HornResp and Mass Break Point - make it make sense !

[Line Array]

i am trying to design a planar wave guide for a line array using BMS 4596Nd as a midrange

https://www.bmsspeakers.com/fileadmin/bms-data/product_data_2015/bms_4596nd_prelim_datasheet.pdf

a planar wave guide is a device like this:

https://www.beyma.com/speakers/Fichas_Tecnicas/beyma-speakers-data-sheet-horn-SG6.pdf

the purpose of which is to convert a spherical wave into a cylindrical one ... but that's besides the point for our purposes here ...

i am just trying to estimate the rough dimensions ( W X H X D ) that it would need to be to cover my target frequency range of 600 hz to 2.2 khz and i am running into the problem of HonrResp showing steep roll off in the highs which i believe is its way of modeling the mass break point ...

mass break point is a semi-mythical concept that appears in this JBL paper:

https://jblpro.com/es/site_elements/tech-note-characteristics-of-high-frequency-compression-drivers

and it gives the following formula:

frequency of mass break point = (BL^2/Re)/(Pi * Mms )

above this frequency the power response of any compression driver rolls off at 6 db / octave ...

now Pi is just a constant factor ( 3.14 etc. ) and BL^2/Re is motor force so really we're just looking at motor force to diaphragm mass ratio which is more or less Acceleration Factor ...

so JBL is basically saying that acceleration factor determines the mass break point frequency ... and HornResp seems to be behaving in exactly this way ...

here is the thing though - i have never found any explanation for what Mass Break Point is and years ago when i tried to find out why my HornResp models roll off in the highs IIRC the author said that he's simply following the Mass Break point in other words there is no underlying physical principle modeled by HornResp that creates this roll off but rather a 6db / octave rolloff is applied on top of calculated response based on mass break point frequency derived from JBL formula ...

because i have no TS parameters for the BMS driver i decided to start modeling a 2" soft dome midrange instead because those do have TS parameters for them and i have used these drivers and know what they are like and the BMS driver has 2" exit so it felt like a natural starting point for examination ... the results looked pretty miserable ( inexplicably steep roll off above 1 khz ) ... then i said what if i simply double the BL and halve the MMS ? BOOM ! suddenly my model looked bang on like BMS spec sheet frequency response. but why ?

i mean obviously BMS is a much more high end driver at about 5 times the price of a 2" soft dome and it's logical to assume it will have higher BL and lower MMS but why does it have this effect on modeled frequency response in HornResp ?

it didn't just make it louder in HornResp - it extended the response to about 3 khz like the real BMS driver should have whereas before it was rolling off already at 1 khz which is just nonsense !

even more insane is when i put in extreme values for BL and MMS it simply keeps extending HF response without any real changes to the FR otherwise. now this may be due to HornResp taking weird inputs like CMS and RMS so maybe when i change BL and MMS without changing CMS and RMS it messes with its internal math - i wish it would just take parameters like Fs and Qms instead of these foolish CMS and RMS but it is what it is ...

the point is no explanation on earth exists for where Mass Break Point comes from and HornResp appears to be simply blindly applying it to the model ...

i have long resolved to ignore this "feature" of HornResp and simply assume the driver will roll off where BMS says it will ( around 3 khz ) but i still need some software ( anybody can recommend something better than HornResp ? ) to model horn dimensions to make sure i get the correct low end response around 600 hz crossover. anybody has TS parameters for the BMS mids ?

in the mean time i am just modeling my modified 2" soft dome in HornResp to get a rough idea for horn dimensions needed to hit 600 hz but this mass break point stuff is driving me insane

i was pretty happy with HornResp when i used it to model Horn Subwoofers ( HF extension not an issue there ) but maybe it is time to try something else ? any recommendations ?

