let's say you're looking for a driver to cover 1.5 khz to 10 khz with high efficiency.
you can use a Planar like the Radian LM8K with response like this:
or you can use a Compression Driver like RCF ND650 with response like this:
between the two of them the Planar slopes up by about 10 db and the Compression slopes down by almost 10 db
i have been trying to research why but the answers are not fully satisfactory.
the explanation for the CD is supposed to be "mass break point" but after extensive googling and reading this JBL paper:
https://jblpro.com/es/site_elements/tech-note-characteristics-of-high-frequency-compression-drivers
i was not able to find a single explanation anywhere on the internet of what exactly mass break point is and what causes it. the formula given by the JBL paper:
takes only motor force ( BL^2 / Re ) and diaphragm mass ( MMS ) as input and magically puts out 3.5 khz as output. it further blatantly states that no matter what driver you use it will always produce about 3.5 khz output because a larger driver will have twice the motor force and twice the diaphragm mass.
this formula is maybe the strangest i have ever seen. why would higher motor force result in higher bandwidth ? my theory is motor force here is simply a stand in for voice coil diameter because all compression drivers have approx 2.0T flux strength in the gap so motor force in real drivers will be proportional to VC diameter and of course MMS will also be proportional to driver size and JBL states in the same paper that Mass Break Point is always around 3.5 khz regardless of what driver you use so it seems the formula is simply designed to basically take driver size as both numerator and denominator in order to have everything cancel out and leave you with just 3.5 khz as result.
the paper further states that the space between diaphragm and phase plug ( about 0.5 mm in most drivers ) is not large enough to matter and is NOT the mechanism behind mass break point.
so what is the mechanism then ?
and it is equally mysterious why Planar response rises. most people intuitively understand that it has something to do with beaming because the power response of the planar is flat, only the on-axis response rises. but why isn't the same effect observed in an array of cone drivers ? why doesn't an array of cones exhibit a rising response ? why only planars and ribbons ?
i was able to come up with a theory that the reason for discrepancy is the low mass of the diaphragm. that is heavy cones are more efficient at lower frequencies where mutual coupling increases acoustical radiation impedance ... while ribbon / planar diaphragms work better with lower acoustical impedance at higher frequencies. this would account for the kind of response rise we see in ribbon tweeters, whereas in the Radian planar there is additional bump around 10 khz due to cavity resonances as well as membrane resonances so i could accept the planar response as being explained by a combination of these factors.
but i still don't understand mass breakpoint of compression drivers. why is it a thing. and what is it ?
i can only assume it has something to do with the phase plug because only drivers with phase plugs seem to exhibit this phenomenon. a 2.5" titanium dome like in RCF in questions should be able to go to 8 khz or so before breaking up yet it begins to roll off much earlier, even in on-axis response, and probably around 3.5 khz as JBL says when measured on plane wave tube / power response.
it must have something to do with the mass of air in the phase plug acting as a bandpass port. but, as i said, i was not able to find a single explanation anywhere online as to exactly what it is.
on a somewhat unrelated note i think it is noteworthy that at 10 khz both the planar and the compression driver are at about the same 105 db efficiency, while at 20 khz a true ribbon beats them both with over 100db efficiency. if radiation patterns could be matched a perfect speaker would use a true ribbon over 10 khz, a planar from about 3 khz to 10 khz and a compression from about 600 hz to 3 khz but nobody optimizes drivers for those frequency ranges and in practice both planars and CDs are designed for the same frequency range and you must pick one or the other, but for that you have to first understand both, which is what i am trying to do.
you can use a Planar like the Radian LM8K with response like this:
or you can use a Compression Driver like RCF ND650 with response like this:
between the two of them the Planar slopes up by about 10 db and the Compression slopes down by almost 10 db
i have been trying to research why but the answers are not fully satisfactory.
the explanation for the CD is supposed to be "mass break point" but after extensive googling and reading this JBL paper:
https://jblpro.com/es/site_elements/tech-note-characteristics-of-high-frequency-compression-drivers
i was not able to find a single explanation anywhere on the internet of what exactly mass break point is and what causes it. the formula given by the JBL paper:
takes only motor force ( BL^2 / Re ) and diaphragm mass ( MMS ) as input and magically puts out 3.5 khz as output. it further blatantly states that no matter what driver you use it will always produce about 3.5 khz output because a larger driver will have twice the motor force and twice the diaphragm mass.
