I had a 5.5 hour flight to Bentonville today, and once I got sick of reading an AWS book I decided to read a B&O patent.
Based on that patent, I thought I'd make a post on how the array works.
I know that I have another thread that's specifically about the DSP in the Beolab 90, but this thread will only focus on the array geometry and why it's shaped the way it's shaped. (It's all in the patent, but there's a lot of gobbledygook to plow through.)
In case you're considering giving it a try, Siegfriend Linkwitz wrote the following about the Beolab 90:
Yesterday, late afternoon, I had the opportunity to listen to these speakers for about half an hour using excerpts from a wide variety of my own demo material, which I had brought with me on a thumb drive. My conclusion: Excellent performance in aspects of neutrality of timbre, of dynamic range, of resolution at all levels, of attack and decay, of spatial rendering in width, depth and focus !!!
The BeoLab90 tops what I have heard from any commercial loudspeaker! (Constant directivity loudspeaker designs)
I agree with him, it is still the best speaker I've ever heard. And not by a small margin. It features imaging like a set of headphones, dynamics like a horn, but without the colorations.
Before we get into the weeds, let's talk about the basics. Why do we build and buy two-way loudspeakers? I believe that the reason that we do this is because we can't get a single driver to cover the entire audible spectrum. For instance, in this two-way Genelec speaker, we have a tweeter covering something like 3.5 octaves and a woofer covering approximately five octaves.
The waveguide is there to control the directivity of the tweeter. I'd say this is generally because we want the directivity of the woofer and tweeter to match at the crossover point. (Understand that a tweeter without a waveguide generally can't do this, unless the woofer was exceptionally small.)
OK, so far, so good?
One thing that might not be obvious is that you can control the directivity of diaphragm with it's shape. For instance, if you wanted a beamwidth of sixty degrees with a diaphragm that's 6" across, you'll want a diaphragm that's shaped like a contact lens. That shape isn't accidental; it's a spherical cap that's one sixth of the circumference of a circle. (Sixty degrees.) The picture above is the exact shape and size for a speaker that meets these requirements.
Obviously, you see shapes like this in tweeters and dome midranges, but you'll rarely find 6" diaphragms shaped like this.
Here's a midrange from Avantgarde Acoustics that follows this rule.
The exceptional beamwidth and frequency response is due to a combination of curvature and shading. The CBT is a 'slice' of that spherical cap that's pictured above. The beamwidth depends on the curvature of the spherical cap.
Now what if you decided that two-way speakers are too much work? You don't want to learn how to make a crossover, you don't want to build a waveguide, etc? What then?
Something like the Tymphany TC9 is probably about as much bandwidth as you'll get out of a single driver that's not exceptionally exotic. The Tympany won't play as low as the Genelec two-way, and the treble isn't as clean either. But the TC9 costs less than $20 and it is legitimately full-range. Although this is an inexpensive driver, this is cutting edge design. It's not easy to squeeze seven octaves out of a $12 driver!
Based on that patent, I thought I'd make a post on how the array works.
I know that I have another thread that's specifically about the DSP in the Beolab 90, but this thread will only focus on the array geometry and why it's shaped the way it's shaped. (It's all in the patent, but there's a lot of gobbledygook to plow through.)
In case you're considering giving it a try, Siegfriend Linkwitz wrote the following about the Beolab 90:
Yesterday, late afternoon, I had the opportunity to listen to these speakers for about half an hour using excerpts from a wide variety of my own demo material, which I had brought with me on a thumb drive. My conclusion: Excellent performance in aspects of neutrality of timbre, of dynamic range, of resolution at all levels, of attack and decay, of spatial rendering in width, depth and focus !!!
The BeoLab90 tops what I have heard from any commercial loudspeaker! (Constant directivity loudspeaker designs)
I agree with him, it is still the best speaker I've ever heard. And not by a small margin. It features imaging like a set of headphones, dynamics like a horn, but without the colorations.
