Hello,
I have been passionately reading up on all I could find on this topic, and I have gathered the following "bits of truth":
(1)
ALL low-pass filters cause a delay (Group Delay) in the output of the filtered speaker unit (e.g. Woofer) in its pass-band, resulting in an apparent backward shift of its acoustic centre
(2)
High-pass filters also cause a similar Group Delay, but in the speaker's stop-band; as a result, the apparent acoustic centre of the unit (e.g. Tweeter) remains approximately coincident with its physical position in the pass-band
(3)
ALL conventional symmetric crossover filters (e.g. 2nd order Linkwitz-Riley, 3rd order Butterworth, 4th oder Linkwitz-Riley, etc.) are designed to sum flat when the physical acoustic centres of the two speaker units (Woofer AND Tweeter) are aligned; however, given (1) and (2) above, this means that the two speaker untis are left to emit their respective portions of the audio band from substantially different apparent positions, which results in an overall NON-time aligned output from the speaker system (incidentally, Linkwitz-Riley crossovers do ensure phase matching of Woofer and Tweeter at all frequencies, which results in regular polar dispersion, but they still do not result in time-aligned output, since the latter depends on Group Delay, and not phase - see (1) and (2).)
(4)
It has been demonstrated that it is impossible to obtain: (A) perfect acoustic summing (flat frequency response), (B) perfect phase match AND (C) flat Group Delay using a simple analogue passive crossover [Vanderkooy, J. and Lipshitz, S. P., “Is Phase Linearization of Loudspeaker Crossover Networks Possible by Time Offset and Equalization?”, J. Audio Eng. Soc., vol. 32 (Dec. 1984)].
(5)
Given (3) and (4) above, a number of efforts have been made to design "quasi-optimal" crossovers that strike the best possible balance between the three goals (A),(B) and (C) (rather than only considering (A) - e.g. conventional 3rd order Butterworth, or (A)+(B) - e.g. even-order Linkwitz-Riley).
Two notable examples of "quasi-optimal" crossovers (5) are the ones developed by SPICA and by Jean Michel LeCleac'h (filtrage).
Both of these "quasi-optimal" crossovers use a physical offset between the physical acoustic centres of the Woofer and Tweeter to try and align their respective emissions over broad portions of the audio band.
The SPICA crossover uses a 4th order Bessel low-pass at Fx (+ polarity) and a quasi-first order high-pass at Fx (+ polarity), with an Offset = 0.435*c/Fx.
Unfortunately, the 1st order HP is often too bland to be usable with real Tweeters, especially of the horn-loaded Compression Driver type that I pefer.
The JMLC crossover uses instead a 3rd order Butterworth low-pass at 0.87*Fc (+ polarity) and also a 3rd order Butterworth high-pass at 1.15*Fc (- polarity), with an Offset = 0.22*c/Fx.
Below are simulations of the frequency response, phase and group delay of this type of crossover for Fx = 650Hz (attachments 1,2,3)
Overall, this is a much more practical solution than the SPICA one, and has been reported to work quite well by a number of users. However, the physical offset between the physical acoustic centres of the Woofer and Tweeter is rather small, and I have found that in the case of a system composed of a large-diametre Woofer and a compression driver + horn, for typical Fx values the horn ends up sticking quite a bit out in front of the Woofer cabinet.
Also, the phase match between Woofer and Tweeter (goal B above) isn't all that good, really, which results in a relatively poor polar response (this is often considered relatively unimportant by the proponents of the JMLC method, who typically listen on axis in the near field).
Finally, the group delay of the Woofer does not match that of the Tweeter at Fx, leaving the two units to emit from non-coincident positions at this important frequency where their output intensities are equal.
So I kept searching for alternative "quasi-optimal" crossover solutions.
One (passive) crossover that always intrigued me and that has developed a bit of a "mythical" aura in some audio circles is that which was used by TAD in their professional monitor models 2401 and 2402 (attachment 4).
By reverse-engineering the published frequency response plots for the 2401 model (attachment 5), and measuring the approximate physical offset between the Woofer's dust cap and the compression driver's diaphragm, I was able to work out the following design criteria for this crossover type:
Woofer: 6th order Linkwitz-Riley low-pass at Fx (+ polarity) (attachment 6)
Tweeter: 2nd order Chebyshev (Q=1) high-pass at 1.3*Fx (- polarity), attenuated -2dB (attachment 7)
Offset = 0.6 * c / Fx
The resulting simulations of the frequency response, phase and group delay of this type of crossover for Fx = 650Hz are illustrated below (attachments 8,9,10).
Well, I must say I quite like it!
This "TAD-style" crossover clearly belongs to the "quasi-optimal" family, and exhibits a nice set of desirable characteristics, namely:
- smooth frequency response
- excellent phase match up until Fx (expected good polar behaviour)
- almost perfect group delay match at Fx, and smooth overall group delay curve, with both Woofer and Tweeter emitting from almost coincident positions over most of their respective pass-bands (i.e. very good "time alignmnet")
- conveniently large offset, which greatly facilitates the physical positioning of the Tweeter horn with respect to the Woofer box
I am posting all this in the hope that others may find it useful, too.
Comments are welcome!
