What’s the Right Power Amp Ratio For Bi-Amping?

It depends on the design of the loudspeaker. It is my understanding that Magnepan recommended the two power amps used to bi-amp their old Tympani T-IVa be of equal power rating (and gain, of course), and chose the speaker’s cross-over frequencies (low pass: 3rd order @250Hz, high pass: 2nd order @400Hz) partly in relation to the speaker’s power "center" (the frequency at which equal amounts of power would be required to achieve the same SPL on each side of the x/o frequency created by the above two filters).

If there is no active crossover, your amp still has to produce the same voltage swings, and therefore needs to have the same voltage rails and rated for similar power, however it may not need a lot of current/low impedance capabilities.

Using an active crossover 5:1 would not be unreasonable.

Erik, I’m using conventional magnetic/voice coil speakers (not electrostatic) operating in bi-amp configuration with the woofer separated, but the crossover still engaged, limiting the band pass to the mid/high drivers. The upshot is that the mid/high frequency side will have an impedance to frequency curve that presents no load to the amplifier below the crossover point. That is why I want to devote my “big” 150 watt per channel amplifier to low frequencies, driving the woofers, and my “modest” 60 watt per channel amplifier to driving the mid/high drivers. The 150 watt per channel amplifier has input level trim controls so I can match its level to the smaller amplifier. I just need an idea of the ratio of power demand so I can be sure I’m not under-powering the mid/high drivers. 

A rule of thumb I’ve seen stated, which seems to me to make sense as a very rough approximation, is that music tends to require similar amounts of power at frequencies above and below 350 Hz. That should be considered in the context of the crossover point of the particular speaker, as bdp24 alluded to in his post. So if the crossover point of the speaker is considerably lower than that figure the high frequency amp will probably have to supply more power than the low frequency amp much of the time, and if the crossover point of the speaker is considerably higher than that figure the converse would be true.

The upshot is that the mid/high frequency side will have an impedance to frequency curve that presents no load to the amplifier below the crossover point.

That is an oversimplification, of course, as you probably realize. Below the crossover point the load impedance presented by the speaker to the high frequency amp will gradually increase as frequency decreases, at a rate roughly corresponding to the slope of the crossover network (e.g., 6 or 12 or 18 db/octave).

Also, Erik makes a good point about the fact that if the two amps are properly gain matched, and a passive biamp configuration is being used (i.e., there is not an electronic crossover "ahead" of the amps), both amps will have to output voltages corresponding to the full frequency range of the signal. As a practical matter what that usually means is that in a passive biamp configuration there should not be a huge disparity between the power capabilities of the two amps. Otherwise the power capability of the low frequency amp that can be utilized, without driving the high frequency amp into clipping, may be limited by the voltage swing capability of the high frequency amp.

Regards,
-- Al