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While outboard electronic crossovers are not widely used nowadays, this information is still relevant because it applies to the internal crossovers built into most car audio amplifiers.
A crossover is a filter. It is used to block some frequencies while allowing others to pass with little or no effect. An electronic crossover is a set of active filters which pass/reject part of the audio band. The crossover point is determined by changing the value of resistors and/or capacitors in the active filter circuit. A high pass crossover will allow frequencies above a predetermined point to pass. The frequencies below the crossover point will rolloff at a rate determined by the crossover's design. A low pass crossover would let low frequencies pass while reducing the level of the high frequency part of the signal. The signal from the head unit feeds the crossover. The signal leaving the crossover goes to an amplifier. If the high pass output is connected to an amplifier, that amplifier would be connected to smaller speakers which may include tweeters. A low pass xover would drive an amp connected to larger speakers, including woofers.
It was stated that an electronic crossover uses active filters to filter/attenuate parts of the audio spectrum. In virtually all instances, the active filters use operational amplifiers (op-amps -- to be covered later). This is in contrast to passive filters (which you'll be introduced to in an upcoming chapter) that use inductors and capacitors to create the filter. Active filters are used where the power passing through the filter is minimal (preamp level audio). Passive crossovers and filters are used when the power passing through the filter is significant (speaker level audio). There is still (at least) one more type of filter. These are digital filters in DSP (Digital Signal Processor) units. The function of a DSP unit is entirely different. They take in analog or digital audio (analog audio has to be converted to a digital format), use algorithms to produce the desired effects and then convert it back to analog audio. They have several advantages but are generally more expensive to implement.
The image below shows how the level of the audio signal rolls off after passing through different types of crossovers. High-pass crossovers pass high frequencies and roll off lower frequencies. Low-pass crossovers pass low frequencies and roll off higher frequencies. If you had a system with a subwoofer for bass and 6x9s for the highs, you would use a low-pass crossover for the woofer and a high-pass crossover for the 6x9s.
Place your mouse/cursor over the crossover frequencies to the left of the graph to see how the slope slides (to pass varying amounts of the audio spectrum) as you change the crossover point. The frequencies that fall on the flat part of the 'curve' are passed without any change in their output level. The part of the audio band that falls on the slope of the curve have their output reduced. Their output level is reduced in proportion to the point where they fall on the curve. If they fall on the higher part of the slope, the output is higher than those frequencies that fall on the lower parts of the slope.
Some electronic crossovers are simple. Many (like the one below) are available with only one set of inputs and one set of outputs and only work as a low pass crossover. This one has both high and low level inputs. High level inputs are designed to accept speaker level signals. Low level inputs are designed for preamp level input. It also has bass boost and multiple options for the bass boost and crossover frequencies. Expect to pay about $20US for a crossover like this.
Crossovers like the next one are more complex and offer more flexibility. It's a 2/3 way crossover which means it can operate in either 2 or 3 way configuration. It's important that you not buy a 3 way crossover if you only need a 2-way crossover because, many times, a 3-way crossover will not allow the entire audio band to play through using only two of the outputs. 2-way crossovers have high and low outputs. 3-way crossovers have low, mid and high outputs. Generally, the midrange cannot extend high enough to play the upper frequencies and the high frequency output cannot pass the lower midrange frequencies. On most crossovers similar to this one, you can use one, two or three pairs of inputs (pair = left and right channels) to produce output from all 3 pairs of outputs.
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