Telex Integrated Signal Processor ISP-100 User Manual

Page 90

8-20

10 July 1998

A properly implemented 2-way, 12 dB/octave Linkwitz-Riley
crossover is characterized by:

• 2

-order Linkwitz-Riley (Butterworth-Squared) lowpass filter, -6

dB magnitude response at crossover frequency

• 2

-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
LP

and HP

, then the low-mid band must be out-of-phase with

the low band. If a 12 dB/octave filter is used for LP

and HP

then the high band must be out-of-phase with the mid-high band.
And if a 12 dB/octave filter is used for LP

and HP

, 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

-order Linkwitz-Riley (Butterworth-Squared) lowpass filter, -6

dB magnitude response at crossover frequency

• 4

-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
LP

and HP

, then the low-mid band must be in-phase with the

low band. If a 24 dB/octave filter is used for LP

and HP

, then

the high band must be the in-phase with the mid high band. And
if a 24 dB/octave filter is used for LP

and HP

, 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

- HP

+ HP