I've posted an embarassing number of threads about Unity horns, going back fifteen years.
Something that's been a big challenge for me is the cost and crossover demands of three way loudspeakers. Basically it's a million times easier to make a two-way speaker than a three way speaker.
When going from a two way to a three way, the crossover tends to get about twice as expensive, and the complexity goes up like a hockey stick.
I had an idea, inspired by my last project that might make it possible to do a full range loudspeaker with controlled directivity using a two way.
I know that it's possible to do a two-way controlled directivity speaker if you put a full range speaker at the apex of a waveguide, like xrk971 did here, or if you use a large format compression driver, like weltersys did here.
But I have a thing for small tweeters and small compression drivers, so those solutions don't work for me, unfortunately.
Something that's been a big challenge for me is the cost and crossover demands of three way loudspeakers. Basically it's a million times easier to make a two-way speaker than a three way speaker.
When going from a two way to a three way, the crossover tends to get about twice as expensive, and the complexity goes up like a hockey stick.
I had an idea, inspired by my last project that might make it possible to do a full range loudspeaker with controlled directivity using a two way.
I know that it's possible to do a two-way controlled directivity speaker if you put a full range speaker at the apex of a waveguide, like xrk971 did here, or if you use a large format compression driver, like weltersys did here.
But I have a thing for small tweeters and small compression drivers, so those solutions don't work for me, unfortunately.
I can't even count the number of times that I've read this paper:
http://www.linkwitzlab.com/Horbach-Keele Presentation Part 2 V4.pdf
There's nothing revolutionary here, but I think it's the most concise and easy-to-read paper about achieving controlled directivity via the use of destructive interference.
Yes, you can build a controlled directivity speaker using CBT technology, but the Horbach Keele paper shows you how to do it without building a super-difficult curved cabinet, and without having to use an array of thirty six tweeters.
The Horbach Keele design, though criminally overlooked, is simple and elegant.
The fundamental idea behind the paper, is that the elements are spaced at 0.757% of a wavelength, and the crossover filters use a specific shape. Each element in the array is underlapped a bit.
In a nutshell, the array uses a specific combination of crossover filter shape, spacing, and xover points to approximate a full range source with controlled directivity. It does this without resorting to the use of a horn or a waveguide or a curved cabinet to control the wavefront shape. The baffle is flat.
http://www.linkwitzlab.com/Horbach-Keele Presentation Part 2 V4.pdf
There's nothing revolutionary here, but I think it's the most concise and easy-to-read paper about achieving controlled directivity via the use of destructive interference.
Yes, you can build a controlled directivity speaker using CBT technology, but the Horbach Keele paper shows you how to do it without building a super-difficult curved cabinet, and without having to use an array of thirty six tweeters.
The Horbach Keele design, though criminally overlooked, is simple and elegant.
The fundamental idea behind the paper, is that the elements are spaced at 0.757% of a wavelength, and the crossover filters use a specific shape. Each element in the array is underlapped a bit.
In a nutshell, the array uses a specific combination of crossover filter shape, spacing, and xover points to approximate a full range source with controlled directivity. It does this without resorting to the use of a horn or a waveguide or a curved cabinet to control the wavefront shape. The baffle is flat.
I've found the H-K paper to simultaneously overcomplicate the crossover design, and fail to generalize the concept of nested arrays. Each "nest" in these nested arrays need not be restricted to 2 drivers. Also, if you follow the spacing requirements, you don't need to apply H-K filters. Fourth order linear phase filters work fine, as shown by Kimmosoto and confirmed by me in this thread:
https://www.diyaudio.com/forums/mul...traight-cbt-passive-xos-eq-4.html#post5606349
Additionally, I find 75 degrees to be too wide. Most people have floor and ceiling reflections between 30 and 45 degrees off the vertical axis. To suppress those more significantly, the beamwidth has to be more like 40 degrees. Unfortunately, the narrower the beam, the more difficult it is to achieve consistency.
I also showed that this can be done with passive crossovers, and I have since designed a simplified 3-way that works in a flat-pack cabinet for about $750 a pair (including drivers, crossover parts, and cabinets). Info available here:
Skylark Flying Towers: Nested Array Speakers in Denovo Cabinet -
Techtalk Speaker Building, Audio, Video Discussion Forum
Those speakers were certainly designed with high output capability for home listening in mind, but aren't for sound reinforcement in large spaces. FWIW, the tweeter is rated at 94 dB and takes 25 watts, for a theoretical 108 dB continuous.
https://www.diyaudio.com/forums/mul...traight-cbt-passive-xos-eq-4.html#post5606349
Additionally, I find 75 degrees to be too wide. Most people have floor and ceiling reflections between 30 and 45 degrees off the vertical axis. To suppress those more significantly, the beamwidth has to be more like 40 degrees. Unfortunately, the narrower the beam, the more difficult it is to achieve consistency.
