A similar thing is seen in some of the Directiva R2 simulations that there is both constructive and destructive interference. They have made a protype with a 5" driver designed for use down to 200Hz where the EQ requirements aren't so severe. As long as the driver has enough excursion even really large boosts can still sound good. You do lose maximum SPL capability and introduce more distortion from the excursion, the Dutch and Dutch shows that doesn't have to be bad thing in the right scenario. The Linkwitz dipoles I used to have had around 20dB of boost on the woofers and the bass sounded really good.
Nice 
Its always a problem how to actually manufacture such box, or conversely how to simulate built box damping material / port(s) in order to be able to tune it.
First suspect explanation for the ~650Hz axial boost is "dipole peak", which relates to path length between front and back source. Hump below which the ~-6db/oct slope of such gradient system is. Testing with VituixCAD diffraction tool, if it was just a flat open baffle then the "dipole peak" would be about where same sized closed box baffle edge main diffraction hump is. But, now with such 3D model the slot is quite far back the hump moves to lower frequency compared to closed box, so I think the axial boost is feature of such "U-Baffle" or what that is called I don't know Path length increased toward back. You can probably move the hump higher or lower frequency by moving the slot front or back affecting path length, but if the response is now what you are looking for then there is no point to.
How is the damping modeled in the simulation? It looks like the slot is open and the walls inside are made of damping material? Would you build it like that or something else?
I suspect it needs some prototyping to get the response, for this reason could you simplify the box simulation, flat top for fast cheap prototype construction? If you get the pattern right with that you'll know it works with the rounded top as well, you can anticipate differences between rounded and flat top from differences in simulation results.
edit. By the way, is the damping constant over whole bandwidth on the simulation? Can you insert absorption coefficients for the material? If not then you'll need to use material and thickness that has ~constant absorption for the bandwidth you need the pattern, which might mean construction insulation in a thick layer, which might give too much attenuation. Usually materials have kind of S-curve on the absorption. Constant absorption happens at high frequencies and its high, like 20db high. On low frequencies there is very little absorption, especially in small thickness, and then some ramp up on the mid frequencies. This is kind of a shelving filter adding some group delay to the system and what not, might change the pattern from ideal unless you can model it?
Basotect seems to work nicely on my cardioid mid prototypes so I suggest try that first if you want to model real damping material: https://insights.basf.com/files/pdf/Basotect_Brochure.pdf I'm using 2.5cm thick melamine sponge on the apertures.
How to convert absorption coefficients to decibels for those who can't calculate dB in their head, I can't
Its always a problem how to actually manufacture such box, or conversely how to simulate built box damping material / port(s) in order to be able to tune it.First suspect explanation for the ~650Hz axial boost is "dipole peak", which relates to path length between front and back source. Hump below which the ~-6db/oct slope of such gradient system is. Testing with VituixCAD diffraction tool, if it was just a flat open baffle then the "dipole peak" would be about where same sized closed box baffle edge main diffraction hump is. But, now with such 3D model the slot is quite far back the hump moves to lower frequency compared to closed box, so I think the axial boost is feature of such "U-Baffle" or what that is called I don't know
Path length increased toward back. You can probably move the hump higher or lower frequency by moving the slot front or back affecting path length, but if the response is now what you are looking for then there is no point to. How is the damping modeled in the simulation? It looks like the slot is open and the walls inside are made of damping material? Would you build it like that or something else?
I suspect it needs some prototyping to get the response, for this reason could you simplify the box simulation, flat top for fast cheap prototype construction? If you get the pattern right with that you'll know it works with the rounded top as well, you can anticipate differences between rounded and flat top from differences in simulation results.
edit. By the way, is the damping constant over whole bandwidth on the simulation? Can you insert absorption coefficients for the material? If not then you'll need to use material and thickness that has ~constant absorption for the bandwidth you need the pattern, which might mean construction insulation in a thick layer, which might give too much attenuation. Usually materials have kind of S-curve on the absorption. Constant absorption happens at high frequencies and its high, like 20db high. On low frequencies there is very little absorption, especially in small thickness, and then some ramp up on the mid frequencies. This is kind of a shelving filter adding some group delay to the system and what not, might change the pattern from ideal unless you can model it?
Basotect seems to work nicely on my cardioid mid prototypes so I suggest try that first if you want to model real damping material: https://insights.basf.com/files/pdf/Basotect_Brochure.pdf I'm using 2.5cm thick melamine sponge on the apertures.
How to convert absorption coefficients to decibels for those who can't calculate dB in their head, I can't
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In a case this would be difficult or impossible to achieve passively (with a mere back side damping), I already like it so much that I'm willing to do it actively - instead of the current port opening I would place an array of small drivers. Maybe even that would be possible passively (i.e. driven with just one amplifier channel).
