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Old 20th July 2009, 06:43 PM   #1
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Default Diaphragm Resonance change with HV bias

Most of the ESLs I have built have been hybrid designs crossing at 250-400 Hz to LF dynamic dipoles or sealed boxes. For these designs, I didn't worry much about the diaphragm resonance...just made sure it was several octaves below the crossover frequency and well attenuated.

Currently I am working on some larger ESLs with the goal of extending ESL coverage down to 70-80Hz. With this in mind, the fundamental resonance of the diaphragm becomes quite important to the design of the LF response. The problem I am running in to is that the resonant frequency and Q seems to be a moving target depending on the level of HV bias applied. I guess this makes sense to me considering the bias can be thought of as adding in "negative stiffness".

The current test panel is 8" wide and 60" long with 3/32" spacing build Audiostatic(or Capaciti) style. With 1/32" felt damping I get the following results for Near Field measurement of the LF response.

HV Fs Q

3kV 55 1.8
4kV 52 1.7
5kV 50 1.6
6kV 46 1.5
7kV 42 1.4
8kV 38 1.2

Based on this data it seems that no matter how carefully you tension your diaphragm, you can't just change the HV and expect the LF response to stay the same.

Has anybody else noticed this before?
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File Type: jpg lf_hv_trend.jpg (79.8 KB, 514 views)
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Old 20th July 2009, 07:26 PM   #2
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Thumbs up pressure & resonans. adjust :)

Simple gear. It is gauged association of a resonance from tension.
Mylar tension a balloon from a bicycle. To fix pressure.
On the extremity of a magnet from the relay we braze a wire fine{thin} with a blob the weak and light.
Just as at major barrel{roll} The Beatles.
Will provide a monotonicity of action on a membrane.
We bring to a membrane. We arrest.
It is gauged a microphone and Spectralab the response
It visual it{him} visually.
We change pressure in a balloon from a bicycle
It visual as the resonance is shaded slide
We attack him{it} pressure in a balloon.
It visual what pressure in a balloon it is necessary, that the resonance was not, if is - minimumly harmful. This reaching will be better than the entering filter can
We adjust. Gives in to adjustment.
The entering filter is not necessary.
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Old 21st July 2009, 12:42 AM   #3
Few is offline Few  United States
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Well I think I've learned something. I'm familiar with the fact that the diaphragm deflects when the bias voltage is applied, even when there's no music signal applied to the stators. I've assumed that the direction of that deflection depends on small deviations from perfect symmetry in the stator-diaphragm-stator construction, or perhaps a small difference between the electric potentials of the two stators.

I--apparently erroneously--also assumed that the deflection of the diaphragm would increase the diaphragm's tension and therefore increase the panel's resonance frequency. As your data show, and the phrase "negative stiffness" implies, increasing the bias voltage actually decreases the resonance frequency. That's certainly consistent with the effect a negative stiffness ought to have, but I guess I hadn't previously paid sufficiently close attention to what was meant.

Is the bias voltage said to contribute a "negative stiffness" because increasing the voltage causes an increase in diaphragm deflection (for a given stator voltage) just as decreasing the diaphragm stiffness would, or am I still missing something?

Few
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Old 21st July 2009, 08:20 AM   #4
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Default Diaphragm resonance change with bad coating

Diaphragm resonance will also change when the coating doesn't work as it should.

That's an extreme case, but I noticed this with the deteriorating Shackman VLC-coating I have tested (See 'Esl diaphragm coating' thread).

First I thought that the Esl was loosing sensitivity because of a failure in the HV-supply. But that was not the case. It was the dying coating which caused an increase in resonance frequency. The nearly uncharged diaphragm is of course nearly non existent from an electrical point of view.

Harry
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Old 21st July 2009, 10:09 AM   #5
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The negative stiffness originates from the fact that the charge on the diaphragm will induce an equal but opposite charge on the stators. As opposite charges attract, a small deflection of the diaphragm will result in a force that tries to increase that deflection, hence 'negative stiffness'. We can lump these compliances together and as the name suggests, the negative stiffness thus has the same effect as lowering the diaphragm tension. Indeed this lowers the resonance frequency.

The magnitude of the force differs for the case where the speaker is constant charge (e.g. very high surface resistance coating) or constant voltage (low resistance coating). With constant charge the force will be linear with diaphragm displacement, with constant voltage it will not be linear because the charge on the diaphragm is allowed to increase (and it will as the capacitance increases when the diaphragm moves towards one of the stators). This means that stability is increased with very high S/R coating and larger deflections of the diaphragm are allowed.

For the constant diaphragm voltage case, the electric compliance is:
Click the image to open in full size.

For the constant diaphragm charge case, the electric compliance is:
Click the image to open in full size.

where (SI units):
A = stator area
d = spacing
V = polarizing voltage
epsilon = diaphragm deflection


If the stators are not connected then there will be no negative stiffness. Or in other words, if you power the stators from a current source there will be no negative stiffness. In reality this is not an option but fun to observe nonetheless.
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Old 21st July 2009, 03:59 PM   #6
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Quote:
Originally posted by arend-jan
The negative stiffness originates from the fact that the charge on the diaphragm will induce an equal but opposite charge on the stators. As opposite charges attract, a small deflection of the diaphragm will result in a force that tries to increase that deflection, hence 'negative stiffness'. We can lump these compliances together and as the name suggests, the negative stiffness thus has the same effect as lowering the diaphragm tension. Indeed this lowers the resonance frequency.

