Acoustic Horn Design – The Easy Way (Ath4)

I think that what has been published on the few last pages is already a solid foundation for making a well-suited horn either for a 1.4 or 2" throat.
I myself hesitated quite a bit with the bigger throats - the same waveguides that work so well with 1" throat just don't cut it when made larger (that's also the reason there's no 1.4" or bigger in the CE series). Now I think we finally found what we need.
 
Ladies and gentlemen!
I would love the thread but it is nearly impossible to keep track with a thread with over 10.000 posts.
I have some may be stupid questions that are probably to be found in some of the > 10.000 posts.
1. The files generated can be used to feed a 3D printer?
2. For larger horns probably there is the need to split the construction in different parts and glue them together?
 
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Is there by the way any reason nobody built yet a ATH using a coax conpression driver like bms 4594 or similar? Searched a while but did not find any attempt to that…
Most of the presented waveguides have poor acoustic loading at low frequencies so it would seem to be a bit of a waste to use a 300Hz capable driver. For example the ATH-CE460-0 has the real part of throat impedance < 0.2 below just over 1kHz. It should be posible to design a deeper waveguide though!
 
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Acoustic loading for the mids may be nice but even unloaded such drivers have more than sufficient output for hifi use. A even addition in directivity would be more important in my view and that would be provided by the ATHs. I also like the few adaptions of ATHs in synergy horn I saw in this forum.

Since already mentioning:
-Real part of throat impedance is 0 unloaded or no more coupling???
- What does the imaginary part tell us?

@MegB: have a look in the firsr post and in the manual ob the ATH Homepage. This might answer some questions. Basicslly answer is „yes“ but for splitting them up you have to CAD a bit yourself or use a published one (there were some already)
 
Since already mentioning:
-Real part of throat impedance is 0 unloaded or no more coupling???
- What does the imaginary part tell us?
Forgive me from copy & pasting an abridged version of a previous explanation. There's some good content on this in the ABEC3 / AKABAK3 help file, which includes the example plot shown.

The vibrating diaphragm of a loudspeaker changes the pressure of the air via displacement, which creates a reactionary force that exerts itself back onto the diaphragm, proportional to the velocity
of the surface. The ratio of this mechanical force to the surface velocity is called the radiation impedance, as defined by
Z_MR = f / u_n

Where f is the force and u_n is the surface velocity normal to the surface boundary. The result is a complex number. The real part represents the resistance (R_A) from the propagating sound waves. The imaginary part consists of the reactance (X_A) from the additional mass created by the air cycling close to the surface.

This reactance creates a phase difference between the pressure and velocity of the surface, which accelerates the diaphragm’s mass rather than making sound - in effect, reducing the available output.

Acoustic impedance is the complex ratio of pressure p, averaged over a one-dimensional surface area S, to the volume velocity U through the surface. The volume velocity can be found by the multiplying particle velocity u at each pressure measurement point by the radiating surface area.

Z_a = p / U = p / uS

It can be helpful to consider the acoustic impedance concerning the characteristic or specific acoustic impedance of air. The value obtained is normalised, which allows easier comparison between data sets.

Z_s = ρc

The mechanical radiation impedance Z_MR has a relation to the acoustic domain by the equation
Z_AR = p / U_n

Where p represents the sound pressure, and U_n is the normal volume velocity across the surface.

It is important to note that this radiation impedance is affected not by the material properties but by the geometry of the surface and the surrounding environment. The shape and size of the diaphragm radius (a) relative to the length of the sound wave, represented by the complex wavenumber (k), dictates the shape of the wavefront.

When ka becomes large, the radiated wavefront becomes planar, showing a high value for R_A, which equates to a high output efficiency. If ka < 1, the reactance X_A dominates, and the sound output is reduced.

The resistive part of the acoustic impedance R_A finds its electrical analogy in a component that converts energy to heat. Since power is only dissipated in resistive electrical components,
the load for a voltage, force or pressure should be purely resistive to ensure maximum energy transfer. The higher the real part of acoustic impedance Z_A value, the greater the acoustic pressure
output.

Conversely, the higher the value of the imaginary part X_A, the greater the acoustic mass, which reduces output and may cause resonance. A negative value for X_A represents an acoustic
stiffness.

1651586638126.png


The red curve is of a flat circular piston, the blue of a concave shape such as a typical loudspeaker cone, and the green of a convex shape or familiar dome source. All three curves become asymptotic at high frequencies, corresponding to plane wave propagation. This is represented by the ratio of the specific impedance of air to the area S of the radiating surface.

The real part of the radiation impedance becomes close to zero at very low frequencies, indicating little to no sound pressure output.

As the wavelength becomes close to the radiator’s dimensions, the radiation impedance for each source begins to deviate. The shape of the curves depends on the geometry and surface vibration of the diaphragm and the environment.

The analytical piston source’s resistance (solid line) rises steeply, without much overshoot, while the reactance (dashed line) is mass-like over the whole passband. The dome shape, equivalent to a soft dome tweeter, is similar to the piston but has a smoother transition to higher frequencies within the resistive part.

The concave-shaped diaphragm, representing a cone speaker, features an apparent overshoot in resistance, which indicates a resonance where the output will be most substantial.
The imaginary part also exhibits negative-valued regions, representing a spring-like stiffness caused by the cone cavity.

This relationship indicates that an increase in the depth of the diaphragm produces an acoustic impedance which begins to approach the behaviour of a horn.

Eventually, the shape would become a straight duct, and pronounced ripples in the radiation impedance would correspond to the standing waves within the pipe.

If the real part of the radiation impedance is low or close to zero, and the imaginary part is high, we can expect resonant behaviour because the diaphragm mass becomes poorly damped.

While a coaxial diaphragm or similar might have sufficient output alone in this region to get a suitable SPL, it may not be a particularly pleasant sound - typical design guidelines suggest using a high pass filter (electrical or acoustic) to roll-off the response before the natural LF resonance of a compression driver.
 
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So…. I understand the drawback for the horns for a coaxial driver.
However: if you want to avoid the vertical narrowing dispersion at Xo frequency using a low/midrange positioned below the horn: what are the alternatives?
Or is this crossover-narrowing in vertical dispersion just something that is commonly accepted here?
 
Is Jab3+ easy to configure?
This is off topic but I'll answer with experience from the older Jab3 without plus. Yeah pretty easy after the process is familiar, but not walk in the park. DSP is programmed with Sigma studio, very flexible, not the easiest one, not too bad as there are plenty of tips on the web. But, the programmer (bought separately) cannot be always connected to the board or otherwise the system doesn't boot up (with sound). Programming needs particular order of hooking and unhooking stuff or custom switches soldered in to manage the connections and make permanent changes to the ADAU1701 chip. Not practical at all, but doable. These boards are not made to be managed daily, more like a set and forget then dump into dumpster after its not working anymore type of product. Can't expect much with equivalent cost of few packs of cigarettes can we. That said, I've used one for three years now. Bluetooth died the first day but otherwise it has been working fine, althought quite noisy with poor PCB design and has too much gain setup, its been good board to prototype speakers with. Cheapest I could find years ago, perhaps still is. You get what you pay for like usual :)
 
So…. I understand the drawback for the horns for a coaxial driver.
However: if you want to avoid the vertical narrowing dispersion at Xo frequency using a low/midrange positioned below the horn: what are the alternatives?
Or is this crossover-narrowing in vertical dispersion just something that is commonly accepted here?

There will always be some polar discontinuity in the acoustic crossover region when using an asymmetrical source arrangement, but it can be reduced with:
1. Matching each individual source's polar patterns in that region
2. Selection of centre-to-centre spacing, baffle mounting (e.g angling or axial offset) for each source
3. Use of asymmetrical or non-standard filtering and processing to reduce the phase differential at off-axis angles from each source
4. Addition of acoustic lenses or similar devices that change the physical radiation pattern of the woofer in the desired plane

One way to work with Option 3 is shown here, with a common "2.5 way" asymmetrical arrangement:
https://www.prosoundtraining.com/2010/03/17/using-all-pass-filters-to-improve-directivity-response/
This method needs good polar data for individual sources - available from Ath/ABEC/AKABAK3 if the mesh is good -and a tool like VituixCAD or AFMG SpeakerLab to work with the filtering.

Since the M2 is a good reference for most folk with lots of data thanks to Erin & others, it makes sense to stick to JBL to explore a few of those ideas.

Options 1 & 2: https://www.jblsynthesis.com/products/loudspeakers/SCL-1.html
Option 4:
https://www.jblsynthesis.com/products/loudspeakers/SCL-5.html
Options 1, 2 & 4 (note the slight angling of the LF drivers):
https://jblpro.com/en/products/c222hp
1651650673071.jpeg


The ‘lenses’ are explored in patent EP 3379845 if you're interested:
09118199-34DB-454D-9261-3BC225BC727E.jpeg

D4FE919F-F723-4FD6-AFCC-08161F5865B7.jpeg

89B0B950-F212-4186-8111-ACC3B19F479D.jpeg



Moving back to horns or waveguides, the loss of resistive loading can be an indicator of resonance or 'horn honk' as I mentioned previously.

A good example of that can be seen on the early prototype horn that B&C sent out with the best performing midrange coaxial CD source:
1651651256272.jpeg

https://audioxpress.com/article/tes...igh-power-coaxial-compression-driver-and-horn

This is a horn of 444.5mm in length, and an elliptical mouth of 597mm x 444.5mm. I think it should be possible to generate in Ath if someone is keen to see the radiation impedance.

While I understand the reasoning, it's a shame there's no polar data for the horn shown in this article. What we do see however is the off-axis response for the MF element, with normalised:
1651651304181.png

1651651316137.png


The frequency response looks good down to 400Hz, and it's pretty well controlled too. But as ever, magnitude response alone doesn't tell the whole story. The CSD and STFT waterfall plots show some interesting things below 600Hz, that don't necessarily appear in the above data:
1651651634220.png

1651651653304.png

This is an issue that becomes more prominent when the reactive part of the acoustic impedance dominates the response.

The lack of resistance can lead to under-damped resonance. Depending on the measurement method, in the example, this appears to be as much as four times the decay time for the majority of the source's frequency range.

Now the question is whether this is much worse than the alternative cone driver... either way, there are other things to consider when choosing your crossover region (acoustic or electronic) than just magnitude response and directivity.
 
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I'm not sure I would agree with the suggested conclusion about the "resonance". This would imply that the horn is not minimum phase which contradics all my experience. I've never seen a time issue that would not be directly related to an amplidude non-flatness (and then, it would not be a resonance anyway). So the suggestion that the amplitude response doesn't show it all is not correct, IMO. It may hide ("smooth") things if the measured time window is too short, that's true.
 
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Now I wonder how strong may be the influence of the whole horn (implies the mentioned issues at low frequencies) at a synergy design. In contrast do a coaxial driver the mf/lf part is intruduced later in the horn and also has some interaction with back-reflections. Maybe I modifiy the st260 to simulate this within the next days.
 
I think there's really no issue below 1 kHz. The measurement is not very telling in this regard either, it's quite hard to make an anechoic measurement in the 300 Hz - 1 kHz region - a one that would reveal the details. For example there's obviously quite a sharp HP knee above 300 Hz - see how smoothed it is in the rest of the measured data. This has also its decay in time that's to be expected to be shown in the CSD (again, here vastly "blured").
 
I think there's really no issue below 1 kHz. The measurement is not very telling in this regard either, it's quite hard to make an anechoic measurement in the 300 Hz - 1 kHz region - a one that would reveal the details. For example there's obviously quite a sharp HP knee above 300 Hz - see how smoothed it is in the rest of the measured data. This has also its decay in time that's to be expected to be shown in the CSD (again, here vastly "blured").
The plots in AudioXpress test bench reviews aren’t generated from a single sweep. Each measurement is done with a different method, and they’re all quite well documented in the text of the article for the sake of repeatability.

The electrical impedance plots given show the driver with (black) and without (blue) horn, using 300-point stepped sine measurements. That’s useful to see the contribution of the horn’s acoustic impedance on the overall response:
1651689075820.png


The time-frequency plots in this particular case are done with a Listen Inc system with the mic at 10cm from the horn mouth, and an adjusted drive voltage to give 2.83 V / 1 m equivalent data. That’s a different set of equipment and software to the magnitude plots, which Vance Dickason typically does with LoudSOFT FINE and CLIO.

Since the maximum time periods shown on the waterfall plots are 5.49 ms, there’d need to be a reflective surface (other than the horn itself) closer than 2 metres for it to be seen in the data. I’ll give you that the anomaly at the edge of the STFT window around 1kHz could possibly be from the mic stand or body, but the Listen Inc SCM capsule is really thin and long:
https://www.listeninc.com/products/...plies-amplifiers/scm-measurement-microphones/