Before we get into the weeds, let's talk about the basics. Why do we build and buy two-way loudspeakers? I believe that the reason that we do this is because we can't get a single driver to cover the entire audible spectrum. For instance, in this two-way Genelec speaker, we have a tweeter covering something like 3.5 octaves and a woofer covering approximately five octaves.
The waveguide is there to control the directivity of the tweeter. I'd say this is generally because we want the directivity of the woofer and tweeter to match at the crossover point. (Understand that a tweeter without a waveguide generally can't do this, unless the woofer was exceptionally small.)
OK, so far, so good?
One thing that might not be obvious is that you can control the directivity of diaphragm with it's shape. For instance, if you wanted a beamwidth of sixty degrees with a diaphragm that's 6" across, you'll want a diaphragm that's shaped like a contact lens. That shape isn't accidental; it's a spherical cap that's one sixth of the circumference of a circle. (Sixty degrees.) The picture above is the exact shape and size for a speaker that meets these requirements.
Obviously, you see shapes like this in tweeters and dome midranges, but you'll rarely find 6" diaphragms shaped like this.
Here's a midrange from Avantgarde Acoustics that follows this rule.
The exceptional beamwidth and frequency response is due to a combination of curvature and shading. The CBT is a 'slice' of that spherical cap that's pictured above. The beamwidth depends on the curvature of the spherical cap.
Now what if you decided that two-way speakers are too much work? You don't want to learn how to make a crossover, you don't want to build a waveguide, etc? What then?
Something like the Tymphany TC9 is probably about as much bandwidth as you'll get out of a single driver that's not exceptionally exotic. The Tympany won't play as low as the Genelec two-way, and the treble isn't as clean either. But the TC9 costs less than $20 and it is legitimately full-range. Although this is an inexpensive driver, this is cutting edge design. It's not easy to squeeze seven octaves out of a $12 driver!
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One of the drawbacks of using a full range like the Tymphany is that it's power handling is fairly low: 30 watts. For comparison's sake, the Genelec two-way has more than 6X the power handling! The additional power handling is very important for dynamics and headroom, and the Genelec is also more efficient.
So the low power handling of the full range is a definite drawback.
So what if we put two of the Tymphany woofers side by side?
You'd end up with something that looks like this. The use of dual midranges raises power handling and efficiency.
This is basically the lower half of the midrange array of the Beolab 50, and a fraction of the midrange array of the Beolab 90.
So... Why doesn't everyone do this? The answer is "comb filtering" of course. Basically the dual midranges create an interference pattern.
The sims above show the polar pattern of a two-element horizontal midrange array, like the one pictured in red above. You can see that the polar pattern is relatively well behaved at 1000Hz, but as you go higher in frequency, the polar pattern becomes a mess.
Sure, we see tons of MTM speakers with VERTICAL arrays, but HORIZONTAL midrange arrays are rare. This is because the polars aren't good. In a vertical orientation, we're not terribly concerned with how the speaker sounds at the ceiling or at the floor. Arguably, bad response on the floor could be a "feature" not a "defect."
So the low power handling of the full range is a definite drawback.
So what if we put two of the Tymphany woofers side by side?
You'd end up with something that looks like this. The use of dual midranges raises power handling and efficiency.
This is basically the lower half of the midrange array of the Beolab 50, and a fraction of the midrange array of the Beolab 90.
So... Why doesn't everyone do this? The answer is "comb filtering" of course. Basically the dual midranges create an interference pattern.
The sims above show the polar pattern of a two-element horizontal midrange array, like the one pictured in red above. You can see that the polar pattern is relatively well behaved at 1000Hz, but as you go higher in frequency, the polar pattern becomes a mess.
Sure, we see tons of MTM speakers with VERTICAL arrays, but HORIZONTAL midrange arrays are rare. This is because the polars aren't good. In a vertical orientation, we're not terribly concerned with how the speaker sounds at the ceiling or at the floor. Arguably, bad response on the floor could be a "feature" not a "defect."
