Single Stator Electrostatic Headphone - issues?

[gentlevoice]

Hey Diy'ers,

I've made this stator to be used for a single stator electrostatic headphone (illustrated in attachments).

However, I realize there's some writing here at DIYaudio & also elsewhere about single stator headphones having higher distortion than two stator designs, yet can one of explain why this should be so?

My own thoughts on this are:

1. The full stator rod surface is very, very close to the membrane so the electric field will vary very little when the membrane moves. The membrane is a high resistance type.

2. Also, since the membrane is very close to the flat stators the electric field variation when the membrane moves will be a linear function and not a square function as it would have been had the stators been an electric point source relative to the membrane. I have attached an illustration of this.

So, I wonder if the high distortion considered to be associated with single stator ES headphones somehow could be a remnant of the past - or if there are other factors that I don't take into consideration?

Insights appreciated

Jesper

[gentlevoice]

Hi again,

I just noticed that I've posted a thread here with a similar question some time ago. If you are interested it is here:

Single stator electrostatic headphone.

My apology for this - have been looking into many topics lately so it slipped... However, the link in post #2 by Godfrey is no longer active so if one of you knows of a new link for a similar overview I'd appreciate this.

Best wishes,

Jesper

[Calvin]

Hi,

both Your assumtions are wrong.
1) the electrical field density varies quadratically with distance. Its just that the field strength increases with smaller D/S-distance, hence the force acting upon the membrane increases with smaller distances. The quadratical relationship applies to any position of the membrane. As such assumption 2 doesn´t apply also. It is just so, that a smaller range of membrane excursion also means less variation in electrical field strength hence less variation of force. Ever decreasing the excursion and the movement approaches a linear movement (though it actually never reaches the linear condition). It is the same as calculating the Derivative of a mathematical function. Since distortion-free working required a true linear relationship, low THD can only be achieved within a very small excursion range.
This should also answer Your last Q. No, physics haven´t changed since the early days.
SE-ESLs inherently distort.

jauu
Calvin

ps. The second sketch contains a mistake. The formula for a circular membrane surface is Pi x r². In praxis under biased conditions the shape would rather follow a chain-contour. But for small excursions the circle formula suffices (talking about a few tenths of an mm). The surface does indeed change but by a miniscule and insignificant amount only. What changes considerably though is the capacitance of the ESL capsule.

[godfrey]

Hi Jesper.

That's a beautiful stator. How did you make it? It looks like some kind of plastic so I guess you'll have to apply some sort of conductive coating?

Originally Posted by gentlevoice

The full stator rod surface is very, very close to the membrane...

Problem 1: Unless the membrane is stretched very tight, it will get sucked on to the stator.

The membrane is a high resistance type.

Problem 2: That won't work, it needs to be relatively low resistance. The resistance and the capacitance between the membrane and stator form an electrical low pass filter. If the resistance is too high, the treble will be rolled off.

As explained in the other thread, the distortion is primarily because the force on the membrane is proportional to the square of the voltage between it and the stator. It's not a linear function, even ignoring the movement of the membrane.

Cheers - Godfrey

[gentlevoice]

Hi both,

& thanks for your replies ;-)

@godfrey: Thank you also for your kind words about the stators I really like the shape myself - it appears aesthetically harmonious and appealing to me, and I hope the shaping is also feasible sound-wise. E.g. the long/short axes are dimensioned so that their longest distances corresponds with the frequency distance of a fifth on my piano - the tonal distance that sounded most pleasing to me. The shape is an ellipse and so is the shape of the rods crossing the frame (long axis perpendicular to the membrane surface - to stiffen the rod on the axis of membrane movement). Hope this supports the sound ...

As it is I made the stators in Moi3D:

MoI, 3D modeling for designers and artists

If you are interested there's a free 30 days trial version which can be downloaded from their site. To me it's quite intuitive to use compared with other CAD softwares I've been able to try (not many, though).

The reason why they look a bit plasticlike is because the picture attached is a screen-dump I made while looking at the stator in Meshlab - I hope to make them either in copper or silver so the attached picture is of a model not the actual stator.

Regarding my question I found out yesterday that the formula for the force between two electrical point sources is:

F=q1*q2/(4*pi*vacuum permittivity*radius(squared))

So, assuming that this - or a similar formula -is the formula that is also used here, I can see that it is a squared relationship.

