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"Analysis" of cardioid speaker radiation via lateral slots - like D&D 8c

ctrl

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First off, I want to temper expectations, I'm certainly not a cardioid radiation expert - but will do my best. I can only touch on a few topics and if something interesting comes up I will expand the post if necessary.

Index
1. Does it work?
2. Comparison speaker with slots to "normal" speaker - does it really matter?
3. Why is there increased harmonic distortion in the low frequency range?
4. What the fuss! Use an open baffle design. Duh!
5. Compare the whole bunch of speaker concepts

1. Does it work?
This is out of the question, the D&D 8c can be referred to as a well functioning example for radiation control via lateral slots, resulting in a cardioid pattern - see Erin's review for more details.

The design team of the forum project "Directiva r2" (design of a loudspeaker with lateral slots for cardioid radiation pattern) has made the experience that BEM simulations of speaker with slots can sufficiently describe the real loudspeaker. I start not with simulations made for the Directiva r2 speaker, but with simulations in which were certain details studied.

For those who can't do much with the terms omnidirectional and cardioid, here's a little refresher, using polar diagrams (WTF is a PD), that I also look at regularly (sorry lost the source link):
1664396886964.png

For a cardioid radiation pattern in some random frequency range, you can just saw a few holes in the side wall of a speaker (or let a woodpecker do it), but with a little more systematic approach, the results will probably be better.
The cardioid radiation pattern is influenced by the driver size, cabinet size and shape, slot position and size, number of slots and their distance from each other, the inner cabinet volume and its damping.

A little more background on cardioid speaker can be found in posts below - for example here.


2. Comparison speaker with slots to "normal" speaker - does it really matter?
There may be one or the other who thinks the whole fuss about radiation characteristics is trendy crap (I can understand that, until recently I used a 17€ flip phone...). If you belong to "one or the other" then this post might not be right for you ;)

We are particularly interested in the upper bass to midrange frequency range of about 100 - 1000Hz. Because below 1000Hz it becomes increasingly difficult to control the radiation. Waveguides are no longer sufficient, horns become very large and specific cabinet designs can control directivity below 1kHz but below 0.5kHz it becomes very difficult.

Let's first look at the radiation of a bass-midrange driver in a "normal" closed box (CB) design. Could also be a BR speaker design, would hardly make a difference for the frequency range we are interested in.

We only take a look at the horizontal radiation pattern. The vertical radiation behavior is also influenced by lateral slots, but not to the same extent.

For those who have difficulty interpreting sonograms and for comparison with the definitions of cardioid behavior shown above, there is also a polar diagram.
In the CB-LS sketch the blue z-axis is our listening axis.
The sonogram is normalized to the axis frequency response and the black line shows the -6dB limit - which is sort of a standard measure of directivity.
The simulation was calculated only up to 4kHz.
The polar diagram shows the radiation pattern for the frequencies 100Hz, 250Hz, 500Hz and 1000Hz.

1664396598972.png 1664396620026.png 1664396644504.png

The radiation below 500Hz expands in two pronounced stages and below 200Hz is almost a omnidirectional radiation pattern. Above 500Hz the cone of the driver acts as a waveguide and controls the radiation of the bass-midrange driver - in the simulation a 10'' driver is used.
A completely "normal" behavior that should be well known to many.

However, when side slots are attached to the same cabinet, the radiation behavior changes completely.
1664396715718.png 1664396766759.png 1664396813277.png 1664547049327.png
Now we have a uniform cardioid radiation pattern down to below 100Hz. The last image shows the axis frequency response of the lateral slots version (LSV) and the individual FR of woofer and the side slots.
The advantages and disadvantages are discussed in more detail in the next section.



3. Why is there increased harmonic distortion in the low frequency range?
Here in the forum it was asked a few times why the D&D 8c shows slightly increased harmonic distortion below 200Hz - more precisely slightly increased HD3*** (compared to a similar CB or BR speaker). This is a purely technical question, as in the listening sessions this did not play a role.

The (my ;)) theory is, that below a certain frequency the slots operate much like similar to an open baffle speaker and therefore SPL is cancelled by interference of front and rear emitted sound of the driver and that the "spring effect" of the air in the cabinet on the cone movement diminishes. This leads to a increased cone excursion which leads to increased third order harmonic distortion.

Whether this is the only reason for the increased HD3, I do not know.

*** This is not correct when formulated in such general terms. Why I assume that mainly HD3 will increase due to the large excursion, I try to explain here.



