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Xmax Investigation


Contrasseur

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Thanks, this is starting to make a lot more sense.

 

I get what's happening, just not exactly why. I think when I get the time to sit down with those equations that SME posted I'll have a lot more good data to work with.

 

That Bl*I variation Kvalsvoll makes a lot of sense too. 

 

Does anyone have Klippel data on any of these drivers? That might offer some clues too.

 

Give me a moment.  I'm working on some plots that might give some better intuition.  I may still have more corrections to do.  This was a more substantial undertaking than I anticipated, and my skills are admittedly quite rusty.

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There is some compression in the burst tests as well.A large amount of it in some cases.

 

SME your math skills are impressive. I think you'll find that the data shows exactly what your formula appears to postulate.

 

Thanks for the compliment.

 

Are you aware of any particular pattern regarding compression in the burst tests?  Like does it tend to be mostly in the low frequencies?  Mostly near resonance?  Or somewhat above resonance?  It does concern me slightly that compression of the fundamental doesn't seem to enter anywhere in my calculations.  It feels like it should at one point or another.  I may be doing something wrong.

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 Harmonic distortion is not the only form of distortion to the waveform. The simple set of TSP specs commonly used for modeling is inadequate or incomplete to describe the behavior of many bass drivers even at small signals. Complex inductance effects must be included. Unfortunately virtually no MFG supply this info and very few simulators could use the info if it was available. This is another deep rabbit hole to go down.

How does one measure complex inductance? Personally, I don't mind a little extra work if it can give us some new insight. This wouldn't be the first time I opened up a can of worms to find a rabbit hole at the bottom.

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How does one measure complex inductance? Personally, I don't mind a little extra work if it can give us some new insight. This wouldn't be the first time I opened up a can of worms to find a rabbit hole at the bottom.

Room Eq Wizard can measure complex inductance I think, but what are you going to do with it?

 

I think there's at least 2 specifications for complex inductance, one authored by Leach and the other by Wright.  There may be more.  I'm not sure which one Room Eq Wizard measures.

 

The only simulator that will accept complex inductance parameters that I know of is Unibox, and for some reason I don't think it will accept the type that Room Eq Wizard measures.

 

 

This issue affects mainly large coil drivers that have above average power handling and/or excursion for the driver cone size.

 

I did a study on this last year and with a very simple Bl tweak I was able to get amazingly accurate results when I simulated 22 drivers in 30 total enclosures as measured by Ricci and posted on data-bass and at this forum.  The tweak is not perfectly accurate but it is worlds better than a simple sim.  Sensitivity will come out a couple db low but the response curve shape is strikingly similar and very accurate compared to a simple sim.

 

I wrote a paper on this tweak, you can download it here - https://sites.google.com/site/amateuraudio/theory/large-coil-simulation-accuracy-issue-and-adjustment

The paper describes the issue, how to determine if the driver is affected by the issue, how the tweak was formulated, and it shows all 30 examples of Ricci's measurements compared to tweaked and untweaked sims.

 

You will find that "regular" drivers don't need the tweak, for example, even if a pro driver has a fairly high inductance sims will still match measurements.  It's the new breed of super excursion drivers that have this problem.  The worst of them are the ones with very high power handling, excursion and inductance.  But even the more moderate one like the Dayton HO with it's low inductance and only slightly above average xmax and the TC LMS with it's fairly low inductance and almost accurate simple sims, both match the measurements better when the tweak is applied.

 

The tweak described in my paper is incorporated right into Hornresp, it's accessible by a check box in the Loudspeaker Wizard.  If you don't use Hornresp you can still use the tweak in any simulator you like, just adjust Bl according to the formula in the paper and run the sim with the new Bl value.

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Here are a few examples of the captured burst signals from various systems. These all have a "pass" grade with THD below the thresholds set as the limit. The first set is all a 16Hz burst and the second set is all a 31.5Hz burst. Look at the differences in the driving waveform and that produced by the system and captured by the microphone. Most of them do not look very good at all.