this formula is maybe the strangest i have ever seen. why would higher motor force result in higher bandwidth ? my theory is motor force here is simply a stand in for voice coil diameter because all compression drivers have approx 2.0T flux strength in the gap so motor force in real drivers will be proportional to VC diameter and of course MMS will also be proportional to driver size and JBL states in the same paper that Mass Break Point is always around 3.5 khz regardless of what driver you use so it seems the formula is simply designed to basically take driver size as both numerator and denominator in order to have everything cancel out and leave you with just 3.5 khz as result.
the paper further states that the space between diaphragm and phase plug ( about 0.5 mm in most drivers ) is not large enough to matter and is NOT the mechanism behind mass break point.
so what is the mechanism then ?
and it is equally mysterious why Planar response rises. most people intuitively understand that it has something to do with beaming because the power response of the planar is flat, only the on-axis response rises. but why isn't the same effect observed in an array of cone drivers ? why doesn't an array of cones exhibit a rising response ? why only planars and ribbons ?
i was able to come up with a theory that the reason for discrepancy is the low mass of the diaphragm. that is heavy cones are more efficient at lower frequencies where mutual coupling increases acoustical radiation impedance ... while ribbon / planar diaphragms work better with lower acoustical impedance at higher frequencies. this would account for the kind of response rise we see in ribbon tweeters, whereas in the Radian planar there is additional bump around 10 khz due to cavity resonances as well as membrane resonances so i could accept the planar response as being explained by a combination of these factors.
but i still don't understand mass breakpoint of compression drivers. why is it a thing. and what is it ?
i can only assume it has something to do with the phase plug because only drivers with phase plugs seem to exhibit this phenomenon. a 2.5" titanium dome like in RCF in questions should be able to go to 8 khz or so before breaking up yet it begins to roll off much earlier, even in on-axis response, and probably around 3.5 khz as JBL says when measured on plane wave tube / power response.
it must have something to do with the mass of air in the phase plug acting as a bandpass port. but, as i said, i was not able to find a single explanation anywhere online as to exactly what it is.
on a somewhat unrelated note i think it is noteworthy that at 10 khz both the planar and the compression driver are at about the same 105 db efficiency, while at 20 khz a true ribbon beats them both with over 100db efficiency. if radiation patterns could be matched a perfect speaker would use a true ribbon over 10 khz, a planar from about 3 khz to 10 khz and a compression from about 600 hz to 3 khz but nobody optimizes drivers for those frequency ranges and in practice both planars and CDs are designed for the same frequency range and you must pick one or the other, but for that you have to first understand both, which is what i am trying to do.
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All of that math is way over my head, but here are some things that may be causing the rise in response:
IMHO, the number one thing that causes a rise in response is when a fraction of the diaphragm is no longer moving. For instance, if you look at the spec sheet of a soft dome tweeter compared to a metal dome tweeter, you may notice that the soft dome begins to beam at high frequencies. Part of this is simply that the wavefront is larger than the diaphragm. For instance, 16khz is 21mm long. Due to the very short length, a 25mm dome will "beam" when radiating a 21mm wavefront.
But another factor is that a lot of soft domes behave like ring radiators at high frequencies. Basically, the apex of the dome becomes decoupled from the part of the dome that's attached to the surround. One way to visualize this, is to picture a trampoline. If you generate a wave in the trampoline at a LOW frequency, that wave will tend to deflect the entire trampoline. But if you generate a wave in the trampoline at HIGH frequency - in other words, you jump up and down at a much faster rate - the peaks and the troughs of the wave will be smaller. And when the trampoline is excited from the EDGE of the trampoline (like the surround on a tweeter), the center of the trampoline will not move at all, when it's excited at high frequencies.
This is the key: although only a fraction of the diaphragm is moving, the motor force is the same.
I hope that makes sense? The size of the tweeter has virtually "shrunk" from a dome to ring, but the motor force is the same. Less mass with the same force, you get higher SPL.
The last factor, which ALSO increases on-axis SPL, is that the beamwidth of the tweeter narrows as you get higher in frequency. This is because at high frequency, the wavelength is smaller than the diaphragm. When you focus all of the energy of the tweeter into a narrow beam, the SPL in that narrow beam gets louder.