Further simulations seem to confirm this theory.
For this purpose we examine three cabinet versions with a 10'' bass-midrange driver:

1. cabinet 10L volume, with lateral slots (red curve below, woofer and slot SPL summed up) - LSV (lateral slots version)
2. cabinet 10L volume, closed box (cyan curve below) - CB10
3. cabinet 18L volume, closed box (green curve below) - CB18
1664408273294.png

In the following picture you can see the on-axis SPL curves of all three versions. For the LSV, the SPL components of woofer (in blue) and the slots (in purple) are also drawn in the diagram.
1664408378013.png

The two SPL curves for CB10 and CB18 (cyan and green) are almost congruent. This may differ more for woofers with lower resonant frequency where the increased cabinet volume has more effect.

In the 200-600Hz frequency range, the on-axis frequency response is increased by up to 3dB compared to the CB versions, which should reduce distortion in this range compared to CB or BR versions at identical SPL. In this frequency range, the LSV is clearly superior to a "normal" CB or BR speaker, since the sound emitted from the rear of the driver increases the on-axis sound pressure level.

In the range around 170Hz the SPL of all three versions are almost identical. Below 170Hz the LSV loses significantly in SPL compared to the CB versions. At 100Hz, the SPL of the LSV is already 3dB below the CB versions. Because the phase-inverse radiated sound of the driver rear interferes with the front radiated sound and there is partial sound cancellation.
For identical SPL, the LSV would have to make significantly more cone excursion.


Now we will have a look at the excursion of the cone for all three versions (to be completely accurate, the simulation shows the excursion of the voice coil).
1664412774501.png
Below about 130Hz the LSV shows a larger excursion than the CB versions. The slots cause a behavior like an open baffle speaker, the "spring effect" of the air in the cabinet on the cone movement diminishes compared to the closed box. The cone movement is hardly damped by the air volume in the cabinet, since the air is shifted back and forth, like in an open baffle speaker.

These two effects (sound cancellation and less membrane damping) lead to a significantly increased cone excursion at the same SPL compared to a CB speaker concept - below 130Hz in our example.

Anyone with a better explanation for this, let me know in the comments.

UPDATE: Another possible reason is given in this post, the acoustic ports could themselves create additional harmonic distortion. In the course of the discussion, however, it is doubted that the slots themselves play a significant role in the distortion in the low frequency range.

Here you can find a simulation of the excursion behavior of the 8'' woofer of the D&D 8c and a bit further below the same simulation but as a BEM-LEM model (including simulation of hor and ver radiation behavior of the D&D 8c woofer).






4. What the fuss! Use an open baffle design. Duh!
One may ask how big the differences are between using a speaker with side slots and an open baffle (OB) speaker.
Are the differences so significant that the additional effort for the LSV is justified?

For the comparison, we redesign our sample speaker (as always woofer only) to an open baffle speaker. There are different baffle variations for OB speakers, for our comparison we choose a classic OB design and at the same time try to change as little as possible on our example speaker.

The images are in the same order, as in the examples above:
The OB speaker sketch, this time the rear view.
The sonogram is normalized to the axis frequency response and the black line shows the -6dB limit.
The simulation was calculated only up to 4kHz.
The polar diagram shows the radiation pattern for the frequencies 100Hz, 250Hz, 500Hz and 1000Hz.
The last image shows the axis frequency response of the OB speaker and the individual frequency responses of woofer front and woofer rear SPL.
1664551494516.png 1664551513941.png 1664551531745.png 1664552797203.png

Below 700Hz, down to 100Hz, the speaker shows almost perfect dipole radiation with the usual null around 90°.

To keep the radiation of the entire OB speaker even, the tweeter must also have dipole characteristics - normal tweeters, WG or horns are not suitable for this (a second rear radiating tweeter may provide satisfactory results).

However, the difference to the cardioid radiation of a speaker with lateral slots becomes clear. The two concepts are too different for one to be considered an alternative to the other.



5. Compare the whole bunch of speaker concepts

In sections 2 and 4 we discussed and compared the horizontal radiation of closed box, lateral slots and open baffle speaker concepts.

Lateral slots can be used to extend the radiation pattern of a CB (or bass reflex) concept to lower frequencies.
The consequences for the improved radiation are that a significantly higher cone excursion is required in the low frequency range for the same SPL.

Let's take another closer look at that. The figure shows the axis frequency responses of the CB (green), LSV (blue) and OB (red) concepts.
1664551395056.png
In our examples with a 10'' bass-midrange driver, significantly higher excursion must be generated for identical SPL below 170Hz with the LSV and OB concepts.
For speaker concepts with slots, the same conditions apply in the low frequency range as for open baffle concepts - you need as much displacement volume as possible to be able to cover the entire low frequency range. Or you need to adjust the crossover frequency when using the bass-midrange driver as second way in a 3-way concept.

