"Quasi-optimal" crossover for high-efficiency loudspeaker system

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Hello,

In response to some insightful comments made by Jean-Michel Le Cléac'h (here and on other French-language forums), I have made new simulations trying to further improve on the TAD crossover.

This is what I have come up with:

- Woofer low pass: 6th order Bessel at Fx * 1.25 (-6dB of attenuation at Fx)
- Tweeter high pass: 2nd order Butterworth at Fx * 1.3 (-6dB of attenuation at Fx)
- Offset = 0.4 * c / Fx

The result is even better phase match and a smoother Group Delay curve, still with a practical offset between Woofer and Tweeter.

Comments welcome.

Marco

Hello Marco,

I just came back from a one week geological field trip and see your message.

Congratulations! This version of the crossover is IMHO far better than the original one.

The group delay curve is more constant in the frequency range inside which our hearing system is the most sensible to phase distortion.

If the response curve "in coincidence" is smooth then this crossover may be called quasioptimal!


Best regards from Paris, France

Jean-Michel Le Cléac'h
 
Hello Jimbee,

From the graph you gave, yes, I can see a very flat summed response and a common -6dB attenuation for the HPF and LPF, meaning that the 2 loudspeakers work in phase at the crossover cut-off (here defined at -6dB).


May be this will give some ideas for improvement for the TAD engineers...

Best regards from Paris,

Jean-Michel Le Cléac'h
 
Seems worth noting that electrical delay and acoustic center shift are only equivalent directly in front of the driver.

Hello,

If the horn propagates parallel isophase wavefronts then the acoustical center will still be at the same apparent (curved) distance from the listener's ear inside the angle inside which the horn radiates . So for HF horns and LF classical loudspeakers the method consisting in cancelling the shift in distance by the group delay of the LPF (if the group delay is most constant) seems relevant.

Best regards,

Jean-Michel Le Cléac'h
 
Hmm, I am having trouble understanding how that could work (I mean work ideally - I do understand how it works out okay as a crossover design strategy).

For an idealized 2-way system like this with a horn and a delayed LF in front of it, where is the point that the listener could rotate around on the horizontal axis and maintain a constant apparent distance to both sources?
 
Hmm, I am having trouble understanding how that could work.

For an idealized 2-way system like this with a horn and a delayed LF in front of it, where is the point that the listener could rotate around on the horizontal axis and maintain a constant apparent distance to both sources?


Hello,

Because in horns the wavefront are curved and for a given wavefront at the mouth (for a good horn ) the travel from the diaphragm of the loudspeaker is the same in every point of the wavefront....

Then , when the listener rotate around the horn, the apparent acoustic center moves maintaining the same distance from the listener ear to the apparent point from which the waves seems to come.

For a non horn loaded loudspeaker, this is different as the apparent acoustic center doesn't move...

This is why most simulations of the lobing due to the crossover is a very rough aproximation when it come to a 2 ways system consisting of a classical LF loudspeaker and a HF horn.

For sure an optimisation of the relative positions of the HF horn over the LF loudspeaker is still needed...

Best regards from Paris, France


Jean-Michel Le Cléac'h
 
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Hello,

In response to some insightful comments made by Jean-Michel Le Cléac'h (here and on other French-language forums), I have made new simulations trying to further improve on the TAD crossover.

This is what I have come up with:

- Woofer low pass: 6th order Bessel at Fx * 1.25 (-6dB of attenuation at Fx)
- Tweeter high pass: 2nd order Butterworth at Fx * 1.3 (-6dB of attenuation at Fx)
- Offset = 0.4 * c / Fx

The result is even better phase match and a smoother Group Delay curve, still with a practical offset between Woofer and Tweeter.

Comments welcome.

Marco

Marco
Have you tried your crossover ?
If not, I intend to do so in coming months.
Thank you very much for sharing your design.

Pierre
 
Actually, I did, yes.
But I found out the hard way that it is practically impossible to obtain a true 2nd order high-pass transfer function for the horn, even when crossed over at Fx > 2*Fc. The phase shift around Fc is just too great, and this ends up messing the phase response of the high-pass and making it closer to a 4th order. Thus, it is impossible to attain the theoretical phase matching shown in the simulations. Alas, such is the real world vs. the ideal!
So I settled for a compromise solution that is, remarkably, much closer to the original TAD version. Low-pass: 6th order L-R; High-pass: quasi-3rd order Butterworth (transitioning to 4th order below Fc). With the right physical offset, this provides a good compensation of the LP group delay, and subjectively a very good integration between the two speaker units. Ideal? No. Practical and good enough? I would venture to say yes (at least for me).

