8-20
10 July 1998
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 4-way crossover the bands associate in non-obvious ways
(see Sum-to-Allpass Characteristics of Linkwitz-Riley
Crossovers). As expected, the polarity reference for the low-mid
band is the low band, and the polarity reference for the high
band is the mid-high band. However, the polarity reference for
the mid-high band is unexpectedly the low band, rather than the
adjacent low-mid band. Thus, if a 12 dB/octave filter is used for
LP1 and HP1, then the low-mid band must be out-of-phase with
the low band. If a 12 dB/octave filter is used for LP3 and HP3,
then the high band must be out-of-phase with the mid-high band.
And if a 12 dB/octave filter is used for LP2 and HP2, then the mid-
high band must be out-of-phase with the low band, not the low-
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 4-way crossover the bands associate in non-obvious ways
(see Sum-to-Allpass Characteristics of Linkwitz-riley
Crossovers). As expected, the polarity reference for the low-mid
band is the low band, and the polarity reference for the high
band is the mid-high band. However, the polarity reference for
the mid-high band is unexpectedly the low band, rather than the
adjacent low-mid band. Thus, if a 24 dB/octave filter is used for
LP1 and HP1, then the low-mid band must be in-phase with the
low band. If a 24 dB/octave filter is used for LP3 and HP3, then
the high band must be the in-phase with the mid high band. And
if a 24 dB/octave filter is used for LP2 and HP2, then the mid high
band must be the in-phase with the low band, not the low-mid
band.
Sum-to-Allpass Characteristics of Linkwitz-Riley Crossovers
A characteristic of 2-way Linkwitz-Riley crossovers is that the output
bands sum to an allpass filter—the frequency response of the sum
has a constant magnitude of one and only phase shift occurs. From
Figure 8-4, this means that
LPx - HPx = θx
or LPx + HPx = θ x