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If you want to know more about the possibility for a cardioid 5-inch. On ASR there is a lot of work done on desiging this type of speaker.
You can see recent simulations (not final design) of this top module, it will need a bass module, crossed over around 200-300 hz. The design of the box, can be seen in the profile picture, of the poster. It's tiny!
It is possible to do passively, the group delay of a low pass filter matched with the corresponding side position for the cancellation woofer is enough to get a good range of cardioid radiation. It's easier and more tunable actively though.
I still don't understand the physics behind these graphs.
To clarify the situation, I played around a bit with simple formulas to clarify at which frequency SPL from two radiating sources (the front and the rear side) exceed SPL of monopole (front side only). I assume for simplicity that SPL of the rear and the front side is eqaul (pf=pb=po), so the total pressure is
pt = po*(exp[-i*fi1] + exp[-i*fi2])
and the module is
|pt| = po* sqrt[(2+ 2Cos[fi1-fi2])]
In order to pt exceed the monopole SPL po, the expression under the square root must be greater than 1,
sqrt[2*(1+ Cos[dfi]) ] >= 1, so the relative phase difference (fi1-fi2) should not exceed 120 deg.
The constructive interference appears when the square root reaches its maximum value which is 2, and relative phase difference (fi1-fi2) is 0 deg.
The destructive interference appears when the square root reaches it minimum value which is 0, so relative phase difference (fi1-fi2) is 180 deg.
Seems that these considerations agrees with your simulated SPL and phase graphs: the phase difference of the front and the rear side reaches 120 deg approx. at ~250Hz. and we can see that above this frequency the cardioid demonstrates SPL gain compared to the monopole SPL, while at the lowest frequencies the phase difference is close to 180deg, so the SPL is considerably decreased.
The second step would be to clarify what physical factors inluence relative phase dif. (fi1-fi2). We have not a lot instruments to influence f1, but f2 can be changed in two ways. The first way is to change acoustic path difference between the front and the rear sides. And a less obvious way is to change the volume of the rear chamber, which is a low-pass acoustic filter, so it also rotates the phase f2.
These will be the initial considerations, perhaps someone will add their thoughts.
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If you move up to a 6" mid, you can target the Purifi PTT6.5, which has 10mm of exceptionally linear Xmax to work with.
It seems you could also seal the back of the front portion of the mid chamber and mount a 2nd driving facing forward into the slot opening from the rear half. with a separate amp and eq channel for that driver, it would be easy to dial in the desired response pattern.
It seems you could also seal the back of the front portion of the mid chamber and mount a 2nd driving facing forward into the slot opening from the rear half. with a separate amp and eq channel for that driver, it would be easy to dial in the desired response pattern.
Hi Dmitrij_S, is the calculation in free space or half space? Baffle step there mixes things up, monopole axial response drops below 1kHz due to bafflestep while the slotted version maintains it to lower frequency due to "wings", increased source separation as the slot is further back. The responses would be more alike, no axial gain difference, if slot was right at the baffle edge and baffle was enlarged instead to have the same path length between the sources.
Sorry I'm too hurry to look into the math to see if something like this is included These are easy to experiment on with VituixCAD so never bothered to familiarize math behind.
You are right, group delay on the back and path length are the main factors for delay. Then if and when there is damping material, absorption is frequency dependent making more group delay.
Sorry I'm too hurry to look into the math to see if something like this is included
These are easy to experiment on with VituixCAD so never bothered to familiarize math behind. You are right, group delay on the back and path length are the main factors for delay. Then if and when there is damping material, absorption is frequency dependent making more group delay.
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About gain in SPL of a leaky port vs. closed vs. open baffle for example is written by user ctrl on ASR too:
"Analysis" of cardioid speaker radiation via lateral slots - like D&D 8c
He also did an analysis and simulation of open baffle types:
Open baffle speaker pitfalls
"Analysis" of cardioid speaker radiation via lateral slots - like D&D 8c
He also did an analysis and simulation of open baffle types:
Open baffle speaker pitfalls
Yeah cool, BEM sims inside!
Main issue with all this gradient speaker stuff is that the smooth usable bandwidth depends on the path length of the sources. When the slots are moved further back, or baffle widened, we get more lows and axial gain because diffraction hump moves to lower frequency, but also the "clean usable bandwidth" comes down with it. Above this main hump the response is not as smooth as it could due to diffraction.
Both ctrl and mabats results show that the good pattern is on longer than the path length difference wavelength and its easy to test in VituixCAD as well. This is where the "2-3 octaves usable bandwidth before problems" rule of thumb arises. Its about two octaves from the "dipole peak" down where good pattern is and before bass loss gets too heavy. Whether any of this matters is of course everyone to decide, perhaps its smooth enough so usable much higher than the hump indicates.
