Acoustic centres vs diaphragm material

[David Gatti]

In an effort to avoid using a sloped baffle, I'm looking for a woofer with a very shallow acoustic centre.
Shopping around has got me wondering how much the acoustic centre varys much with diaphragm material.
For example does an Aurasound aluminium cone have an acoustic centre that is significantly more forward than that of say a Scanspeak paper cone?

Another possibility is to use a B&W approach of a very large voicecoil woofer, presumably as this allows a shallow cone & hence also moves the acoustic centre forwards without sacrificing rigidity. Any comments on this?
Does anyone know of a suitable make of shallow cone/large voicecoil woofer iwth around 88-90dB sensitivity?

[Lynn Olson]

Originally posted by David Gatti
In an effort to avoid using a sloped baffle, I'm looking for a woofer with a very shallow acoustic centre.
Shopping around has got me wondering how much the acoustic centre varys much with diaphragm material.
For example does an Aurasound aluminium cone have an acoustic centre that is significantly more forward than that of say a Scanspeak paper cone?

Another possibility is to use a B&W approach of a very large voicecoil woofer, presumably as this allows a shallow cone & hence also moves the acoustic centre forwards without sacrificing rigidity. Any comments on this?
Does anyone know of a suitable make of shallow cone/large voicecoil woofer iwth around 88-90dB sensitivity?

Unfortunately, it's a little worse than that. The acoustic delay is a direct function of not only of the physical center of radiation, but the added delay of the lowpass crossover. This can be estimated by adding an 1/8th wavelength (at the crossover frequency) for a 6 dB/octave filter, 1/4 wavelength for 12 dB/octave, and so on. Speed of sound is about 345 m/Sec, or looking at it another way, 1 kHz is about 14 inches long.

Even without any crossover, the woofer low-pass filters itself thanks to its internal voice-coil inductance. That's one inductor you can never remove - although some woofers have much less VC inductance than others, thanks to copper rings on the pole-piece and other linearizing techniques.

The net result of all this are acoustic centers that are a one to several inches behind the voice coil. Now you know why linear-phase speakers put the tweeters in short horn waveguides, have sloped baffles, or use digital time correction. Your choice which technique you employ.

[David Gatti]

Thanks Lynn
I'm not too concerned about the lowpass-filter effects as that will be accounted for in the x-over. My goal is to start the design with the driver's native acoustic centres on as close to a flat plane as possible, hopefully making crossover work much easier.
Being minimum phase, a Hilbert transform from the driver's frequency response will allow me to quantify the net effect of voicecoil inductance, diaphragm materials and cone geometry. From there it's a matter of working out the time-of-flight difference to the listening point using the usual LspCAD methods.
So then, when I'm shopping for the optimum woofer, good indicators of acoustic-centre depth would be :
1. voicecoil inductance (or put it another way, how high the frequency response extends and how quickly it rolls off)
2. cone depth.
3. diaphragm rigidity
Is this a fair summation?
Unfortunately, shallow diaphragms with large voicecoils also usually have highish inductance, so its a bit of a compromise.

[DSP_Geek]

Originally posted by Lynn Olson


Unfortunately, it's a little worse than that. The acoustic delay is a direct function of not only of the physical center of radiation, but the added delay of the lowpass crossover. This can be estimated by adding an 1/8th wavelength (at the crossover frequency) for a 6 dB/octave filter, 1/4 wavelength for 12 dB/octave, and so on. Speed of sound is about 345 m/Sec, or looking at it another way, 1 kHz is about 14 inches long.

Even without any crossover, the woofer low-pass filters itself thanks to its internal voice-coil inductance. That's one inductor you can never remove - although some woofers have much less VC inductance than others, thanks to copper rings on the pole-piece and other linearizing techniques.

The net result of all this are acoustic centers that are a one to several inches behind the voice coil. Now you know why linear-phase speakers put the tweeters in short horn waveguides, have sloped baffles, or use digital time correction. Your choice which technique you employ.

I would argue with the lowpass crossover phase being significant, because lowpass and highpass filter phase is already taken into account when the networks are designed, so summing the woofer and tweeter should work out to unity gain assuming perfect drivers.