 

 

 

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These come from 5 different systems which are all radically different. The same systems for both sets. There is at least one sealed, vented, FLH, and TH represented and both active closed loop systems and passive systems driven by the big amp. If anyone wants to try guessing which systems are which (sealed, horn, active, etc...) I'd be very surprised if anyone got most of them right.

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One can have nearly 40% THD and still get a passing CEA grade. I think CEA is much too lenient. One might argue that it might not be audible, but a very clean passing CEA burst sounds very different than a barely passing burst. You definitely do not need golden ears to hear that difference. The ridiculous thing is they made the passing CEA-2010 thresholds even more lenient in CEA-2010-B! They should have went in the other direction. I think the CEA-2010 thresholds are based more on where the mechanical limits of the subwoofer then on perceptual research. These subs don't seem to have much more oomph left once they have reached the CEA-2010 thresholds. You can maybe squeeze a decibel or two after failing thresholds, but the subs seem to be at their limits. I would rather the thresholds be based on perceptual research. 

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Whooh thems is some squiggly lines. Especially #7. There's a lot of non-harmonic content here too, which surely must be audible. The amplitude of the center peak is even lower than the outer ones. Crazy that this massive nonlinearity didn't cause enough harmonic distortion to break the threshold.

 

If you band-pass that signal, you'll surely measure a much higher average amplitude of the fundamental than measuring a cleaner reproduction that maintained the original signal's windowing. It certainly would show up in my Xmax calculations as an excursion much higher than the driver ever even produced.

 

Probably explains shadyJ's claim of "running out of oomph"

 

It seems like it cheated the test. It never really peaked at the intended SPL, it just compressed the largest peaks without adding much harmonic distortion. 

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    |H3| = 9 * k3 * om0^2 * sqrt{ 1 + 9*om^2*(Le/R)^2 } / sqrt{ [om0^2 - 9*om^2]^2 + 9*om^2*[om0/Qtc + Le/R*(om0^2 - 9*om^2)]^2 }

 

I'm making some plots to determine compliance limited Xmax by varying different parameters of the driver and the enclosure. All I should have to do to solve for relative excursion is to solve this equation for k3 and then take the square root, right? Then I just pick values for H3 and it should give me relative excursion values to reach said distortion level. But I did that and everything looks all wonky. I'm getting an excursion minimum at Fb/3 regardless of Qts. Is my math wrong or my whole methodology?

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Here's the updated calculated excursions. You can see the excursions are largely consistent with large, wide, bumps centered at Fb, consistent with SME's Qts vs H3 calculations.

 

Some interesting points:

 

The XXX design must be BL limited in the low end. They have the same suspension but the overhung coil has much greater BL nonlinearity. The Split Coil version's higher Qtc should have a greater Xmax boost at Fb according to SME's graph, but the Overhung shows greater excursion. Some other mechanism must also be involved at Fb.

 

Higher Qtc => Higher Distortion is supported by the B&C 21SW152-4. This is the only driver we have multiple sealed enclosures for. The dual opposed cabinet shows lower excursions across the board. Some of this could certainly be air-spring nonlinearity, as the SPLs are higher coming out of this similarly sized. Other factors could be at play.

 

The 21IPAL demonstrates nearly twice the excursion of the 21SW152-4. Only the XXX 18D2 ported produced more 10Hz out of all the tested systems. We can certainly expect some really exciting performance from the Palehorn or Othorn v2 or whatever kickass enclosures this driver ends up in.

 

The Orion HCCA-15 has a large Xmax bump AROUND fb, but a small dip AT fb. It's the only system exhibiting this unusual behavior. Could be a just a blip, but it could be significant too.

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I wrote a paper on this tweak, you can download it here - https://sites.google.com/site/amateuraudio/theory/large-coil-simulation-accuracy-issue-and-adjustment

The paper describes the issue, how to determine if the driver is affected by the issue, how the tweak was formulated, and it shows all 30 examples of Ricci's measurements compared to tweaked and untweaked sims.