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To understand why there are three midranges in the Beolab array, we need to understand what causes comb filtering. Here's the math:
Here's an illustration of the pathlength from a loudspeaker to the person listening to it. The person is two meters away from the loudspeaker and they're 24 degrees off axis. Because the array is horizontal, one of the elements is a little further away than the closer element. The difference is minor - a pathlength difference of 41mm, or just 1.73"
Here's why that makes a difference: 8300Hz is 41mm long. When the array plays 4150Hz, the two drivers are out-of-phase. This is due to that pathlength difference of 41mm. (4150Hz is one-half-wavelength of 8300Hz, and 8300Hz is 41mm long.)
This stuff always makes my head hurt, but I think it's important to understand what causes comb filtering. We know it's there, but it may not be obvious how even very small pathlength differences can create peaks and dips in the response of an array.
The addition of a third element in the array does something very valuable: It makes the array behave as if the center-to-center spacing was half as much. The Bang & Olufsen patent has a nice illustration of this. The third element basically behaves as if it's 'sandwiched' in between the other two elements.
For instance, as illustrated earlier in this post, you can see that a 41mm pathlength difference between the two drivers creates a dip at 4150Hz. The dip is caused by the pathlength difference, and the fact that the additional pathlength caused one driver to be out-of-phase with the other. (180 degrees out of phase, to be specific.) So the addition of a third element means that there's another driver playing that's 90 degrees out-of-phase. That has the effect of 'filling in' the dip.
If you look at the polar response of the three element array, you can see that it basically behaves as if the center-to-center spacing was half as much.
Here's an illustration of the pathlength from a loudspeaker to the person listening to it. The person is two meters away from the loudspeaker and they're 24 degrees off axis. Because the array is horizontal, one of the elements is a little further away than the closer element. The difference is minor - a pathlength difference of 41mm, or just 1.73"
Here's why that makes a difference: 8300Hz is 41mm long. When the array plays 4150Hz, the two drivers are out-of-phase. This is due to that pathlength difference of 41mm. (4150Hz is one-half-wavelength of 8300Hz, and 8300Hz is 41mm long.)
This stuff always makes my head hurt, but I think it's important to understand what causes comb filtering. We know it's there, but it may not be obvious how even very small pathlength differences can create peaks and dips in the response of an array.
The addition of a third element in the array does something very valuable: It makes the array behave as if the center-to-center spacing was half as much. The Bang & Olufsen patent has a nice illustration of this. The third element basically behaves as if it's 'sandwiched' in between the other two elements.
For instance, as illustrated earlier in this post, you can see that a 41mm pathlength difference between the two drivers creates a dip at 4150Hz. The dip is caused by the pathlength difference, and the fact that the additional pathlength caused one driver to be out-of-phase with the other. (180 degrees out of phase, to be specific.) So the addition of a third element means that there's another driver playing that's 90 degrees out-of-phase. That has the effect of 'filling in' the dip.
If you look at the polar response of the three element array, you can see that it basically behaves as if the center-to-center spacing was half as much.
As noted in the first post in this thread, a spherical cap will give you directivity control, similar to what a waveguide can do. This technology is used in the CBT arrays. IMHO, the curvature in the cabinet of the Beolab 90 and Beolab 50 is there for directivity control. IE, it's not just cosmetic.
You can see with the three element array it's not quite a perfect spherical cap, but the baffle isn't flat either.
Another benefit of tilting the baffles is that it reduces interference between elements in the array. In this measurement of the Tymphany TC9, you can see that it's starting to 'beam' at 4000Hz. So tilting the baffle not only changes the beamwidth, it also extends the upper response of the array.
At this point, there's an obvious enhancement to the array:
You can low pass two of the three elements when they begin to interfere with each other.
