# Software speaker simulation weirdness

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#### jteef

I took Dr. Leach's Audio Engineering class at georgia tech, and in the process learned a great deal about this stuff. His textbook sits on my desk at all times. So I am playing around with various drivers to be considered for my first pair of real speakers. His method for sealed box systems entails choosing the QTC.

I will be referring to the focal 15KX in the examples as it was what i was working with at the time. (i wish i could afford it!)
Vas = 280.3L fs = 25.8, QTS = 0.39, QES = .40, QMS = 9.71

anyways, Dr. Leach says to choose your QTC. so lets go with 0.707. Then estimate the value of QMC. he suggests using 5-10 for unfilled systems, and 2-5 for filled systems. so lets use 3.5.

Then calculate the electrical quality factor QEC by the equation QEC = QMC*QTC/(QMC-QTC)... .886
Then calculate the compliance ratio alpha

alpha = (QEC/QES)^2 - 1 = 3.91

then VAB is simply Vas(280.3L) / alpha. or 71.76L
and fc is fs*sqrt(alpha+1) = 57.19hz. to accomodate the effects of filling this volume must be reduced further. Leach suggests 25% for uncompressed home fiberglass insulation. So Vb = 71.76/1.25 = 57L So final box volume would be 57L + bracing + driver displacement.

This varies significantly from winISD which gives me an enclosure size of 121L and an Fc of 46.8hz(extrapolated from the phase plot...freq when phase = 90)

unibox gives 131L with an Fc of 54.4hz with Ql = 30 and Qa = 5. would QMC be the parallel combination of these two? In which case i'll recalculate the Leach way with a QMC of 4.3. I get a VAB of 81L and FC of 54.6.

It seems leach and unibox are very close with their calculation of Fc. which means both should calculate the compliance ratio similarly, but why the big difference in Vab? Both in my acoustics class and my audio engineering class, Vab was always Vas/alpha.

What am I missing? I like Dr. Leach's method because it follows with his PSPICE loudspeaker models that I use to simulate driver + crossover interactions. If it is grossly inaccurate however, I need to find something new!.

jt

#### AudioFreak

a= (Qtc/Qts)^2 - 1

Vb = Vas / a

Fc = (Qtc x Fs) / Qts

So if Qtc = 0.707

a = 2.286

Vb = 122.6L

Fc = 46.77

#### jteef

Alright, I have it figured out now.

Can somebody explain how unibox gets the volume ?

With similar QMS' (4.28) i get a box size of about 80L using the method from my textbook, the same fs, and the same alpha.

Unibox shows a "physical Vb" of 134L while leach's is 80L. using the compliance ratio from unibox to calculate Vb, you get 80L, why would they report 134L though? The box still needs to be reduced in size to accomodate the effects of the filling that you desigined for.

thanks

jt

#### jahonen

jteef,

I think there is a problem adding leak Q (Ql) into this. Because if we add that, then the system is of third order instead of second. It doesn't have one simple Qtc in same sense that second order system has. It is probably the reason why you get differing results. If you set Ql to very high value, then you should get equal results. Mr. Leach's box calculations seems to omit Ql as I have seen others to do also. I believe it is because of mentioned difficulty.

This has been a royal headache for me, as I have been working with mathematics of next generation WinISD.

BTW, you might want to play with new WinISDpro 0.50a4, downloadable from www.linearteam.org site (check programs menu). We have done (hopefully) some improvements over "classic" versions, although there is still much work which needs to be done. There is no consideration for Qa in "synthesis" phase, but at least you can play with it, as well as with Ql. The box synthesis part is probably one thing what needs complete rework.

With Best Regards,
Janne

#### f4ier

just my thoughts...

I took Dr. Leach's Audio Engineering class at georgia tech, and in the process learned a great deal about this stuff. His textbook sits on my desk at all times.

That is one book I REALLY would like to buy, unfortunately, it's not available, locally, in Australia Ordering online is still not an option due to currency exchange rates.

.... with Ql = 30 and Qa = 5. would QMC be the parallel combination of these two?

No.

Can somebody explain how unibox gets the volume?

I'm not entirely sure, but I think Unibox is based on the model described at http://www.hal-pc.org/~bwhitejr -- it might give you an idea of how Unibox works. Kristian might have some time for a comment or two

This has been a royal headache for me, as I have been working with mathematics of next generation WinISD.

I've just tried the new winISD and I think it's great that it is finally offering more graphs aside from gain and spl I can't wait to try the finished product. (And yeah, the math for this 'hobby' is a real headache!)

I think there is a problem adding leak Q (Ql) into this. Because if we add that, then the system is of third order instead of second.

I guess it depends on the complexity of the Ql model. The simplest model, being a resistor to ground, won't change the order of the model.

Mr. Leach's box calculations seems to omit Ql as I have seen others to do also. I believe it is because of mentioned difficulty.

Leach's models can be as simple as a resistor, with an infinite resistance in the case of a well-sealed box, or as hair-raising as a full-blown thermo-mechanic circuit block when trying to model the full effects of fibre filling. His model for box filling is quite easy to calculate, but getting the necessary details like the aerodynamic drag coefficient, resistance, compliance and mass of each single fibre is 'almost' impossible... some simplifications and assumptions have to be made... that's why I haven't touched the closed-box feature of my simulator.

Speaker design is like second nature to Leach. I think, if his methods say, "Vb = 71.76/1.25 = 57L" then you can rest assured that the results won't be disapointing.

#### jteef

I did some more simulations in Unibox, and oddly, the Focal KX15 was the only driver that didn't make sense in the simulations. Who knows...

leach doesn't go into the aerodynamics of the filling in his textbook

Just the density of filling, the volume ratio of air to filling, and the specific heat of air, and of the filling. In the model, they are neatly integrated into the acoustical air mass of the enclosure, and the acoustical losses in the enclosure.

jt

#### f4ier

jteef, have you seen his paper -- Electroacoustic-Analogous Circuit Models for Filled Enclosures -- JAES Vol.37, No.7/8 July/August. It's a great article, but a bit too demanding of data about the candidate filling

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