You're explaining this on rather complicated way.
Any system has a total Q factor as well as a Fs.
Which than can be divided again in mechanical Q (often called Qms) and electrical Q (often Qes)
How that translates from one driver to multiple drivers isn't relevant.
We just measure the drivers all together as if it is just one system
This will give us a total Q of this system as well as a Fs of this system.
The math behind all of that isn't needed to do the above calculations to determine the total change in Q (of the entire system) and calculate how much effective volume has been gained by adding damping material.
The only exception here, is when you want to give each driver its own and different EQ compensation.
But this topic is only about change in total Q and increase in volume.
SQR = Square root, LOL, thanks. Geeeeez....
So:
Qtc = Qts x SQR ( alpha + 1)
Fc = fs x SQR (alpha + 1)
where alpha = Vas / Vb.
Vas is doubled for the two drivers, which I measured free air, to be between 4.1~5.06 ft^3. So maybe 9.16 ft^3 as an average doubled?
Vb = 2.6 ft^3
Alpha = 9.16 ft^3 / 2.6 ft^3 = 3.523
Qtc = 0.5795 * square root (3.523+1)
Qtc = 1.232
Fc = 23.11hz * square root (3.523+1)
Fc = 49.15hz
Qtc 1.2 doesn't make a lot of sense though I don't think?
Very best,
Naming is important if I don't understand the naming scheme. Sorry, I haven't read every text on all of this. I'm learning. Any help is great, so thanks.
Just working through what I've measured and comparing to the snippet:
Single driver in free air:
Re = 3.847
Fs = 24.83
Qts = 0.5308
Qes = 0.5896
Qms = 5.317
Vas = 4.147 ft^3
For snippet use:
Fs = 24.83
Qms = 5.317
Qes = 0.5896
Both drivers in the enclosure without filling:
Fct = 47.54hz
Qmct = 5.317
Qect = 1.203
Both drivers in the enclosure with filling:
Fc = 42.66hz
Qmc - 4.824
Qec = 1.136
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So I think I have most of what I need.
However, I don't know what Mac / Mact are.
==============================
And the last bit, says the ratios of Qtcto in the snippet represent the unfilled system. And to compare it to Qtco of the filled computed system. But compare how? Do I just use the filled measurements for the calculation in place of any unfilled measurements?
Example from snippet (5):
Qtcto = QmctQect / (Qmct+Qect)
Qtcto = 5.317*1.203 / (5.317+1.203)
Qtcto = 6.396 / 6.52
Qtcto = 0.981
However, if I assume the above for filled:
Qtco = QmcQec / (Qmc+Qec)
Qtco = 4.824 * 1.136 / (4.824 + 1.136)
Qtco = 5.48 / 5.96
Qtco = 0.919
What am I missing there? If that's true, then Q went up? But the efficiency changes suggest Q should have went down? Maybe I have that incorrect? A larger Qtc suggests my box is "smaller" for the drivers' behavior. Stuffing shows the Q droped a tiny bit (0.060).
Thanks so much.
Very best,
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The ratio between total moving mass.
Mac corresponds to Qmc, driver in filled enclosure.
Mact corresponds to Qmct, driver in unfilled enclosure.
Se previous text 🙂
They are both not very important to know, just there for clarification.
Since you have a DATS system, in your case the procedure is very straightforward
1 - Measure Qms, Qes, Fs and Re of driver free-air
2 - do the same with unfilled box
3 - same again with stuffed box
That's all you have to do.
For just knowing only the Q factor of the total system + damping material, you can just only do step 3.
Connect the speakers as you're gonna use them in the system.
Just see this as DUT.
If you're interested in how much volume has gained, see the Vab/Vb formula.
This will just give you a ratio (like a percentage) of increase.
There is literally nothing more to it.
No deep dive needed into the math, unless you're just curious about the why and how.
Thank you so much, this is very helpful.
It is all about the why & how for me, part of the fun to learn it so I understand and not just mimic something. I'm a hobbyist only, but I'd like to understand it better when designing and building speakers.
And the Vab/Vb formula will be helpful, it would be interesting to know the effective volume increase like a percentage. I calculated a 42% gain previously from simulation based on my measurement of +2db at 10hz. I'd like to check that to see if it's close and understand better why via this relationship with stuffing/filling an enclosure and how it changes things.
I did the measurements and calcs above in my edited post, if you perhaps you will review there. I got Qtc > 0.9 on both accounts. Does that seem appropriate to you?
Very best,
I don't know, just simulate the drivers in a enclosure and you know lol 🙂
Getting Qt is quite simple by just measuring all the drivers all at once with DATS and measure the DC resistance as well.
No calculations needed 😉 🙂
So, going back to moving mass ratio:
Mac / Mact = FctQec/FcQect
Mac / Mact = 47.54hz*1.136 / 42.66hz*1.203
Mac / Mact = 54.005 / 51.31998
Mac / Mact = 1.0523
This ratio implies its minimal I assume?
Now, volume change:
Vab / Vb = ((FctQect / FsQes) - 1) / ((FcQec / FsQes) - 1)
= ((47.54hz*1.203) - 1) / ((42.66hz*1.136) - 1)
= 56.19062 / 47.46176
= 1.1839
Or 18.39% change in volume?
Very best,
Mac / Mact = FctQec/FcQect
Mac / Mact = 47.54hz*1.136 / 42.66hz*1.203
Mac / Mact = 54.005 / 51.31998
Mac / Mact = 1.0523
This ratio implies its minimal I assume?
Now, volume change:
Vab / Vb = ((FctQect / FsQes) - 1) / ((FcQec / FsQes) - 1)
= ((47.54hz*1.203) - 1) / ((42.66hz*1.136) - 1)
= 56.19062 / 47.46176
= 1.1839
Or 18.39% change in volume?
Very best,
This is the simulation.
Qtc = 0.770
My measurements are of the built enclosure after this.
Just trying to see what the Qtc is now effectively, not simulated, and after stuffing to see what it is.
From my measurements and these calculations, the Qtc > 0.9 implication and the effective volume increase of about 18% don't seem to match what I would expect. Qtc > 0.9 implies a smaller volume, and an increase in 18% of effective volume from stuffing means my Qtc should go down, correct?
Very best,
I assume that's simulated with the parameters from the datasheet, not your actually measured parameters?
We know the Qt of the actual driver(s) from your free-air measurements.
How much is the difference between the datasheet values?
Correct, this is from published values.
I'll model based on the measured values. This is probably where the difference really is. I've yet to see a driver close to its measured values, unless I'm measuring incorrectly or unless my calibration is way off.
Edit: Welp, I tried to simulate the driver in WinISD with the measured values, but it won't pass integrity and fails. I think the values just don't allow the derived values to come together properly. It crashes. So I don't think I can really check this. But that said, the measured values are significantly different from published, so this is likely the problem. In reality it probably never was 0.770 Qtc and was probably over Qtc 1.0 based on measurements I'm rough guessing and came down from there, implied by calculations from measurements.
Very best,
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Or when manufactures don't cherry pick 😉
We can always determine Re, Qms, Qes, Qts and Fs very accurately and there won't be any very significant changes with that.
So it's mostly all about at what voltage manufactures determine their parameters.
Which isn't always at 0.1V unfortunately.
Also, some extrapolate Re (DC resistance), which in some cases will be very different compared to the actual DC resistance.
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OP, how did you take this measurement? driver resting on a table?
a jig needs to be used to support the driver so it is "in free air" away from other surfaces
test out your measurement setup with some 5R and 47R 0.1% resistors
It was supported on a jig so the vent pole was open and away from a surface. The only contact points were small areas on the magnet.
Very best,