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Old 12th March 2015, 06:19 PM   #1
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Default Accessible acoustics theory for electrostatic microphone?

Hi all,

I'm in search of some literature that describes the acoustics in "technical layman's terms" for an electrostatic loudspeaker playing into a cabinet on the backside. It would also be very helpful if one of you know of e.g. a webpage/calculator of some kind which could assist in calculating the resonance frequency with respect to:

- cabinet volume (also a vented system),
- wire/mesh damping,
- the tensioning of the membrane,
- thickness/weight of the membrane
- and other relevant parameters ... ?

Hmmm... I realize I may be asking "some" here but hope one of you may now about these aspects of electrostatic design ...

Have a good day (or evening as it is here in Denmark)

Jesper
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Old 13th March 2015, 07:29 AM   #2
Calvin is offline Calvin  Germany
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Hi,

IIrc P.Walker described that issue in a understandable way in his article "Wide range electrostatic loudspeakers".
In short, due to the extremely low mass of a ESL membrane a classic CB casing rules out for all, but highly xovered hybrids.
If the ESL is intended to reproduce LF also Walker suggested kind of tapered, dampened Transmissionline.
Think of something similar to the B&W Nautilus.
Under all circumstances should it be a design where nothing of the backside sound is reflected back to the membrane.
Considering the associated wavelengths simply think BIG

jauu
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Old 13th March 2015, 11:38 AM   #3
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Hi Calvin,

... I'm tempted to say "as always" thanks for your very useful input I found the articles you refer to from Peter Walker and have read them (not all understood in one read-through though).

Quote:
Think of something similar to the B&W Nautilus.
That has actually been my thought, and along this line also to not have anything reflecting back towards the electrostatics' membrane.

I'll just consider how to progress but reading Peter Walker's article suggests that I have been in the (for me) right direction.

Have a good weekend when you get to that Calvin ;-)

Jesper
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Old 13th March 2015, 01:01 PM   #4
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I don't think you meant "microphone"?

In order to reproduce bass, most ESLs are fairly high Q designs. Talking T/S parameters.

One could measure the ESL's T/S parameters more or less the same way one tests a dynamic speaker. This would tell you a lot about the effect at LF for an enclosure.

The idea enclosure for an ESL is likely to be and IB (infinite baffle), since then the rear energy never reaches around to the front to cancel.

The Nautilus idea is simply an approximation of an IB...

As far as calculating things like tension, I suppose this is possible, but what the calculations will look like are generic equations for a flat membrane with a given stiffness and tension. It's more practical to do it empirically, I expect. MathCad can likely be set up to automate the process if you wanted to calculate it. But to duplicate the results you'd need a fairly precise way to do the build, and the membranes do stretch anyhow... one is counting on the electrostatic force to dominate in terms of control, for the most part. Of course the bass rolloff will still be dominated by the results of the tension vs. mass vs. size of the ESL cell.

that's my seat-of-the-pants thoughts on the matter...
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Old 16th March 2015, 07:41 PM   #5
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@bear:

Thanks also for your reply

Quote:
I don't think you meant "microphone"?
As it is I actually meant both "microphone" and "loudspeaker" but somehow my words slipped between the headline and the rest of the text ... Hopefully a rare occurrence However, the link Calvin gave to Peter Walker's article was very helpful so I got a reply to many of my question regarding both the "microphone" aspect and the "loudspeaker" aspect reading that article.

Quote:
One could measure the ESL's T/S parameters more or less the same way one tests a dynamic speaker. This would tell you a lot about the effect at LF for an enclosure.
Now, this is interesting but not something I'm very familiar with ... I do, however, (hopefully soon) have a fine measurement microphone (B&K 4133 capsule) and so should be able to measure down to about 3 Hz and up to at least 40 kHz (frequency response appears to be completely straight up to 40 kHz). I don't have immediate access to an anechoic chamber though so would need to find an alternative way of measuring a small membrane ESL's frequency and impulse response. Besides LF resonance frequency information I would be looking at breakups, and HF resonance frequency.