I also showed that this can be done with passive crossovers, and I have since designed a simplified 3-way that works in a flat-pack cabinet for about $750 a pair (including drivers, crossover parts, and cabinets). Info available here:
Skylark Flying Towers: Nested Array Speakers in Denovo Cabinet -
Techtalk Speaker Building, Audio, Video Discussion Forum
Those speakers were certainly designed with high output capability for home listening in mind, but aren't for sound reinforcement in large spaces. FWIW, the tweeter is rated at 94 dB and takes 25 watts, for a theoretical 108 dB continuous.
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Elegance . you are right. But there is no "magic", fixed ratio in Horbach-Keele at all. 0.757 is as right as any ratio between some <0.5 ... >1.0, which will uniquely influence on the constant vertical polar.... The Horbach Keele design, though criminally overlooked, is simple and elegant.
The fundamental idea behind the paper, is that the elements are spaced at 0.757% of a wavelength ...
To understand Horbach-Keele as a DIY-er it is mandatory to read part 2 of this (!) paper:
400 Bad Request
I did understand this paper even as a non-mathematician and also built several functional Horbach-Keele arrays with the help of filters generated by Acourate. It really works.
And then maybe you may also read part 1 for a more gereralized and thus more theoretical approach:
400 Bad Request
This paper was too theoretical for me. I did not understand it fully, but as said, it is not necessary to be successful. Working through the aforementionned part 2 will do.
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Again, and as in my prior post: The vertical behavior of the resulting, frequency independent dipole characteristic of Horbach Keele can be tailored to one's needs.
Ceiling/Florr reflection inhibition? Yes, please ... Exactly here is where Horbach-Keele shines: Configure your physical array and your parameters of the Xover such as to decently send the dipole null precisely into the angle of the reflection:
Horbach-Keele Lobing.jpg
By this trick, the null will be reflected. Null=nothing at all. This holds true for only one hearing distance = one projection angle, but you can adjust the angle of the null from 90° to <30°. This works very well, as shown by a prototype of mine:
Array_HK.jpg
Step.png
The step response shows the result of the full array (red) and the more traditional bottom half of the array (green). The highlighted area shows where the floor reflection happens. The measurement was made once and at the theoretically expected minimum. Further refinements such as adjusting the measurement distance to even better matching of the null were not performed.
This shows that Horbach-Keele is very well able to inhibit floor reflection and thereby to minimize the ceiling reflection. You are encouraged to try it yourself!
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I didn't mean to imply that the response can't be tailored, only to warn people that the target beamwidth identified earlier in this thread wasn't necessarily ideal.
It's not clear to me why you have decided to refer to array beam response patterns as a "dipole" characteristic.
I agree this is an approach to speaker design that can be quite effective and should be tried by more people. I also want to provide options for people who don't want to take the H-K approach, though that one is well documented. It can be done digitally with 4th order linear phase crossovers. It can be done passively with mixed-order minimum phase crossovers.
I have discussed the option of turning off the top half of the array with other builders, but never done it (harder to do with passive crossovers since impedance changes). It's cool that you were able to do that. Did you have any listening impressions to go along with that change?
I forgot to mention that one thing I hope to be able to do with the skylark speaker build is to rotate the speakers 90 degrees in the middle of listening; thus switching the dispersion control from vertical to horizontal, to get a sense for how that impacts perception.
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You are right in being puzzled! It's my error, sorry for this one: Of course we are not speaking of (inversely poled) dipoles. It's rather pairs of equally poled point sources: In theirs paper, Horbach and Keele write of "pairs". The term "dipole" is wrong in this context.
Horbach-Keele filters will be best in terms of polar control, but do produce much ringing because of theirs steepness. They are also not available everywhere. Linphase LR-Filters instead are more common, and could lead to a compromise in terms of less ringing at the price of less control of the polar pattern. And it would certainly also be interesting to investigage in the further compromising introduced by minphase xovers. But I doubt that this last option would really work.
I am sorry, no. I had another goal - I only was interested in the answer to the question about the nulled floor reflection. The HK model of radiation pattern is, strictly seen, only defined for theoretical point sources and for the infinitely distant soundfield. Therefore, I did this experiment because I was uncertain if it would work or not in the relative near field and with real, twodimensional sound sources. So I was already very happy to see it worked. And another pity, referring to your above comment: I have also missed the opportunity to measure/investigate this setup along with a compromise linphase LR4 xover with/at the same xover frequencies than HK's.
No worries. I like to keep things simple for readers who might be trying to follow, and thought it might be confusing, so wanted to get it cleared up.
Do you have a source for the HK filters offering better polar control than the 4th order linear phase filters? Having read the papers, I figured there was no way that a simple 4th order linear phase filter would work at all, but kimmosto showed that it was possible. My suspicion is that it's actually easier to derive the HK filter because all frequencies are covered by only 2 nests. Perhaps something was missed, or else avoided for purposes of patenting or marketing.