Cheers,
Marco
I have been passionately reading up on all I could find on this topic, and I have gathered the following "bits of truth":
(1)
ALL low-pass filters cause a delay (Group Delay) in the output of the filtered speaker unit (e.g. Woofer) in its pass-band, resulting in an apparent backward shift of its acoustic centre
(2)
High-pass filters also cause a similar Group Delay, but in the speaker's stop-band; as a result, the apparent acoustic centre of the unit (e.g. Tweeter) remains approximately coincident with its physical position in the pass-band
(3)
ALL conventional symmetric crossover filters (e.g. 2nd order Linkwitz-Riley, 3rd order Butterworth, 4th oder Linkwitz-Riley, etc.) are designed to sum flat when the physical acoustic centres of the two speaker units (Woofer AND Tweeter) are aligned; however, given (1) and (2) above, this means that the two speaker untis are left to emit their respective portions of the audio band from substantially different apparent positions, which results in an overall NON-time aligned output from the speaker system (incidentally, Linkwitz-Riley crossovers do ensure phase matching of Woofer and Tweeter at all frequencies, which results in regular polar dispersion, but they still do not result in time-aligned output, since the latter depends on Group Delay, and not phase - see (1) and (2).)
(4)
It has been demonstrated that it is impossible to obtain: (A) perfect acoustic summing (flat frequency response), (B) perfect phase match AND (C) flat Group Delay using a simple analogue passive crossover [Vanderkooy, J. and Lipshitz, S. P., “Is Phase Linearization of Loudspeaker Crossover Networks Possible by Time Offset and Equalization?”, J. Audio Eng. Soc., vol. 32 (Dec. 1984)].
(5)
Given (3) and (4) above, a number of efforts have been made to design "quasi-optimal" crossovers that strike the best possible balance between the three goals (A),(B) and (C) (rather than only considering (A) - e.g. conventional 3rd order Butterworth, or (A)+(B) - e.g. even-order Linkwitz-Riley).
Two notable examples of "quasi-optimal" crossovers (5) are the ones developed by SPICA and by Jean Michel LeCleac'h (filtrage).
Both of these "quasi-optimal" crossovers use a physical offset between the physical acoustic centres of the Woofer and Tweeter to try and align their respective emissions over broad portions of the audio band.
The SPICA crossover uses a 4th order Bessel low-pass at Fx (+ polarity) and a quasi-first order high-pass at Fx (+ polarity), with an Offset = 0.435*c/Fx.
Unfortunately, the 1st order HP is often too bland to be usable with real Tweeters, especially of the horn-loaded Compression Driver type that I pefer.
The JMLC crossover uses instead a 3rd order Butterworth low-pass at 0.87*Fc (+ polarity) and also a 3rd order Butterworth high-pass at 1.15*Fc (- polarity), with an Offset = 0.22*c/Fx.
Below are simulations of the frequency response, phase and group delay of this type of crossover for Fx = 650Hz (attachments 1,2,3)
Overall, this is a much more practical solution than the SPICA one, and has been reported to work quite well by a number of users. However, the physical offset between the physical acoustic centres of the Woofer and Tweeter is rather small, and I have found that in the case of a system composed of a large-diametre Woofer and a compression driver + horn, for typical Fx values the horn ends up sticking quite a bit out in front of the Woofer cabinet.
Also, the phase match between Woofer and Tweeter (goal B above) isn't all that good, really, which results in a relatively poor polar response (this is often considered relatively unimportant by the proponents of the JMLC method, who typically listen on axis in the near field).
Finally, the group delay of the Woofer does not match that of the Tweeter at Fx, leaving the two units to emit from non-coincident positions at this important frequency where their output intensities are equal.
So I kept searching for alternative "quasi-optimal" crossover solutions.
One (passive) crossover that always intrigued me and that has developed a bit of a "mythical" aura in some audio circles is that which was used by TAD in their professional monitor models 2401 and 2402 (attachment 4).
By reverse-engineering the published frequency response plots for the 2401 model (attachment 5), and measuring the approximate physical offset between the Woofer's dust cap and the compression driver's diaphragm, I was able to work out the following design criteria for this crossover type:
Woofer: 6th order Linkwitz-Riley low-pass at Fx (+ polarity) (attachment 6)
Tweeter: 2nd order Chebyshev (Q=1) high-pass at 1.3*Fx (- polarity), attenuated -2dB (attachment 7)
Offset = 0.6 * c / Fx
The resulting simulations of the frequency response, phase and group delay of this type of crossover for Fx = 650Hz are illustrated below (attachments 8,9,10).
Well, I must say I quite like it!
This "TAD-style" crossover clearly belongs to the "quasi-optimal" family, and exhibits a nice set of desirable characteristics, namely:
- smooth frequency response
- excellent phase match up until Fx (expected good polar behaviour)
- almost perfect group delay match at Fx, and smooth overall group delay curve, with both Woofer and Tweeter emitting from almost coincident positions over most of their respective pass-bands (i.e. very good "time alignmnet")
- conveniently large offset, which greatly facilitates the physical positioning of the Tweeter horn with respect to the Woofer box
I am posting all this in the hope that others may find it useful, too.
Comments are welcome!
Cheers,
Marco
Attachments
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