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

OWC

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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.
At these frequencies, there are no "individual sound sources", since the wavelength of the frequencies are much bigger than those sources.
This is called the lumped element or control system region.

About the distortion coming from the ports and damping material.
I doubt about its significance, and if so it results in even order harmonics.
Damping material does add addition distortion, that is certainly true, I only have never seen it so significant.

I mostly likely think it's the just distortion from boosting, which I agree with @ctrl
Speaking of which, how much is being boosted is a bit of a way of how you look at the whole problem.
Even from your simulation @ctrl there is a peak around 650Hz at +9dB
So seen from this peak, the 100-150Hz region is even 10dB lower.
A usual baffle-step correction is 6dB in a closed box, so it will be AT LEAST 6dB
On an open baffle system this will be more.

Which is in term of excursion at least twice as much = 10^(6/20) = 2
Which is equal in double the amount in percentage in distortion.

D&D is using some custom Seas Prestige line woofer.
The base model has been around for decades, and is most certainly not as optimized as speaker drivers nowadays.
So I don't know if the distortion will be totally symmetrical or not.
I don't disagree with you on that, but I was just saying that it really depends as a general statement.
As a general rule of thumb, most 8 inch woofers are starting to get much higher distortion levels from 50-60Hz and below.
Depending on the impedance peak. So roughly twice the frequency of the impedance peak would be still a low region in sense of distortion.

And still, here is an example with a relative symmetrical BL and Kms, yet the distortion below 150Hz is mostly even order.
Probably because there seems to be a dynamic offset towards one direction.

Since the 8C is completely symmetrical as a stereo pair, (seen from the listener point of view), I think I would have crossed a little higher.
Especially because room modes are much more of an issue at those frequencies.

I get that you might want to write certain things a bit more "lightly" and "with humor".
There is nothing wrong with that, but just keep in mind that for a lot of people this style of writing is not really respectful.
That doesn't have anything to do with lack of fun, just a difference in culture.
 
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OWC

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It is interesting though.

I have been looking at a couple of 6-8 inch woofers, and this region is usually the lowest as well as being predominantly even order distortion.
(Something I was already expecting, but just did a double check).
H3 often even dips in this region.

Which is very unfortunate that the reviewers don't take out the individual drivers and test those as well.
Because that will give an awful lot more information.
Hack even a simple impedance curve can sometimes already answer many questions.

For example, it also could be that they are using some kind of limiter or compressor around this region, since it's the woofer's weakest point.
Which also wouldn't surprise me when we look at the distortion graph at difference SPL's.
All other frequencies change as being expected, yet this region stays relatively constant, just higher.
 
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ctrl

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Thanks @Kvalsvoll and @OWC for the stimulating and informative discussion.

You both have motivated me to get to the bottom of the driver excursion - at least I will try ;)


First of all, it should be clarified whether a speaker with slots behaves similarly to an open baffle speaker in terms of cone excursion.
For this we compare the voice coil excursion from the BEM-LEM simulations (closed box, slots, open baffle) from our example with the 10'' midwoofer.
1664707110386.png
The "spring effect" of the air on the driver suspension, as with a CB speaker, is no longer present in a speaker with slots, rather the excursion of the driver behaves like an OB speaker.
If a lot of damping material is used, minimal deviations in the excursion behavior may occur, but they should not be decisive.

From here on, the simulations refer to an 8'' woofer as used in the D&D 8c to have a better comparability with the real 8c speaker.

First we need the frequency response of the woofer in the speaker under free field conditions.
This can be roughly simulated in VCAD:
1664708209500.png
The plot in orange, as a comparison, the frequency response of the woofer front - similar to a CB speaker. In blue the frequency response of the open baffle simulation. So we have our free field frequency response of the 8'' woofer in the cabinet.

This frequency response will be imported into the "Enclosure-Tool" of VCAD:
1664708891885.png
There we see in brown the free field frequency response of the woofer in the cabinet from above. In black the frequency response of the woofer in an infinite baffle, i.e. under half-space conditions, and in orange our high pass filter target function [email protected] as used in the D&D 8c (ignore the low pass at 2kHz).