Regarding the minphase (passive) crossovers, they do in fact work, which I showed, and which kimmosto and BYRTT verified in the link I posted. There are even equations to calculate the necessary Qs of the cascaded filters that are required. They don't result in a linear phase speaker the way the others do, since each nest has opposite polarity to the nests around it. Of course, if that was important, it could be fixed with a linearizing DSP tool after the fact, and would still only require one channel of amplification.
Too bad. If you ever try switching the top of the array on and off, I'd love to hear your impression of the result.
As to my knowledge, no other filter seem to work as neatly as the specific HK-Filters:
Google: US7991170
See also the paper part I
Everything seems transparentls and completely published within the scientific papers - no hidden secrets for patent's sake:
Google: US8160268
There is a indeed a bunch of different patents regarding these HK arrays and filters. I count 12 copies of pdf's of different HK-patents in my home collection. But despite of this armada of patents there is no legal risk of trying HK's at home for non-profit-hobbyist's interest. Mr. Horbach himself told me so in an email.
For a real-world polar response of my very first HK-Prototype you may have a look at:
http://www.acourate.com/freedownload/Horbach_Keele_Dipole_Prototype.pdf
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They seem to work, but cannot really close up to HK.
Kimmosto/BYRTT (KB):
Vertical_Polar.png
KB shows min 5dB amplitude fluctuation at 30°:
HK:
HK1.png
HK2.png
HK is almost linear to 40°
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I'm glad you've come around regarding the ability to use minimum phase passive crossovers. However, you're comparing a 5-way minimum phase speaker with narrower beamwidth to a 6 way HK speaker with wider beamwidth. The HK plots show how much easier it is to achieve consistency with the wider beamwdith, and using an extra nest allows for even more consistency. Additionally, the minimum phase speaker was not simulated with theoretical point sources, as I suspect the HK speaker was.
An advantage of using the minimum phase target slopes is that you can focus exclusively on the magnitude of the response when designing the crossovers (unless your chosen drivers have vastly different z-offsets in acoustic centers, creating a delay between them that's significant compared to the period of the crossover frequency). When using HK filters, you're expected to linearize the minimum phase characteristic of the drivers.
You are perfectly right, and also closer to the original thread title than I am: You definitely advocate a cheaper and simpler way to approximate controlled directivity. HK is neither simple nor cheap.
One question remains: Are there some measurements of real-world working Kimmosto/BYRTT systems? If so, I would be very interested to see how they compare against the described HK-prototype in my pdf.
What do you mean with "much easier"?
The beamwidth as a value is one of the main parameters in a HK design, and will take an influence on the vertical pattern, and on the xover frequencies: the wider the desired beamwidth is declared, the lower the xover frequencies will get. Logical, isn't it? HK will give perfectly consistent results for beamwidth values between 60° ... 120°. And with some compromises beyond these values. So beamwidth is not an issue. It's a parameter to play with, fine for optimizing the system to fit into an environment. Such to null a floor reflection ...
Therefore I don't understand your statement.
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As I understand it, when you have a pair of drivers they'll generate an interference pattern. If the spacing is between zero and one third of a wavelength, the two drivers will basically behave as one.
As the spacing approaches one half wavelength, the beamwidth narrows to about sixty degrees.
As the spacing approaches one full wavelength, the on-axis beamwidth narrows, but you also get lobes OFF axis.
Arguably, the strongest and most consistent nulls are at 30 degrees off axis. I think this is part of the reason that the array's beamwidth is in a range between 30 degrees and 75ish degrees.
The nulls are geometric. They're caused by the fact that the pathlength from the top radiator to a point 30 degrees off axis, is about one half wavelength shorter than the path from the BOTTOM radiator.
All of this is complicated by the fact that we have three drivers playing at the crossover frequency.
The idea that I had - is that it might be possible to use a higher center-to-center spacing by placing some type of phase plug over the woofers. This is because the nulls are 30 degrees off axis. So if it's possible to reduce the woofer's beamwidth to sixty degrees or less, then it should be possible to 'stretch' the center-to-center spacing.
This was something I (accidentally) discovered in one of my Unity horn projects. I'd used a single midbass instead of four, and I discovered that the polar response was way different than expected. Basically the midrange taps in front of the midbass were 'flattening' the wavefront. If the midbass was mounted to the baffle normally, it would radiate spherically. But because it radiated through a set of midrange taps, the wavefront was close to flat.
Yes! I would like to encourage you to read the aforementionned 2nd part of Horbach & Keele's paper, where exactly these topics are discussed and elaborated, included the three-driver's behavior. The following picture is a photo out from this very paper, which might act as an appetitizer:
PolarPattern.png
PS: I appreciated very much to read about yours, as you say, zillions of horns protos and your reports about them, this ongoing story of trial and error and of best iterative research on new path's!
