of the signal passes through the inductors, in a high pass all of the signal passes through the caps, and in a bandpass all of the signal passes through both caps and coils that aren't shunts.
The losses due to passive filters are not very significant,
3dB is not uncommon, that's half your power. 2dB is considered very good, 1dB is rare.
The main issue is that the power is being divided among multipe drivers, again this makes the biggest difference when mid-drivers are present.
In a typical three way system 75% of the power is dissipated in the woofers, 20% in the midranges, 5% in the tweeters. The main use for multi-band amplification is in pro-sound, and it's used there for the driver protection offered by 4th order and higher filtering that would be prohibitively expensive with passive components capable of handling the load without excessive insertion loss.