Here's an example. This is a polar response prediction of a three element array of drivers that are the size of a Tymphany TC9. You can see that the beam is getting quite narrow at 4000Hz. By 8000Hz, the beam will be a mess. The change in beawidth is due to interference between the drivers cause by pathlength differences. So there's a dead-easy solution, just lowpass two of the drivers at 4000Hz. This would yield an array that behaves like a single driver above 4000Hz, but with 3X the power handling of a single driver below 4000Hz. Plus, you get beamwidth control when all three drivers are active.
But at that point, you're getting into a discussion of the Beolab 50 & 90 DSP, which is better suited to the other thread:
B&O Beolab 90 - adjustable directivity by DSP
If you tinker with the simulations, you'll see something fairly quickly:
This three element array is REALLY GREAT for midrange. It's pretty trivial to come up with a three element array with substantial advantages over a single driver.
Rumor has it, the Nola Brio Trio uses a very minimalist crossover. Picture something like the Nola, but with 50% more power handling and better beamwidth control. Very easy to implement using B&O's array.
But when you do the math for a tweeter array, you can start to see why B&O went back to waveguides for the Beolab 50. It's just REALLY difficult to get the tweeters close enough together.
I'm not saying it DOESN'T work with tweeters, just saying that it's more compelling with midranges.
This three element array is REALLY GREAT for midrange. It's pretty trivial to come up with a three element array with substantial advantages over a single driver.
An externally hosted image should be here but it was not working when we last tested it.
Rumor has it, the Nola Brio Trio uses a very minimalist crossover. Picture something like the Nola, but with 50% more power handling and better beamwidth control. Very easy to implement using B&O's array.
But when you do the math for a tweeter array, you can start to see why B&O went back to waveguides for the Beolab 50. It's just REALLY difficult to get the tweeters close enough together.
I'm not saying it DOESN'T work with tweeters, just saying that it's more compelling with midranges.
And for my last post, I'd like to editorialize for a bit.
What's the point of all this? B&O obviously could have used a single conventional midrange for the Beolab 50 and 90.
I think there are three things going on:
1) If you compare the response of a 3.5" woofer to a 6.5" woofer, you'll see that 3.5" woofers are generally better behaved above 2000hz. So the use of multiple small woofers allows B&O to do things that they couldn't do with a single conventional driver. For instance, in the Beolab 5 they had to use a dome midrange between the tweeter and the woofer in the speaker. The use of multiple small midranges allows the designer to get response that's nearly as good as a dome, but with more displacement. "win-win."
2) You can do the sound steering with a single driver.
1) And, duh, it looks cool.
In other words, if the Beolab 50 didn't have beam steering, you could potentially replace that three driver midrange array with a single 6.5" or 8" woofer. But you're going to have a heck of a time finding one that can play nice with a dome tweeter in a waveguide. Though the inventor of the B&O lens uses BMS compression drivers in his speakers, B&O is still using soft dome tweeters. So that's going to place a 'hard limit' on how low the tweeter will play. I'd guess somewhere around 3000Hz.
What's the point of all this? B&O obviously could have used a single conventional midrange for the Beolab 50 and 90.
I think there are three things going on:
1) If you compare the response of a 3.5" woofer to a 6.5" woofer, you'll see that 3.5" woofers are generally better behaved above 2000hz. So the use of multiple small woofers allows B&O to do things that they couldn't do with a single conventional driver. For instance, in the Beolab 5 they had to use a dome midrange between the tweeter and the woofer in the speaker. The use of multiple small midranges allows the designer to get response that's nearly as good as a dome, but with more displacement. "win-win."
2) You can do the sound steering with a single driver.
1) And, duh, it looks cool.
In other words, if the Beolab 50 didn't have beam steering, you could potentially replace that three driver midrange array with a single 6.5" or 8" woofer. But you're going to have a heck of a time finding one that can play nice with a dome tweeter in a waveguide. Though the inventor of the B&O lens uses BMS compression drivers in his speakers, B&O is still using soft dome tweeters. So that's going to place a 'hard limit' on how low the tweeter will play. I'd guess somewhere around 3000Hz.
