Editing Audio crossover (section)

===Classification based on filter order or slope===
Just as filters have different orders, so do crossovers, depending on the filter slope they implement. The final acoustic slope may be completely determined by the electrical filter or may be achieved by combining the electrical filter's slope with the natural characteristics of the driver. In the former case, the only requirement is that each driver has a flat response at least to the point where its signal is approximately −10dB down from the passband. In the latter case, the final acoustic slope is usually steeper than that of the electrical filters used. A third- or fourth-order acoustic crossover often has just a second-order electrical filter. This requires that speaker drivers be well behaved a considerable way from the nominal crossover frequency, and further that the high-frequency driver be able to survive a considerable input in a frequency range below its crossover point. This is difficult to achieve in actual practice. In the discussion below, the characteristics of the electrical filter order are discussed, followed by a discussion of crossovers having that acoustic slope and their advantages or disadvantages.

Most audio crossovers use first- to fourth-order electrical filters. Higher orders are not generally implemented in passive crossovers for loudspeakers but are sometimes found in electronic equipment under circumstances for which their considerable cost and complexity can be justified.

====First order====
First-order filters have a 20 dB/[[Decade (log scale)|decade]] (or 6 dB/[[octave]]) slope. All first-order filters have a Butterworth filter characteristic. First-order filters are considered by many [[audiophile]]s to be ideal for crossovers. This is because this filter type is 'transient perfect', meaning that the sum of the low-pass and high-pass outputs passes both amplitude and phase unchanged across the range of interest.<ref name="Ashley1962" /> It also uses the fewest parts and has the lowest insertion loss (if passive). A first-order crossover allows more signal content consisting of unwanted frequencies to get through in the LPF and HPF sections than do higher-order configurations. While woofers can easily handle this (aside from generating distortion at frequencies above those that they can properly reproduce), smaller high-frequency drivers (especially tweeters) are more likely to be damaged, since they are not capable of handling large power inputs at frequencies below their rated crossover point. 

In practice, speaker systems with true first-order acoustic slopes are difficult to design because they require large overlapping driver bandwidth, and the shallow slopes mean that non-coincident drivers interfere over a wide frequency range and cause large response shifts off-axis.

====Second order====
Second-order filters have a 40 dB/decade (or 12 dB/octave) slope. Second-order filters can have a [[Bessel filter |Bessel]], [[Linkwitz-Riley filter |Linkwitz-Riley]] or Butterworth characteristic depending on design choices and the components that are used. This order is commonly used in passive crossovers as it offers a reasonable balance between complexity, response, and higher-frequency driver protection. When designed with time-aligned physical placement, these crossovers have a symmetrical [[wiktionary:polarity|polar]] response, as do all even-order crossovers. 

It is commonly thought that there will always be a [[Phase (waves)|phase]] difference of 180° between the outputs of a (second-order) low-pass filter and a high-pass filter having the same crossover frequency. And so, in a 2-way system, the high-pass section's output is usually connected to the high-frequency driver 'inverted', to correct for this phase problem. For passive systems, the tweeter is wired with opposite polarity to the woofer; for active crossovers the high-pass filter's output is inverted. In 3-way systems the mid-range driver or filter is inverted. However, this is generally only true when the speakers have a wide response overlap and the acoustic centers are physically aligned.

====Third order====
Third-order filters have a 60 dB/decade (or 18 dB/octave) slope. These crossovers usually have Butterworth filter characteristics; [[phase response]] is very good, the level sum being flat and in phase [[Quadrature phase|quadrature]], similar to a first-order crossover. The polar response is asymmetric. In the original [[Joseph D'Appolito|D'Appolito]] [[Midwoofer-tweeter-midwoofer|MTM arrangement]], a symmetrical arrangement of drivers is used to create a symmetrical off-axis response when using third-order crossovers. Third-order acoustic crossovers are often built from first- or second-order filter circuits.

====Fourth order====
[[File:Smaart 4 crossover traces.jpg |thumb |300px |Fourth-order crossover slopes shown on a [[Smaart]] transfer function measurement.]]

Fourth-order filters have an 80 dB/decade (or 24 dB/octave) slope. These filters are relatively complex to design in passive form, because the components interact with each other, but modern computer-aided crossover optimisation design software can produce accurate designs.<ref name="AdamsRoe1982" /><ref name="Schuck1986" /><ref name="Waldman1988" /> Steep-slope passive networks are less tolerant of parts value deviations or tolerances, and more sensitive to mis-termination with reactive driver loads (although this is also a problem with lower-order crossovers). A 4th-order crossover with −6 dB crossover point and flat summing is also known as a [[Linkwitz-Riley filter |Linkwitz-Riley crossover]] (named after its inventors<ref name="Linkwitz1978" />), and can be constructed in active form by cascading two 2nd-order Butterworth filter sections. The low-frequency and high-frequency output signals of the Linkwitz–Riley crossover type are in phase, thus avoiding partial phase inversion if the crossover band-passes are electrically summed, as they would be within the output stage of a [[Dynamic range compression#Multiband compression |multiband compressor]]. Crossovers used in loudspeaker design do not require the filter sections to be in phase; smooth output characteristics are often achieved using non-ideal, asymmetric crossover filter characteristics.<ref name="Hughes" /> Bessel, Butterworth, and Chebyshev are among the possible crossover topologies.

Such steep-slope filters have greater problems with overshoot and ringing<ref name="Bohn2005" /> but there are several key advantages, even in their passive form, such as the potential for a lower crossover point and increased [[power handling]] for tweeters, together with less overlap between drivers, dramatically reducing the shifting of the main lobe of a multi-way loudspeaker system's radiation pattern with frequency,<ref name="Linkwitz1978" /> or other unwelcome off-axis effects. With less frequency overlap between adjacent drivers, their geometric location relative to each other becomes less critical and allows more latitude in speaker system cosmetics or (in-car audio) practical installation constraints.

====Higher order====
Passive crossovers giving acoustic slopes higher than fourth-order are not common because of cost and complexity. Filters with slopes of up to 96 dB per octave are available in active crossovers and loudspeaker management systems.

====Mixed order====
Crossovers can also be constructed with mixed-order filters. For example, a second-order low-pass filter can be combined with a third-order high-pass filter. These are generally passive and are used for several reasons, often when the component values are found by computer program optimization.  A higher-order tweeter crossover can sometimes help to compensate for the time offset between the woofer and tweeter, caused by non-aligned acoustic centers.

====Notched====
There is a class of crossover filters that produce null responses in the high-pass and low-pass outputs at frequencies close to the crossover frequency. Within their respective stopbands, the outputs have a high initial rate of attenuation, while the sum of their outputs has a flat all-pass response. Their two outputs maintain a constant zero-phase difference across the transition, thus enhancing their lobing performance with noncoincident loudspeaker drivers.<ref name="Thiele2000" />