There are active and passive crossovers. Crossover are devices (or networks) to split a signal in signals with different bandwidths, for different drivers in the loudspeakers.
Passive crossovers have only passive components. Without active components the signal can only be attenuated, never amplified. In practice the gain is always lower than one, because there is always some insertion loss. (Actually, a passive crossover can have some gain in a small bandwidth (a peak) if the crossover acts as a resonator. And a crossover can also give peaks in the response at the crossover frequency when the sound of the different drivers add up).
Active crossovers have also active components and give much more possibilities, especially, amplifying a certain bandwidth.
Crossovers can be placed anywhere in the audio chain. A usual place for a crossover is between power amplifier and loudspeaker drivers, in the loudspeaker or as a separate device. And because of the high voltages, high currents and high power, crossovers placed after the power amplifier are passive crossovers.
Another place for crossovers is before the power amplifier, and then you need more power amplifiers. Now the crossover only has to deal with low level signals which makes the use of active devices possible. So active crossovers are usually placed before the power amplifiers.
A crossover can also be placed before the digital to analog conversion (DAC), which means you need more DAC’s (a multi-channel DAC for stereo). This opens up even more possibilities, like very high order filters with very high precision (without extra components) and time alignment.
Why active crossovers?
The actual question should read: Why passive crossovers? Because I don’t see any reason, sound wise and cost wise (more on this later) to use passive crossovers.
The only possible reason to use passive crossovers is because lot of others use passive crossovers in their speakers, and by doing that also, you can mix and match amplifiers with that type of loudspeakers.
On the other hand, the main reason for me for using (digital) active crossovers is that it gives far more possibilities to mix and match: drivers, enclosures, power amplifiers, DACs, DSP-hardware, filter algorithm implementations and filter specifications. And now even level dependent crossover frequencies are possible. The only ‘problem’ in using off-the-shelf loudspeakers that I have to pass the crossover.
Active crossovers are more common in the professional market. And in the mean time there are more and more active speakers where crossover, power amplifier and drivers are integrated into one box: subwoofers, wireless speakers, computer speakers, but also hifi and audiophile speakers. Bi-amped two-way and tri-amped three-way loudspeakers also need active crossovers.
Passive crossovers are unstable
Crossover filters are designed to a specific load impedance. But the impedance raises and lowers with the average power of the music. Between 90 % with 102 dB efficient drivers, till 99.9 % with 82 dB efficient drivers, of the power is turned into heat, which makes, in the worst case (a power compression of 6 dB), the impedance four times higher. The raise of the impedance influences the cutoff frequency of the crossover filter and/or the rolloff curve of the crossover filter.
Passive crossovers suck up power
Passive crossovers suck up power of the power amplifier. The passive crossover operates between the power amplifier and the loudspeaker drivers. Drivers normally have a nominal impedance of 8 or 4 ohms, so one ohm or a part of an ohm resistance for the crossover suck up a lot o power. Better coils for passive crossover ar between 0.2 and 0.5 ohm. So, an 0.4 ohm coil with an 8 ohm driver costs 5 % of the power, and with a 4 ohm driver 10%! And besides that, the most efficient drivers of the loudspeaker get a resistor in series to temper its efficiency to equal it to the driver with the least efficiency.
Passive crossovers are expensive
The passive crossover must deal with high voltages, high currents and high power and needs very expensive components to sound good under those circumstances.
Active crossovers make more efficient use of amplifiers
The usual argument against active crossovers was that you need more amplifiers which raises the costs.
An example. Suppose you have a two-way loudspeaker with two 4 Ω drivers and that you have a signal that requires 20 V and 5 A for each driver (for example a sine for the woofer and a sine for the tweeter). In the case of an active crossover you need two amplifiers each capable of delivering 20 V and 5 A, which is 100 W. And a power supply to feed two of those amplifiers. In the case of passive crossovers one amplifier must handle the combined signal: 40 V and 10 A, which is 400 W. Actually, you need some more, because there is a passive crossover between the power amplifier and the drivers. And you need a power supply feeding four times the power of one amplifier in the active case.
So, in the passive case you need only one amplifier in stead of two (for that two-way loudspeaker), but it must have at least a four times bigger power handling and a power supply with at least double capacity. And this is a two-way case.
In the case of a three-way with passive crossovers, the amplifier must be (at least) nine times as big and the power supply three times as big.
In the case of a four-way with passive crossovers (or three-way and sub), the amplifier must be (at least) sixteen times as big and the power supply four times as big. An active four-way system with 100 Watt amplifiers is the equivalent of about 1600 Watt in the passive case! In practice, the crossover frequencies are not chosen for equal distribution of power over the drivers, but you get the point.
So, passive crossovers need much bigger amplifiers, bigger power supplies and very expensive crossover components to handle the high powers.
Or, the other way around, with active crossovers you can easily create large amounts of headroom in the amplifiers.
Active crossovers give better clipping behavior
If, despite the extra headroom, an amplifier of one of the drivers clips, the signal for the other drivers stays clean.
The tweeter is most sensitive to added harmonics, but the tweeter amplifier is the least likely amplifier to clip. If the woofer amplifier clips, the tweeter doesn’t get more harmonics.
Active crossovers give better intermodulation behavior
Each amplifier has only a part of the total bandwidth, so there are less modulating signals per amplifier. For example, if you have two tones, one for the woofer and one for the tweeter, they are separated in different amplifiers, so there cannot be any intermodulation between those tones.
And if there is intermodulation, there is only intermodulation for that particular driver.