I've read your paper and I find it exceptionally useful. It just doesn't explain why this happens. Lowering the BL shows uncanny agreement with reality. So good that I doubt a complex inductance formula would give the same results. But the BL can't ACTUALLY be lower, right? Why would a woofer in a mass-added test behave as though it had a certain motor strength, but once you put it in an enclosure it behaves like one with 70% of the BL?! The mind boggles.

 

Josh, when you were measuring T/S parameters did you get complex inductance values as well? Would you still have this data? I'm wondering if they might generate a better fitting curve than the one diysg generated based on normalized inductance.

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Yes I have the complex inductance data from LIMP. We know that the BL can't really be lower because it would lower the sensitivity quite a bit but this isn't happening. I do have multiple cab sizes for 18 and 21 drvers now. The bigger sizes are much larger too over twice the volume. I plan to get some data to compare against the smaller cabs. Distortion will be lower in the bigger cabs.

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I've read your paper and I find it exceptionally useful. It just doesn't explain why this happens. Lowering the BL shows uncanny agreement with reality. So good that I doubt a complex inductance formula would give the same results. But the BL can't ACTUALLY be lower, right? Why would a woofer in a mass-added test behave as though it had a certain motor strength, but once you put it in an enclosure it behaves like one with 70% of the BL?! The mind boggles.

 

Josh, when you were measuring T/S parameters did you get complex inductance values as well? Would you still have this data? I'm wondering if they might generate a better fitting curve than the one diysg generated based on normalized inductance.

 

 

The paper doesn't explain why it happens because I don't know why it happens.  A guy on diyaudio suggested this:

The force field (BL) is a constant and cannot change. Losses have to be compensated with Re. The problem here is in the inductive reactance (XL), which opposes the change in current and becomes the dominant force here. You can increase or lower this force by increasing or lowering the force field (BL). If you look for driver indications: high Le and/or high Mms (for its size) in relation to a low EBP value.

 

From here - http://www.diyaudio.com/forums/subwoofers/278876-large-coil-simulation-accuracy-issue-adjustment-3.html#post4434166

I haven't bothered looking into that yet so for now the best I can do at this time is give guidelines for the type of driver that exhibits this issue, as described in the paper.  And clearly higher inductance points to a larger issue, but only the really big coil high excursion high power handling drivers are really bad.  The part that surprised me was that drivers with an exceptionally low normalized inductance (Le/Re) like the Dayton HO also benefited from using the tweak with a clearly more accurate frequency response compared to the measurement.  Even the TC LMS, which is considered to be almost immune from inductance effects matched better with the tweak.

 

No the Bl can't actually be lower, the measured t/s parameters have to be correct.

 

The reason why this method uses a tweaked Bl value is simply because empirical testing shows that it works to give a much more accurate picture of the frequency response (and although I can't test it, I'm sure it gives a more accurate excursion graph too).

 

As I think I mentioned in the paper this all came about because for a couple of years every time I looked at data-bass measurements of these big coil drivers it was clear just by looking that they wouldn't sim like the measurements suggested.  But I had seen that frequency response curve shape before, many times.  I saw it every time I added some series Re (or Rg) to a sim to simulate the effect of heavy power compression.  So I started comparing the measurements to sims using 2x the driver's Re and the frequency response started to match much better (although sensitivity was obviously way off using that method, but I had a tweak for sensitivity correction too).  After a bit of discussion on avs and a bit of help from David McBean and LTD02 (and of course all of Ricci's measurements) the result was the Bl adjustment method.  The only 3 problems are:

1. The method is not perfectly accurate at predicting frequency response, although it is a lot better than an untweaked sim.

2.  Impedance results are not accurate - compared to measurements the untweaked impedance is closer to reality, although it's not a big difference and not a big deal.

3.  Sensitivity is consistently about 2 db lower in the tweaked sims than in the measurements.  The tweak does not address this, but you can easily just mentally add a couple of db to the Bl adjusted sim.

 

Hopefully one day there will be a lot more measured examples of this type of driver in all different types of enclosures so the method can be validated to a higher degree (as far as I'm concerned it's already validated as this tweak worked on every single driver of this type in every enclosure type that I simulated and compared to measurements, even with the generic tweak as shown in the paper, but more data is better than less) and possibly the tweak can be even further refined with a more robust data set.  But I don't really trust anyone's measurements except Ricci's and therein lies the problem.  His measurement dataset isn't growing very quickly.  But it is the best data available as far as I'm concerned.

 

I'm also interested to see how the complex inductance parameters sim, but what program are you going to use to do the sims?

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I'm making some plots to determine compliance limited Xmax by varying different parameters of the driver and the enclosure. All I should have to do to solve for relative excursion is to solve this equation for k3 and then take the square root, right? Then I just pick values for H3 and it should give me relative excursion values to reach said distortion level. But I did that and everything looks all wonky. I'm getting an excursion minimum at Fb/3 regardless of Qts. Is my math wrong or my whole methodology?

 

Something is probably wrong if you are getting a minimum at Fb/3 regardless of Qts.  It's possible that there's an error in the formula that I posted.

 

While I didn't show it explicitly, the model suggests that the absolute level of the third harmonic should grow with the cube of excursion.  Thus, the *relative level* of third harmonic distortion (as a percent) should grow with the square of excursion.  Equivalently, third harmonic distortion should double with each 3 dB increase in output of the fundamental.  Unfortunately, this trend does not appear in the few examples I looked at from Ricci's data, so this conclusion may not be very sound.  This calls into question whether I was doing *my math* correctly.  I'm thinking I missed something key.  (FWIW, the excursion in the model is the excursion required to reproduce the fundamental cleanly, *not* the actual excursion including distortion harmonics.)

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These come from 5 different systems which are all radically different. The same systems for both sets. There is at least one sealed, vented, FLH, and TH represented and both active closed loop systems and passive systems driven by the big amp. If anyone wants to try guessing which systems are which (sealed, horn, active, etc...) I'd be very surprised if anyone got most of them right.

 

It's fun to try to guess, but I honestly have no idea.  One thing that stands out is that the drivers seem somehow "better behaved" at 16 Hz than 31.5 Hz.  The overall shape of the burst wave seems to be better reproduced in the 16 Hz tones.  The phase of the harmonics relative to fundamental has a lot of impact on the shape of the wave, so the implication is that the distortions in the 31.5 Hz tones involve more/weirder phase shifts.

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Yes I have the complex inductance data from LIMP. We know that the BL can't really be lower because it would lower the sensitivity quite a bit but this isn't happening. I do have multiple cab sizes for 18 and 21 drvers now. The bigger sizes are much larger too over twice the volume. I plan to get some data to compare against the smaller cabs. Distortion will be lower in the bigger cabs.

MORE DATA POINTS!! *squeals in excitement*

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While I didn't show it explicitly, the model suggests that the absolute level of the third harmonic should grow with the cube of excursion.  Thus, the *relative level* of third harmonic distortion (as a percent) should grow with the square of excursion.  Equivalently, third harmonic distortion should double with each 3 dB increase in output of the fundamental.  Unfortunately, this trend does not appear in the few examples I looked at from Ricci's data, so this conclusion may not be very sound.  This calls into question whether I was doing *my math* correctly.  I'm thinking I missed something key.  (FWIW, the excursion in the model is the excursion required to reproduce the fundamental cleanly, *not* the actual excursion including distortion harmonics.)