Problem 2: That won't work, it needs to be relatively low resistance. The resistance and the capacitance between the membrane and stator form an electrical low pass filter. If the resistance is too high, the treble will be rolled off.

And this is what made it dawn on me "why?" not to use a single stator (I hope ). If the membrane is high resistance - and there's only one stator - then the power available to move the membrane is very low (the membrane is a high value series resistor). Whereas if there's a second stator the energy can be transferred through this stator - grounded or not. Right? And the efficiency for a grounded stator vs. +/- driven stators is a loss of 6 dB SPL (half the level) - could it be so?

I also remember reading about why a low resistance membrane in a normal EL speaker would lead to distortion. I can't remember the exact reasoning but might it be so that the need for a low(er) resistance membrane on a single stator ELS is the main reason for the distortion compared with a double stator ELS?

Problem 1: Unless the membrane is stretched very tight, it will get sucked on to the stator.

Hmmm... can you say a bit about why this is not an issue with the double stators?


@calvin: Thank you also for replying ;-) Part of your reply puzzles me, though, so just to clarify:

The formula for a circular membrane surface is Pi x r²

I looked it up in my high school formula collection and yes it is a (4)*pi * r(square) relationship.

1) the electrical field density varies quadratically with distance.

I'm puzzled about this ... I would say that this is the case if it's a circular surface because the surface area increases quadratically with the radius and the field "density" is now distributed across a larger surface (see above). However, in a plate capacitor the electrical field "density" is the same anywhere between the two plates - as far as I understand. And an ELS resembles a plate capacitor more than a sphere...

would rather follow a chain-contour.

I'm not sure what this is ... In Danish chain is "kæde" and in German I think it would be "Kette". But never mind - I hope I now have a grasp of why a single-ended ELS may be compromised from a theoretical point of view ...

Again, thank you both for considering & replying & best wishes for your day,

Jesper

[Calvin]

Hi,

the area of a circle is Pi times r². The factor 4 relates to the surface area of a sphere.
You´re right though about field density. E = V/d , hence a linear relationship of field intensity over plate distance. I used the wrong term. Meant was not field density but Force.
The force is: F= Q x E (Charge times field density), with Q= C x V (capacitance times applied Voltage)
This leads to F = C x V²/d.
With C = epsilon0 x A/d (epsilon0: 8.854exp-12 F/m, dielectric constant of vacuum, A: Area of ESL plate, d: distance of ESL-plates)
F becomes: F = epsilon0 x A x V²/d²
Hence the inverse quadratical relationship of Force over distance.

If the membrane is high resistance - and there's only one stator - then the power available to move the membrane is very low

Not power but current. The alternating signal current charges/discharges the ESL-capacitance up to the applied voltage. The more current the faster the process of charging and discharging happens. Reducing the current with a large resistance slows down the charging --> reducing bandwidth.

I can't remember the exact reasoning but might it be so that the need for a low(er) resistance membrane on a single stator ELS is the main reason for the distortion compared with a double stator ELS?

The reason is within the drive principle, if it is either constant voltage or constant charge.

Look at the formula Q=CxV and the effect of Q on the force-relationship. With a low resistance diaphragm, the ESL runs under constant voltage condition, hence Q variies. With a high resistance (or even more extreme an electret membrane) Q remains constant. Then the Force is proportional to the field density (d beeing the distance of the fixed ESL-plates of a symmetrical ESL. So d remains constant also)

would rather follow a chain-contour.

If You take a crossection of the membrane and its contour this would be a straight line if no voltage is applied. If voltage is applied the membrane bows towards the fixed stator plate. It takes up a contour similar to a chain which is fixed at both ends. Thats a similar but still different contour compared to teh circular crossection of a sphere. The change of the bowed membranes surface area compared to the no-signal circular area is insignificant in this application. It may though be significant with regard to the distribution of charge over the membrane surface. The charge concentrates where field density is higher, which gives a self amplification effect of the forces with low-ohmic membranes where the excursion of the membrane is highest.
A high ohmc resistance coating of the membrane reduces the movement of the charge. It virtually fixes the charge locally.