So, why just not use any size and be happy with it? The thing is that we lose the lows and benefit as large cone area as possible to have some SPL capability. For this reason, cleanest mids and highest SPL capability is attained when there is minimal path length between the sides, situation with minimal baffle and aperture basically at the driver edge. Now diffraction hump is as high of a frequency as possible and we have as big of a cone as fits.
What comes to system design one wants to use crossover frequency from tweeter to cardioid mid as low as possible, to extend cardioid response to a low frequency with the 2-3 octaves available. Crossover frequency is pretty much around baffle (driver) size wavelength or bit longer, somewhere around 1-2kHz for 5-8" drivers. Two octaves from 2kHz is 500Hz, from 1kHz its 250Hz. Better target to schroeder so perhaps 8-10" driver and 1" compression driver in ST260 sized waveguide is fine Double up to 15" woofer to get into 100Hz comfortably.
Main issue with all this gradient speaker stuff is that the smooth usable bandwidth depends on the path length of the sources. When the slots are moved further back, or baffle widened, we get more lows and axial gain because diffraction hump moves to lower frequency, but also the "clean usable bandwidth" comes down with it. Above this main hump the response is not as smooth as it could due to diffraction.
Both ctrl and mabats results show that the good pattern is on longer than the path length difference wavelength and its easy to test in VituixCAD as well. This is where the "2-3 octaves usable bandwidth before problems" rule of thumb arises. Its about two octaves from the "dipole peak" down where good pattern is and before bass loss gets too heavy. Whether any of this matters is of course everyone to decide, perhaps its smooth enough so usable much higher than the hump indicates.
So, why just not use any size and be happy with it? The thing is that we lose the lows and benefit as large cone area as possible to have some SPL capability. For this reason, cleanest mids and highest SPL capability is attained when there is minimal path length between the sides, situation with minimal baffle and aperture basically at the driver edge. Now diffraction hump is as high of a frequency as possible and we have as big of a cone as fits.
What comes to system design one wants to use crossover frequency from tweeter to cardioid mid as low as possible, to extend cardioid response to a low frequency with the 2-3 octaves available. Crossover frequency is pretty much around baffle (driver) size wavelength or bit longer, somewhere around 1-2kHz for 5-8" drivers. Two octaves from 2kHz is 500Hz, from 1kHz its 250Hz. Better target to schroeder so perhaps 8-10" driver and 1" compression driver in ST260 sized waveguide is fine
Double up to 15" woofer to get into 100Hz comfortably.
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Very curious to what you'll come up withBetter target to schroeder so perhaps 8-10" driver and 1" compression driver in ST260 sized waveguide is fine
Prototypes have been running long time, beginnings here https://www.diyaudio.com/community/...eaker-insipired-by-d-d-8c.369939/post-6763700 and pretty much all my posts more or less relate since Fear not, its not final version and I'm also eager to hear what comes up I'm also eager to see what others come up with, hence sharing what I've found out so far to help others step on it.
Fear not, its not final version and I'm also eager to hear what comes up I'm also eager to see what others come up with, hence sharing what I've found out so far to help others step on it.
Hi Dmitrij_S, is the calculation in free space or half space? Baffle step there mixes things up, monopole axial response drops below 1kHz due to bafflestep while the slotted version maintains it to lower frequency due to "wings", increased source separation as the slot is further back. The responses would be more alike, no axial gain difference, if slot was right at the baffle edge and baffle was enlarged instead to have the same path length between the sources.
Sorry I'm too hurry to look into the math to see if something like this is included
You are right, group delay on the back and path length are the main factors for delay. Then if and when there is damping material, absorption is frequency dependent making more group delay.
Hi, tmuikku !
Only assumption I made is that we analyze pressure from two sources in a fixed point of space. It is very generalized analysis without going into deails on radiation condition, a shape of the the wavefront etc. We have complex pressures from source 1 |po|*exp[-i*fi1] and source 2 |po|*exp[-i*fi2] that are simply summed and the modulus of the sum is found to see an influence of the phase difference.
Such a generalized simple analysis helped me to undestand very basics relations, because it was not entirely clear to me how cardiod gains SPL in the mid range compared to the monopole SPL. We are all heard that cardiod suppresses SPL at low frequencies, however, I have not seen anywhere discussed, that cardioid gains SPL in the midrange, which is the quite interesting fact
. Once the basic relationships and physics are understood, one can think about the details of how to implement them technically. It is more or less clear to me how to set up acoustic path, however, it is not entirely clear to me how to configure acoustic filter (rear chamber + damping material) to get a cardioid radiation pattern.
By the way, maybe someone knows the mathematical definition of a cardioid ?
tmuikku, this is just a basic vector algebra: https://www.desmos.com/calculator/r8djnn41lg
You add two vectors of the same length (blue and green, see the Desmos link) and ask what must be the angle (=phase difference) so the sum (red) is longer than the original vector(s).
