Editing Audio crossover (section)

====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.