The converse happens when the wavelengths are larger than the diaphragm; they get spread out into a wider beamwidth, and since the energy is the same, you get lower SPL on-axis.
TLDR: you have a fixed amount of output, assuming that the input power stays constant. But that output can be focused into a narrow beam (increasing SPL on-axis) or it can be spread out into a wider beam (decreasing SPL on-axis.) The size of the diaphragm also changes at high frequencies, because it's not rigid.
IMHO, the number one thing that causes a rise in response is when a fraction of the diaphragm is no longer moving. For instance, if you look at the spec sheet of a soft dome tweeter compared to a metal dome tweeter, you may notice that the soft dome begins to beam at high frequencies. Part of this is simply that the wavefront is larger than the diaphragm. For instance, 16khz is 21mm long. Due to the very short length, a 25mm dome will "beam" when radiating a 21mm wavefront.
But another factor is that a lot of soft domes behave like ring radiators at high frequencies. Basically, the apex of the dome becomes decoupled from the part of the dome that's attached to the surround. One way to visualize this, is to picture a trampoline. If you generate a wave in the trampoline at a LOW frequency, that wave will tend to deflect the entire trampoline. But if you generate a wave in the trampoline at HIGH frequency - in other words, you jump up and down at a much faster rate - the peaks and the troughs of the wave will be smaller. And when the trampoline is excited from the EDGE of the trampoline (like the surround on a tweeter), the center of the trampoline will not move at all, when it's excited at high frequencies.
This is the key: although only a fraction of the diaphragm is moving, the motor force is the same.
I hope that makes sense? The size of the tweeter has virtually "shrunk" from a dome to ring, but the motor force is the same. Less mass with the same force, you get higher SPL.
The last factor, which ALSO increases on-axis SPL, is that the beamwidth of the tweeter narrows as you get higher in frequency. This is because at high frequency, the wavelength is smaller than the diaphragm. When you focus all of the energy of the tweeter into a narrow beam, the SPL in that narrow beam gets louder.
The converse happens when the wavelengths are larger than the diaphragm; they get spread out into a wider beamwidth, and since the energy is the same, you get lower SPL on-axis.
TLDR: you have a fixed amount of output, assuming that the input power stays constant. But that output can be focused into a narrow beam (increasing SPL on-axis) or it can be spread out into a wider beam (decreasing SPL on-axis.) The size of the diaphragm also changes at high frequencies, because it's not rigid.
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a perfect ribbon superb light should , just like a ESL have a perfect rising response. (i believe Bolserts did one with 1 micon (just to proof this) and its rising to 20khz and beyond.) why most planars are falling off is weight and or siize. so a small planar with rather heavy foil still reach 20khz, a long thin one might roll off earlier. top end wont add up after a certain length size, width or length. i had the same length tweeter here 10cm long, one lighter then the other. the light one reaches beyond 20khz, not rising anymore but more like flat. the heavier one fell of at 16khz. making the heavy one wider makes it possible to have more high frequencies on axis possible and then it does the same as the light panel. if you would make it even wider then it would drop just like it would with more length.
besides that the curve i see looks just like a B&G or something. they have more trouble besides the weight that makes this 12-13Khz Peak and then drop. like width of unsupported/undriven mylar between traces etc. it might be nice for efficiency noit so much for FR response, adding only coil in the strongest field and leave the rest of the mylar to move out of sync with the traces (bit like breakup) i chose in most tweeters to leave as little undrivven mylar above the magnet, to have a smoother response
besides that the curve i see looks just like a B&G or something. they have more trouble besides the weight that makes this 12-13Khz Peak and then drop. like width of unsupported/undriven mylar between traces etc. it might be nice for efficiency noit so much for FR response, adding only coil in the strongest field and leave the rest of the mylar to move out of sync with the traces (bit like breakup) i chose in most tweeters to leave as little undrivven mylar above the magnet, to have a smoother response
AFAIK, rising response from planar drivers is caused by constructive interference between the waves emitted at different points on the same side of the diaphragm, especially as the wavelength being produced becomes a fraction of the size of the driver area. You see the same sort of rising response in electrostatic speakers, especially ones that use large flat panels. That's why such speakers have a very narrow sweet spot to listen in. It's also why ribbon tweeters are made long and narrow and oriented vertically - that gives them good horizontal dispersion, but very narrow vertical dispersion.