8-20
A properly implemented 2-way, 12 dB/octave Linkwitz-Riley crossover is characterized by:
•2nd-order Linkwitz-Riley (Butterworth-Squared) lowpass filter, -6 dB magnitude response at crossover frequency
•2nd-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:
•4th-order Linkwitz-Riley (Butterworth-Squared) lowpass filter, -6 dB magnitude response at crossover frequency
•4th-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-wayLinkwitz-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
10 July 1998
