I was responding to an earlier post that stated power delivered by both amps in a passively bi-amped system was the same. Not sure how I got so far out of synch, the "False" statement was about that, not the immediately preceeding posts. I am leaving this mess in case it helps. >
False. Here is a hand-waving idealized explanation that might help:
AVR -> LF amp, HF amp -> speaker LF input, HF input
Each amp sees the same signal from the AVR. Assuming identical amps, the output voltage
from each amp will be the same, over all frequencies. However, the speaker's crossover will reject out-of-band signals so the LF amp, whilst delivering a full-range voltage at its outputs, will only deliver current and thus power (the product of voltage and current, P = V*I) to the LF driver, and the HF amp will deliver HF power to the HF driver. Assuming ideal (lossless, brick-wall) crossovers, the LF amp will not provide power at higher frequencies, and the HF amp will not provide power at lower frequencies. They will both provide voltage at all frequencies, and that is the main drawback of passive bi-amping. Most amplifiers for most loads are limited by their voltage rails, and passive bi-amping does not change the voltages.
Restated: The LF amp delivers the same output voltage as the HF amp; both deliver the same voltage over all frequencies. However, the LF amp delivers only LF current and power to the speaker, and the HF amp only HF current/power, because the crosover inside the speaker will "block" the other frequencies from the driver. In a passive bi-amp system there is no additional voltage headroom and thus no sonic benefits (in the vast majority of cases; I am sure all passive bi-amp proponents have one of those special cases, everybody is above average
In an active system there is a crossover before the power amps, so they only deliver voltage and power in the appropriate frequency band, preserving voltage headroom.
If you have a 100 W amp it delivers 100 W over all frequencies. If you bi-amp with two 100 W amps the LF driver can see up to 100 W and the HF driver can see up to 100 W. If you are passively bi-amping, since both amps have the same voltage output over all frequencies, there is no voltage headrooom added. You have split the output across two amps but essentially no additional power is gained; 100 W to all drivers vs. 100 W to the low driver and 100 W to the high driver, still limited by voltage rails in the amp, each driver sees no more power than before.
Note that in an active system each driver still sees no more max power than before, but there is in general extra headroom because the frequency range is limited by the crossover before the amplifiers so the LF amp only puts out LF voltage (and current, and power), and of course the HF amp only puts out HF energy.
This would be much easier in person with a whiteboard.
HTH - Don