Dipole Horn

introducing "Dipole Directivity Control Device" (DDCD) to the audio community

Never heard?
Its a "brand new" player in the game intended to perfectly mate open baffle low-mid designs.

by Ing. Michael Gerstgrasser

Foreword

Open baffle designs perform great up to the point where the (first) baffle peak occurs, which - in case of a 8" mid driver - for example - this covers a usable bandwidth of roughly 300 to 1500 Hz - *if* we make the baffle small. Besides some other advantages, OB's enjoy with increased gain, no suffering from cavity resonances and no need for all that diffuse and greyish sounding dampening materials. In addition, OB sports a fairly stable dipole / figure eight directivity pattern over frequency.

Unfortunately the mechanisms that guarantee for the dipole pattern for the low-mid frequency range no longer work above roughly the first baffle peak and "dipole operation" becomes kind of "bipole operation". For a seamless sonic blending to a tweeter though, we would like to have a mating dipole / figure eight directivity for the tweeter over its entire band width as well.

The Problem

What happens if we mount a tweeter - like an electrostat, an air motion transformer, or a magnetostat - into an open baffle of reasonable size in "dipole configuration" (radiating equally to front and back) is shown below for angels of 0 / 10 / 20 / 30 / 40 degree:

Fig. 1

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Fig. 1 (AMT in 30cm wide baffle, flat on axis response due to advanced equalising done with ACOURATE here) shows that we get severe deviations at different frequencies. Meaning - we get pretty unpredictable power response from that configuration or - seen from a more common point of view - smooth FR is limited to a very narrow sweet spot. *or* a very small band width.
Also notice the severe peak at the lower end of the pass band at non-axis angels - right in the middle of our most sensitive hearing ability.

A Solution

Obviously we need some degree of "Dipole Directivity control" to apply.
Sorting out a bunch of ideas about the "how to" - the easiest and most proven way to do so seemed to be using kind of horn attached at front and back of the driver - though I had severe reservations regarding the sonic outcome, dating back some centuries where I was investigating in horn's for domestic use the last time.

Anyway...
In my search for a good starting point for my "Dipole Directivity Control Device" I found Jean-Michel LeCleach ideas about wave front propagation and wave front shape development most intriguing - telling us that the big issue of mouth reflections can be overcome to a vast extent.

Fig. 2

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Fig. 2 shows how a wave front (black) propagates along a LeCleach contour (red) - or better put - how Jean-Michel corrects the contour for hyperbolic horns due to the simple law of time of flight.

Implementing the contour Jean-Michel sent me when I asked what he would suggest to my specific application, I was happy to find out that the excellent sonic reputation of the LeCleach contour also applies for my cylinder wave dipole horn.

Fig. 3, 4, 5, 6, 7

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Fig. 3, 4, 5, 6, 7 show how a "Dipole Directivity Control Device" may look like if done for an air motion transformer and when limited in vertical space available.

Performing measurements at different angels from above DDCD yield excellent results as well:

Fig. 8

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In Fig. 8 we see that the nasty peak at 1.5 kHz at non- axis positions is all gone *and* the off axis traces are really smooth and pretty consistent considering the high zoom range - at least up to roughly 12 kHz.
Again, on axis frequency response in this measurements is shaped by ACOURATE and PC XO for being flat on-axis (4th order Butterworth HP).

To sum up what we have got from my "Dipole Directivity Control Device" until now is the first and most important step towards seamless blending between an OB mid and the tweeter department in avoiding "off axis baffle peak" (resulting from flat on-axis equalisation) plus smoothing out the upper part.

It may be worth to note that a dipole horn obviously acts like any conventional horn / wave guide - no mess in acoustic impedance or other calamities due to radiation into two horns at the same time.

I first introduced this concept in Lynn Olson's thread "Beyond the Ariel".

Second Step of Optimisation

Now - considering the enormous capabilities of advanced equalising there is even more to get.

As John Kreskovsky pointed out several times the benefits of looking at speaker behaviour from a minimum phase point of view, we clearly see that an OB arrangement in the tweeter range (Fig. 1 ) isn't exactly minimum phase for more than a very narrow angle around the axis. Though the dipole horn arrangement (Fig. 8) with the LeCleach contour clearly is a huge improvement over Fig. 1, both from measurements and form auditioning - the LeCleach contour obviously isn't intended to be "minimum phase" over a considerable room angle.

The point in having a speaker acting "minimum phase" over a broad room angle is, that any equalisation applied, will perfectly fit for the whole room angle where the speaker can be seen to be close to "minimum phase". Simply put - we would like to achieve "constant directivity" - or at least something close *and* as stable as possible over the entire frequency range of our speaker.

