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3.11 Should I get an active or a passive crossover? [JSC, JR]
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[note: Related question: What is a crossover?
Active crossovers are more efficient than passive crossovers. A typical insertion loss (power loss due to use) of a passive crossover is around 0.5dB. Active crossovers have much lower insertion losses, if they have any loss at all, since the losses can effectively be negated by adjusting the amplifier gain. Also, with some active crossovers, you can continuously vary not only the crossover point, but also the slope. Thus, if you wanted to, with some active crossovers you could create a high pass filter at 112.3Hz at -18dB/octave, or other such things.
However, active crossovers have their disadvantages as well. An active crossover may very well cost more than an equivalent number of passive crossovers. Also, since the active crossover has separate outputs for each frequency band that you desire, you will need to have separate amplifiers for each frequency range. Furthermore, since an active crossover is by definition a powered device, the use of one will raise a system's noise floor, while passive crossovers do not insert any additional noise into a system.
Many people find it advantageous to use both active and passive crossovers. Often, a separate amp is dedicated to the subwoofers, to give them as much power as possible. The other amplifier is used to power the mids and tweeters. In this scheme, an active crossover is used to send only the sub-bass frequencies to the sub amp, and the other frequencies to the other amp. The passive crossovers are used to send the correct frequencies to the individual speakers (e.g., mids and tweeters).
Thus, if you have extra money to spend on an active crossover and separate amplifiers, and are willing to deal with the slightly more complex installation and possible noise problems, an active crossover is probably the way to go. However, if you are on a budget and can find a passive crossover with the characteristics you desire, go with a passive.