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26th November 2009, 12:23 AM  #1 
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Location: Austria, at a beautiful place right in the heart of the Alps.

Min Phase Horn with Faital Drivers at German DIY Show in Gelsenkirchen
I start this split thread on the topic of “Min Phase Horns” to no longer occupy Earl Geddes ones with what he isn’t directly involved in.
Roots of “Min Phase Horns” go back some month in discussion here on diyaudio in several threads – where I – considering myself a noob in horns developed towards the idea and the term “min phase horn” which finally got reality ready to purchase for the DIY’er from German Strassäcker company due to the effort “jzagaja” has taken as a manufacurer. The whole min phase philosophy originally stems from John Kreskovsky who repeatedly was teaching the very basic fact that speakers actually *can* be seen as min phase device. Meaning that by advanced equalization a close to perfect behaviour can be achieved. My contribution here was to look at horns as to be seen as pure “diffraction alignment device” meaning that if we want to achieve min phase behaviour over an as wide as possible room angle we have to concentrate on the effects of diffraction in a way to hit exactly that goal. The basic philosophy behind my min phase horns is presented in my paper down from the capture “Second step of Optimisation” http://www.kinotechnik.edis.at/pages...pole_horn.html There was a lot of contribution of others to this concept evolving in several threads on diyaudio especially “soongsc” and “rcw” which are somewhere on the same line. It may be worth to go back some month of this discussion. The first public appearance of a Min Phase Horn took place at German DIY show 2009 in Gelsenkirchen – though it’s wrongly have been announced or anticipated as Kugelwellenhorn there. Some pretty pictures can be seen in a German DIY forum: http://www.roehrenundhoeren.de/php...pic.php?t=7528 It’s a huge min phase horn for which I have calculated the contour, but have not been any further involved in the design process. It may be helpful to read through following ( not only ! ) postings too: Geddes on Waveguides Geddes on Waveguides Geddes on Waveguides Geddes on Waveguides There is a lot more to read about though to get the whole picture – anyway – I hope to having made a useful starting point to a good discussion about min phase horns  in particular the very *first one in public* as well as any other ones to come (sooncs and rcw  do you hear me? ) Michael
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Audio and Loudspeaker Design Guidelines Last edited by mige0; 26th November 2009 at 12:39 AM. 
26th November 2009, 12:45 AM  #2  
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Michael
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26th November 2009, 12:55 AM  #3  
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For any piston like source – moving back and forth – we have 180 deg of diffraction each side to fill 4 PI space. What really counts is the *alignment of diffraction in space* to get the lowest possible sound field defects *in combination* with controlled directivity over a as wide as possible room angle and a as wide as possible frequency range. This is actually what’s min phase horn philosophy is all about. Michael
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26th November 2009, 08:19 AM  #4 
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26th November 2009, 05:22 PM  #5 
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Actually my sentence:
“What really counts is the *alignment of diffraction in space* to get the lowest possible sound field defects *in combination* with controlled directivity over a as wide as possible room angle and a as wide as possible frequency range.” …is nothing less than my statement regarding a radically new paradigm of how to look at any speaker design and *especially* at horn speaker design. 1. I set the *main* goal in speaker design to be a smooth and consistent resulting sound field 2. I set the goal in speaker design that this sound field has to be of min phase behaviour to an as widely as possible range in space and frequency 3. I claim diffraction to be seen as an “alignment tool” – in fact the only one we actually have (!) – in the process to achieve the goal of 1) and 2) 4. I’m aware that to some degree the basis to benefit from 1) – 3) is nowadays availability of *advanced equalizing* (response shaping at will) – which was not the case at any reasonable price until now One can argue that neither 1) nor 2) is any new at all, and many good speakers already have been optimized to come close to this goal in the end. I certainly agree – though the combination of all three points to a stringent philosophy (with quite some impact) *is* new – to my honest knowledge. *Diffraction*, on how I learned to look at things (during the last several month) is key. By many seen as some crude mix of “action / reaction”  diffraction got bad reputation as an ill effect in loudspeaker design to be avoided or suppressed at any price  with Earl Geddes to be the most famous and outspoken proponent of this thesis around here. In my point of view I set *diffraction* or even more precisely *alignment of diffraction* to be the ultimate tool to achieve considerable progress in speaker design. Quite some difference! ###### To have a semantically precise handle on the subject, I strictly restrict “diffraction” to be a “term of cause” in the historically meaning of “bending around the corner” In German its maybe more intuitively to do so, as “diffraction” in a technically understanding here is closely connected to “Beugung” = “bending” Anyway  to my knowledge “diffraction” as a word of science, prominently entered public awareness with the most famous photos of solar eclipse being taken to prove Einstein’s theory a long time ago. The most important benefit to stay clear about that sharp definition is that now we immediately see the big bunch of diffraction *effects* as a pure result of alignment. 1.) Any bending of a wave front causes a “second source” – no matter how. 2.) To fill 4 PI space or 2 PI space (in case of infinite baffle) a “one vector” wave front  from a piston moving back and forth  has obviously to be bent by 180deg (4 PI space) respectively by 90deg (2 PI space) either side – no matter how The alignment of the inevitable “second source” points in space is what I call “diffraction alignment” in short. Whether we look at a speaker mounted in closed box or at a horn – the outcome in sound field smoothness and consistency depends *only* on “diffraction alignment” ##### Undertaking a short survey on dampening measures in the light of what I said above, we immediately see that applying dampening materials to “avoid” diffraction is a double sided sword at best and a “nonsense claim” at a closer look. For one  there simply is *no* way to avoid diffraction. All space available gets filled with sound – no matter how – so its nonsense to claim “avoiding diffraction” by dampening measures. On the other hand – if we look at how dampening materials actually work like regarding diffraction *effects*, we might get a better feeling in what dampening measures can do for us at most. For example  let’s take an extreme case of an ideal dampening material and apply that magic dampening material at the *whole surface* of a horn contour. In its sound field outcome one would have a hard time to distinguish that experimental setup from the compression driver playing without any horn. The reason behind is, that any ideal dampening material applied at a surface makes that surface virtually disappear and also creates a sharp discontinuity – building for a stoooong second source – comparable to intentionally bending the wave front all around 360deg at a knife like edge. Obviously – current dampening materials (foam etc.) are far from being ideal absorbers. So the effects taking place will be that there is gradual diffraction / bending at the point where this foam is applied to a surface – meaning it will be a matter of try and error what possibly more easily and more predictably can be achieved by a clever designed solid contour. As for a dampening foam *plug* inside a horn  as is done by Earl in his OS – IMO, the positive effect is limited to dampen the specific cavity resonance (horn honk) caused by sub optimal contour and mouth reflections. IMO – basically a “end of pipe” measure and something not even being in *direct* relation to “avoiding ( controlling – at best) diffraction by dampening measures” Michael
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Audio and Loudspeaker Design Guidelines Last edited by mige0; 26th November 2009 at 05:28 PM. 
26th November 2009, 07:32 PM  #6  
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Refraction is unidirectional depending of environment, diffraction is omnidirectional depending of geometry. For me: Reflection: return or rebound Refraction: bending Difraction: decomposing or separating (due to the interferences from reflection for one source) So I don't know, because I don't understand everything, if your concept is based on an interesting global point of view but developed with some false details. 