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Thank you Patrick for this! Here is a link to the Beolab 50 whitepaper/manual
https://www.bang-olufsen.com/~/medi...ab-50/bang-olufsen-beolab50-whitepaper-v3.pdf
Looks like that the three bass units and three mid units are playing same way all the time, unlike in Beolab 90. Beam width control affects only the tweeter, by moving it's wings. My guess is that there is some delay for rear woofers to create cardioid response in upper bass.
It would be nice to see 3D acoustic measurements of this! Could be worth cloning...
https://www.bang-olufsen.com/~/medi...ab-50/bang-olufsen-beolab50-whitepaper-v3.pdf
Looks like that the three bass units and three mid units are playing same way all the time, unlike in Beolab 90. Beam width control affects only the tweeter, by moving it's wings. My guess is that there is some delay for rear woofers to create cardioid response in upper bass.
It would be nice to see 3D acoustic measurements of this! Could be worth cloning...
I believe Geoff Martin from B&O stated that the Beolab 50 does beam steering. With the high frequencies that IS accomplished using the waveguide. The waveguide is mechanized, it physically varies the beamwidth and the angle.
I can only speculate on how the beam is steered on the midranges, but I'd be willing to bet that they just use DSP to alter the arrival times so that they're simultaneous at the listener's seat.
IE, the beamwidth itself is simply a product of the device size and the shape of the baffle, same as any radiator. But since there are three drivers with their own amp, the *direction* of that beam can be steered.
I can only speculate on how the beam is steered on the midranges, but I'd be willing to bet that they just use DSP to alter the arrival times so that they're simultaneous at the listener's seat.
IE, the beamwidth itself is simply a product of the device size and the shape of the baffle, same as any radiator. But since there are three drivers with their own amp, the *direction* of that beam can be steered.
Cool thread. I'm surprised it hasn't excited more comment / interest.
I like this point:
"It makes the array behave as if the center-to-center spacing was half as much."
If combined with this point:
"You can low pass two of the three elements when they begin to interfere with each other."
...I'm thinking it could be interesting to try this layout where the 3 'elements' are about the same size, but do different jobs.
-dedicated mid as the upper element
-less efficient, higher excursion midwoofers as the lower two elements
As I see it, the (effective) reduction of C-to-C spacing would mean the midwoofers could be run to a high frequency with less ill effect, so you could use a simpler crossover (lower order filters) than otherwise, as long as you chose midwoofers that roll off smoothly.
e.g system would be something like this:
DSP --> stereo amp --> stereo subs
DSP --> stereo amp --> 3 way with 1st order filters
Seems legit?
I like this point:
"It makes the array behave as if the center-to-center spacing was half as much."
If combined with this point:
"You can low pass two of the three elements when they begin to interfere with each other."
...I'm thinking it could be interesting to try this layout where the 3 'elements' are about the same size, but do different jobs.
-dedicated mid as the upper element
-less efficient, higher excursion midwoofers as the lower two elements
As I see it, the (effective) reduction of C-to-C spacing would mean the midwoofers could be run to a high frequency with less ill effect, so you could use a simpler crossover (lower order filters) than otherwise, as long as you chose midwoofers that roll off smoothly.
e.g system would be something like this:
DSP --> stereo amp --> stereo subs
DSP --> stereo amp --> 3 way with 1st order filters
- pair of 6" ~88dB efficient midwoofers (run in parallel for an effective sensitivity of 94dB)
- ~94dB pro mid
- waveguide loaded soft dome tweeter
Seems legit?
I should ask Geoff is all three are playing at the same time. He's been quite open about his designs.
If so, then it will behave a lot like the spherical cap described in Keele's CBT paper. Basically the array will approximate a transducer that's shaped like a giant contact lens.
