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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.
* 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
Linkwitz Lab: CrossoversGlossary: Linkwitz–Riley
{{DEFAULTSORT:Linkwitz-Riley filter Linear filters Network synthesis filters Audio engineering Filter theory
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.
* 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
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of a ...
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 ''n''th-order Butterworth filters will give a (2''n'')th-order Linkwitz–Riley filter, theoretically any (2''n'')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.
Common types
Second-order Linkwitz–Riley crossover (LR2, LR-2)
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. Inloudspeaker
A loudspeaker (commonly referred to as a speaker or speaker driver) is an electroacoustic transducer that converts an electrical audio signal into a corresponding sound. A ''speaker system'', also often simply referred to as a "speaker" or ...
s 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
An operational amplifier (often op amp or opamp) is a DC-coupled high- gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op amp produces an output potential (relative t ...
.
Fourth-order Linkwitz–Riley crossover (LR4, LR-4)
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)
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
* Audio crossover * Butterworth filter *Partition of unity
In mathematics, a partition of unity of a topological space is a set of continuous functions from to the unit interval ,1such that for every point x\in X:
* there is a neighbourhood of where all but a finite number of the functions of are ...
* Siegfried Linkwitz
References
Linkwitz Lab: Crossovers
{{DEFAULTSORT:Linkwitz-Riley filter Linear filters Network synthesis filters Audio engineering Filter theory