With advanced equalising available as DSP processing or PC based solutions we nowadays can shape frequency and phase response completely to our will. Meaning - the impulse response of such a system can be made extremely close to ideal - subsequently including virtually no decay (extreme rapid) to be seen in CSD / waterfall plots. The room angle this perfectly works for is limited to the range we can call "constant directivity" though.

To sum up - "constant directivity" here is not the aim for getting wide and smooth audience coverage at first but to provide the necessary basis to gain the benefits of advanced equalising. Very different starting points - yielding comparable results in the end !

The concept of "constant directivity" is best known regarding horn and wave guide designs and tells us that the directivity pattern does not alter with frequency. Meaning - off axis listening does exhibit exactly the same sonic impression - usually at somewhat lower SPL though. This isn't the case in its precise meaning for all the CD horns out there but everybody still is happy in using the term "true constant directivity" as long as there is *fairly stable* directivity over a "relatively wide" frequency range of the unit.

;)

One other thing to notice about "constant directivity" is that we can see an ideal omni source to be "constant directivity", as well as figure eight or any other pattern - as long as this SPL pattern in the room remains stable over frequency.

As a side note, there is ongoing discussion about whether or not CD is favourable from a sonic point of view. Meaning - no one can tell if presentation in a room benefits from CD pattern or not, as there are more technical facts and personal preferences to consider for perception of sound then a fix ratio of power response compared to direct arrival frequency response.

Of course, open baffle designs can be seen to be true "constant directivity" (in the range up to the first baffle peak) as well. So, at some point it seemed to be the most logically thing to me to pair an open baffle low-mid with a tweeter that provides dedicated "directivity control". In addition to that, the dipole character has to be retained of course.

The syntheses of all above came out to what I call a "Dipole Directivity Control Device" (DDCD) or "Dipole Horn" for short. The aim for a DDCD intended to mate OB is *not* to maximise efficiency (as is the main goal for horns) but to provide a directivity pattern close to that of the open baffle dipole low-mid unit, up to as high frequencies as possible. Sure - we will keep in mind that high efficiency is always a good thing to have as is to minimise the impacts of subsequent "diffraction > reflection > delay > interference" (to which HOM is a subset of). Thus - regardless of how we look at the subject of DDCD - in the end its simply a kind of horn / wave guide and all the endless discussion points about superiority of one concept over the other apply almost equally.

We have to be aware that there are several ways to achieve the goal with horns / wave guides which may result in severe compromises for the sake of maximising efficiency or minimising cost or any other rigor "single spec" optimisation.

In the Light of Ancient versus Nowadays Knowledge

An excellent overview about current horn related design criteria can be found in Bjorn Kolbrek's articles published in AudioXpress 2008:

"Horn Theory: An Introduction, Part 1 & Part 2 "

(as kind of follow up I should mention that there is "horn theory replay.pdf" form Earl titled "Letter to the Editor Audio-X-Press")

Digging deeper into the subject of "directivity control devices" / "wave guides" / "horns" we see that a lot regarding gain control over frequency was already done by the ancients but there is ongoing debate and a lot of confusion regarding sound field defects / wave front propagation and its impacts in "directivity control devices" / wave guides / horns. Even the current "masters" ain't clear about this subject - sometimes "completely wrong" even ;) - to my noob surprise.

Hence I thought best is to make up my own mind about this subject to gain some deeper understanding of the underlying mechanisms involved.

Looking at the "ancient" measurement of W.M. Hall (1932) and compare those with some "up to date" simus form mine probably makes a good start to enter the topic.

Fig. 9

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Fig. 9 (taken from Bjorn's article) shows what W.M. Hall thought to be wave fronts (and not only he !).
Already having seen some illustration of wave fronts - like Jean-Michel looks at the topic - we see that the so called "wave fronts" from W.M. Hall look quite different. This brings us towards the question what actually is a wave front?

I once illustrated that with the following "picture":

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Say we take Grand Canyon and shape it into a horn - put a glass roof, and invite a few thousand fans of DIYAUDIO as audience sitting right in and in front of our mega-horn. Then we ask Zeus to assist and throw one of his lightning's into the throat.

We have instructed our lovely audience to raise arms once they hear something.
Watching our experiment from a bird's eye view we see the arms going up like when wind goes through a corn field.

Now - so far so clear - having defined what is meant with the term "wave front". Telling us that there is only one thing important to the term "wave front" - time of flight. Meaning - the contours of subsequent "wave fronts" - like shown in the pix of W.M. Hall simply ain't possible

What we should focus on is that time of flight depends *only* on the distance nothing else (well - in the first place). Quite in contrary to the term "sound field" which basically mirrors "what comes after"

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If we use simus to visualise what's going on we first may look at a wave front propagating through a simple conical contour like W.M. Hall's conical horn

Fig. 10

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Fig. 10 showing that a wave front travels like "wind through a corn field"

Meaning - its not affected by reflections and interference.

