[NiToNi]

A few things I would like to understand better:

1. The rule of thumb says baffe width should be less than ~2.2 times the driver's diameter - why is that really? Modelling an 8" on a 24" wide open baffle gives much better extension below 200 Hz than an 18" baffle so it is tempting to do the trade-off (whatever it may be). Given I use DSP, can I negate those negative effects of going with 24"?

2. Both 18" and 24" wide baffles have their dipole peaks way above the pass band of my 15" woofers (30-120 Hz) so the 6dB/octave roll-off will apply to the whole pass band for both those baffle widths. In an active system with EQ, are there any benefits then to go for the wider 24" baffle rather than the slimmer 18" baffle? Is there a difference in sensitivity and if so how many dB difference are we talking about?

3. Since it is a given that the woofers will roll-off by 12dB over their two-octave pass band, correcting for this alone with digital EQ will use up precious bits in the digital domain (reducing the resolution of 16 bit redbook source material to 14 bits), and this is even before DSP correcting the actual room response (peaks and dips). In an effort to preserve digital headroom, is it common (or at least a good idea) to combine digital XO/EQ with a first-order electronic crosssover on the woofers amps to compensate at least for the dipole roll-off prior to EQ'ing?

[JohnR]

Where did you read the 2.2x rule of thumb? I suspect this may be more to do with the behavior at higher frequencies - with smaller drivers (on a given baffle) it's harder to position the driver to avoid an on-axis notch.

Digital EQ/xovers use 24 bit DACs (not 16), all that I've seen anyway.

[NiToNi]

Several places, including on here. I think it has to do with dispersion if anything and applies to a 8" fullrange driver as well.

The DAC may be 24 bit but if the source material is 16 bit, digital EQ must reduce resolution , e.g. a 9 dB EQ cut would reduce resolution to 15 bits.

[JohnR]

Why ask questions if you're going to argue with the answers  If you add 8 bits to a 16-bit signal, then shift the top 16 bits down one bit, what do you get?

[JohnR]

Several places, including on here. I think it has to do with dispersion if anything and apllies to a 8" fullrange driver as well.

It is explained here by Rudolf: http://www.audiocircle.com/index.php?topic=64048.0

As I understand it, he is saying that the crossover frequency should be below the dipole peak. The baffle width rule of thumb then comes about in order to keep the dipole peak above some nominal "upper frequency" that the driver can be used, based on its size.

If you are using a full-range driver, then you won't be low-passing it anyway. Angling the baffle edges will reduce the problem, try it in Edge.

For the sub, wider is better but it's not a huge amount (again, try it yourself in Edge). Much more benefit can be obtained by moving the sub closer.

[JeffB]

I did an open-baffle build a while back.  It showed promise, but I now think my biggest problem is that I need to deal with the roll-off.  This is my current understanding.  I hope someone will correct me if I am wrong. 
If we have speed of sound = 1135ft/sec, then an 1135Hz tone is 12" long.
If I have an 18" baffle, then the 6db per octave roll-off will begin at 12"/18" * 1135Hz * 2 = ~1500Hz.
How many octaves can I stretch a driver across, seems like 2 at the most, however if I want a smallish mid-range driver like 3" or 4", these are normally not very efficient and so would only be good for 1 octave.  I mean if I start at say 86 db, then I will be down to 81db after correcting for the 6db roll-off.  I chose 18" here because that is what I used originally, but now I think maybe I should go narrower.  If I use 16", so that I can still use a 15" woofer, then I get the following:
12"/16" * 1135 * 2 = ~1700Hz.
Now I can use a tweeter from 1700Hz without the need for baffle step correction.
I can use a 3" driver for one octave from 850Hz to 1700Hz.
I can now bring in something bigger with high efficiency.  Some sort of pro-audio 8" or 10" to cover two octaves from 212Hz to 850Hz.  Then I can use a 15" to cover two octaves from 53Hz to 212Hz.
I am now up to 4 drivers and still don't have the bottom 1.5 octaves.
If I go with a wider baffle, then my 3" driver covers a range where it will change from 2pi space to 4pi space.
This might be advantageous though as it could run lower.  So lets try a 24" baffle and see what happens.
Now the 6db roll-off starts at 1135.
So now I need to deal with the 3" in both 2pi and 4pi space. I think I will just it run without a tweeter to save 1 speaker.  I can now run the 3" driver from 567Hz all the way up.  A high efficiency 10" for two octaves from 142Hz to 567Hz, and a 15" from 35Hz to 142Hz.  Ok, this is starting to look doable.  How come most of the open baffle designs I see are 2-way.  Seems like 3-way is the bare minimum.  Unfortunately, I think 24" is a bit too wide for my room.  18 is really about the max.  Maybe 20".  Perhaps the 15" could be stretched a little beyond 2 octaves.  Or perhaps I am ok with the bass rolling off a little early.  It is kind of nice not having bass bother the neighbors.