Now the crossover must be adjusted so that the free-field frequency response in brown corresponds to our target filter function in orange:
1664709315582.png
Since the black curve refers to half-space conditions, the SPL must be increased by 6dB to satisfy free-field conditions.
So if we are interested in the excursion for 86dB SPL, then the brown FR must be raised to 86+6dB.

Excursion simulation 8'' woofer (speaker with slot or OB) at 86dB and 96dB with HP [email protected]
1664721585552.png 1664721608835.png

Harmonic distortion D&D 8c 86dB and 96dB
1664721269588.png 1664721625949.png
The shape of the exaggerated harmonic distortion and the cone excursion match very well, the cause of the HD is most likely related to the excursion.
However, even at 96dB, the woofer has only +-3.6mm (0.14'') excursion (Update: Even small changes in the FR, for example, lead to 4mm excursion, it would be better to say the excursion is around 4mm), which is below the Xmax of most 8'' woofers (e.g. Seas L22RNX/P Xmax=6mm).

Is the 3.6mm excursion enough to explain the roughly 8% [email protected] of the D&D 8c woofer around 100Hz or is there an additional effect (as @Kvalsvoll suspects) caused by the slots?
 
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OWC

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@ctrl

Thanks for the effort.
As far as I know, VituixCAD is not optimized for modelling and simulating open-baffle or dipole systems (but I might be wrong).
I am talking about dipole here, because it simplifies thing a bit.

One very important parameter for dipole systems (which also counts for passive cardioid systems), is the path length difference between the front wave and the back wave.
Back in the day MJ King used to have some great MathCAD sheets about this, but Linkwitz also has a quick spread sheet to (roughly) calculate this.

This is separate from the bafflestep simulation, since the thickness of the baffle for example, is also very important.
For this reason U-frames or H-frame dipole systems (or open baffles) will perform differently.
As far as I know, this can not be modeled in VCAD.

The reason why I am mentioning this, is because the slots on the 8C are basically right behind the woofer.
Meaning that for lower frequencies (< 200/300Hz or so), the shortcut ratio for the back- vs front wave is rather high.
This can have a very negative effect on the output and therefor things like cone excursion.

Best way to simulate this would probably AKABAK (there is a free home use license available, but learning curve is rather steep)
Otherwise Hornresp might give an "okay" result. I am not 100% sure if it's optimized well for this.

So it could be that the 4mm cone excursion is even on the low side, but that is a little difficult to determine at this point.

The slots themselves don't distort, only the uneven/asymmetric load on the woofer caused by the slots and damping material will.
Which will always result in even order distortion. Linkwitz has a section on his page about this for example.
Although the physics behind it can also be found in plenty of other books and literature (see my sig for some examples)
An easy reminder is that asymmetric distortion, meaning only either the top or bottom of a sine wave is being distorted, always results in even order harmonics.

That's not what we see in the distortion plots.

Which bring be back to my previous post.
If we see how the rest of the distortion of frequencies overall move, it's not really in line with what one would expect around de 100-200Hz region.
Compare that for example with measurements from Hificompass as well.
In this case here, we see all harmonics moving up from 86dB to 96dB as a bunch.
Higher in level that's true, but the relative difference between the different harmonics seems to stay the same (more or less).

So to sum up.
In this region I would expect a couple of things.
1 - Even order harmonics should be more dominant than 3rd order harmonics / or 3rd order harmonics lower
2 - With higher SPL's I would expect that the different order harmonics would change at a different rate relative to each other.
 

sigbergaudio

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So, we use a very high capacity driver, but we did not see any significant change in distortion with/without the cardioid loading in our design. One reason is probably that we have a more narrow bandwidth design with two separate cardioid systems. The lower chamber only operates from ~100-600hz, and distortion is very low even at high SPL.

We do see an increase in THD as frequency goes down, I suspect this is because the chamber itself is pretty small, as it's not designed to play much below 90-100hz.