There *is* an influence on the shape of the "wave front" by the mechanism of diffraction though (not visualised by my CARA sims), but it is a relative simple straight forward effect (plus some reflection part) involved in "bending the wave front around the corner" as presented and outlined by Jean-Michel LeCleach and David McBean on several occasions.

If we next look at the sound field that is created inside the horn at a certain frequency:

Fig. 11

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In Fig. 11 we can see that the islands seen in W.M. Hall's measurements clearly reflect the sound field inside the horn.

I took some liberty here to stretch the term "sound field" to characterise pressure distribution inside the horn speaker whereas it usually is meant to describe pressure distribution in the listening room . This pressure distribution is nothing else than the SPL level (for a specific frequency) at any point in space - meaning - we easily can localise hot spots.
One thing to stay clear about is that the SPL distribution shown is for a specific frequency *only* - meaning - it is calculated to reflect / visualise W.M. Hall's measurements at 800Hz. The islands usually would change their shape and place inside the horn if the frequency is altered.

So - at a certain point in space there can be a hot spot for one frequency - translating to a peak in the frequency response for that very frequency taken at exactly that point in space - whereas for other frequencies the sound field looks totally different - making up for the ragged FR's we are all familiar with. Going back to my Grand Canyon example - people at different seats would - most probably - have different impression of the "sound quality" of Zeus' lightning.

From a horn design point of view it is desirable to keep the islands in place as what is cooked inside the horn is spilled out into the room and we would like to be able to correct for that raggedness for an as wide as possible room angle. All above is more or less a side note to CD characteristics - or better put - how deviations from CD translate from the underlying mechanisms.

Further looking into the details of how the phase gradients in W.M. Hall's measurements are visualised by my simus :

Fig. 12

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Fig. 12 above shows a CARA simu of a sinus stimulus - plus the interference due to mouth reflection.
If there were no mouth reflection we simply would see a smooth sinus wave "from right to left". Now - if we draw the lines along its zero crossing (for 0 (180) 90 (270) deg) we would get the equi-phase gradients in space shown by W.M. Hall.

To sum up, the hot spot island and the phase gradients seen in W.M. Hall's measurements - this is what's diffraction > reflection > delay > interference (and thus HOM included) is all about.

Nothing new under the sun !

The point to pay attention to is that the "wave *front*" isn't affected by any interference mechanism (beside what's already outlined).

Impacts

Now that we have seen the impacts of the subsequent actions of "diffraction > reflection > delay > interference" (basically what's creating the "swiss cheese" defects in sound fields) we also might explore the topic of how these subsequent actions of "diffraction > reflection > delay > interference" kick back.
Obviously there is some amount of energy reflection back to the throat. These reflections also hit the diaphragm causing "defects" in the acoustic impedance. So if we look after "what" comes back to the diaphragm in detail - we just have to follow this parts of the wave front that got reflected and hit the diaphragm after some delay.

And last but not least we can look into the details of what additional second order effects may be anticipated due to the non-uniform sound field shown somewhere above (first order effect simply being a "rugged" sound field and its impacts on impulse response homogeneity over points in space).

This admittedly I expect to be sublime effects but nevertheless worth to bring up.

As also outlined in Bjorg's article, we will be hit by rays of sound that "have a record". Meaning - if waves get higher in SPL they get deformed - more seriously - in a very specific way.
There are two effects that count in here :

This occurs from the wave itself for any change from compression to decompression and for any cycle it takes to reach our ear. But it also occurs for any high SPL space a wave has to pass - meaning - the law of the "linear superposition principle" does not tell us the whole story.

Third Step of Optimisation

To proceed towards an end and coming back to a less philosophical level, I'd like to show how excellent the latest contour - figured out by soongsc - performs.

Fig. 13

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In Fig. 13 (taken from http://www.diyaudio.com/forums/showthread.php?postid=1851334#post1851334) we see soongsc's approach to merge the ideas of Earl Geddes and Jean-Michel LeCleach and mixing in some own thoughts.

This contour he gained by extensive use of BEM simulation.

Fig. 14

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Fig. 14 (taken from http://www.diyaudio.com/forums/showthread.php?postid=1851004#post1851004) shows soongsc's BEM simu for the above contour (Fig. 13)

Outlook towards a Fourth Step of Optimisation

Below my measurements of how sonngsc's horn contour ( that I slightly adapted to fit my needs) turns out in my "cylinder wave" dipole horn.