For one or the other might be new that conversely at higher frequencies the on-axis SPL output of OB and LSV is significantly higher than that of CB (or BR) concepts.
Here LSV and OB have clear advantages over the "classic" speaker concepts.
In the frequency range 200-1500Hz OB produces the highest SPL. Because of the damping of the cabinet interior, LSV performs somewhat worse, if less damping is needed, there is room for improvement.
 
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ctrl

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Added the next part in the opening post.

I don't know any studies that deal with this topic, so not everything I claim has to be right.
 

Blumlein 88

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An open baffle would result in a dipole pattern not a cardioid.

Don't know if you've seen this thread.


There are number of articles in cardioid subs in live sound applications.



 
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ctrl

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An open baffle would result in a dipole pattern not a cardioid.
You're right about that, it's worded a little sloppily in section 3. As already announced, I would like to discuss the exact difference in section 4. The phrase "similar to an open baffle system" would probably be more accurate - would it?

The total area of the slots and thus the possible rear sound radiation is of course significantly smaller than with open baffle (complete cone backside area).
The spring stiffness of the air, which counteracts the cone movement in a closed cabinet, seems to have little effect in the simulation below 130Hz, so it behaves more like an open baffle system.
This could be a possible explanation for the fact that the lateral slot version (LSV) shows a slightly higher cone excursion than the two CB versions.

As I said, maybe there is a better explanation for the excursion behavior.
 
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ctrl

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Very interesting! What SW are you using?
I use the former version of AKABAK3, which was called ABEC (both are BEM and LEM based simulation tools). And in addition VCAS a software that can graphically display the data from AKABAK or ABEC.
 

alex-z

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Is it possible to model aperiodic venting with this software? I am curious if it would be possible to engineer the cardioid slots so they only work below 200Hz. That way a significant directivity benefit could be experienced with less leakage of internal reflections. Perhaps some form of high density foam.
 
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ctrl

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I am curious if it would be possible to engineer the cardioid slots so they only work below 200Hz. That way a significant directivity benefit could be experienced with less leakage of internal reflections. Perhaps some form of high density foam.
In the sectional drawings of the cabinets, the green color represents areas that have a damping surface.

By default the wall surface absorption coefficient seems to be frequency independent or a fixed absorption profile - I can vary the absorption between 0-1.
But it's possible to use your own data file with frequency depended absorption coefficients.
So in theory your described case is possible.

Different absorption profiles might also be decisive for the difference in radiation between simulation and real measurement with the Directiva r2.
 

Mnyb

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Fyi have you seen this ?


A manufacturer tread but never the less some interesting measurements
 

Scgorg

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Great post as usual ctrl! I have played around with this myself in AKABAK, with varying results. Based on the models you've posted pictures of here, you only model damping on the enclosure walls, and not the slots themselves? When I worked on this I assumed there had to be an impedance at the slots, as speakers from Dutch&Dutch and ME Geithain use damping material in their slots (presumably to slow the speed of sound so they can obtain the correct time delay for cardioid or supercardioid radiation pattern). Do you even use an interface at all between the inside of the cabinet, the inside of the slots, and the exterior domain?

If you can simply model them as ports with no impedance without any interface that makes things a whole lot simpler.
 
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ctrl

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A manufacturer tread but never the less some interesting measurements
Yep, I watch it.

Based on the models you've posted pictures of here, you only model damping on the enclosure walls, and not the slots themselves?
That is correct. In the end, it depends on the frequency-dependent absorption coefficient that is used. If I put the "WallImpedance" layer over the slots, probably no sound will come through (haven't tried it).
With a separate file for the absorption coefficients, one should also be able to simulate, for example, a layer of felt over the slots.

When I worked on this I assumed there had to be an impedance at the slots, as speakers from Dutch&Dutch and ME Geithain use damping material in their slots (presumably to slow the speed of sound so they can obtain the correct time delay for cardioid or supercardioid radiation pattern).
Impedance at the slots, see above.
I have not yet calculated how large the change in sound velocity must be to have a significant effect on the sound addition/summation of front and rear sound components - apart from the existing propagation time differences due to the cabinet.

Do you even use an interface at all between the inside of the cabinet, the inside of the slots, and the exterior domain?
I'm using only eight interfaces and six subdomains ;) Two interfaces for each slot and a subdomain between the slot interfaces.
 