Well we need an example that is mostly compliance limited and not BL limited. Seeing the difference in performance between the two motors in the RE XXX versions, this driver is surely BL limited below Fb. I'm not sure which data set would be a good candidate. Ricci only bothers with high end drivers, which are (generally) well engineered. Enough so that they won't add the cost and inductance of extended BL linearity without a compliance that can support it. The LMS Ultra 5400 is definitely compliance limited, but this driver certainly doesn't have a parabolic K curve. At least not at the very end where it hits its hard limit.

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Well we need an example that is mostly compliance limited and not BL limited. Seeing the difference in performance between the two motors in the RE XXX versions, this driver is surely BL limited below Fb. I'm not sure which data set would be a good candidate. Ricci only bothers with high end drivers, which are (generally) well engineered. Enough so that they won't add the cost and inductance of extended BL linearity without a compliance that can support it. The LMS Ultra 5400 is definitely compliance limited, but this driver certainly doesn't have a parabolic K curve. At least not at the very end where it hits its hard limit.

 

What makes you say that the LMS Ultra is definitely compliance limited?  My thinking is that it has unusually linear compliance, but this is in some ways its Achilles heel.  By not stiffening enough at the extremes of its stroke, it allows a hard bottom to occur.

 

If my analysis is at all relevant here, my guess is that compliance linearity will often be of lower priority to most manufacturers because it really doesn't impact things much until you get well below the resonance frequency.  In contrast, the importance of BL linearity remains relevant in the resonance region and above.  Consider that most applications will use the sub predominantly in the resonance region or above or will use the sub in an alignment where the physics change completely.  For example, I would bet that suspension has little impact on driver distortion in a ported system until the driver/port unloads.

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I use LIMP for all of my driver parameter measurements. Here is an example from a SI HST-18d2. There are 3 different " lossy inductance" models available in LIMP. Generally I use LE+L2/R2. Unibox has entry for these data points. However I've found even using this it isn't an accurate simulation. It's better but still not all that close. Expensive dedicated development/measurement software can likely use these inductive models but I'm not aware of any free-ware.

 

 

 

 

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What makes you say that the LMS Ultra is definitely compliance limited?  My thinking is that it has unusually linear compliance, but this is in some ways its Achilles heel.  By not stiffening enough at the extremes of its stroke, it allows a hard bottom to occur.

 

If my analysis is at all relevant here, my guess is that compliance linearity will often be of lower priority to most manufacturers because it really doesn't impact things much until you get well below the resonance frequency.  In contrast, the importance of BL linearity remains relevant in the resonance region and above.  Consider that most applications will use the sub predominantly in the resonance region or above or will use the sub in an alignment where the physics change completely.  For example, I would bet that suspension has little impact on driver distortion in a ported system until the driver/port unloads.

Well here's my reasoning. An LMS voice coil wind theoretically could generate a completely linear BL curve, only drooping at the very ends of travel. Given TC Sounds' record, I'd give them the benefit of the doubt and assume they came pretty darn close.

 

Now looking at every other driver, they get a huge linear excursion bump at Fb. Sometimes they're still yielding CEA-2010 passing results when the voice coil would be almost completely beyond the gap, even after accounting for distortion. Clearly the BL linearity is of less importance at a system's natural resonance frequency. This is supported by your calculations that show reduced H3 distortion at Fs for alignments Qtc ~0.3 and higher, which is every system tested.  At these frequencies, the driver is at Xmech, which is why Ricci reports tapping, mechanical noises, etc. 

 

I suspect that after the stretchy elements of the LMS Ultra's suspension reach ~34-35mm, a flexible but non-stretchy element (I'm guessing some nylon or Kevlar woven in the spider) is pulled taut, preventing any further excursion. The driver should have more usable stroke at Fs, but the hard limit stops this. This makes sense from a design standpoint because you would want to create a soft bottom where you're pulling on kevlar threads instead of smashing into the back plate or spider landing. If it were a failure of the suspension to stiffen up, then the driver would continue on to have more linear stroke, just like every other driver tested.

