Linkwitz–Riley Filter
   HOME

TheInfoList



OR:

A Linkwitz–Riley (L-R) filter is an
infinite impulse response Infinite impulse response (IIR) is a property applying to many linear time-invariant systems that are distinguished by having an impulse response h(t) that does not become exactly zero past a certain point but continues indefinitely. This is in ...
filter used in Linkwitz–Riley
audio crossover Audio crossovers are a type of electronic filter circuitry that splits an audio signal into two or more frequency ranges, so that the signals can be sent to loudspeaker drivers that are designed to operate within different frequency ranges. Th ...
s. It is named after its inventors
Siegfried Linkwitz Siegfried Linkwitz (November 23, 1935 – September 11, 2018) was a German American engineer who was noted co-inventor of the Linkwitz–Riley filter along with Russ Riley. He submitted several important technical papers to the ''Journal of th ...
and Russ Riley and was originally described in ''Active Crossover Networks for Noncoincident Drivers''. It is also known as a ''Butterworth squared'' filter. A Linkwitz–Riley crossover consists of a parallel combination of a low-pass and a high-pass L-R filter. These filters are typically designed by cascading two
Butterworth filter The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter. It was first described in 1930 by the B ...
s, each providing a gain at the cut-off frequency. The resulting Linkwitz–Riley filter has a gain at the cut-off frequency. This means that when summing the low-pass and high-pass outputs, the gain at the crossover frequency is . As a result, the crossover network behaves like an all-pass, exhibiting 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 am ...
response with a smoothly changing
phase response In signal processing, phase response is the relationship between the phase of a sinusoidal input and the output signal passing through any device that accepts input and produces an output signal, such as an amplifier An amplifier, electro ...
. This is a primary advantage of L-R crossovers compared to even-order
Butterworth filter The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter. It was first described in 1930 by the B ...
crossovers, whose summed output has a peak around the crossover frequency. Since cascading two ''n''th-order
Butterworth filter The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter. It was first described in 1930 by the B ...
filters creates 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 be less practical due to their complexity and an increasing peak in
group delay In signal processing, group delay and phase delay are functions that describe in different ways the delay times experienced by a signal’s various sinusoidal frequency components as they pass through a linear time-invariant (LTI) system (such as ...
around the crossover frequency.


Common types


Second-order Linkwitz–Riley crossover

Second-order Linkwitz–Riley crossovers (LR2, LR12) have a () slope. They can be realized by cascading two one-pole filters or by using a
Sallen Key filter Sallen () is a commune in the Calvados department in the Normandy region in northwestern France. Population See also *Communes of the Calvados department The following is a list of the 526 Communes of France, communes of the Calvados ...
topology with a Q0 value of 0.5. There is a 180° phase difference between the
low-pass A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filt ...
and
high-pass A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency de ...
outputs, which can be corrected by inverting one signal. In
loudspeaker A loudspeaker (commonly referred to as a speaker or, more fully, a speaker system) is a combination of one or more speaker drivers, an enclosure, and electrical connections (possibly including a crossover network). The speaker driver is an ...
s, this is usually done by reversing the polarity of one driver if the crossover is
passive Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive * Passive language, a language from which an interpreter works * Passivity (behavior), the condition of submitting to the influence of ...
. For active crossovers, inversion is typically achieved using a unity gain inverting
op-amp An operational amplifier (often op amp or opamp) is a DC-coupled electronic voltage amplifier with a differential input, a (usually) single-ended output, and an extremely high gain. Its name comes from its original use of performing mathem ...
.


Fourth-order Linkwitz–Riley crossover

Fourth-order Linkwitz–Riley crossovers (LR4, LR24) are currently the most commonly used type of audio crossover. They are constructed by cascading two 2nd-order Butterworth filters. Their slope is (). The phase difference is 360°, meaning the two drivers appear in phase, although the low-pass section has a full period time delay.


Eighth-order Linkwitz–Riley crossover

Eighth-order Linkwitz–Riley crossovers (LR8, LR48) have a very steep, () slope. They can be constructed by cascading two 4th-order Butterworth filters.


See also

*
Partition of unity In mathematics, a partition of unity on a topological space is a Set (mathematics), set of continuous function (topology), continuous functions from to the unit interval ,1such that for every point x\in X: * there is a neighbourhood (mathem ...


References


External links


Linkwitz Lab: CrossoversGlossary: Linkwitz–Riley
{{DEFAULTSORT:Linkwitz-Riley filter Linear filters Network synthesis filters Audio engineering Filter theory