It's been a while since we did these tests, and the design of the cabinet including the ports have changed since then. So I have to report back again when we've been to the Klippel with the new design, but from our previous prototype:

[email protected] = ~1.5% THD (here we will have significant overlap with the subwoofer(s), so in practice it will be lower)
[email protected] = ~0.3% THD
 

Kvalsvoll

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There may be some misunderstanding of how this works, I can try to explain and show the essentials of why and how. Simple and incomplete.

Here is the output from such an acoustic port, note that the fr is not necessarily flat, most important, look at the phase, it is flat at 180 deg across a wider freq range:
F205 port1 nf 600 w.jpg


A different speaker:
nf port sum.png

Same behavior of phase at 180 deg, different freq response.

When this 180 deg out-of-phase sound sums with the output from the cone at 0 deg, the sound cancels out, and this happens towards sides and backwards, while attenuation on-axis is less, due to distance/position of the radiators and a small phase difference. Since there will be some attenuation also on-axis, there is a loss of sound pressure, and it is this loss of spl that may cause problems with capacity limitations and distortions.

A bass reflex port is different, it acts like an acoustic mass, and this mass comined with the air volume inside the box rotates the phase so that the port output is in-phase with the sound radiated from the cone.

Clearly, this is quite complicated to model and simulate and design, compared to just putting a driver into a sealed box. The advantage is the possibility to design a small speaker with radiation pattern control. It is possible to design the freq response of the port output, adjust port output level, and then shape of the front baffle, driver cone size and placement, port placement, also are factors that determine the resulting frequency response and radiation pattern.

Copying from others, or simply making some holes on the side of the box, may or may not result in something that works, sort of, after some experimentation. Kind of like a ruzzian approach - do something, make a boom/hole, see what happens next.

Simulation is required to make a design that behaves according to some sort of specification, a spec that defines a desired radiation pattern. Then the big question actually is how this radiation pattern should be. Because the speaker can now be made to match. There is a choice.
 

OWC

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I am a little confused what you're trying to show with the phase here?
That might be as well as an artifact, which makes me believe when looking at the totally erratic phase behavior above 800Hz.

The in- or out-of-phase part only contributes in the polar response, but looking from on single angle (on-axis in this case), one can not determine if an unknown DUT is a dipole, cardioid or monopole. This can only be seen when a polar plot is being made with different angles.
I have worked on plenty of dipole systems (and contributed in a few cardioid systems), and an on-axis response will typically not have such phase jumps by itself.

I don't understand why bassreflex or sealed boxes are being mentioned.
One can make a cardioid pattern with two sealed boxes, or even two BR-boxes.
In fact, this is done very often in PA/sound-reinforcement applications (in particular outdoor).
One would get similar principles from these systems.

Significant attenuation on-axis is certainly not always the case.
Totally untrue for dipole systems, and only sometimes true for active cardioid systems.
In a proper design it's less than 3dB, so nothing that is considered for any kind of distortion.
Keep in mind that a dipole is worse in output than a cardioid system.
So the reason why it is helpful to approach it that way, is to give us a worse case scenario.
In practice this means it will only be better, not worse.
Keep in mind the bafflestep in practice, which always needs to be corrected for!

Still those are only the acoustic parts of the system.
It's being rather nitpicky on details, with only minor changes, but not on the general scope.

Or in other words, going back to the original question from @ctrl , it doesn't give any answers why the distortion might be (so much) higher.
The only good way to know this, is to just measure the loudspeaker in question (T/S paramters, impedance as well as distortion at different voltages/power/cone excursion) as well as knowing what's going on in the DSP.
The reason why T/S can matter, is that depending on some parameters like Qt, BL and Vas we get an idea how much more we need to "boost" a woofer.
Also de Fs can have a role in this.

But probably more importantly, it also still doesn't explain why the distortion curves of the different harmonics are so bunched up, moving as a whole and are this high in an area were distortion is usually lowest.
Coming from measurements where these speakers are being tested in an open baffle or even in free air (= max possible cancellation! ), this doesn't make any sense.

