the “trick” with the WW analysis is that the 2 conductive coatings on the micron thin Mylar membrane is a huge capacitance and therefore the front and back coatings are AC short circuited regardless of an R between front and back
the principle that the charges can move in the conductive coating is fine though and the E field force is proportional to the density of charges – they just totally miss the real geometry effect
the problem with conductive membranes is that the charges can move around within the conductor under the influence of the E field which varies as the distance between the conducting, polarized surfaces move
so even if no new charge comes in from the polarizing supply because of the big resistor, if the membrane coating is low resistance the charges can move over the surface of the diaphragm in the low resistance coating to be closer to the oppositely polarized stator
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I believe the ideal “constant charge” ESL implementation would be to “glue” some charges uniformly distributed over the surface of the membrane without having any surface conductor at all
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Yet you don't want the charge to move when excursion of the diaphragm happens, I suppose? That'll introduce distortion as jcx lines out?
What is the minimum coating resistance that allows "constant charge" to avoid migration within the diaphragm surface and what is the minimum coating conductance to charge the diaphragm?
How long it takes to achieve full surface charge of the diaphragm with such "high resistance coating"?
With uncoated membranes, what is the sensitivity? If I push them hard, can the stators achive the air voltage breakdown?
Suppose one could laser or photo etch shields with several patterns* and spray gun the coating chemical solution at a certain pressure and during certain time so that the coating is made at certain regions at certain thickness according to a given precision (variables: shield accuracy, proportion accuracy of elements in the solution, pressure in the spray gun, time spraying…).
When the animation starts, in diaphragm to the right, green color regions are coated surfaces of the diaphragm and blue color then represents uncoated Mylar. There are traces that connect the concentric coated regions. Which length and coating thickness the traces that connect the concentric coated regions must have in order to its resistance reduce charge migration from circle to circle?
Suppose 24 hours or more (48 hours, i.e.) to fully space charge all the concentric circles at the rated voltage bias. Since the traces seem to add serial resistance, what is the charge gradient or voltage gradient from the inner circles to the outer circles and how they scale up from hour one to hour 48?
Urghh, this seems very hard to achieve, so now a different perspective.
Now the diaphragm depicted to the left. The outer coating in the front side of such diaphragm (green) could be connected to 580V pro bias and the inner coating in the back side (yellow) could be connected to +230V normal bias**. Blue color represents uncoated Mylar at each side of such “double bias” and “double side” coated diaphragm. Would that increase linearity?
I have drawn the pattern according to low frequency vibration modes that arnaud described. I presume low frequencies cause more diaphragm displacement and charge displacement than midrange. But vibrations modes also change as we go up in frequency (arnaud simulated the stators, is the same vibration mode for diaphragms?):
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Examples below with the first 2 stator resonances at about 750Hz and 1400Hz, left is the old stator, right is the new one with smaller perforated area. In both cases I ignored the copper trace / etching so this is assuming 1mm FR4 (also I used isotropic average properties for the material even though its mechanical properties are actually somewhat direction dependent):
Mode 1 (730Hz for both stators):
Mode 2 (1460Hz for old stator, 1350Hz for new stator):
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Maybe segregating the pattern in east and west portion with 230v bias within the surfaces in the peak of the 1400Hz vibration mode?
Yellow (front 580V pro bias); green (back 230V bias); blue (uncoated Mylar).
Urghh, this also seems very hard to achieve. Perhaps there is no optimum diaphragm coating pattern for all vibrations modes of the diaphragm in the audio spectrum.
I do not know much about the physics behind this transducers, but this is certainly the coolest thread***.
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* Shields only used in production process.
** Or a -230V negative normal bias or -80V unstandardized negative bias, changing the coating pattern, I honestly do not know…
*** if I had a lab, I would build all crazy or stupid configurations just to test if they work… Maybe with theory background to simulate their behavior, I would probably build considerably less “prototypes”. Knowledgeable people in ee please do not shoot me if I said something stupid.