[JohnR]

Hi Jeff

If we have speed of sound = 1135ft/sec, then an 1135Hz tone is 12" long.
If I have an 18" baffle, then the 6db per octave roll-off will begin at 12"/18" * 1135Hz * 2 = ~1500Hz.

Something's not right there... I measured around 400 Hz for the dipole peak on my 18" baffle.

How many octaves can I stretch a driver across, seems like 2 at the most

That is derived from the idea that a driver should not be operated above the dipole peak - ? I think that might be limiting the design process a bit. (see below)

How come most of the open baffle designs I see are 2-way.  Seems like 3-way is the bare minimum.

My take on it is that, for a truly full-range system system using "conventional" drivers, four-way works out well. Note that many closed-box systems are like that too - i.e. "3-way plus sub." Speaking in general terms, if you don't need the full extension and impact at the bottom, you can drop the sub. If you use an extended range driver you can drop the tweeter, with some compromises in the treble response. Combine them and you have a two-way. I'd like to do a two-way at some point, to explore this a bit further.

The thing is, the shape (not just the size) of the baffle has an enormous effect on the response. Rather than just going by rules of thumb derived from circular or rectangular baffles, I think it would be more helpful to model different baffles to explore what is optimum for a given driver and operating range. The ripples above the dipole peak can be greatly reduced by moving the top edge closer to the driver and providing varying distances to the edge horizontally. You lose low-end response, but then again, there is no need for a baffle that supports 100 Hz on a driver that will be highpassed at 300 Hz (for example).

[JeffB]

Ok, I must have read some bad info before.
From http://www.musicanddesign.com/Gradient_woofer_eq.html the dipole peak is computed as
C - the speed of sound
D - the effective separation of the speakers.
F = C / (2D). 
So for 18", you get 1135/(2 * 18/12) = 378hz.  I was thinking it was 4 times higher.
I was using a basic surround sound receiver with a 200Hz cross-over point with a 3" and a 15".
The 3" was then down 6db at 200Hz.  This explains why it got close to working good, but not quite.

[JohnR]

The 3" was then down 6db at 200Hz.

It depends on the baffle and where the driver is. Here is a 65mm diameter driver in a 50x120mm baffle, modeled in Edge (roughly a 3" driver in 18x48"):



The only difference between these is the vertical location of the driver.

[scorpion]

As John's diagram shows the dipole peak of a 500 mm wide baffle will be about 340/0.5 Hz. The formal difference in the formula will be half the widht of a rectangular baffle or the radius of a circular baffle.
/Erling

[Crumbs]

As I remember the 2.2x width rule was devised in part to limit temporal smearing. The time it takes for the back wave to travel along the baffle and then 'appear' to the front sound stage means you effectively have two sources in time. The second a delayed 'copy' of the other. Obviously this ignores the fact that you would also have the back-reflected wave off nearby wall(s) but that is why most people space their open-baffles out from the nearby wall to limit multiple sources in close temporal proximity. Obviously you could go the other route and have really big (infinite) baffles but most peoples houses aren't that big.

Bill

[Rudolf]

This "2.2 rule" thing started when I read this essay: http://www.wvier.de/texte/Dipollautsprecher-FV.pdf. Equation (6) shows for a pistonic driver of diameter d on a baffle of average diameter D, that lobing and the related diffraction effects will be minimal for D/d < 2.2 . See Fig. 4 and 5 too. Note that this will be true even above the first dipole peak.
But real life can't be reduced to pistonic drivers, circular baffles and a single number. Edge certainly gives a better picture of the relation between baffle size, driver size and driver placement.

Rudolf

[NiToNi]

Thanks, Rudolf. I had thought it was related to those things. But if I use a 8" full-range driver far above its upper beaming frequency and the baffle's dipole peak (and break the rule anyway) as well as DSP, all this does not really matter anyway and it would be better to try to get a bit more bass response out of the FR driver...?

I have been playing around a lot with Edge (as well as with ABC Dipole and BDBS) and I think I have come up with a baffle design that might work - see attached Edge file:

Base design.edge - 1kB

Instead of off-setting the fullrange driver on a recangular baffle, I have trimmed the baffle itself to reduce diffractions. The two 15" woofers would be vertically aligned below the FR driver. To me, off-axis performance (as tested by moving the mic position around) seems pretty alright (save for the normal beaming of a 8" with corresponding roll-off in the treble of course) but opinions and tips are greatly welcome before I get the saw out 

Bill, my listening is strictly on-axis in the sweet spot, 120 cm listening height. There is no free-standing sub, the woofers are on the same OB as the fullrange driver.

Erling, how would this turn out in your model (SV 215B, AE OB15) for a more complete picture- or can you only model rectangular baffles? Schysta... 

[scorpion]

Using the MJK model you can simulate a three or four corner straight line baffle and for the specific speaker you will also need TSP-data.
So your six corners are too many. But never the less the Edge simulation will in the dipole peak/dipole hump area be as good as an MJK-simulation
if the element is in itself linear on axis here.

By the way, playing around with your figure in EDGE I could reduce diffraction effects to no more than 1 dB by altering the top three corners
moving sides even closer to the element. So if you don't mind a bit unusualshaped baffle you could design one that could go un-DSPed for shape reasons. 

/Erling

[NiToNi]

Thanks, Erling.

I have downloaded MJK's spreadsheets and will play around a bit with them too but if Edge is just as good as far as the shape of the baffle is concerned, I think this design could work. I may add more "corners" in Edge and try rounding the shaved-off part (i.e. making that bit elliptic) which would improve aesthetics.

I also noticed that performance could be improved by moving the side closer to the driver but the trade-off is an earlier roll-off in the bass and I want to keep some space above the FR driver for a possible super tweeter.

[Rudolf]

But if I use a 8" full-range driver far above its upper beaming frequency and the baffle's dipole peak (and break the rule anyway) as well as DSP, all this does not really matter anyway and it would be better to try to get a bit more bass response out of the FR driver...?

Keeping the optimal baffle width throughout the complete 20-20.000 Hz range would demand a four way system - at least. So you have to make some compromise of course. I always try to keep the baffle shape and the driver position symmetric to the vertical axis - with the driver as near to the baffle top edge as possible.

"Sculpting" the baffle to get extremely flat on-axis diagrams in Edge doesn't lead very far. I simulated the +/- 30° response in your Edge model:



In most cases the best on-axis-response compromises the off-axis response to one side. But don't judge this picture too high. The off-axis precision of Edge looses any precision beyond 15°.

[johnk...]

I haven't visited this site for some time. I saw this thread and thought I might comment. The relationship between baffle size (width) and driver size is really one which relates to driver directionality. Small baffles, or unbaffled drivers, will typically become directional before the dipole peak. As a result, the dipole peak does not achieve the full +6dB level. More importantly is that the first dipole null will not occur because of the lack of front to rear cancellation. If you go to a wider baffle then it is possible that the first null will be at a frequency where front/rear cancellation will still occur. This is very undesirable because it can not be corrected by equalization without having adverse effects on the off axis response. Additionally, if you are interested in true dipole response and uniform polar response, the dipole response should only be used up to a frequency of about 1/2 to 1 octave below the peak. Pushing the response higher on a wider baffle generally leads to a response that broadens off axis and the -3dB point moves past the 60 degree point. The 2 or 2.2 times driver size rule is a guide which places the dipole peak high enough in frequency so that driver directionality takes over and prevents the appearance of the first null and maintains a  quasi-dipole response due to driver directionality in the front hemisphere.  But the bottom line is that you really need to buil dand measure the polar response to see what you have.

[NiToNi]

Thanks Rudolf and John for these excellent clarifications!

I always try to keep the baffle shape and the driver position symmetric to the vertical axis - with the driver as near to the baffle top edge as possible. "Sculpting" the baffle to get extremely flat on-axis diagrams in Edge doesn't lead very far. In most cases the best on-axis-response compromises the off-axis response to one side.

OK so you recommend I keep the 8" FR driver centered on my 18-24" baffle (horizontally) for a symmetric off-axis response (+30° response equals -30° response) although this would compromise the on-axis response itself? And this is despite the fact that I will be (i) listening strictly on-axis, (ii) use DSP for room correction (Audiolense) and (iii) try to achieve an RFZ with an ISD gap of 15 ms at the sweet spot with treatments? Wow, the off-axis response must be more important than I could have imagined - and I don't mean that in an ironic way!

I cannot place the FR driver close to the upper edge since I would like to leave real estate for a potential super tweeter - unless I put tweeter below the midrange, i.e. between it and the woofer. Is that kosher...?

The 2 or 2.2 times driver size rule is a guide which places the dipole peak high enough in frequency so that driver directionality takes over and prevents the appearance of the first null and maintains a  quasi-dipole response due to driver directionality in the front hemisphere.  But the bottom line is that you really need to build and measure the polar response to see what you have.

I guess so... sigh... I do realise that I violate your (and Rudolf's) OB design philosophy by using a 8" FR driver for most of the response (140-8,000 Hz) on an 18-24" wide baffle but a lot of people seem happy with this kind of setup (including Thorsten Loesch), so perhaps the in-room response - or at least the perception of it- deviate a bit from simulations and theory... let's hope so...

So to go back to my two other questions, how much sensitivity do I gain in practise by going with a width of 24" versus 18" for my two 15" woofers? Playing around with Edge etc seems to indicate only about 2dB, i.e. hardly worth it, but is this what could be expected in reality too?

And also, is it necessary (or advisable) to compensate for the 6dB/octave roll-off in the analogue domain prior to applying digital EQ in order to preserve maximum headroom in the digital domain? Taking room boundary effects into account, what kind of roll-off is typically experienced in reality, especially with woofers designed for OB (in my case, AE OB15)? If it is less than 6dB over the 30-120 Hz pass band (as opposed to dipole theory of 12dB roll-off), then I may not bother with things like the Linkwitz transform or the T-bass circuit or electronic line-level shelving filters...     




 

[Rudolf]

OK so you recommend I keep the 8" FR driver centered on my 18-24" baffle (horizontally) for a symmetric off-axis response (+30° response equals -30° response) although this would compromise the on-axis response itself?

The "natural" on-axis response of a dipole is NOT flat. It starts with a continuous rise from low frequencies, peaking at some point and falls off to a rather steady response "plateau" some dB below the peak - if you follow the 2.2 times driver size "rule". This behaviour applies to all other directions too (more or less). To me it seems advisable to equalise this global "non-linearity" by electric/electronic means first.

And this is despite the fact that I will be (i) listening strictly on-axis, ... Wow, the off-axis response must be more important than I could have imagined - and I don't mean that in an ironic way!

What you hear on axis, is probably less than 1 % of the entire energy emitted into the room. This first wave is certainly the most important, but you should have a clear idea, what the other 99 % are made of. Reflections have up to 20 ms time to alter the impression of the first wave.

I cannot place the FR driver close to the upper edge since I would like to leave real estate for a potential super tweeter - unless I put tweeter below the midrange, i.e. between it and the woofer.

I wouldn't integrate a super tweeter into the main baffle. It robs you of the option to direct the super tweeter to the ceiling or the back wall - sometimes a better solution than boring on-axis