 

A failure to stiffen up would actually be a good thing. The stiffening up is what causes distortion. If it had the most linear suspension, then that means it would have the lowest compliance related distortion and the k3 in your formula would be near zero.

 

Given that, I'm pretty sure it's compliance limited.

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Whooh thems is some squiggly lines. Especially #7. There's a lot of non-harmonic content here too, which surely must be audible. The amplitude of the center peak is even lower than the outer ones. Crazy that this massive nonlinearity didn't cause enough harmonic distortion to break the threshold.

 

If you band-pass that signal, you'll surely measure a much higher average amplitude of the fundamental than measuring a cleaner reproduction that maintained the original signal's windowing. It certainly would show up in my Xmax calculations as an excursion much higher than the driver ever even produced.

 

Probably explains shadyJ's claim of "running out of oomph"

 

It seems like it cheated the test. It never really peaked at the intended SPL, it just compressed the largest peaks without adding much harmonic distortion. 

 

It's fun to try to guess, but I honestly have no idea.  One thing that stands out is that the drivers seem somehow "better behaved" at 16 Hz than 31.5 Hz.  The overall shape of the burst wave seems to be better reproduced in the 16 Hz tones.  The phase of the harmonics relative to fundamental has a lot of impact on the shape of the wave, so the implication is that the distortions in the 31.5 Hz tones involve more/weirder phase shifts.

 

Here are the 5 systems...

 

1.) Dayton UM18-22 sealed

2.) Velodyne DD18+

3.) HSU VTF15H both ports open

4.) JTR OS-LFU

5.) Gjallarhorn

 

Interestingly #7 that Contrasseur mentioned as being particularly ugly is a sealed , closed loop,servo controlled system.

 

Now granted all of these systems are being driven very hard at the point these waveforms were captured and they will clean up a lot once the  demands are lowered significantly. The DD18+ is likely DEEP into the limiter circuit. Unfortunately, while I do have some recorded waveforms produced when the systems are not being driven so hard, they are random and not standardized. What I may do is capture the maximum passing result as normal and then capture the waveform 6dB reduced. Some of the waveforms from systems driven past the distortion threshold are truly ugly indeed. Clearly harmonic distortion is not the only form of distortion happening in these waveforms.

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Contrasseur,

The LMS driver hard bottoms the cone against the spider spacer ring at around 33-38mm, depending upon which model you have and which spacer ring height is used. Xmech is met. This is why it is limited where it is in most of the CEA-2010 tests. The driver is destroyed if pushed further. It has nothing to do with the soft parts, distortion or running out of motor force. The surround is beginning to become very tight at this point that is true, but the 10" spiders are no where near becoming a limitation. When a driver has a lot of motor force at the point that the surround or spiders become stretched tight it generally wins that fight and something breaks in the soft parts. If the LMS did not mechanically limit on the spider landing it would likely rip the surround on the out stroke as a next step or fold the cone up.

 

Mechanical limit.

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Out of all of the drivers you've tested, do you think any of them were compliance limited? Maybe some of the smaller drivers?

 

These are my guesses. The BMS 18n862 and pro5100 possibly but I believe they run out of motor and suspension at roughly the same time. The split coil XXX possibly. The Chase/Chane subs using the 18" Eminence sourced driver and also the Powersound subs using Eminence drivers may be worth looking at. (Eminence's surround just doesn't have the size or profile to allow huge excursion.) All of these may be partly compliance limited primarily due to the surrounds used. Most drivers are not designed with a motor that is linear well past the suspension limits because that's how drivers break themselves.

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  • 4 months later...

Thread Necromancy engage.

 

I'm resurrecting this thread because it was a great discussion and another discussion today reminded me of these posts.

 

Compliance limited drivers. 21-IPAL could be added to that list. Possibly the old Funk FW18.0C test which is no longer a current model.

 

Also we now have data for the GUJ18v1 in a very large sealed cab and the smaller standard one which may help this discussion a bit.

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