Scgorg

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I'm using only eight interfaces and six subdomains ;) Two interfaces for each slot and a subdomain between the slot interfaces.
Same as I have done then :p Except I've not been enough of a madman to do multiple slots yet. Perhaps it is less of a chore in the script-based ABEC compared to AKABAK :oops:
Thank you very much for the answers. It is hard to find information and comparison with real-life measurements when talking about ABEC/AKABAK, so every little crumb helps.

Also, speaking of applying an impedance to the slots, you will get sound, but if you use a very high impedance it will practically behave as a solid wall. Looking at the change in radiation pattern from a change in slot interface impedance was interesting, but not very useful.
 
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ctrl

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Added section
4. What the fuss! Use an open baffle design. Duh!
5. Compare the whole bunch of speaker concepts
in the opening post and made some minor corrections and additions.

If you find any mistakes or if I have made a complete mess, please let me know so that I can correct it.
 
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OWC

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Added section
4. What the fuss! Use an open baffle design. Duh!
What's always with the screamy, provoking sentences and titles here?
Can we just phrase it on a more objective, constructive and neutral way?
Thumbs down for using these things. The same goes for "If you belong to "one or the other" then this post might not be right for you"
That is already disclosing people from a discussion, even if they might have more knowledge and experience.

anyway.

I don't know any studies that deal with this topic, so not everything I claim has to be right.
Well D&D has plenty of prio-art in their patent, so it's just a matter of reading those?
Also there is absolutely tons and tons of experimental findings that can be found on the Diyaudio forum.
Some in direct relationship with the speakers in question.
The concept of a cardioid system has also been explained in enough books about loudspeakers and acoustics.
So if you say that you don't know about any studies, that means you haven't done proper literature investigation yet.

As for distortion.
Most speakers naturally distort.
A cardioid design falls kind of in between a dipole and a closed box seen from the lumped element/control system point of view.
So if we just simulate this speaker in a dipole (with whatever your favorite program is, Edge, VituixCAD etc), you will see that you have to boost quite a bit.
Around 100Hz, that's about 6dB relative to the nominal output levels.

You're saying that this is mostly 3rd order harmonic distortion.
I don't understand where that claim is coming from, but that as a general statement is absolutely untrue.
Or rather, can't be known beforehand.

That totally depends how the speakers is distorting, if the non-linear elements distort in a symmetrical fashion (= odd order harmonics) or asymmetrical fashion (= even order harmonics). If you have been following enough Klippel and distortion measurements like here; https://audioxpress.com/categories/vc-testbench , you should know that it really differs per driver. They are using a custom Seas woofer from the Prestige line.
Having experience with Seas myself, I can't say if that will be mostly even or odd order.
Totally depends on the suspension.

As far how cardioid works, I see you're going over it extremely briefly and quickly with very poor 3rd party references.
I think it's best to read into books from Beranek for example, although there also seems to be a decent explanation on sciencedirect.com
(I have to look up a link, has been a while)
But a cardioid system is nothing more than two monopole sources that are out of phase next to each other, were one of them is delayed as well as attenuated.
Which is fundamentally different than a dipole. Which on consists of two monopole source that are out of phase.
The main difference is that a dipole has cancellation on the side, while a cardioid has cancellation on the back.

A cardioid system can be made passively or actively.
Both have been done for absolutely decades and there are just different solutions to create the same thing basically.

Technically D&D is not using slots, but just damping material to delay the back wave as well as using a mesh.
This mesh does add some additional delay, but as far as I know, was mostly chosen for esthetic reasons.
It has been a while but I think Martijn explained and discussed this very well.
I have seen other solutions with just only an open back full of damping material that worked also really well.
Obviously this can't be done with two additional woofers in the back of the cabinet.

In the end it's mostly just avoiding other peoples patent, so one has to come up with a different solution.
It could be as well as that D&D is even using a hybrid approach, since they have two woofers on the back as well.
Which already points out the shortcomings of a Klippel NFS system, since we can't measure the individual drivers as well as output from the amplifiers to determine the filter response.
 

Blumlein 88

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It might be interesting to know that in the early 20th century, cardioid pattern mikes were made by combining an omni and a ribbon. You could do the same with speakers. A panel combined with an omni woofer. Otherwise, time delay or spacing (effectively for time delay) is how cardioid woofers are made.
 

ernestcarl

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I don’t know much about this topic, but I know Geithain and Fulcrum Acoustic uses some kind of flow/port resistive network to achieve cardiod patterns. Their method is more “invisible” to the eye or not so obvious until it’s pointed out to you.


