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 26th December 2016, 04:59 PM #1 Patrick Bateman   diyAudio Member     Join Date: Oct 2006 Location: San Diego An Improved Array I had some time off work, so I've been trying to decipher how the Beolab 90 works. I'm looking forward to hearing it again in a couple weeks. (At CES.) While studying the patents, I stumbled across an interesting one from Enrique Stiles. In this thread I'll take a stab at describing it. Mr Stiles' patent is based on the work of Philips. About 35 years ago, Philips patented a novel array named 'the Bessel array.' The concept of the Bessel array is very simple: In a conventional line array, the elements sum constructively at low frequency, and destructively at high frequency. Specifically, they'll sum destructively when the frequencies reproduced are shorter than the center-to-center spacing, and they'll sum constructively when the frequencies reproduced are longer than the frequencies reproduced. The reason that this happens is due to phase and amplitude. At low frequencies, all of the array elements are in phase due to the long wavelengths. At high frequencies, this is no longer true, because the wavelengths are so short. And this gets worse the further you go off axis. (Due to the phase differences.) So the Bessel array addresses the phase and amplitude issues in two ways. First, two of the five elements are driven with a reduced amplitude. Second, the phase of one element is flipped. The net result is an improvement in the off-axis response, at the expense of overall amplitude. The overall output of a five element Bessel array is equivalent to the output of a two element line array. More info can be found here : Bessel Array Arguably, nearly all attempts to improve array performance are based on attempts to manipulate the phase and amplitude of the array elements. For instance, 'shading' manipulates the amplitude. CBT arrays manipulate phase via physical placement, and also 'shade' the array. IMHO, 'log spaced arrays' are a clever method of shading an array without modifying the voltage. Here's a comparison of a conventional five element array, versus a five element Bessel array. Note the improvement in off-axis response, at the expense of overall output. Data is source from Mr Stiles' patent, #US20060018491 A1 Last edited by Patrick Bateman; 26th December 2016 at 05:02 PM.
 26th December 2016, 06:26 PM #2 Patrick Bateman   diyAudio Member     Join Date: Oct 2006 Location: San Diego As noted in the first post, arrays behave differently at high and low frequencies. At low frequencies, the elements are combining constructively, because the wavelengths are long. Basically the phase difference between elements is very little. At high frequencies, the phase differences are large (because the wavelengths are short) and due to this, the array elements combine destructively. Mr Stiles patent addresses this discrepancy. In his patent, he's doing a couple things to improve the performance. In a conventional Bessel array, the voltages look like this: 1 2 2 -2 1 What that means is that the outermost elements in the array get one half the voltage. (The array is "shaded.") The innermost elements get full voltage but one element has flipped polarity. Flipping the polarity of that element improves the off-axis response, at the expense of overall efficiency. In Mr Stile's array, he's recognized that a conventional line array is superior at low frequency, but a Bessel array is superior at high frequency. So he's made an array that combines both. The way that he's done this is that the array uses the following voltage at high frequency: 1 2 2 -2 1 And it uses this voltage at low frequency: 2 2 2 2 2 I hope that makes sense. It's a clever enhancement to an array. Here's a measurement of his design. Note that at low frequency, it's a straight line array. At high frequency, it's a Bessel array. Note that the response is not flat. One might use the design 'as is', perhaps they'd like the bass-heavy sound. Another option is to flatten out the response using an equalizer. One 'neat' thing about this improved array is that it would have significantly higher output potential than a conventional Bessel array, due to the higher efficiency at low frequencies. I discovered Mr Stiles' patent because it was referenced by Bang & Olufsen in their Beolab 90 patent. Above is the frequency response of the Beolab 90. Not sure if there's a relation between the frequency response of the Beolab and the Stiles design. (IE, is the Beolab 90 an improved circular Bessel array with DSP controlled beamwidth?) That may be possible; note that the number of drivers used in the Beolab 90 midrange and tweeter arrays is compatible with Bessel wiring/shading.
 26th December 2016, 07:11 PM #3 Patrick Bateman   diyAudio Member     Join Date: Oct 2006 Location: San Diego Okay, so how does someone build this thing? Here's how: Possibly the simplest way to build this array is using a MiniDSP. Remember, here's how we wire this thing: At high frequency, these are the voltages: 1 2 2 -2 1 And at low frequency, the voltages are : 2 2 2 2 2 This means that we need three channels of filtering: 1) In the first channel, we have a filter that reduces the voltage from 50% to 100%. IE, we need to use a MiniDSP 'shelf' filter that looks like this: Note that the filter won't look exactly like this; I just stole this online. 2) The second speaker and the third speaker in the array have no filtering whatsoever. 3) The fourth speaker has the most interesting filter of all. The third speaker has no changes to the amplitude whatsoever, but the phase shifts 180 degrees at high frequency. Here's how you implement the filter for the fourth channel : Advanced filters (Allpass/LT etc) with MiniDSP - Car Audio | DiyMobileAudio.com | Car Stereo Forum Thanks to Hanatsu for documenting this. 4) The fifth speaker in the array has the exact same filter as the first. Unfortunately, this set of filters uses three of the four channels in a MiniDSP. It would be nice to reduce this down to two filters, so that one MiniDSP could be used for a stereo signal. One 'obvious' way to do it with a single MiniDSP would be to use a splitter to bypass the MiniDSP for elements #2 and #2 in the array. (Since they use no filtering whatsoever.) Unfortunately, this probably wouldn't work, because the MiniDSP introduces latency.
 26th December 2016, 07:27 PM #4 Patrick Bateman   diyAudio Member     Join Date: Oct 2006 Location: San Diego Can we build this thing passively? At high frequency, these are the voltages: 1 2 2 -2 1 And at low frequency, the voltages are : 2 2 2 2 2 This means that we need three channels of filtering: 1) In the first channel, we have a filter that reduces the voltage from 50% to 100%. This can be accomplished passively using a baffle step compensation filter. Instructions on how to do this passively are here : mh-audio.nl - Home 2) The second speaker and the third speaker in the array have no filtering whatsoever. 3) The fourth speaker has the most interesting filter of all. The third speaker has no changes to the amplitude whatsoever, but the phase shifts 180 degrees at high frequency. I am not aware of a simple way to implement this passively. But note that it is only one element in the array; it may be possible to get very close to the active performance by simply flipping the polarity of this element. 4) The fifth speaker in the array has the exact same filter as the first. Okay, so the paragraph above documents how to do all this passively. But it's not the ONLY way. Here's another option: The passive filter describe in the previous paragraph can be quite expensive. As much as \$20-\$30. That can be kinda silly when you're using 5cm drivers in an array that cost ten bucks. So an easy way to simplify things would be to use a dual voice coil driver, with a low pass filter on ONE of the TWO voice coils.
 26th December 2016, 08:09 PM #5 Patrick Bateman   diyAudio Member     Join Date: Oct 2006 Location: San Diego In post #4, I speculated that the array could be done passively, and suggested how to do it. In another patent, I found a simpler way to do it: Here's the polar response of this array: One thing to note, in all of these polar plots, is that the array is oriented vertically. But this array type is really intended to be flipped on it's side. The entire point of these patents is for soundbars. So if you've been thinking about building a 'soundbar' type of speaker, this could be a great option. Instead of using an expensive passive filter to roll off the highs of the outer elements, one could simply *rotate* the outer elements. Bob Carver's Sunfire Cinema Ribbon does a similar 'trick' with his loudspeaker. Note that putting the outer elements of the array on the *side* of the enclosure, like Carver did, also moves the voice coils backwards. This has the net effect of curving the array, and may widen the directivity. Basically a very rudimentary way of doing what Monte Kay did in his CBT pictured above. Another possibility with this improved array is to use it as the 'tweeter' in an MTM. The advantage of using this improved array instead of a conventional tweeter is that the improved array will have directivity control that a single tweeter does not. It will also have higher power handling. In this respect, the improved array could offer you the advantages of a waveguide or horn without using a waveguide or horn. As noted earlier in the thread, the whole reason I stumbled on this patent was because it's referenced by B&O. So it's possible that this technology could be an interesting substitute for waveguides or horns. (Since that's exactly what B&O is doing.) BTW, all the details you could ever want can be found here: Patent US20060159287 - MTM of bessels loudspeaker - Google Patents
 26th December 2016, 09:43 PM #6 PeteMcK diyAudio Member   Join Date: Feb 2002 Location: Western Sydney Thanks Patrick, I always find your posts thought provoking, even if they go down paths I may not follow myself. (There isn't enough of this innovative thinking around here...) __________________ Impedance varies with frequency, use impedance plots of your drivers and make crossover calculations using the actual impedance of the driver at the crossover frequency
 26th December 2016, 10:04 PM #7 mayhem13   diyAudio Member   Join Date: Sep 2008 Then there's also Costas arrays which deal with phase by the physical alignment of the drivers in that the phase cancellations are greatly reduced. Wouldn't be a narrow speaker by any means but an interesting use of full range drivers in say a shallow, on wall speaker.
 27th December 2016, 12:33 AM #8 Jim Griffin   diyAudio Member   Join Date: Jun 2003 Location: Tennessee Don Keele wrote a very good treatment of Bessel arrays in an AES paper several years ago. See the discussion at the end of section 4.4.4 and the conclusions in section 6.0 for a quick summary. See Don's work at: http://www.xlrtechs.com/dbkeele.com/...l%20Arrays.pdf
FoLLgoTT
diyAudio Member