26th November 2009, 07:50 PM  #7 
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In researching this problem I have come to certain conclusions outlined bellow.....
You can define a general minimum phase system as one that is positive definite.(ref. available). The usual definition used in signal processing is that in the transfer function there are no zeros in the right half of the complex plane, this breaks down however for spatial systems since pure time delays have this property and yet are non minimum phase. We can then say that if we have a class of spatial phenomena that can be described as minimum phase, then they must have a symmetrical matrix which has all positive eigenvalues, it is usual to call these Hermitian, but any other solution to a square matrix that also yields all positive eigenvalues is by this definition minimum phase. We also don't need to consider all solutions to wave equations in a sphere, all we need is a solution for a unidirectional beam, and there are a class of solutions that are called the parabolic approximations that are suitable for this purpose. Those that use a Pade series approximation are close to exact over + 40, degrees from the axis, and useful over a full hemisphere. A convenient feature of this equation is that it is also the Schrodinger equation, and since all solutions to this are matrices with all positive eigenvalues, then all solutions to the Schrodinger equation are minimum phase. To be minimum phase the field from the radiating element, and the field caused by its interface with the outside space, via the duct, must be potential fields that sum to a third potential field that then maps conformally to the listening area. If you can design a device that conforms to all of these criteria then it should be possible to get an exact replication of the input electrical waveform at a useful set of points defining a listening area. I will not ask for comments because I am sure there will be plenty so I leave it there for now. rcw. 
26th November 2009, 07:55 PM  #8 
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Join Date: Jul 2005
Location: sydney nsw

In researching this problem I have come to certain conclusions outlined bellow.....
You can define a general minimum phase system as one that is positive definite.(ref. available). The usual definition used in signal processing is that in the transfer function there are no zeros in the right half of the complex plane, this breaks down however for spatial systems since pure time delays have this property and yet are non minimum phase. We can then say that if we have a class of spatial phenomena that can be described as minimum phase, then they must have a symmetrical matrix which has all positive eigenvalues, it is usual to call these Hermitian, but any other solution to a square matrix that also yields all positive eigenvalues is by this definition minimum phase. We also don't need to consider all solutions to wave equations in a sphere, all we need is a solution for a unidirectional beam, and there are a class of solutions that are called the parabolic approximations that are suitable for this purpose. Those that use a Pade series approximation are close to exact over + 40, degrees from the axis, and useful over a full hemisphere. A convenient feature of this equation is that it is also the Schrodinger equation, and since all solutions to this are matrices with all positive eigenvalues, then all solutions to the Schrodinger equation are minimum phase. To be minimum phase the field from the radiating element, and the field caused by its interface with the outside space, via the duct, must be potential fields that sum to a third potential field that then maps conformally to the listening area. If you can design a device that conforms to all of these criteria then it should be possible to get an exact replication of the input electrical waveform at a useful set of points defining a listening area. I will not ask for comments because I am sure there will be plenty so I leave it there for now. rcw. 
26th November 2009, 09:28 PM  #9  
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Refraction ('"Brechung" in German)  at least as I understand it  is a variation in the vector (inangle versus outangle) when a ray changes from one medium to another one *and* does not pass the border at *exactly* perpendicular angle. So light going through a lens at any non perpendicular angle gets "bent" or "refracted"  whereas the "bending" of light rays at the very rim of the lens (aperture) is called "diffraction"  basically *this* bending / diffraction would also happen if there is no lens mounted and there would only be a hole of a certain diameter. Its the physics experiment in school where they show us how slits widen the parallel light beam going through. In all photographers all days experience its the fact that pix do *not* get any sharper below a aperture of ~8 – 16 quite in contrary. Also  in my reference example of the historic photos captured to prove Einstein's hypothesis its *diffraction* which was the underlaying mechanism of bending the sun's light around the moon  not refraction. These crazy guys form England traveled around halve the world to take a picture of the total eclipse of 29 May 1919, that in the end made Einstein famous even in his days. So, I can't exactly see how "refraction" enters the picture in audio  no? Michael
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Audio and Loudspeaker Design Guidelines Last edited by mige0; 26th November 2009 at 09:41 PM. 

26th November 2009, 09:36 PM  #10  
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Michael
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