I also have a frequency oscillator going from ~0.7 Hz to ~110 kHz so may provide a signal for this. And I was thinking of just measuring where the LF & HF electrical resonances are as a way of identifying the acoustic ones as well. However, if you, or one of the other DIY'ers here know of a better kitchen-table-like-reasonable solution I'd appreciate hearing about it

Thanks again for your feedback!

Cheers,

Jesper
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Old 17th March 2015, 06:12 AM   #6
golfnut is offline golfnut  New Zealand
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Hi Gentlevoice

T-S parameters make absolutely no sense in the context of electrostatic speakers and microphones - the physical models of the two types of speakers are completely different.

If you want to find a model for a ESL resonance, the best place to look is a book that explains the physics of drums. A normal (open-backed) ESL - it is essentially a drum with an open back. If you close the back by putting a cabinet around it, the physics will change A LOT.

hope this helps
Rod
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Old 19th March 2015, 07:58 AM   #7
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Hi Rod/golfnut,

Hmmm... suppose you have more than one interest or hobby

Quote:
T-S parameters make absolutely no sense in the context of electrostatic speakers and microphones - the physical models of the two types of speakers are completely different.

If you want to find a model for a ESL resonance, the best place to look is a book that explains the physics of drums. A normal (open-backed) ESL - it is essentially a drum with an open back. If you close the back by putting a cabinet around it, the physics will change A LOT.
Just in case you read this I would be interested in any possible links or references you may have on this (drum physics; ESL with a back - other than calvin's Peter Walker article if you know this one?) ....

Have a good day

Jesper
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Old 19th March 2015, 08:50 AM   #8
golfnut is offline golfnut  New Zealand
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Hi Jesper
First: head to Links & info - The wire electrostatic Loudspeaker page where you'll find a copy of Baxandall's paper on ESLs. Baxandall worked with Walker on the ESL 63. The paper is an absolute mine of information - the best resource on ESLs.

Second, I've just done a bit of fishing around. Most acoustics texts have the basic theory for the stretched membrane, which describes how to calculate the various resonant frequencies for a conventional ESL with an open back and minimal baffle. If you send me a PM, with your direct email, I'll send some pages.

The ESL is a little more complicated than the simple membrane because the electrostatic motor is inherently unstable without some diaphragm tension - the effect is equivalent to negative tension so that the resonant frequencies are lower than the model says, but the physics is the same. Baxandall discusses the stability problem in some detail. The most important resonance is the lowest one, because it has the least natural damping.

Third, the nearest thing I can think of for a model of an ESL with a cabinet behind it is a kettle drum - highly resonant things. I was unable to find anything useful in a text book. But if you use google scholar to search on kettledrum, you'll pick up a couple of acoustics papers describing them - the papers are pretty impenetrable unless your maths is good, but if you read it slowly while sipping on a nice red and mumble ah ha to yourself every now and again, you'll get the gist. Its not a simple problem.

regards
Rod
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Old 20th March 2015, 06:13 PM   #9
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Hello Rod,

Thanks also for the additional comments & suggestions and the link to the Baxendall paper. I've just briefly read through it which made me realize that if I am to more thoroughly understand what it says I need more time (& focus) to read it ... I would, however, be interested in the additional pages you mention and will send you my email in a PM.

Quote:
- the papers are pretty impenetrable unless your maths is good, but if you read it slowly while sipping on a nice red and mumble ah ha to yourself every now and again, you'll get the gist. Its not a simple problem.
;-) Well, weekend is approaching and admittedly I need a break - so I may not read about this over the weekend but probably/hopefully will have the opportunity to sip on something delicious ... Don't know what a "red" is though, but maybe a good tea or the like (teas are my favorites ...).

Best wishes from up North :-)

Jesper
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