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The function of the crossover is to separate low, mid and high frequencies according to the number of drive units in the loudspeaker. A crossover can be passive or active. A passive crossover is generally internal to the cabinet and consists of a network of capacitors, inductors and resistors. Having no active components, it doesn't need to be powered. An active crossover on the other hand does contain transistors or ICs and requires mains power. It sits between the output of the mixing console and a number of power amplifiers - one for each division of the frequency band. A system with a three-band active crossover would require three power amplifiers.
Crossovers have two principal parameter sets: the cut off frequencies of the bands, and the slopes of the filters. It is impractical, and actually undesirable, to have a filter that allows frequencies up to, say, 4 kHz to pass and then cut off everything above that completely. So frequencies beyond the cutoff frequency (where the response has dropped by 3 dB from normal) are rolled off at a rate of 6, 12, 18 or 24 dB per octave. In other words, in the band of frequencies where the slope has kicked in, as the frequency doubles the response drops by that number of decibels. The slopes mentioned are actually the easy ones to design. A filter with a slope of, say, 9 dB per octave would be much more complex.
As it happens, a slope of 6 dB per octave is useless. High frequencies would be sent to the woofer at sufficient level that there would be audible distortion due to break up. Low frequencies would be sent to the tweeter that could damage it. 12 dB/octave is workable, but most systems these days use 18 dB/octave or 24 dB/octave. There are issues with the phase response of crossover filters that vary according to slope, but this is an advanced topic that few working sound engineers would contemplate to any great extent.
Passive crossovers have a number of advantages:
And the disadvantages:
Likewise, active crossovers have advantages:
And the disadvantages:
Some loudspeaker systems come as a package with a dedicated loudspeaker control unit. The control unit consists of three components: