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10 July 1998
band and LP2 lowpass filter in the low band. The inclusion of
these filters is mandatory for proper implementation of the 3-way
Linkwitz-Riley crossover; they ensure that the phase shift and
magnitude response in each band match those of the other
bands to maintain the fundamental Linkwitz-Riley sum-to-allpass
quality. A detailed explanation of the use of compensation filters
such as these may be found in “Active Realization of Multiway
All-Pass Crossover Systems” by Joseph A. D’Appolito;

Journal

of the Audio Engineering Society

, Volume 35, Number 4, April
1987.
A 3-way Linkwitz-Riley crossover is essentially a combination of
two 2-way Linkwitz-Riley crossovers. This means that the
polarity requirements associated with a 2-way Linkwitz-Riley
crossover carry over to a 3-way crossover.
A properly implemented 2-way, 12 dB/octave Linkwitz-Riley
crossover is characterized by:
•2
nd-order Linkwitz-Riley (Butterworth-Squared) lowpass filter, -6
dB magnitude response at crossover frequency
•2
nd-order Linkwitz-Riley (Butterworth-Squared) highpass filter,
-6 dB magnitude response at crossover frequency
• polarity of highpass band opposite that of lowpass band
In a 3-way crossover the bands associate in non-obvious ways
(see Sum-to-Allpass Characteristics of Linkwitz-Riley
Crossovers), and the polarity reference for the high band is
unexpectedly the low band, rather than the adjacent mid band.
Thus, if a 12 dB/octave filter is used for LP1 and HP1, then the
mid band must be out-of-phase with the low band. If a 12 dB/
octave filter is used for LP2 and HP2, then the high band must be
out-of-phase with the low band, not the mid band.
A properly implemented 2-way 24 dB/octave Linkwitz-Riley
crossover is characterized by:
•4
th-order Linkwitz-Riley (Butterworth-Squared) lowpass filter, -6
dB magnitude response at crossover frequency
•4
th-order Linkwitz-Riley (Butterworth-Squared) highpass filter,
-6 dB magnitude response at crossover frequency
• polarity of high band the same as that of low band
In a 3-way crossover the bands associate in non-obvious ways
(see Sum-to-Allpass Characteristics of Linkwitz-riley
Crossovers), and the polarity reference for the high band is
unexpectedly the low band, rather than the adjacent mid band.
Thus, if a 24 dB/octave filter is used for LP1 and HP1, then the
mid band must be in-phase with the low band. If a 24 dB/octave
filter is used for LP2 and HP2, then the high band must be the in-
phase with the low band, not the mid band.