You add two vectors of the same length (blue and green, see the Desmos link) and ask what must be the angle (=phase difference) so the sum (red) is longer than the original vector(s).
Thanks mabat! Desmos is great tool to visualize and interact with maths, loving it!
Dmitrij_S, yeah best way to learn is to do it what ever means, get some understanding whats going on and then expand !
If it helps, I've been simplifying the damping material out as its the hardest part to simulate and fiddle with. I figured out it is best to rely on it as little as possible and instead just use basic acoustic low pass consisting of a chamber and a port, and then use location and shape of the port to adjust path length. Damping material is used barely enough to ease out any resonances.
How to make acoustic low pass filter? bass reflex box port is one! Add another chamber to make higher order low pass filter if needed. See Fulcrum acoustics patent https://patents.google.com/patent/US20170353787A1/en
Basically, use VituixCAD electrical filter block to emulate cardioid system and find out what kind of low pass you need. Then use some reflex box calculator to make Helmholz resonance there abouts to get second order acoustic low pass. Is pretty much there when you make minimal internal volume and start with 2-4 apertures totalling about driver Sd and adjust from there. Then there is no need to make "long" ports, thickness of typical ply 1-2cm is fine. Then use some damping material to reduce peaking of the resulting filter. Damping material affects some as its another filter in the system so experiment a little. Simplified emulation of absorption coefficients can be emulated with shelving filter in VituixCAD. Here is recent run through about how to approximate the stuff in VituixCAD https://www.diyaudio.com/community/...w-distortion-with-a-2-way.334757/post-7244275. Bonus of the emulation method is real time adjustment. One can measure a prototype box and then try to match it in the emulation, then if the response is off one can just fiddle around to find out what needs to be changed to get toward target response.
Whether this is what actually happens or not is beyond me, it seems to work so worthy starting point for everyone trying things out, if nothing else To me the "resistance box" has been a myth from the get go, never figured out what the resistance is and how its related to anything, just ignored it as it didn't seem to make sense Stuff seems to work fine without thinking about resistance at all, think about acoustic low pass filter and damping and thats it. Damping seems to reduce resonance but also the attenuation affects the pattern, better to design so that as little damping is needed as possible.
What I'm hoping to see here is to understand more about the system, perhaps to learn what the "resistance box" is all about. BEM sims are new to me, fun to see it happening Perhaps function of the damping is better understood after the process on this thread, perhaps its very key. I think ability to really simulate it properly would be needed though.
Dmitrij_S, yeah best way to learn is to do it what ever means, get some understanding whats going on and then expand !
If it helps, I've been simplifying the damping material out as its the hardest part to simulate and fiddle with. I figured out it is best to rely on it as little as possible and instead just use basic acoustic low pass consisting of a chamber and a port, and then use location and shape of the port to adjust path length. Damping material is used barely enough to ease out any resonances.
How to make acoustic low pass filter? bass reflex box port is one! Add another chamber to make higher order low pass filter if needed. See Fulcrum acoustics patent https://patents.google.com/patent/US20170353787A1/en
Basically, use VituixCAD electrical filter block to emulate cardioid system and find out what kind of low pass you need. Then use some reflex box calculator to make Helmholz resonance there abouts to get second order acoustic low pass. Is pretty much there when you make minimal internal volume and start with 2-4 apertures totalling about driver Sd and adjust from there. Then there is no need to make "long" ports, thickness of typical ply 1-2cm is fine. Then use some damping material to reduce peaking of the resulting filter. Damping material affects some as its another filter in the system so experiment a little. Simplified emulation of absorption coefficients can be emulated with shelving filter in VituixCAD. Here is recent run through about how to approximate the stuff in VituixCAD https://www.diyaudio.com/community/...w-distortion-with-a-2-way.334757/post-7244275. Bonus of the emulation method is real time adjustment. One can measure a prototype box and then try to match it in the emulation, then if the response is off one can just fiddle around to find out what needs to be changed to get toward target response.
Whether this is what actually happens or not is beyond me, it seems to work so worthy starting point for everyone trying things out, if nothing else
To me the "resistance box" has been a myth from the get go, never figured out what the resistance is and how its related to anything, just ignored it as it didn't seem to make sense Stuff seems to work fine without thinking about resistance at all, think about acoustic low pass filter and damping and thats it. Damping seems to reduce resonance but also the attenuation affects the pattern, better to design so that as little damping is needed as possible. What I'm hoping to see here is to understand more about the system, perhaps to learn what the "resistance box" is all about. BEM sims are new to me, fun to see it happening
Perhaps function of the damping is better understood after the process on this thread, perhaps its very key. I think ability to really simulate it properly would be needed though.
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