On the other hand, I agree with the woofer series inductance adding another lowpass term which would affect phase, with the addition of the mechanical lowpass also adding its own delay. Tweeters typically have second-order highpass transfer functions, so they'd have their own phase lead, with the amount roughly depending on how far the tweeter resonance is below the crossover point. Both effects together can add close to 90 degrees of phase shift at crossover for typical drivers.

[john k...]

Hi Dave,

Sorry I can't help you with woofer choice but, don't worry about the GD of the low pass filter. If you are working with a symmetric crossover, B3 or LR4, etc the HP and LP sections have the same GD vs. frequency. So if the acoustic roll off of the drivers is symmetric then the GD variation in the crossover region is the same for the HP and LP sections. The only concern is the AC offset.

Voice coil inductance is also already in the picture since its effect is mirrored in the drivers frequency response. Again, matching the acoustic target will cover this. I don't believe cone rigidity will be a significant factor.

Cone depth and VC length (or former length) would seem to be the most significant considerations. However, if you want to use a flat baffle there are other ways to deal with the offset by employing asymmetric HP and LP filters. For example, a LR4 LP on the woofer with an 6th order HP designed to follow the LR4 amplitude response through the crossover can often be designed to compensate for the offset while retaining the symmetric polar response characteristics of an true LR4 crossover. The order of the HP filter will depend of the crossover frequency and the amount of offset to be compensated for. Additionally, to get correct phase matching through the crossover region the HP may need to be connected with inverted polarity, like the LR2 crossover.

[David Gatti]

G'day John and thanks for the feedback guys, you've confirmed my thoughts.
As you may or may not be aware, I'm more interested in linear phase speakers, so high order slopes are not an option and anyway, I'm not too keen on applying an electrical bandaid to a problem that shouldnt be there to begin with.

It appears the simplest solution is to bring the tweeter acoustic centre back using a waveguide/horn style tweeter as Lynn suggested. I have just now managed to get hold of a nice pair of Dynaudio d21 horns on ebay which, with their greater depth, should help bring things in line with the cone midrange and woofer. I have no data on the old d21, it's a bit of a leap of faith, and it will be interesting to see how they sound and measure compared to my d21/2s, which reach 40kHz by the way!

Dynaudio d21:


Why all this trouble? Well I'm looking at building a plasmaTV/room/waf friendly 3-way floor stander based somewhat on the old Boston Acoustics A200, or maybe the A150.
The wide flat plasma-style baffle has a lot of aesthetic and practical appeal for me in my space-limited flat.

Boston Acoustics A200:




Boston Acoustics A150:



Midrange will probably be the nice Audiotechnology Cquenze 15h520613sdk,woofer probably the Scanspeak 26W8861 (as used in Delta ).
The enclosure will be about 20cm (8") deep! The woofer will see a kind of horn loading due to the close proximity of the floor and wall, hence NO baffle-step compensation required

Still lots of design theory and simulations to do, but it's looking promising ...

David Gatti

[DSP_Geek]

Originally posted by David Gatti

Why all this trouble? Well I'm looking at building a plasmaTV/room/waf friendly 3-way floor stander based somewhat on the old Boston Acoustics A200, or maybe the A150.
The wide flat plasma-style baffle has a lot of aesthetic and practical appeal for me in my space-limited flat.

Midrange will probably be the nice Audiotechnology Cquenze 15h520613sdk,woofer probably the Scanspeak 26W8861 (as used in Delta ).
The enclosure will be about 20cm (8") deep! The woofer will see a kind of horn loading due to the close proximity of the floor and wall, hence NO baffle-step compensation required

It won't be horn loading per se, more like quarter-space loading. That'll work well. You can cross the woofer fairly high (around 200 Hz) and still avoid comb filter effects from the first bounce off the floor.

I'd avoid the precise A150 and A200 shapes, however, because they could set up some serious internal resonances. As an example, the A200 seems to be about 42 inches high. Take away 2 inches of that for wood, you get 40 inches. The first mode would be a half-wave with nodes at the top and bottom, so a whole wavelength would be 80 inches, leading to a frequency of 13600 inches/second / 80 inches = 170 Hz. Even if you cross over below that point, you'd get distortion amplification of the 85 Hertz second harmonic, the 57 Hz third harmonic, and so on. Analyzing side-to-side resonances is the same exercise with different numbers.