I like the shape of Your stator. But what are those three ´ears´ and teh small beam at the lower edge for? Are thy meant as fixation points?
How do You intend to produce the really complex shape of the stator? Looks like a task for a rapid prototyping printer to me.
How will You create the conductive surface and how will You insulate it?

jauu
Calvin

[gentlevoice]

Hey Calvin,

Wow - thanks for outlining the theory behind. When I read it I can see that I'll have to ponder the contents and its implications so probably won't comment (if any appears) in the days to come ...

However, you also ask some questions about the stator and I can say that:

- The three "ears" (they may like being called this ;-)) are for fixation. I've chosen somewhat random varying distances between them to break up waves in the material. I intend to fix it firmly on one of the ears and less firmly with the other two ears (like single-point firm spike for a loudspeaker).

- The small extrusion at the bottom is for soldering the amplifier wire onto the stator.

- Regarding making the stator I was thinking of casting it from a model made by a 3D printer. Probably in copper but I've also been considering silver since it's less prone to tarnishing. I've had a model 3D printed by Shapeways (with an additional support on the non-membrane side) and to me it looks fine except that there was a deep curvature on the surface where the membrane is to be mounted. So I can't use it for casting but was positively surprised to see the level of detail in the printing. From their selection of materials I chose strong & flexible plastic which has a somewhat grainy surface. This surface is not ideal for a casting but it was a trial and they have other materials. BTW they also do castings in bronze I think - price is about a 100 EUR whereas I paid ~ EUR 22 for the plastic model including shipment to Denmark.

- for insulation between the stators and the membrane I'm currently considering plain paper... Very low dielectric coefficient, readily available, may absorb moisture but only from the small outside surface area towards the membrane, probably an even thickness, easy to work with.

Now that you have explained some theory related to single stator ES headphones I might have to move the "ears" so that they are symmetric allowing for two stators to be assembled together ...

Hope this answers your questions ... ;-)

Jesper

[oshifis]

The formulas of Calvin are correct, but they will give non-constant F and hence 2nd harmonic distortion. In the case of electrostatic transducers we want to keep Q constant, so that we get linear displacement with applied voltage. The electrical power is converted to mechanical movement of a constant charge in the electrical field. All electrostatic transducers have high resistance (constant charge) diaphragm. Please correct me if I am wrong.

[godfrey]

Originally Posted by gentlevoice

Hmmm... can you say a bit about why this is not an issue with the double stators?

If the membrane is centered between the plates, it will be equally strongly attracted to both of them, so the forces cancel.

Interestingly, if it's not centered then the forces don't balance and the membrane is pulled more strongly towards whichever plate it's closer to. So the electrostatic forces act as a kind of anti-spring, partly counteracting the stiffness due to the membrane tension.

[Calvin]

Hi,

Yes, a conductive coating of the membrane (and low ohmic HV-bias supply to be precise) leads to non-constant Q, non-linear F and THD. A conductive membrane but a high-Ohmic HV Bias-supply lead to a constant amount of charge on the membrane, but uneven distribution over the surface area of the membrane, which also leads to uneven distribution of F and an increase in THD.
Only a high ohmic value coating distributed evenly over he membrane surface guarantees for constant and locally fixed charge. Then F is proportional to Vsignal and THD becomes minimal.

In a symmetrical ESL the membrane would stay centered, because the attracting forces of the two stators upon the membrane would cancel. Would, if everything were theoretically perfect. In praxis, the membrane will be pulled towards one stator, the harder the higher the bias voltage level. Unfortuantely we want and need as much bias as possible, since this immediately effects the efficiency of the panel and efficiency is the mantra of any good ESL.

All electrostatic transducers have high resistance (constant charge) diaphragm

Most ESL work under the constant charge premise, but there were and there are ESLs with low ohmic membranes. The older Beveridge, APS, Rennwald, Final and the actual Phios (which are Finals under new name but without the burdon of service for broken finals ) and maybe more. The latter two wouldn´t function with high-R membranes, they are true constant voltage ESLs with all the inherent deficiencies, regardless of what their marketing department tries to tell us.

Jesper, I wouldn´t cast the stator in metal, but just metallize the stator surface toward the membrane side. Thinking of using conductive ink (maybe printing) or glueing on metall foil. The Q regarding insulation related to the insulation of this conductive layer (with laquer or similar).
You could maybe design the spacers directly (which You interpreted as the "insulation") into the stator, in forming a outer rim into the plastic frame (regarded the tolerances of the rapid prototyping are are low enough).
See pic.

jauu
Calvin