Unless the speaker is already at its max around 86dB @ 1m.
Which I found very hard to believe and also knowing Martijn (from D&D) personally for many years, I would highly doubt that he would be designing things that way.
 

OWC

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So, we use a very high capacity driver, but we did not see any significant change in distortion with/without the cardioid loading in our design. One reason is probably that we have a more narrow bandwidth design with two separate cardioid systems. The lower chamber only operates from ~100-600hz, and distortion is very low even at high SPL.

We do see an increase in THD as frequency goes down, I suspect this is because the chamber itself is pretty small, as it's not designed to play much below 90-100hz.

It's been a while since we did these tests, and the design of the cabinet including the ports have changed since then. So I have to report back again when we've been to the Klippel with the new design, but from our previous prototype:

[email protected] = ~1.5% THD (here we will have significant overlap with the subwoofer(s), so in practice it will be lower)
[email protected] = ~0.3% THD
I am missing total context here, who is we, what kind of driver, what design are you referring to?
 

sigbergaudio

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I am missing total context here, who is we, what kind of driver, what design are you referring to?

My apologies, we have a dual cardioid speaker under development (due to be released next summer), a link to our development thread here on ASR was shared by another user earlier in this thread.

Here it is again:


And link to a preliminary product page:
 
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ctrl

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As far as I know, VituixCAD is not optimized for modelling and simulating open-baffle or dipole systems (but I might be wrong).
I am talking about dipole here, because it simplifies thing a bit.
VCAD has the option to simulate an open baffle speaker using its "diffraction tool". With the "enclosure tool" and infinite baffle setting the free field response can then be used to simulate excursion within the "enclosure tool".

One very important parameter for dipole systems (which also counts for passive cardioid systems), is the path length difference between the front wave and the back wave.
Back in the day MJ King used to have some great MathCAD sheets about this, but Linkwitz also has a quick spread sheet to (roughly) calculate this.
When considering the low frequency response, this is not critical in our examples and the D&D 8c, as the slots are close to the front of the enclosure and therefore the additional delay difference due to the enclosure does not matter much.
In the BEM simulation, of course, all possible runtime differences are taken into account.

The reason why I am mentioning this, is because the slots on the 8C are basically right behind the woofer.
Meaning that for lower frequencies (< 200/300Hz or so), the shortcut ratio for the back- vs front wave is rather high.
This can have a very negative effect on the output and therefor things like cone excursion.
Ha, ha. I should have kept reading. Totally agree with you.
You can find this exact result under section 5 in the opening post:
The on-axis SPL of the OB example and the example with slots is identical below 200Hz and so is the excursion of the voice coil (shown in the post#23 above). That is, the speaker with slots behaves, apart from the radiation, similar to an OB speaker in the low frequency range.

Best way to simulate this would probably AKABAK (there is a free home use license available, but learning curve is rather steep)
Otherwise Hornresp might give an "okay" result. I am not 100% sure if it's optimized well for this.
I'm using the previous version of AKABAK (called ABEC), because my parameterized scripts were not taken over without errors (at least in the first AKABAK versions).

I agree with you to clear the last doubts we need confirmation. So I created a BEM-LEM simulation of the D&D 8c, so we have a possibility to compare with the results of the VCAD simulations - the results will be presented in a separate post.

An easy reminder is that asymmetric distortion, meaning only either the top or bottom of a sine wave is being distorted, always results in even order harmonics.

That's not what we see in the distortion plots.

Dashed is the base tone, the upper image shows HD2, the lower HD3.
1664810928441.png
It is not clear to me how you can draw conclusions from a single frequency that shows influence of HD2 or HD3 to the frequency response of the distortion measurement.

Or do you simply mean that if the slots had a significant influence on the distortion, then HD2 (and others with even order) should increase more than those with odd order.
 