 

[bmc0]

I can't fully explain the physics in play at the moment, but playing around with a simple HF compression driver model attached to a plane-wave tube in ABEC3 seems to suggest that there's a missing parameter in the JBL formula: the compression ratio. The Cms and Rms in my model are set to physically impossible values (1 meter/N and 0 Ns/m) to remove the influence of the suspension, the voice coil inductance is zero, and the distance between the diaphragm and phase plug is essentially zero.

Using a constant acceleration source produces a -6dB/oct response regardless of frequency, as expected. Using the CD model results in this response for fairly typical parameters other than those previously mentioned:

This is with a compression ratio of 10, which is typical of HF compression drivers. Changing the compression ratio to 2 results in this:

Here's a compression ratio of 50:

Since the compression ratio of HF devices tends to fall within a fairly narrow range, JBL's formula is a reasonable approximation (ignoring secondary resonances, etc.). The BMS driver is quite different in its design, however, so I don't know how applicable the formula is.

Edit: Forgot to mention that decreasing Mms and increasing Bl both extend the HF response, just like in Hornresp.

 

[NTK]

I am fully aware that OP was a troll and, I think, has already been escorted out of the premise. However, the question was interesting. I had earlier spent some time looking into the physics behind the Thiele/Small parameters, and hopefully this post will shed some light (or may be adding confusion) to this question.

My background is in mechanical engineering, and I have lots of trouble understanding and following the use of equivalent electrical circuits in Professor Small's vented loudspeaker papers. As an ME, I am much more comfortable with equations of motions, force balance, etc. So I'll use my own derivation and it starts with the basic model of a loudspeaker driver in free air.

The mechanical part of the driver is modeled as a spring-mass-damper system. The driving force from the driver motor is equal to the force factor Bl times the voicecoil current.

For the electrical circuit, the sum of the voltage drop across the voicecoil resistance, the voicecoil inductance, and the back EMF from the motor (equal to the force factor Bl times the cone velocity) is equal to the driving voltage.

The JBL compression driver tech notes (link in post #1) simplified the model by assuming the mechanical damping, suspension stiffness, and voicecoil inductance to be negligible.

Now, here are the things I am not completely sure. If I take the the diaphragm velocity as the output, its transfer function (response) shows the first order roll off at high frequencies just as what was in the JBL tech notes. The only difference is that my cutoff frequency (the location of the pole) is exactly 1 octave lower than (half) of what JBL says. May be they chose -9 -6 dB as cutoff point? I have no idea. I hope it wasn't simple coincidence.

The way compression drivers work, AFAI understand, is that the diaphragm compresses the air inside the compression cavity, and the compressed air exits the cavity, and with the help of the phase plugs, generates plane wave pressure waves, which means pressure and particle velocity are in phase, with one being the other multiplied by a constant factor.

From the Purifi blog we know that for direct radiating drivers the acoustic pressure is proportional to the acceleration of the diaphragm instead of velocity. However, the transfer function for diaphragm acceleration will not have high frequency roll off as with the velocity since the acceleration transfer function will have an additional "zero" at s = 0. The system will have a high pass response instead of one with a low pass response per the JBL tech notes. So the diaphragm acceleration transfer function will not match the JBL tech notes.

Comments?

 

[bmc0]

I am fully aware that OP was a troll and, I think, has already been escorted out of the premise.

Looks like it. I was not aware of this when I responded.

From the Purifi blog we know that for direct radiating drivers the acoustic pressure is proportional to the acceleration of the diaphragm instead of velocity. However, the transfer function for diaphragm acceleration will not have high frequency roll off as with the velocity since the acceleration transfer function will have an additional "zero" at s = 0. The system will have a high pass response instead of one with a low pass response per the JBL tech notes. So the diaphragm acceleration transfer function will not match the JBL tech notes.

I'd have to look into the physics more to explain precisely why, but unless I screwed up my ABEC3 sims, an ideal constant acceleration source (without a phase plug) coupled to a plane wave tube results in a -6dB/oct slope (looks like an integrator, in other words). The same constant acceleration source on the surface of an infinite baffle results in a flat response.