Fig. 14.

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Fig. 14 tells us in comparison to Fig. 1 (AMT operating dipole in OB) and Fig. 8 (AMT radiating into LeCleach contour dipole horn) that we can realise excellent constant directivity (up to roughly 15 kHz here) with "Dipole Directivity Control Device" / dipole horn.

Again my plot is referenced to flat on axis response.

Very impressive indeed!

Investigating some more into the irregularities at the top end reveals that these can look pretty different as they are most certainly caused by interference due to throat dimension - *plus* reflections at the horn contour

Fig. 15

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Fig. 15 shows the sound field inside a horn for a specific frequency, providing an on-axis peak at that frequency

This specific sound field behaviour (Fig. 15) most certainly applies for my measurements shown for the LeCleach contour (Fig. 1) - just that I have equalised for flat on-axis response, making for a dip at all other angels.

Fig. 16

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Fig. 16 shows the sound field inside a horn for a specific frequency, providing an on-axis dip at that frequency

This specific sound field behaviour (Fig. 16) most certainly applies for my measurements shown for the soongsc's contour (Fig. 14) - just that I have equalised for flat on-axis response, making for a peak at all other angels.

Fig. 1 (again)

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Fig. 1 dipole horn with LeCleach contour

Fig. 14 (again)

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Fig. 14 dipole horn with soongsc contour (on axis referenced / no HP filter)

The funny thing to note is that CARA seems to capture a behaviour we are strongly interested in, whereas BEM does not - at least from what I can conclude from my discussions with soongsc. Not knowing enough about the limitations of BEM simulation it seems to calculate the pressure distribution along the wave front rather than the sound field - meaning it possibly does not account for the interference of rays of sound - I could be completely wrong though.

We have to stay clear that CARA sims are not meant to be "scientifically correct". CARA was written for calculating and visualising acoustic room effects and hence has severe limitations for the application I stretch it to. All the useful numbers CARA calculates about RT60, STI and so on are meaningless in our context. Keeping this in mind we nevertheless can gain a lot of qualitative understanding about the mechanisms involved due to CARA's excellent visualisation tools.

One issue with stunning impacts is the limitation of CARA regarding diffraction. It simply doesn't calculate for diffraction. Kind of exceptions - in *my* simus - are the diffraction at the mouth that is fairly well modelled by a simple reflection - and for the diffraction at the throat that is fairly well modelled by the directivity of the source attached to the horn.

That I got my CARA sim's such congruent to W.M. Hall measurements tells us that these sources are by far dominant to diffraction effects along the horn contour itself (at least in this very case).

Very interesting - no ?

All in all there are possibly several ways to deal with the imperfections horns (same issue with wave guides of course) show at their top end:

Cut to the bones of HOM

Any discussion to be tangent to horns wouldn't be complete unless the issue of HOM isn't addressed (at least until now ;) ).

As even the "master of HOM" himself is confused how to translate the beauty of his HOM-math into terms of "wave front" and "sound field" - I found it especially exhausting to cut through all the woodoo dancing Earl likes to wrap around the issue.

HOM (as an abbreviation)- first of all - is short for High Order Modes.

HOM (as incisive term) - secondly - was introduced by Earl Geddes to the audio community along with his wave guide theory.

HOM (as kind of special rays) - thirdly - hasn't been "really" measured yet nor is there any valid data about any specific sonic impacts.

HOM (in general) - fourthly - lacks some clear definition - meaning we have to deal with something we don't really know where it begins and ends.

My take on HOM is to limit it to

What HOM looks like is best visualised for ducts - the most simple boundary contour available.

Fig. 16

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Fig. 16 shows us how a wave front travels along a (infinite) duct right after "thrown in" without matching the requirements of being the "right" shape *and* the "right" pressure distribution. We see the wave front straightening out ahead to become flat - followed by a tail of reflections bouncing between the boundaries.

Same scenario like in Fig. 16 but with the sound field visualised for a certain frequency instead:

Fig. 17

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In Fig. 17 we see that the bouncing wave front from Fig. 16 indicates subsequent defects in the established sound field due to interference.

Same scenario like in Fig. 16 but visualising the pressure distribution of a sine wave stimulus instead:

Fig 18

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In Fig. 18 we see that the bouncing wave front from Fig. 16 indicates subsequent defects in the established pressure distribution at a certain frequency due to interference.

Again - lets stay clear, that the defects in the sound field created by HOM vary with frequency.

We could state that:

HOM creates deviations (in an established sound field) of isophase points in space from the "natural shape" of a wave front, propagating in limited space (along boundaries).