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ctrl

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So, we use a very high capacity driver, but we did not see any significant change in distortion with/without the cardioid loading in our design. One reason is probably that we have a more narrow bandwidth design with two separate cardioid systems. The lower chamber only operates from ~100-600hz, and distortion is very low even at high SPL.
Thanks for the information, this is another indication that the quality of the driver, or its behavior in the low frequency at greater excursion is decisive and that the slots contribute little or nothing to the distortion.
A driver with a rather rigid suspension system should not hurt either - which is the case with your project, if I remember correctly.

but from our previous prototype:

[email protected] = ~1.5% THD (here we will have significant overlap with the subwoofer(s), so in practice it will be lower)
[email protected] = ~0.3% THD
You can't complain about that ;)


When this 180 deg out-of-phase sound sums with the output from the cone at 0 deg, the sound cancels out, and this happens towards sides and backwards, while attenuation on-axis is less, due to distance/position of the radiators and a small phase difference. Since there will be some attenuation also on-axis, there is a loss of sound pressure, and it is this loss of spl that may cause problems with capacity limitations and distortions.
Yes exactly, to show this in more detail the on-axis frequency response was compared for three different speaker concepts (identical baffle and driver) - closed box, slots and OB.
1664813665333.png
The results are only intended to give a rough indication of the advantages and disadvantages of the three concepts in terms of on-axis SPL. The details, of course, depend on the project.

Copying from others, or simply making some holes on the side of the box, may or may not result in something that works, sort of, after some experimentation. Kind of like a ruzzian approach - do something, make a boom/hole, see what happens next.
I agree with you, that is exactly what is said in the opening post.
 
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ctrl

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Simulation of the D&D 8c (without WG)
To provide confirmation to the VCAD simulations in post#23 on the excursion behavior of the woofer of the D&D 8c, a BEM-LEM simulation of the 8c was created.

A BEM (Boundary Element Method ) model was created:
1664815416196.png 1664815434066.png
I did not know how big the internal volume for the 8'' woofer is, for the simulation I took 6L.

The crossover frequency of the woofer ([email protected]) was modeled with LEM (Lumped Element Method). Modeling a crossover in LEM is a PITA, so forgive me that the target function ([email protected]) is only accurately met below 200Hz:
1664815548490.png
In black you can see the target function and in red the SPL of the simulated 8c speaker under free field conditions.
For those interested in more details, in blue is the SPL of the woofer alone and in pink the SPL of the slots (summed up, taking into account the phase frequency responses, the red graph results).


All this was done just to get three paltry graphs with the voice coil excursion of the woofer. Shown is the excursion at 86dB, 96dB and at 106dB.
1664817410284.png 1664817442319.png 1664817628232.png
Excursion of the 8'' woofer is
86dB --> 1.2mm
96dB --> 3.7mm
106dB --> 11.8mm
Of course, the [email protected] SPL can not be performed by the woofer despite crossover frequency with [email protected], because the voice coil would probably hit the woofer back plate.

It seems that the used woofer in the D&D 8c already shows slightly increased harmonic distortion at excursion of +-4mm. Since the slots do not (or only slightly) contribute to the distortion according to the current state of the discussion.



Digression:
Since the radiation pattern of the simulated 8c is a "by-product" of the simulations, I attach it here. In comparison with Erin's measurements of the 8c, the agreement of the normalized sonograms are quite good (especially since I had to assume an arbitrary damping of the inner volume).

Hor and ver sonogram of the 8c woofer without crossover - the top and bottom of the vertical sonogram are reversed.
1664816741956.png 1664816794245.png
 
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puppet

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Doesn't the cardioid enclosure more closely resemble an expanded or morphed aperiodic enclosure? The function seems quite similar.
 

Kvalsvoll

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I am a little confused what you're trying to show with the phase here?
That might be as well as an artifact, which makes me believe when looking at the totally erratic phase behavior above 800Hz.
The phase graph wraps at 180 degrees, and behavior when level is down say more than -20dB is not really relevant, and also will be affected by noise. What this graph shows, is that the phase is quite smooth at -180 degrees across a wider frequency range, in the range where the level of sound output from the ports are high enough to make a significant contribution to the overall sound emitted from the speaker. Acoustic ports without resistive damping that act like acoustic mass elements do not work like that.
 

Kvalsvoll

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The technical properties of how this works is one thing. But why bother, what is the purpose, what is gained in terms of improvement to sound.

It would be interesting to learn how others see the more practical implications for sound; how do you expect the sound to be affected and presumably improved, is there any improvement, how does such a speaker sound compared to a standard box.
 
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ctrl

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It would be interesting to learn how others see the more practical implications for sound; how do you expect the sound to be affected and presumably improved, is there any improvement, how does such a speaker sound compared to a standard box.
We will certainly have long discussions about this as well.

Once Tim and Rick have finished their prototypes of the Directiva r2, they will certainly give their subjective opinion.

My own project, this thread (2-way top-speaker) is a by-product of it, also uses slots, instead of a 6'', like Directiva r2 with target crossover frequency of 200-300Hz, a 10'' bass-midrange driver is used. One goal there is to be able to lower the crossover frequency if necessary to 150Hz or even 100Hz without increased harmonic distortion (with usual Hifi SPL):
1664834924814.png 1664834938660.png
Simulation, ignore Frequencies above 12kHz, normalized hor and ver sonogram, possible XO.
 
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ctrl

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Doesn't the cardioid enclosure more closely resemble an expanded or morphed aperiodic enclosure? The function seems quite similar.
The main distinguishing feature would be the extremely flattened impedance curve compared to a CB concept.
1664835904234.png
Whether such an impedance curve also occurs in concepts with slots would depend on the type of damping and the area size of the slots.

The slot area is often in the size range of the cone area of the woofer which is totally different to aperiodic concepts (much smaller area dependend on cabinet volume).
The impedance curves of the simulations show no relation to "resistive vents" of aperiodic concepts (maybe real measurements show different outcome).
 

sigbergaudio

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The technical properties of how this works is one thing. But why bother, what is the purpose, what is gained in terms of improvement to sound.

It would be interesting to learn how others see the more practical implications for sound; how do you expect the sound to be affected and presumably improved, is there any improvement, how does such a speaker sound compared to a standard box.

My impression so far with our prototype is that the most significant difference is improved imaging/soundstage - so records that uses any kind of effect with regards to placement of instruments or vocals and/or any immersive effect that makes you feel like you're surrounded by sound feels wider / deeper / bigger / more immersive compared to a regular speaker. As opposed to the more regular "wall of sound", you get individual sounds and individual placement of whatever happens in the soundstage. We also have measurable reduction in SBIR effects resulting in improved midbass response and midbass "punch".

Finally it sounds more open and clear in midrange/highs, so more information / energy while still not sounding harsh compared to our other speaker that uses the exact same coax. Not exactly sure what to attribute this last thing to.
 

Rick Sykora

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Thanks @ctrl for your continued contributions to ASR! I really appreciate your sense of humor and your respectful responses when challenged (especially when responding to me). Your experience was invaluable to the success of Directiva r1.

That said, Directiva is a team effort and want to also point out that the project often consults with experts beyond the team. These experts often do not get any credit despite making key contributions. Some of those contributing dialog to this thread are indirectly contributing to a better Directiva outcome. So, thanks to you as well!
 

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We will certainly have long discussions about this as well.

Once Tim and Rick have finished their prototypes of the Directiva r2, they will certainly give their subjective opinion.

My own project, this thread (2-way top-speaker) is a by-product of it, also uses slots, instead of a 6'', like Directiva r2 with target crossover frequency of 200-300Hz, a 10'' bass-midrange driver is used. One goal there is to be able to lower the crossover frequency if necessary to 150Hz or even 100Hz without increased harmonic distortion (with usual Hifi SPL):
View attachment 234990 View attachment 234991
Simulation, ignore Frequencies above 12kHz, normalized hor and ver sonogram, possible XO.
Lovely read! Thanks for all the insights you share. You have a great way of explaining, and the visualizations via the graphs makes it so much easier for a layman hobbyist like me to understand.

Do you post any of your progress regarding your personal project?
 
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