Is % open area the wrong parameter for ESL stator design?

[Few]

I’m trying to select the spacing to use between wires in a tensioned wire ESL stator. The question of percentage open area for an ESL stator has been discussed in several ways in several different threads but I suddenly found myself questioning the conclusions I had been drawing from the those discussions. Can someone please verify or correct the following assumptions and conclusions?

Assumptions:
1) ESL sensitivity scales with the panel’s useful capacitance, in other words, the total capacitance minus the “stray” capacitance associated with those parts of the panel that can’t produce sound.
2) As long as the holes in a stator are small compared to the distance between the two stators, the capacitance depends on the outer dimensions of the stator but not on the area of the holes that perforate the stator.

Proposed conclusion:
1) The spacing between wires in a tensioned wire ESL should be selected to be a bit smaller than the stator-stator distance rather than selected to yield a particular percentage of open area.

The conclusion would imply that, assuming a given stator-stator distance, the gap between wires should be the same no matter what the diameter of the wires is (assuming the wires aren’t more than a few millimeters in diameter). In other words, the percentage open area really isn't the key parameter. What matters is hole size compared to stator spacing. Is this consistent with everyone’s observations? Also, would it be better to use the stator-diaphragm distance rather than the stator-stator distance as the maximum gap between wires in a tensioned wire stator?

Few

 

[BillH]

Hi, Few. I'll try to answer what I can.

1) ESL sensitivity scales with the panel’s useful capacitance, in other words, the total capacitance minus the “stray” capacitance associated with those parts of the panel that can’t produce sound.

That's true. Here's a follow up question for the group: If you only coat the diaphragm within the active area of the stators, is the stray capacitance still there?

2) As long as the holes in a stator are small compared to the distance between the two stators, the capacitance depends on the outer dimensions of the stator but not on the area of the holes that perforate the stator.

The capacitance calculations I've seen all assume the perforations aren't there.

In other words, the percentage open area really isn't the key parameter.

In my limited experience, it seems to be true. You've got to keep the open area small enough so the electric field stays equal at all points on the diaphragm and large enough not to choke the air movement caused by the diaphragm. I'm not sure what the range of acceptable values is, though. So far I've used 50% and 35% open area perforated metal and they both worked fine.

On a related note, is the diaphragm to stator distance on a wire stator measured from the outer edge of the insulation or the copper underneath? It wouldn't make much of a difference with magnet wire, but could with PVC coated wire and a small d-s distance.

Here's a diyAudio post from JohnG with an attachment showing a wire stator simulated using FEMM.

 

[BillH]

Hi, Few. I tried out a few FEMM sims of different stator wire spacing and it turns out there is a difference between them. It's not a lot of difference, but the voltage near the diaphragm does change with different spacings. Closer spacing means more voltage. It's something to consider if you're trying to maximize efficiency.

See the details and pictures in the .pdf file attached below.

 

[Coffee]

PVC has a relative permitivity of 3,4 - 4 so the field intensity in a PVC insulation will be about 4 times weaker then in the air gap, so about 75% of the intensity will remain where it should be, in the air gap, between the outer edge of the insulation and the diaphragm

this is true when we made a presumption that the two sections (PVC and air gap) are of the same thickness

for thinner insulation then the air gap, it would be even better case for us

IMHO

 

[Few]

BillH:
Thanks for the replies and for your FEMM efforts. I've been meaning to explore the use of that software for this purpose but haven't yet found time. I find your results interesting because they make sense, but I don't know how to fit them together with the fact that others claim that the capacitance is unaffected by small holes in the stator ("small" meaning smaller than the stator/diaphragm spacing). Your FEMM results show fairly significant changes in the electric field at the diaphragm even when the gaps between the wires are quite a bit smaller than the stator/diaphragm spacing.

Few

 

[BillH]

I don't know how to fit them together with the fact that others claim that the capacitance is unaffected by small holes in the stator

Me either. I'd like to see someone measure the capacitance of an actual ESL to see if it's close to the theoretical value.

Thanks for the information, Coffee. I'm getting a quote on some #24 wire with 0.010" thick insulation. I'm bracing for a shock as the price of copper has jumped lately.

 

[Few]

The following excerpt:

In summary, what we found was that the measured capacitance depended on the total area inside the perimeter, if the hole sizes were smaller than, or comparable with, the plate spacing; whereas the capacitance depended on just the area of metal in the wires (total) if the hole sizes were much larger than the plate spacing.

is taken from this site.
The context is different, but at least there's an experimental study of the capacitance as a function of hole size and plate spacing. Unfortunately, it doesn't clear up my confusion.