Uff - not that much intuitively - neither very clear "from scratch"!

So, better lets go step by step and let's focus at the two most easiest contours, duct and cone. By the way the two only ones, where *no HOM* occurs *when driven properly*. Key here is that HOM refers to "Higher Order Mode" - meaning we first have to look at the fundamental mode:

The "natural" shape of a wave front in a duct is - of course - a plane one. This kind of wave front can travel infinitely through a duct without any need to alter its shape ever - it also would not leave behind any tail - it's completely balanced.

Another "natural" shape of a wave front is the spherical - propagating along an infinite conical horn (with it's origin coincident with the origin of the spherical wave front!) - it also is completely in balance - no need to ever change its shape (besides getting bigger in radius).

For a second step, let's say we take the duct and enlarge its diameter abruptly.

At the point of discontinuity our lovely plane wave front will radiate into the enlarged space - according to the laws of

  1. sound speed limit
  2. pressure balancing

- summing up to rays of sound with its origin at the point of discontinuity - or put it different - a "second source" at the point of discontinuity has been created. Same creation of a second source will happen if we deliberately change the conical contour at some point.

Its important to note that any "second source" is a "point source" at first hand - meaning - it radiates in all directions - forth / back / to the sides. Thus we see that "reflection" occurs.

To sum up - what currently has a revival due to Earl Geddes' specific interest in HOM as an incisive term is more easily described and understood by the common concept of "sound fields" stretched to the topic at hand (superposition of diffraction artefacts inside horns).

It has to be stressed that there is HOM *free* sound propagation only for the two "natural" wave fronts "flat" and "spherical" - meaning - with respect to real world horns - there is no contour without HOM (conical would require to be driven by a virtual point source *and* to be of infinite length whereas a duct isn't exactly a "horn" at all)

Further more, the "ancients" V.A. Hoersch (Non-radial Vibrations Within a Conical Horn, Physical Review, Feb. 1925) and W.M. Hall (Comments on the Theory of Horns, 1932) have already revealed the basic principles of "non-radial vibrations" by theory and measurements, according to Bjorn's excellent summary.

To sum up - all the fuss about HOM is basically nothing else than "non radial vibrations". Though "non radial vibrations" didn't reveal the deep insight modern simulations provide by a "mouse click" nor does it account for the beauty of Earl's math. With our understanding of the underlying mechanisms we also can conclude that Earl Geddes has found the oblade sheroide contour to have the least diffraction effects - by math - *for a transition from plane to spherical wave fronts* and hence the most uniform sound field for the part of his contour that mostly performs this transition. I may add that Earls OS contour asymptoticly approaches the conical - so it might be better - to refer to that part where the OS has its strongest wave front bending effect (at the throat). There is some questioning what the "lowest diffraction by math" is meant here though - maybe come back later on that *if* I find a easy way to visualise Earls claim "the lowest diffraction proven by math".

There are two pitfalls however

A note of personal preference regarding the benefits of foam to dampen reflections inside the horn contour - I found out that I simply can't stand the coloration *any* dampening material I've came across adds to the sound.

Obsession and Fulfilment

Below I'd like to show kind of documentation about "long lasting" development on the subject I recently "exhumed" from the attic.

Fig 18 19 20 21

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in Fig.18 -20 we see my early attempt to join a "breathing source" (bent Shackman electrostat) with horns.
Would that horn have been pure conical and of infinite length - "non radial vibrations" wouldn't have occurred (even better than any oblade sheroide transition ever can do).

:)

Well - besides some guts feeling not knowing much more than what the booklets of Hans Peter Klinger (who has inspired a whole generation of German speaking DIYers) provided at that time - the outcome of my implementation was .... and I buried the whole horn issue in the deepest grave for centuries.

Its been a long time since but with my current concept I got fulfilled all my wishes from then - clarity, high resolution, beautiful presentation, reasonable SPL capability .

This wouldn't have been possible without the intense and productive discussion / exchange of ideas about benefits and issues of current approaches on DiyAudio with Lynn Olsen, John Kreskovsky, Jean-Michel Lecleach, Earl Geddes, Soongsc and many, many others
Thanks to all of you - also to the "invisible" ones that manage to keep this outstanding platform going!

Michael

PS:

Regarding the semantics of "Dipole Directivity Control Device" I found it kind of pleonasm in the strict scientific sense but on the other hand it perfectly tells us what I'm after:

mimicking dipole directivity where it can't be achieved "naturally".




keep swingin' !

** PLEASE DESCRIBE THIS IMAGE ** Austria, in Mai / June / July 2009

Rev2 / 3rd July 2009