The magnitude of the force differs for the case where the speaker is constant charge (e.g. very high surface resistance coating) or constant voltage (low resistance coating). With constant charge the force will be linear with diaphragm displacement, with constant voltage it will not be linear because the charge on the diaphragm is allowed to increase (and it will as the capacitance increases when the diaphragm moves towards one of the stators). This means that stability is increased with very high S/R coating and larger deflections of the diaphragm are allowed.

For the constant diaphragm voltage case, the electric compliance is:
Click the image to open in full size.

For the constant diaphragm charge case, the electric compliance is:
Click the image to open in full size.

where (SI units):
A = stator area
d = spacing
V = polarizing voltage
epsilon = diaphragm deflection


If the stators are not connected then there will be no negative stiffness. Or in other words, if you power the stators from a current source there will be no negative stiffness. In reality this is not an option but fun to observe nonetheless.
First off, thanks for verifying the validity of my data. At first I thought I was losing my mind(or at least my diaphragm tension)
I had always read about people carefully tensioning their diaphragms to achieve specific resonant frequencies, but never any discussion about how it changes later once HV bias is applied to the panel.

Now that you mention it, I did notice that my test panels made with a lower resistance coating showed more variation in resonant frequency with HV than the higher resistance coated panels. I had been trying the different coatings to get a feel for their effect on LF odd harmonic distortion. I had assumed that the differences I was seeing in Fs shift were, perhaps, from inconsistent tensioning. Then I finally noticed the Fs vs HV trend while measuring distortion at various levels of HV bias and drive levels.

I had a few questions concerning your Force formulas...

1) Did you derive these yourself? or is there a reference you could point us to for further study.

2) What is the variable definition for xi?

3) Where does the non-linearity come from for the constant voltage formula?

If epsilon is the diaphragm deflection, then BOTH formulas show the Force (Fe) being directly proportional to deflection, or linear with displacement.
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Old 21st July 2009, 04:19 PM   #7
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Quote:
Originally posted by bolserst
I had a few questions concerning your Force formulas...

1) Did you derive these yourself? or is there a reference you could point us to for further study.

2) What is the variable definition for xi?

3) Where does the non-linearity come from for the constant voltage formula?

If epsilon is the diaphragm deflection, then BOTH formulas show the Force (Fe) being directly proportional to deflection, or linear with displacement. [/B]

OK...guess I should have studied the formulas just a bit more before firing off a post. I now recognize them from my physics text book and some old Peter Walker(Quad) papers.

- xi should be deflection.
- epsilon0 is Coulombs constant, not deflection.

With these definition changes you can plot an exponential rise in Fe as the diaphragm approaches the stator for the constant voltage case.

For the constant charge, Fe grows linearly with displacement all the way to the stator.

arend-jan, Thanks again for pointing me in the right direction with formulas to back up the observations.
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Old 23rd July 2009, 04:43 PM   #8
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Default Negative Stiffness

After arend-jan opened my eyes a bit, I went back thru some of the papers and articles I'd collected on ESLs. And, I found this...

Wireless World, March 1956 “Letters to the Editor”

Peter J. Walker comments on article from February,
“Distortion in Electrostatic Loudspeakers: Conditions Necessary for Linear Operation”

“…The author points out that if, with constant total charge, the diaphragm is moved mechanically then a force appears on the diaphragm. He states this force is linear with displacement, but is not due to the signal and is therefore a distortion. The force is indeed linear with displacement and acts away from the central position. This is a negative stiffness. It causes no distortion, but it does of course require the introduction of positive stiffness in order to avoid diaphragm collapse to one or other of the fixed plates…”


I also found a fairly detailed discussion of this topic by Peter Baxandall in the ESL portion of the book “Loudspeaker and Headphone Handbook, 3rd edition”. Not sure how I missed it before, but obviously my focus was on other matters at the time. I’ve attached a figure from the book that illustrates the negative stiffness effect of constant charge and constant voltage ESLs.

Looks like that P.J. Walker considered this negative stiffness when tensioning the diaphragms on the Quad ESLs to achieve the desired LF response; making the diaphragm mechanical stiffness due to tension 3.5 times as strong as the constat charge negative stiffness.
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Old 22nd November 2010, 09:25 PM   #9
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Default Negative Stiffness posts

For those reading this thread based on search results, thought I would add a link to some additional posts on the topic which include comparisons of experimental and theoretical negative stiffness trends.

Current vs voltage drive ESL?
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Old 25th November 2010, 09:31 AM   #10
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Quote:
Originally Posted by bolserst View Post

...

HV Fs Q

3kV 55 1.8
4kV 52 1.7
5kV 50 1.6
6kV 46 1.5
7kV 42 1.4
8kV 38 1.2

Based on this data it seems that no matter how carefully you tension your diaphragm, you can't just change the HV and expect the LF response to stay the same.


...
Maybe a strange idea, but could the "negative stiffness"
introduced by HV be utilised in making the effective
membrane stiffness varying over its area ?

I guess this would call for a multisectional conductive
coating, each section having noticeably different HV.

Making the membrane more compliant at its
circumference - and also ineviteably driving it with
increased force there - would change the shape of
moving at LF.

Surely not a good idea for mid- to higher frequencies.

I was thinking sort of "increasing effective membrane area"
by modfifying the LF motional pattern / distribution of excursion.


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Last edited by LineArray; 25th November 2010 at 09:37 AM.
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