Assuming a two-way speaker, the crossover itself must produce a pair of signals that sum to the original waveform. The drive units themselves must have sufficiently good phase and frequency responses and directivity characteristics that there is a reasonably wide band of frequency in which either drive unit could be used. The crossover frequency can then be placed within this band. Finally the physical arrangement of the drive units must be such that the acoustic summation of sounds from two drive units must be the inverse of the subtraction that took place in the crossover. Failure to address any one of these problems will result in a system that has audible deficiencies.
Looking first at the crossover itself, it’s an obvious requirement that the two output signals, high pass and low pass, should be capable of being summed together to recreate the original signal. Unfortunately in the vast majority of loudspeakers this doesn’t happen. It’s a simple fact that in order to get a pair of complementary signals it is necessary to use a subtraction stage in the crossover. This is fundamentally impossible in a passive crossover because passive circuitry can’t subtract. Thus passive crossovers are not crossovers at all, but a pair of filters, one high pass and one low pass, whose turnover frequencies happen to be similar.
The outputs of these crossovers cannot and do not sum to the original waveform. Instead the crossover frequency range is subject to a variety of deficiencies in amplitude, power and timing. The vast number of passive crossover topologies available simply fuels an endless debate about which one does the least harm, when the goal ought to be to do no harm at all. Thus, by definition, a passive two-way loudspeaker cannot reproduce the input waveform and cannot display linear phase through the crossover band...
The way forward in loudspeaker performance is clearly to use active technology. The problem is that just because a loudspeaker is active it doesn’t mean that it meets any of the criteria explained here. An active loudspeaker may be no more than a passive loudspeaker and passive crossover with a built in amplifier. An active loudspeaker having a line level crossover might be a better bet, but the crossover may just be a line level version of the traditional passive crossover. In this case the only benefit is reduced intermodulation. A further problem is that when the speaker is active, it costs more, so the manufacturer may be tempted to cut corners to get the price down. This isn’t logical, as the purchaser doesn’t need to buy a power amplifier, but then we don’t live in a logical world.