Dave Gunness said that the resistive mesh material they have (dunno about Geithain) is the same type used in our tiny smartphone speakers.
 
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ctrl

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What's always with the screamy, provoking sentences and titles here?
It's simply more fun to write when you're not deadly serious the whole time - and it took me a lot of time to write it up.
I actually assumed that the phrases were so exaggerated that no one would take them seriously. The rest of the text is worded in a deadly serious manner.

So if we just simulate this speaker in a dipole (with whatever your favorite program is, Edge, VituixCAD etc), you will see that you have to boost quite a bit.
Around 100Hz, that's about 6dB relative to the nominal output levels.
Yep, that's consistent with what I stated in the text. Except that it's not 6dB SPL difference between CB and OB in the example with the 10'' driver, but only about 3dB at 100Hz.

The BEM simulation takes into account the complete cabinet design (not just the baffle) and the damping material placed in the inner walls (whose frequency-dependent absorption coefficients I don't know - but is chosen low at 0.3 on a scale of 0-1).

A very simple simulation of a 10'' driver in VCAD on a similarly sized baffle, results in about 4.5dB for the difference between front sound and open baffle SPL with free field conditions.
1664638438566.png



You're saying that this is mostly 3rd order harmonic distortion.
I don't understand where that claim is coming from, but that as a general statement is absolutely untrue.
Or rather, can't be known beforehand.
That totally depends how the speakers is distorting, if the non-linear elements distort in a symmetrical fashion (= odd order harmonics) or asymmetrical fashion (= even order harmonics). If you have been following enough Klippel and distortion measurements like here; https://audioxpress.com/categories/vc-testbench , you should know that it really differs per driver.
You're right, in my opening post it's not the correct way to put it. Needs more explanation.

I wanted to say that in my experience (seems different than yours ;)), at extreme excursion HD3 is often dominant - because with "modern" drivers Kms and Bl is symmetrical, the motor and suspension system at extreme excursion thus produces odd harmonic distortions of which HD3 usually dominates - see for example ScanSpeak or SBAccoustics driver tested by Erin.
Which could explain why HD3 is dominant in the range around 100Hz with the D&D 8c where the crossover frequency is around 100Hz for the 8'' midwoofer. Which will cause large cone excursion (since the frequency response is equalized to a flat curve - [email protected]).

See documents on Klippel website:
5.1. Symmetry and asymmetry
The most obvious feature of a nonlinear parameter is the symmetry of the curve. A well-made loudspeaker should have symmetric K ms (x) and Bl(x) curves. At high positive and negative excursion the suspension will be limited by unfolded and stretched suspension material and the voice coil will leave the gap.
A symmetric curve usually produces 3rd - and other odd-order distortion components as illustrated in Table 2.
1664641827759.png
Source: Loudspeaker Nonlinearities – Causes Parameters Symptoms by Wolfgang Klippel



As far how cardioid works, I see you're going over it extremely briefly and quickly with very poor 3rd party references.
Yes, I'm more interested in the specific effects of slots than the general workings of cardioid concepts - will refer to your post.


Technically D&D is not using slots, but just damping material to delay the back wave as well as using a mesh.
This mesh does add some additional delay, but as far as I know, was mostly chosen for esthetic reasons.
Technically, the 8c uses a single slot (per side) ;)
I would also assume that the mesh is mainly for aesthetic reasons (and to hold back the damping material).
 
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Kvalsvoll

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3. Why is there increased harmonic distortion in the low frequency range?
...
Anyone with a better explanation for this, let me know in the comments.
Several unfortunate effects work together to increase distortion in such designs, and the end result of this misfortune may be a speaker that has so high distortion it is unusable for high performance sound reproduction. So the problem is real, and it has to be addressed.

The first problem is that the output at the fundamental is reduced, partially due to cancellation from the acoustic port outputs, partially due to low q in the box.

Then there is the problem of radation patterns from the individual sound sources, the driver cone and the acoustic ports, which does not necessarily sum in a similar way across the frequency range, leading to harmonics actually getting amplified, and this amplification can be very different at different radiation angles.

Then the acoustic ports will introduce harmonic distortion themselves, due to non-linear properties of the acoustic resistive material in use. This distortion can be very significant, and actually larger than the distortion from the active driver.

It is possible to reduce this harmonic distortion to acceptable levels, but it is not necessarily easy, if the speaker is very small and very high attenuation of rear sound radiation is a requirement.

Don't know if this was a better explanation, my intent here was more to fill in with some more information.
 
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