You might want to try slanting the sides toward each other to make the top not quite as wide. Not only will it reduce the strength of internal resonances, the imaging will also improve from the narrower cabinet at the tweeter/midrange.

[john k...]

Originally posted by David Gatti
As you may or may not be aware, I'm more interested in linear phase speakers, so high order slopes are not an option and anyway, I'm not too keen on applying an electrical bandaid to a problem that shouldnt be there to begin with.

David Gatti

Linear phase is another issue all together. Let's call it a minimum phase speaker, that is, a speaker where there is no corssover induced phase distortion. You know that is my forte. Your choices basically boil down to 1st order or 2nd order transient perfect designs for 2-ways if you are sticking to analog crossover types. These will require aligned ACs.

The other approxinate approach if the old Spica type crossover where the LP is a 4th order Bessel and the tweeter has a 1st order with the tweeter AC significantly behind the woofers. The idea there was the the Bessel has maximally flat GD so it retains linear phase further towards the crossover point. The tweeter AC is then offset to align the AC so that the higher frequencies are delayed by something less that the DC GD of the Bessel LP section and the HP crossover frequency is optimized to yield as flat a response as possible. This comes close but is never a pefectly flat response. It does achieve minimum phase response though, relative to the tweeter AC.

[David Gatti]

Originally posted by DSP_Geek


It won't be horn loading per se, more like quarter-space loading. That'll work well. You can cross the woofer fairly high (around 200 Hz) and still avoid comb filter effects from the first bounce off the floor.

I'd avoid the precise A150 and A200 shapes, however, because they could set up some serious internal resonances. As an example, the A200 seems to be about 42 inches high. Take away 2 inches of that for wood, you get 40 inches. The first mode would be a half-wave with nodes at the top and bottom, so a whole wavelength would be 80 inches, leading to a frequency of 13600 inches/second / 80 inches = 170 Hz. Even if you cross over below that point, you'd get distortion amplification of the 85 Hertz second harmonic, the 57 Hz third harmonic, and so on. Analyzing side-to-side resonances is the same exercise with different numbers.

You might want to try slanting the sides toward each other to make the top not quite as wide. Not only will it reduce the strength of internal resonances, the imaging will also improve from the narrower cabinet at the tweeter/midrange.

Yes, simulations of the low frequency response in this setup look very promising. Virtually an infinite baffle repsonse.
The midrange/tweeter enclosure will take up the top 12" of the cabinet, so that should raise the resonant frequency of the woofer enclosure to a safer region. It will also be well stuffed. It will be a square flat enclosure, no angled sides - I did own a pair of Boston Acoustics A100s once so I have some idea of what to expect in terms of imaging. Behind the midrange I'll have a kind of V section deflecting the back wave 90 degrees, i.e. towards the sides of the enclosure, as they do internally in some tweeters. Of course bracing of that huge baffle will be paramount and a real challenge.

[David Gatti]

Originally posted by john k...


The other approxinate approach if the old Spica type crossover where the LP is a 4th order Bessel and the tweeter has a 1st order with the tweeter AC significantly behind the woofers. The idea there was the the Bessel has maximally flat GD so it retains linear phase further towards the crossover point. The tweeter AC is then offset to align the AC so that the higher frequencies are delayed by something less that the DC GD of the Bessel LP section and the HP crossover frequency is optimized to yield as flat a response as possible. This comes close but is never a pefectly flat response. It does achieve minimum phase response though, relative to the tweeter AC.

From memory those Spicas had REALLY sloped baffles.
But I'm determined to go for a flat baffle this time, and I dont think the tweeter horn is deep enough, so that probably rules out the Bessel approach.
I'll likely go for the usual simple 1st order acoustic crossovers at least around the crossover point, letting it asymptope to 12 or 18dB further away from Fc. That way, the crossover is minimal and I don't get too much damage on the overall phase response.