Marco
 
You could also try a quasi_optimal of another kind composed of Bessel_18 on the high pass with a Linkwitz_24 on the low pass finding different frequencies and offset adjust.

For example, about LP 500 Link4, HP Bessel 700 -3dB -180°, offset 200mm.
This gives in theory a good correspondance between on-axis and off-axis response.
You need 1'4 or 2' compression driver I guess

Don't be afraid to fiddle with values ... :)

I found measuring curves with my horn + compression driver to exhibit a 18 Bessel curve when passive XO designed and adjusted for Link24@-6dB.
For now I try a quasi_optimal 4/4 Butt24/Link24, but real life often calls for practical adjustments ...

A crossover for a horn mixed with direct radiation speaker is always a challenge !

Best regards,

nAr
 
You could also try a quasi_optimal of another kind composed of Bessel_18 on the high pass with a Linkwitz_24 on the low pass finding different frequencies and offset adjust.

For example, about LP 500 Link4, HP Bessel 700 -3dB -180°, offset 200mm.
This gives in theory a good correspondance between on-axis and off-axis response.
You need 1'4 or 2' compression driver I guess

Don't be afraid to fiddle with values ... :)

I found measuring curves with my horn + compression driver to exhibit a 18 Bessel curve when passive XO designed and adjusted for Link24@-6dB.
For now I try a quasi_optimal 4/4 Butt24/Link24, but real life often calls for practical adjustments ...

A crossover for a horn mixed with direct radiation speaker is always a challenge !

Best regards,

nAr

Thanks, interesting and helpful.
I have just modelled your proposed 4 L-R LP + 3 Bess HP and it does work very nicely. However, the optimal offset is only ~0.29*c/Fx, which is a little short. The LP+HP combination I used (similar to TAD's) calls for a more practical ~0.63*c/Fx (but produces a worse combined phase response...)

Marco
 
Thanks, but the one to congrat is Jimbee, all credits to him for that one ;)

Marco I'm curious about your setup.

What do you use as LP driver, in which enclosure,
which kind of horn and what is the compression driver you use with it ? :)

Horns are not so practical to match with direct radiation speaker -
one could think the LP driver also needs to be horn mounted, as in VOTT
so offsets become more practical, but with other caveats.

I'm also in "dire straits" because offset for the 4/4 @ 700 is about 140-150 mm,
depending on the real acoustic phase result ... It's dangerous to live like this ! :) :) :)



I've been a little sceptical achieving in real life a Butterworth 2nd order with a horn + compression driver,
because the phase shift will often be naturally more pronounced than a theoritical 2nd order.

I think it's because the compression driver has it's own acoustic cut-off, and according phase shift;
and the horn also has a phase shift (another) of his own at acoustic cut-off.
The combination of both may produce greater (at first unexpected) phase shifts,
even if using the horn at more than 2x acoustic cut-off @ xo fc.

But maybe I'm totally wrong here ... :confused: :D

Best,

nAr
 
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Thanks, but the one to congrat is Jimbee, all credits to him for that one ;)

OK, thanks to him then!

Marco I'm curious about your setup.

What do you use as LP driver, in which enclosure,
which kind of horn and what is the compression driver you use with it ? :)

My system consists of a Fostex FW405N 15" woofer in a damped 180L bass reflex box + Fostex D1400 1" AlNiCo compression driver & Fostex H400 maple radial horn (Fc = 455 Hz) + Fostex T925A AlNiCo horn tweeter (pic attached).

Horns are not so practical to match with direct radiation speaker -
one could think the LP driver also needs to be horn mounted, as in VOTT
so offsets become more practical, but with other caveats.

Very true!

