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Old 2nd May 2010, 03:30 PM   #1
gpapag is online now gpapag  Greece
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Hi all

We are able to plot the impedance versus frequency of a speaker either in air or installed on an enclosure.

We can thus have a set of impedance parameters of this speaker for every frequency in Z (Ohm) and V to I Phase Angle (degrees) data, or in R, Zl, Zc (Ohms) and Zx to R Phase Angle (degrees).

Is it possible from all these data sets to reverse engineer (construct) the electrical network from L,C,Rs (equivalent circuit) which will exactly model this speaker in this very installation?

Best Regards
George
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Last edited by gpapag; 2nd May 2010 at 03:53 PM.
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Old 2nd May 2010, 04:26 PM   #2
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Sure, that's how the Thiel-Small calcs work.

Click the image to open in full size.
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Old 2nd May 2010, 08:38 PM   #3
gpapag is online now gpapag  Greece
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Hello Dennis

Thanks for contributing.

One question please.

How do you manage to assign values to the electrical model constituents (Ohms on R, mF on C, mH on L), when your calculations –using the formulas at the bottom of the schematic- are in Length, Mass, Force ect?
I tried to use this h ttp://en.wikipedia.org/wiki/SI_derived_unit

Farad=m−2∙kg−1∙s4∙A2
Volt=m2∙kg∙s−3∙A−1
Ohm=m2∙kg∙s−3∙A−2
Henry=m2∙kg∙s−2∙A−2


But I don’t come to any meaningful units.

Nevertheless, even if I was able to assign values to the electrical symbols, this wouldn’t be the answer to my question.

For, this is fixed model ( I have seen others as well, representing speakers on other enclosure types), onto which one assigns values derived from calculations.

What I have asked is, if it is possible to derive a speaker electrical model from it’s impedance versus frequency data

Best Regards
George

Last edited by gpapag; 2nd May 2010 at 08:41 PM.
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Old 2nd May 2010, 10:15 PM   #4
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T/S parameters are calculated from the impedance curves by the software. Behind the scenes, it is calculating electrical components and converting them to the parameters we are used to. Linkwitz's pic shows the relationships between the two.
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Old 3rd May 2010, 12:39 AM   #5
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So you have 2 sets of readings, one in free air and one in a sealed enclosure of known volume?

The impedance curves are already showing you something. You can see the free air resonant frequency fs

You can see the resonant frequency of the closed-box system fc

You can calculate Qts and Qtc. These are the ratio of reactance to resistance at fs and fc

From these you can calculate alpha = ((Qtc/Qts)^2) -1

You know the box volume Vb, so you can calculate Vas = alpha * Vb

You know RE

Some of the other parameters are directly measurable, such as cone effective area.

You can easily determine the cone mass by adding a weight and remeasuring fs. This, with the cone effective area A, the density of air and the speed of sound will tell you Cms. And so on... As you measure and calculate more values, you will get to cross check parameters. Once you determine values for the impedance simulation, you can compare the result with your measurements.

This isn't my field. Do you have Dickason's book? I'm just picking the maths out of it. Have a look on Rod Elliott's site too.

w
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Old 3rd May 2010, 03:29 AM   #6
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I don't know if there's any foolproof deterministic way to do this. I divide the curve up into regions like the resonant peak, figure out the Q, design a generic tank circuit, then scale it to the correct impedance. The rest of the curve is a slow rise at some dB/octave, so that's done similarly. No doubt there's some better way, but I just use the basic L-C formulas and charts in almost any edition of Terman. You do a model of a crystal in a similar manner and some of the values can be remarkably large. Check your results with a quick plot in LT Spice or similar.
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Old 3rd May 2010, 03:45 AM   #7
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Old 3rd May 2010, 04:44 AM   #8
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Old 3rd May 2010, 05:00 AM   #9
godfrey is offline godfrey  South Africa
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Hi George

To convert between mechanical and electrical impedances, the "magic number" in the specs is BL.

BL = strength of magnetic field in the gap * length of voice coil wire in the gap
and BL = Force on diaphragm / current in voice coil
and BL = Induced voltage across coil / diaphragm velocity

So: Induced voltage / Current = BL * BL * Velocity / Force

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To get back to your original question (if I understand it correctly): I think in general it could be extremely difficult or impossible to treat a loudspeaker system as a "black box" and derive the equivalent circuit purely from impedance measurements.

For simple systems e.g. sealed box or reflex, one could pick the appropriate "off the shelf" equivalent circuit and fill in the values.

For something like that shown below (a horn) it's not so easy. One could (with difficulty) invent an LCR circuit with similar impedance and phase curves, but it would not be equivalent - the transient behavior would be totally different.

Cheers - Godfrey
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Old 8th May 2010, 10:41 PM   #10
gpapag is online now gpapag  Greece
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Hello all
Thank you for your responses.

I have looked on the internet for a possible answer to my quest (which is as godfrey wrote “treat a loudspeaker system as a "black box" and derive the equivalent circuit purely from impedance measurements”.

My wish is, this electrical circuits that is born out of the measured electrical impedance of the driver/enclosure, to be used to study the effect that the value of each component has on the outcome. Also, to calculate/simulate the acoustic frequency response of this driver/enclosure..

There are some less demanding utilizations of this model, e.g. the study of the amplifier and/or x-over interaction with this model.


It seems that indeed all the software packets that deal with speaker/enclosure simulation, are adopting some electrical model of the speaker driver and some electrical model for the enclosure.
Alas, these models ( their structure and the components value ) are not “accessible” by the user.

I understand that even if the software packets were making their models accessible, the success would depend entirely on the precision (adequacy ?) of the embodied model.

Yes, there are some simulators, which predict the acoustic output of a certain speaker (modeled by entering it’s T/S parameters).

This prediction is OK but only for the bass range.
We may optimize the bass response using these simulators and the actual acoustic results may- in the bass range - follow the modeled response, but I have found in the proccess of building loudspeakers, that the midfrequency response (sound) may be dramatically affected while optimizing the bass range acoustic response.
The simulators do predict some changes in the midfreq. Range, but only through the harmonic series of the low resonance frequency of the speaker/enclosure system.

I do not think that this harmonic series is enough to explain the acoustic effect the enclosure imposes on the midfreq. Response of a speaker. I suppose that this is attributed to the lack of a very detailed equivalent circuit.

For example, I have seen on the various published speaker/enclosure equivalent circuits, the radiation acoustic resistance of the cone to be modeled by a resistive element. Isn’t this not an oversimplification (as much as is the use of a pure 8 Ohm resistor to model a real speaker as an amplifier load)?

What do you think? Are the published speaker/enclosure equivalent circuits detailed enough to let us model speakers over an extended frequency range, or there is a need for a more precise customized model generation ?

Best regards
George

Last edited by gpapag; 8th May 2010 at 10:45 PM.
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