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>To give credit where it's due, I believe your critically damped version
>would properly be called a 4th order Linkwitz-Riley filter. Linkwitz and
>Riley introduced it to the Audio Engineering Society in the mid 70s in a
>paper called "Active Crossover Networks for Noncoincident Drivers." It's
>a Q=.5, critically damped filter, down 6dB at Fc, commonly (although
>it's not the only way) constructed by cascading two Q=.7 Butterworth
>filters.
I found the reference:
S. Linkwitz, ‘Active Crossover Networks for Non-Coincident
Drivers,’ J. Audio Eng. Soc., vol. 24, pp. 2-8 (Jan./
Feb. 1976).
There is a good discussion of this at:
http://www.rane.com/pdf/note119.pdf
It looks to me as though the Linkwitz-Riley filter uses cascaded standard Butterworth filters where as the paper Alex referenced uses modified Butterworth filters (for critical damping). The Linkwitz-Riley filter is not critically damped and has overshoot.
The filter seems to be better than the Ehlers filter I referred to earlier. See picture.
Bob Fulks
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