I'm also in "dire straits" because offset for the 4/4 @ 700 is about 140-150 mm,
depending on the real acoustic phase result ... It's dangerous to live like this ! :) :) :)


That looks like a nice system too! Care to elaborate a bit? Woofer? Compression driver? Nice Guigue-style horn!
The search for a more "comfortable" offset is what drove me to the crossover configuration that I ended up adopting. I get 240 mm with a 900Hz crossover (~0.635*c/Fx).


I've been a little sceptical achieving in real life a Butterworth 2nd order with a horn + compression driver,
because the phase shift will often be naturally more pronounced than a theoritical 2nd order.

I think it's because the compression driver has it's own acoustic cut-off, and according phase shift;
and the horn also has a phase shift (another) of his own at acoustic cut-off.
The combination of both may produce greater (at first unexpected) phase shifts,
even if using the horn at more than 2x acoustic cut-off @ xo fc.

But maybe I'm totally wrong here ... :confused: :D

You are NOT wrong at all. This has been exactly what I have measured, and your explanation makes perfect sense. That's also part of the reason why I settled for a quasi-3rd order acoustical high pass on the compression driver (transitioning to 4th order below Fc). The electrical filter to get there is 2nd order.

Cheers!

Marco
 

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nAr and Marco - Many thanks to both of you.
Your systems are awesome and I can hardly wait to join the two-way horn and direct radiation woofer club :).

Getting the optimal offset in the right ballpark is one of the reasons that attracted me to Marco's approach. The TAD filter requires more offset than I need, and nAr's filter not quite enough... Although I guess that the horn sticking out would be better than recessed behind the woofer cabinet's baffle.

The horn is the AH425 (axial length of 260mm and fc 425 Hz). I figured an offset of 250 mm or slightly less is probably right. For Marco's filter, this corresponds to fx=575 Hz. Not all 1.4" compression drivers can reach this low, but there are a few. It is getting close to the horn's fc though. But overall workable I thought - until I read your insights. For my target offset, the TAD filter requires fx above 850 Hz. nAr, your filter gives an offset of 166 mm for fx = 600 Hz. A bit shorter than I would like, but very tempting.

Is either of you using an autoformer with a swamping resistor on the compression driver? The reason I ask is that intuitively this could affect the phase response.

Pierre
 
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My system consists of a Fostex FW405N 15" woofer in a damped 180L bass reflex box + Fostex D1400 1" AlNiCo compression driver & Fostex H400 maple radial horn (Fc = 455 Hz) + Fostex T925A AlNiCo horn tweeter (pic attached).

Marco - Very interesting woofer. I just looked up the specs and they are very close to the TAD's. A rare combination of low Rms, light Mms, and low Fs/Qts ratio. Is it readily available or hard to obtain? Are you pleased with its sound?

Pierre
 
nAr and Marco - Many thanks to both of you.
Your systems are awesome and I can hardly wait to join the two-way horn and direct radiation woofer club :).

Getting the optimal offset in the right ballpark is one of the reasons that attracted me to Marco's approach. The TAD filter requires more offset than I need, and nAr's filter not quite enough... Although I guess that the horn sticking out would be better than recessed behind the woofer cabinet's baffle.

The horn is the AH425 (axial length of 260mm and fc 425 Hz). I figured an offset of 250 mm or slightly less is probably right. For Marco's filter, this corresponds to fx=575 Hz.

Not sure how you calculated this. "My" filter calls for an offset = 0.635*c/Fx, so if you set offset = 250mm, the required Fx is actually 0.635*344/.25 = 873 Hz, which BTW is just about right for a horn like yours having an Fc = 425 Hz. Going much lower is IMHO asking for trouble! (not necessarily because the driver can't handle it, but because the sound quality will suffer)

Is either of you using an autoformer with a swamping resistor on the compression driver? The reason I ask is that intuitively this could affect the phase response.

No, I am using a simple variable L-Pad (Fostex R82B).
Why do you think the autoformer would affect the phase response? (Not saying that it doesn't - just asking)

Marco
 
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Why do you think the autoformer would affect the phase response? (Not saying that it doesn't - just asking)

The HP filter will see at its output not the impedance of the driver, but the resistance of the swamping resistor in parallel with the input impedance of the autoformer, which itself is the impedance of the driver times the square of the turn ratio of the autoformer. I don't have simulation handy to show the outcome, but intuitively I would expect this to affect the phase response. Hope this helps...
 
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