Make it worse to make it better???

[moray james]

having balanced push and pull force is as far as I know subject to having the two stators equal distance from the diaphragm (at rest). So if the system is symmetrical then the drive force is always equal regardless of where in between the two stators the diaphragm is positioned. As soon as the system balance is skewed it all falls apart.

[frank ziel]

Wrong, I think the same way as Few.
It only seems to be unequal: if you push the diaphragm towards one
stator, all over sudden it is sucked into the stator. But that is because the load can travel to the nearest point -
even when the coating is very high resistiv.
Regards
Frank

[Ed Holland]

The simple electrostatic model - a charge situated within a parallel plate capacitor would suggest that the force is independant of the charge's proximity to either plate.

I think to add distortion via electrostatic design, one would have to engineer a design wich incorporated a non-zero electric field gradient between the stators. in this way, field strength and hence driving force would vary with diaphragm displacement.

Ed

[moray james]

can you provide the english Coles Notes defination of this statement? "a non-zero electric field gradient between the stators"
Seems very logical to me that if you move away from a force be it magnetic or electroststic the affect of that force is diminished. So if you shift one stator farther away from the diaphragm than the other stator you have reduced the force of that stator on the diaphragn with respect to the closer stator. The combined balanced pushing and pulling force is lost. My understanding is that the two parallel stator plates must be equally spaced from the diaphragm at rest to make this trick work. Thanks Moray James.

[Ed Holland]

OK I'll try... The old physics is a bit rusty though

Simple case. A paralel plate capacitor, i.e. our two stators separated by distance d. Say there is a peak in the music signal at some instant in time, and the stators have a potentlial difference V between them. If they are parallel, an electric field E =V/d, extends between them and is uniform. Thus a point charge Q placed within this field experiences a force F=QE. Since the field is uniform, the force does not depend upon the position of charge Q. i.e. in this case, you can't move away from the force.

Ed

[Few]

I'll tack this on to the end of Ed's response:

The electric field is a "vector field." At each point in space we can define the electric field's magnitude and direction. Here's an example taken from Wikepedia:

It shows the electric field surrounding a positive charge (red) in the neighborhood of a negative charge (cyan). The blue arrows indicate the direction and magnitude of the electric field at many points in space (the locations of the arrows' tails). At a given location a positively charged particle would feel a force in the direction indicated by the arrow and the magnitude of the force would be proportional to the arrow's length. Since in this example the arrows have different lengths and directions, the electric field is not uniform. Ed's gradient (I think, strictly speaking, it ought to be the Jacobian since the electric field is a vector field) measures how the electric field changes from one location to its neighboring locations. If the gradient (Jacobian) at some point "A" is large then the electric field's magnitude and/or direction at some of the points surrounding "A" must be quite different from the electric at "A". In the example above the Jacobian would have large magnitudes near the charges because that's where the electric field changes most rapidly.

The electric field between two infinite parallel plates (ESL stators) would be indicated by an array of arrows all pointing in the same direction (from positive stator to negative stator), and all with the same length (proportional to the voltage difference between the stators). In other words, the electric field is uniform. Since all points have identical electric field magnitudes and directions, the Jacobian is zero at all points. Since the arrows are all identical, and they indicate the force felt by a positively charged particle at the various points in space, we see that a charged particle placed anywhere between the plates feels the same force as it would at any other place between the plates.

Moray James, if it troubles you that the force does not vary with distance, consider that as you move farther from one stator you move closer to the other, by exactly the same amount.

Or, if that doesn't help try an audio example. The SPL from a point source of sound drops off as 1/distance^2. It drops off as 1/distance as you move away from an infinitely long linear source. It doesn't drop off at all as you move away from an infinitely large planar source.

I hope I haven't just further muddied the waters...

[Ed Holland]

Thanks, Few.

Yes, what I meant by gradient should really be termed divergance, to use accepted definitions.

The electric field between parallel stators has zero divergance, but is established by a potential gradient (the difference in voltage between the electrodes).

To create a field divergance, it would be necessary to devise some non planar stator electrode geometry. I envisage all sorts of technical difficulties with this...

Of course another way to introduce distortion would be to add a little music signal to the diaphragm, thus changing the charge level (I know about the high surface resistivity etc...)

Ed

[moray james]

I cannot find anything that would support my belief that the stators have to be equally spaced from the diaphragm for the force vectors to always add up the same. I asked a buddy who knows better than I and he told me the same. I still have to imagine that at some distance things stop working the same way but I have no idea how much different the stator spacers could be and still have things equal out. I made the assumption a long time ago and just ran with it. Live and learn.
So what would be an easy way to introduce some second order harmonic distortion short of a single ended esl?

[Ed Holland]

As I mentioned in my previous post - addition of some music signal to the diaphragm would achieve this.

This would modulate the static charge (achieved by the DC bias). Say the diaphragm is biased at some positive DC voltage + 10% music. On positive portions of the waveform, bias is increased, hence diaphragm driving force is increased. The reverse is true on negative going portions of the music signal.

It is simple to show that this would in theory add a perfectly controllable amount of 2nd harmonic distortion.

The problem would be in actually delivering music signal to the diaphragm, as the sheet resistivity is usually high to restrict charge flow on the surface...

Ed

[el`Ol]

Originally posted by Ed Holland

The problem would be in actually delivering music signal to the diaphragm, as the sheet resistivity is usually high to restrict charge flow on the surface...

Maybe one could modify a Final ESL that way. The smaller ones are quite inexpensive.
http://www.final.nl/electro.html#advantage