Beyond the Ariel

Kolbrek said:

I view it like this: the horn throat impedance forms the load for the compression driver. For steady-state simulations, the average complex throat velocity and pressure can then be found if we know the throat impedance, the parameters of the driver, and the input voltage. Changes in the throat impedance will be reflected in the throat velocity, diaphragm displacement, electrical impedance and so on, so there is a coupling.

-The parameters for the waveguide (throat diameter and angle, length from the throat to where the mouth radius starts, and the waveguide angle [theta0])
-The end areas and length of the internal driver flare, including the phase plug, and if the flare is conical or another shape
-The driver parameters, at least Sd, Bl, Cms, Rms, Mmd, Le and Re
-The volume and size of the rear chamber
-The volume and size of the front chamber

I assume the mouth flare radius is 4 inches, as per your earlier posts.

Best regards,

Bjørn


Yes, the above procedure works, but you just can't assume that the complex throat velocity is independent of the load for a real device, especially at or near the lower cutoff. That was more my point. The resonance that you show presents a large load which reduces the velocity of the driver - an effect not shown in your simulations.

The throat of my larger waveguide is 1" and has a 6 degree entrance. It goes to 45 degrees to a mouth that is 15" in diameter. There is a 4" radius at that junction. Hence the radius would start at 5.6 " from the throat and end at the baffle which is at about 7" from the throat.

The drivers internal flare has to be estimated, but should be close to 1" at the open end, a 6 degree conical section about 2" long, but it could be a little shorter than that. I don't have an exact model of the DE250. I could measure it and get you those exact numbers but that would take some time. I have a model of a typical driver - lumped parameter they are all close to the same. My estimate for the DE250 would be:
Sd = 15 cm^2
Bl = 1.8 Tor
Cms = 1.7 x 10-7 m/Nt (approximately)
Rms = 1 ohm (also a guess)
Mmd = 15 grams (a decent guess)
Le = .11 mH
Re = 6.3 ohms
The volume and size of the rear chamber = just consider this as part of the diaphragm compliance
The volume and size of the front chamber = this is also hard to get, but you can assume that it is about Sd x 1mm = 1.5 cm^3 or less.

When you use these parameters you can adjust them from the simulated impedance curve versus the published data from B&C or your own measurements. I will do that too when I get a chance to see how eell they fit.


I thinks thats all you need.

Thanks - looking forward to it.
 
Forums like DIYAudio are one of the treasures of the Internet.

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There are CEO's and managers throughout corporate America who are confident once the Powerpoint presentation is dreamed up and pitched and sold, the hard part is already done. The wreckage in the military, diplomatic, financial, and economic spheres is mute testimony to the quality of managerial "thinking" - if it can even be called that - over the last decade.

Although we are more heavily cost-constrained than the corporate world, there are no MBAs, managers, marketing directors, magazine reviewers, or a legacy base of customers to satisfy. Thus no reason we can't outperform commercial products, once we leave behind "DIY is only for beginners or cheapskates" mindset.
 
Lynn Olson said:
Forums like DIYAudio are one of the treasures of the Internet.

There are CEO's and managers throughout corporate America who are confident once the Powerpoint presentation is dreamed up and pitched and sold, the hard part is already done.

Yes nicely said!
I've been there when the VP's typical pitch to the troops after the sale, "Now all we have to do is execute". Sometimes I think US management is in different world and language to go with it.
 
Earl,

The driver parameters look a bit odd - but perhaps I'm using the wrong units? I ran a lumped parameter plane wave tube simulation with these parameters, and the response is in the form of a sharp spike at 3.1kHz.

So just to make sure:
Bl = 1.8 Tesla*meters
Cms = 1.7 x 10^-7 meters/Newton
Rms = 1 Newton*second/meter (or should it be electrical ohms?)

or did you use other units?

To me, both Bl and Cms seem to be too low. The values above gives a driver with a Qes of over 500.

Best regards,

Bjørn
 
Hello Bjorn,

a MMd of 15grams fro the DE250 seems to me an indecent guess.

I am using according to Kinoshita a Mmd value of 1.6 grams for my model of TAD TD2001.

Best regards from Paris, France

Jean-Michel Le Cléac'h



Kolbrek said:
Earl,

The driver parameters look a bit odd - but perhaps I'm using the wrong units? I ran a lumped parameter plane wave tube simulation with these parameters, and the response is in the form of a sharp spike at 3.1kHz.

So just to make sure:
Bl = 1.8 Tesla*meters
Cms = 1.7 x 10^-7 meters/Newton
Rms = 1 Newton*second/meter (or should it be electrical ohms?)

or did you use other units?

To me, both Bl and Cms seem to be too low. The values above gives a driver with a Qes of over 500.

Best regards,

Bjørn
 
Jmmlc said:
a MMd of 15grams fro the DE250 seems to me an indecent guess.

I tend to agree, especially considering that the Beyma 102Nd 10" paper cone driver is specified with a moving mass (possibly including air load) of 33 grams.

From other data I have seen, typical moving mass for 1" compression drivers seems to be in the 1-2 grams range. Perhaps it should be 1.5g?

Bjørn
 
Kolbrek said:
Earl,

The driver parameters look a bit odd - but perhaps I'm using the wrong units? I ran a lumped parameter plane wave tube simulation with these parameters, and the response is in the form of a sharp spike at 3.1kHz.

So just to make sure:
Bl = 1.8 Tesla*meters
Cms = 1.7 x 10^-7 meters/Newton
Rms = 1 Newton*second/meter (or should it be electrical ohms?)

or did you use other units?

To me, both Bl and Cms seem to be too low. The values above gives a driver with a Qes of over 500.

Best regards,

Bjørn


Bjorn - I checked on the moving mass and that was a typo, its more like 1.2 grams. Compliance would then be about 2 x 10^-5. See if those numbers work better. I got the flux data from the B&C website and that number is just the flux density not BL. BL would be more like 18. Sorry for the mix-up.
 
Thanks Earl, that looks better.

I attach the resulting lumped parameter PWT simulation resulting from this. Does it makes sense?

I have included an internal driver flare, per your suggestion 2 inches (5.08 cm) long, 2.54 cm exit diameter (S=5.07cm^2), and a 1:10 compression ratio, giving a start area of 1.5cm2.

Bjørn
 

Attachments

  • de250_pwt.gif
    de250_pwt.gif
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Agree the overall waveguide should make a much larger difference than throat length of the driver. I thought a longer driver throat would provide a bit lower extension.

The top end is what I'm really curious about...no real clue how zero/long driver throat lengths would change performance on a short/zero throat WG like the OS or conical.
Paul
 
gedlee said:

.....
The volume and size of the rear chamber = just consider this as part of the diaphragm


For a first order effect yes, and maybe good enough for the simu intended – I agree.



Looking slightly under the surface there are interesting things going on with drivers having a non dampened or a only slightly dampened rear chamber.

If we recall what John Kreskovsky brought into our mind about Doppler modulation – and take this a little bit further - we see strange things happening in the time domain.



To put things into perspective, I set up a quick and simplified simulation.

What we will see is that the SPL reflected by the rear chamber wall and transmitting through the diaphragm as a kind of mirror source adds another - pretty unique - sonic pattern to such drivers.

In order to show the effects happening, I set a extraordinary high modulation depth for the Doppeler_IM in this simulation.






An externally hosted image should be here but it was not working when we last tested it.


In the first picture we can see how Doppler-IM varies frequency by comparing the elecrical input signal of the voice coil (GREEN plot) to the SPL output of a speaker membrane (RED plot) – nothing very new.

Here it is assumed that *only* the front of the membrane is radiating – all the SPL radiating from the back side of the membrane is dampened to dead.

We see the already known frequency modulation of Doppler IM.






An externally hosted image should be here but it was not working when we last tested it.


In the second picture we can see what happens if we overlay the SPL radiating from the front with the SPL mirrored at the chamber.
The membrane is considered to be completely transparent in this case - *and* no dampening of the rear chamber at all.
The delay is set to roughly 12mm / half an inch to mimic a rear wall in the distance of 6mm / a quarter inch behind the diaphragm.

The SPL of the front (GREEN plot) and the delayed SPL from the back (GREEN plot) have inverse frequency modulation as can be observed immediately.
The sum of both frequency modulated SPL's (RED plot) result in a *pure* amplitude modulation !
Its easy to see that the summed SPL (RED plot) sine curve is exactly in between of the green ones.

Wow – surprise, surprise– we get *amplitude* modulation from Doppler IM !






An externally hosted image should be here but it was not working when we last tested it.



In the third picture we see demonstrated that in reality we more likely will end up with a mix of amplitude *and* frequency modulation.
Here I attenuated the mirrored SPL – in order to mimic some dampening in a rear chamber and also a transfer loss through the membrane – i.g. the membrane isn't considered to be 100% acoustically transparent

If we compare the SPL overlay plot *without* dampening (GREEN plot) that does *not* have any frequency modulation – as shown in the picture above – with the SPL overlay plot *with* dampening (RED plot) – the variations in frequency become most apparent.

The amplitude modulation is slightly less though – kind of trade in.


Keep in mind:
Doppler IM *can not* be avoided – it always happens with speakers.


Michael
 
There is no end of the hypothesis that one can make about "problems" in loudspeakers. What one has to do is to "close the loop" by showing their significance in terms of audibility.

Since in blind tests (published AES paper on Distortion in Compression Drivers) no listener could detect nonlinear distortion in any of three different compression drivers, I would have to conclude that any effects like this - assuming that they do actually occur - are not audible.