The loudspeaker designer can vary the vertical and horizontal beamwidth by varying the dimensions of the cap. A bowl shaped cap will have a beamwidth of around 90 degrees, while a contact-lens-shaped cap will have a beamwidth of around 45 degrees.
Just thinking out loud here, the array should have three distinct modes of operation:
1) At very high frequency, the radiators are beaming. Because the faces of the array are angled away from each other, the high frequencies of the array are extended. This works the same way as a curved array, but now it's curved in two dimensions, not one.
2) Things get complex as the radiators become omnipolar. For instance, when I made a design with 2" drivers, the tightest that I could pack them together was about 3.5". This means that there's going to be a range between 6,750Hz and 3900Hz where the interaction between drivers is quite complex. Basically we'll probably see some comb filtering in this range, because the wavelengths are long enough to be omni, but short enough where the three drivers aren't summing perfectly.
3) As the frequencies get lower and lower and lower, the three drivers beging to behave like a single driver with a diameter of approximately eight inches. (At least in this example.) Every octave that you go below 3900Hz, the three drivers are starting to sum in a more constructive fashion.
From the looks of it, there's a "magic range" where the three drivers are summing really nicely. But as you go lower in frequency, the device will lose directivity control. This is probably why B&O made a multiway speaker, instead of simply building a giant spherical cap. For instance, in the example cited above, a three driver array of 2" drivers measures about 8" in diameter. So the directivity control will be very good in the octave from 1700Hz to 3400Hz, but as frequencies go higher things get trickier, due to comb filtering.
There's a few ways to extend the bandwidth:
1) By putting speakers on the side of the Beolab 90, they can use cancellation to control the beamwidth at low frequencies. So basically you'd have the three-driver spherical array do it's thing in the midrange, but at low frequencies, the side drivers start to contribute to beam forming.
2) A simpler solution is to simply build a larger spherical cap. But this gets big in a hurry. Like a horn or a waveguide, you need a big cap to work at low frequencies. A cap that works down to 500Hz needs to be 68cm in diameter! On the upside, these devices aren't as physically large as a horn, because they're not as deep. We're talking about a speaker that's about 20cm deep.
3) Like a CBT, shading can be used to improve the frequency response and the consistency of the beamwidth. This comes at the expense of efficiency. But arrays are pretty darn efficient.
It occurred to me today that this project of mine from last year works a lot like the B&O cap. That wasn't my plan, I just stumbled across the idea on accident. It worked very very well, and I now realize that the important part of these designs is simply the shape of the cap.
IE, you don't necessarily need to build these caps with three drivers, or six drivers, or fifteen drivers. You can build these caps with ONE driver.
The reason why is because the apparent source of the sound is the surface of the cap.
IE, if you take a single driver, and you put a cap over it's face, and then create a 'channel' where the sound can radiate, you just moved the apparent source of the sound. The source is no longer the speaker itself, it is the channel that rings the cap.
This works the same way as bandpass boxes; the apparent source of the sound is the port, not the loudspeaker inside of the box.
Of course, you still need to compensate for the delay that is introduced, but that is easily done via DSP or even a simple passive xover.
And all of this is 'fractal' in nature. You could nest three drivers under one cap to make a three way loudspeaker that radiates consistently across a broad spectrum. Basically a speaker with directivity control on both the X and the Y axis. Heck, you can even tweak the Z axis via DSP or the crossover.
Neat!
Thinking of spherical cap may have led you to this but it looks to me like you've created a co-axial driver. The natural next step would be to add a horn to the front of it and be on your way to cloning a Danley SM-60F
I see some similarities to the Genelec 8351A. That has 2 oval woofers slot-loaded behind a waveguide out of which a MT coax fires. That design seems to have some issues with turbulence/compression from the slot loading that you might also have to consider here.
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Thanks Patrick!
Great post Patrick, you explain complex subjects in a clear and logical way....Inspirational dude!
A.
Great post Patrick, you explain complex subjects in a clear and logical way....Inspirational dude!
A.
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