Join Date: Oct 2006
Location: Hannover, Germany
With my line array with waveguide prototype I also tried the Bessel array a time ago. The directivity is close to that of the single driver. This means beaming above 10 kHz is the same, too.

Bessel array with 1" drivers:

Directivity index is not very good. An 1-dimensional Waveguide does a better job and takes not much more space than such an horizontal array.

The idea to change directivity "on the fly" is tempting. But I still don't see the real benefit in home use.
Attached Images
 Bessel vertikal ohne Stege.png (27.7 KB, 1987 views)

Last edited by FoLLgoTT; 27th December 2016 at 01:38 PM.

 27th December 2016, 01:59 PM #10 Grasso789   diyAudio Member   Join Date: Mar 2016 Location: Juelich Hi, forget money. I have seen JBL's CBTs, Don's long-bows, Don's and Mister Horbach's and Follgott's FIR stuff, Follgott's CBT+horn combinations, Bessel arrays, simple and J-shaped line arrays and beaming by destructive interference as in Kiii, open baffles and now Beolabs. But the only effective arrays, effective in ratio of sound quality to building effort, are some big-*** Public Adress ones, because 18" is maximum driver size yet too few for a stadium, JBL's inobtrusive church CBTs, Follgott's principle of combining array and horn, and my Krassolito. Krassolito: Wide-range drivers, possibly stopped (read: less than) first-order filters and possibly bent baffles. Combine simple bricks well, avoid what is bad. Forget money.

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