Linkwitz-Riley filter
A Linkwitz-Riley filter (LR filter) is an electronic filter that is used in Linkwitz-Riley crossovers . It is named after its inventors Siegfried Linkwitz and Russ Riley . It is also known as a Butterworth Double Filter because it is formed by cascading two Butterworth filters .
General
An LR crossover consists of a parallel arrangement of an LR low pass and an LR high pass, the outputs of which are e.g. B. can be used to control power amplifiers for operating multi-way active speaker systems. The rated frequency of both filters is the same and is called the takeover frequency in the case of crossover arrangements.
LR filters are implemented by cascading two Butterworth filters , each of which has a gain of −3 dB at its rated frequency. The resulting Linkwitz-Riley filter now has a gain of −6 dB at the rated frequency.
If the high-pass and low-pass outputs are added, the gain at the crossover frequency is 0 dB. The whole arrangement behaves like an all-pass filter with a flat amplitude response and a phase that changes slowly over the frequency . The flat amplitude response is the greatest advantage compared to Butterworth crossovers, because when the outputs are added together, they have a gain of +3 dB at the takeover frequency.
Cascading two Butterworth filters of the nth order result in a Linkwitz-Riley filter of the 2nd order. Theoretically, every 2nd order LR crossover can be built in this way. Crossovers with a higher than 4th order are hardly used, as the group delay increases too much around the crossover frequency . In addition, for orders larger than 4, the complexity of the electrical structure increases too much. The increased number of components makes the system prone to errors and malfunctions and is too dependent on the tolerances of the individual components.
Often used types
Second order (LR2, LR-2)
Second order Linkwitz-Riley crossovers have a slope of 12 dB / octave (40 dB / decade). They can be built from two first-order passive filters or according to Sallen-Key topology with a quality factor of Q 0 = 0.5. The phase difference of 180 ° between the low-pass and high-pass output of the crossover can be compensated by inverting a signal. In loudspeakers this is achieved by reversing the polarity of a chassis when using passive crossovers. With active crossovers, an operational amplifier (OPV) connected as an inverting unit amplifier is added or an OPV can be used to invert the signal. With symmetrical cabling , both signal wires (the "cold" with the "hot" wire) can be exchanged.
Fourth order (LR4, LR-4)
Fourth-order Linkwitz-Riley crossovers are the most widely used speaker crossovers . Two Butterworth filters are cascaded for this. The slope is 24 dB / octave (80 dB / decade). The phase difference between the low-pass and high-pass output of the crossover is 360 °, so they seem to be in phase, with the low-pass lagging a full period.
Eighth order (LR8, LR-8)
Linkwitz-Riley crossovers of the eighth order are very steep at 48 dB / octave (160 dB / decade) . They are built from two cascaded 4th order Butterworth filters.
Web links
- Linkwitz Lab: Crossovers
- Linkwitz Lab: Active Filters
- Linkwitz-Riley Crossovers: A Primer
- Glossary: Linkwitz-Riley