A Linkwitz–Riley (L-R) filter is an infinite impulse response filter used in Linkwitz–Riley audio crossovers, named after its inventors Siegfried Linkwitz and Russ Riley. This filter type was originally described in Active Crossover Networks for Noncoincident Drivers in the Journal of the Audio Engineering Society.[1][2] It is also known as a Butterworth squared filter. A Linkwitz–Riley "L-R" crossover consists of a parallel combination of a low-pass and a high-pass L-R filter. The filters are usually designed by cascading two Butterworth filters, each of which has −3 dB gain at the cut-off frequency. The resulting Linkwitz–Riley filter has −6 dB gain at the cut-off frequency. This means that, upon summing the low-pass and high-pass outputs, the gain at the crossover frequency will be 0 dB, so the crossover behaves like an all-pass filter, having a flat amplitude response with a smoothly changing phase response. This is the biggest advantage of L-R crossovers compared to even-order Butterworth crossovers, whose summed output has a +3 dB peak around the crossover frequency. Since cascading two nth-order Butterworth filters will give a (2n)th-order Linkwitz–Riley filter, theoretically any (2n)th-order Linkwitz–Riley crossover can be designed. However, crossovers of order higher than 4 may have less usability due to their complexity and the increasing size of the peak in group delay around the crossover frequency.
Comparison of the magnitude response of the summed Butterworth and Linkwitz–Riley low-pass and high-pass 2nd-order filters. The Butterworth filters have a +3dB peak at the crossover frequency, whereas the L-R filters have a flat summed output.
Second-order Linkwitz–Riley crossovers (LR2) have a 12 dB/octave (40 dB/decade) slope. They can be realized by cascading two one-pole filters, or using a Sallen Key filter topology with a Q0 value of 0.5. There is a 180° phase difference between the low-pass and high-pass output of the filter, which can be corrected by inverting one signal. In loudspeakers this is usually done by reversing the polarity of one driver if the crossover is passive. For active crossovers inversion is usually done using a unity gain inverting op-amp.
Fourth-order Linkwitz–Riley crossovers (LR4) are probably today's most commonly used type of audio crossover. They are constructed by cascading two 2nd-order Butterworth filters. Their slope is 24 dB/octave (80 dB/decade). The phase difference amounts to 360°, i.e. the two drives appear in phase, albeit with a full period time delay for the low-pass section.
Eighth-order Linkwitz–Riley crossovers (LR8) have a very steep, 48 dB/octave (160 dB/decade) slope. They can be constructed by cascading two 4th-order Butterworth filters.
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^ abcLinkwitz, Siegfried H. (February 1976). "Active Crossover Networks for Noncoincident Drivers". Journal of the Audio Engineering Society. 24 (1): 2–8. Retrieved 2024-05-05.
^Linkwitz, Siegfried H. (1976). "Active Crossover Networks for Noncoincident Drivers". Linkwitz Lab. Retrieved 2024-05-05.
^ abcBohn, Dennis (2005). "Linkwitz-Riley Crossovers: A Primer (RaneNote 160)" (PDF). Rane Corporation. Retrieved 2024-05-05.
January 01, 1970
linkwitz, riley, filter, linkwitz, riley, filter, infinite, impulse, response, filter, used, linkwitz, riley, audio, crossovers, named, after, inventors, siegfried, linkwitz, russ, riley, this, filter, type, originally, described, active, crossover, networks, . A Linkwitz Riley L R filter is an infinite impulse response filter used in Linkwitz Riley audio crossovers named after its inventors Siegfried Linkwitz and Russ Riley This filter type was originally described in Active Crossover Networks for Noncoincident Drivers in the Journal of the Audio Engineering Society 1 2 It is also known as a Butterworth squared filter A Linkwitz Riley L R crossover consists of a parallel combination of a low pass and a high pass L R filter The filters are usually designed by cascading two Butterworth filters each of which has 3 dB gain at the cut off frequency The resulting Linkwitz Riley filter has 6 dB gain at the cut off frequency This means that upon summing the low pass and high pass outputs the gain at the crossover frequency will be 0 dB so the crossover behaves like an all pass filter having a flat amplitude response with a smoothly changing phase response This is the biggest advantage of L R crossovers compared to even order Butterworth crossovers whose summed output has a 3 dB peak around the crossover frequency Since cascading two nth order Butterworth filters will give a 2n th order Linkwitz Riley filter theoretically any 2n th order Linkwitz Riley crossover can be designed However crossovers of order higher than 4 may have less usability due to their complexity and the increasing size of the peak in group delay around the crossover frequency Comparison of the magnitude response of the summed Butterworth and Linkwitz Riley low pass and high pass 2nd order filters The Butterworth filters have a 3dB peak at the crossover frequency whereas the L R filters have a flat summed output Contents 1 Common types 1 1 Second order Linkwitz Riley crossover LR2 LR 2 1 3 1 2 Fourth order Linkwitz Riley crossover LR4 LR 4 1 3 1 3 Eighth order Linkwitz Riley crossover LR8 LR 8 3 2 See also 3 ReferencesCommon types editSecond order Linkwitz Riley crossover LR2 LR 2 1 3 edit Second order Linkwitz Riley crossovers LR2 have a 12 dB octave 40 dB decade slope They can be realized by cascading two one pole filters or using a Sallen Key filter topology with a Q0 value of 0 5 There is a 180 phase difference between the low pass and high pass output of the filter which can be corrected by inverting one signal In loudspeakers this is usually done by reversing the polarity of one driver if the crossover is passive For active crossovers inversion is usually done using a unity gain inverting op amp Fourth order Linkwitz Riley crossover LR4 LR 4 1 3 edit Fourth order Linkwitz Riley crossovers LR4 are probably today s most commonly used type of audio crossover They are constructed by cascading two 2nd order Butterworth filters Their slope is 24 dB octave 80 dB decade The phase difference amounts to 360 i e the two drives appear in phase albeit with a full period time delay for the low pass section Eighth order Linkwitz Riley crossover LR8 LR 8 3 edit Eighth order Linkwitz Riley crossovers LR8 have a very steep 48 dB octave 160 dB decade slope They can be constructed by cascading two 4th order Butterworth filters See also edit nbsp Wikimedia Commons has media related to Linkwitz Riley filters Audio crossover Butterworth filter Partition of unity Siegfried Linkwitz Linkwitz Lab Crossovers Linkwitz Lab Active Filters Linkwitz Riley Crossovers A Primer Glossary Linkwitz RileyReferences edit a b c Linkwitz Siegfried H February 1976 Active Crossover Networks for Noncoincident Drivers Journal of the Audio Engineering Society 24 1 2 8 Retrieved 2024 05 05 Linkwitz Siegfried H 1976 Active Crossover Networks for Noncoincident Drivers Linkwitz Lab Retrieved 2024 05 05 a b c Bohn Dennis 2005 Linkwitz Riley Crossovers A Primer RaneNote 160 PDF Rane Corporation Retrieved 2024 05 05 Retrieved from https en wikipedia org w index php title Linkwitz Riley filter amp oldid 1222312139, wikipedia, wiki, book, books, library,
