8-19
Processing Components - Crossover
Four-way Linkwitz-Riley Crossovers
Figure 8-10
Four-way Linkwitz-Riley crossover implementation.
In the ISP-100, 4-way Linkwitz-Riley crossovers are
implemented as shown in Figure 8-10.
Linkwitz-Riley designs constitute a special, even-order in-phase
class of 2-way sum-to-allpass response crossovers, and they
must be configured in accordance with very strict phase and
polarity requirements. Because the basic Linkwitz-Riley
crossover is a 2-way design, extra steps must be taken in 4-way
Linkwitz-Riley crossovers to ensure that these phase and
polarity requirements are met.
Note the presence of the unexpected θ1 allpass filter and HP2
highpass filter in the high band, the θ1 allpass filter in the mid-
high band, the θ3 allpass filter in the low-mid band, and the LP2
lowpass filter and θ3 allpass filter in the low band. The inclusion
of these filters is mandatory for proper implementation of the 4-
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 4-way Linkwitz-Riley crossover is essentially a combination of
three 2-way Linkwitz-Riley crossovers. This means that the
polarity requirements associated with a 2-way Linkwitz-Riley
crossover carry over to a 4-way crossover.