Hi BillH,
By my calculations your small panels have an area of about 1/3 ft^2. You said your large ones have an area of 3 ft^2 so they're different by about a factor of 9.
The d/s spacings are 0.060" and 0.025", for a ratio of 2.4. All else being equal the sensitivity should scale as (1/spacing)^2 so neglecting the area differences, the small panels should be about 5.8 times more sensitive than the large ones.
Combining both effects we get 5.8/9 = 64%, so the small panels should be about 64% as sensitive as the large ones. That's not what you're reporting, so I wonder where the glitch is. Probably in my reasoning! I realize that you're saying the amp runs out of steam when you try to crank things up, but below that level (so the amp is happy driving either panel) I guess I'd still expect the large panels to be more sensitive.
Even if we include the different radiation patterns I can't quite make sense of it. The large panels should be beamier than the small ones so at a distance of a few meters the large ones should sound even louder relative to the small ones.
Any chance it's something insidious like charge leakage in the large panels that doesn't exist in the small ones? Or even more likely, perhaps someone can point out an error in my arithmetic... Do you have any way to measure the capacitances of the panels? Just wondering if they come out about where you'd expect based on the intended dimensions.
Few
By my calculations your small panels have an area of about 1/3 ft^2. You said your large ones have an area of 3 ft^2 so they're different by about a factor of 9.
The d/s spacings are 0.060" and 0.025", for a ratio of 2.4. All else being equal the sensitivity should scale as (1/spacing)^2 so neglecting the area differences, the small panels should be about 5.8 times more sensitive than the large ones.
Combining both effects we get 5.8/9 = 64%, so the small panels should be about 64% as sensitive as the large ones. That's not what you're reporting, so I wonder where the glitch is. Probably in my reasoning! I realize that you're saying the amp runs out of steam when you try to crank things up, but below that level (so the amp is happy driving either panel) I guess I'd still expect the large panels to be more sensitive.
Even if we include the different radiation patterns I can't quite make sense of it. The large panels should be beamier than the small ones so at a distance of a few meters the large ones should sound even louder relative to the small ones.
Any chance it's something insidious like charge leakage in the large panels that doesn't exist in the small ones? Or even more likely, perhaps someone can point out an error in my arithmetic... Do you have any way to measure the capacitances of the panels? Just wondering if they come out about where you'd expect based on the intended dimensions.
Few
Hi, Few.
I took some time off from DIY, so wasn't able to answer you earlier. I'm back now.
Near the beginning of this thread, you asked about the lobing I heard in my large ESLs. As I reconnected the wiring on one of them after using its electronics to test the small ESL, I had a chance to try some different things. Long story short, the lobing wasn't caused by one ESL. It was a result of the beaminess (hehe, Firefox says that's not a word) of both ESLs together. I was just moving in and out of the sweet spot and perceived it as a fault of the individual speakers.
Back to the efficiency of the small vs. large ESLs. Again it turned out to be something other than what I thought it was, it just took me a while to figure it why the small ESL played so much louder than the larger one. One of my large ESLs, the left one always had leakage problems. I had done everything I could to correct it and ended up lowering the bias voltage to stop the arcing. To balance the right ESL, I turned down its bias too. With a higher bias, the right ESL can play considerably louder than the left without arcing. I tested the small ESL on the right side electronics, biased as high as I could, and used the left large ESL without modification. At the time I thought the small ESL was much more efficient than the larger ESL. Now I know it was a flawed test.
I've been reading 'Telestar-Shaped Electrostatic Speaker' by R. J. Matthys and grabbed some math from it to help me understand what went wrong. The math agrees with yours, Few.
If we have two different speakers tested at the same frequency, then:
Efficiency = (Vb/d)sqrd x a
Where:
Vb = bias voltage
d = diaphragm-stator distance
a = diaphragm area
After assuming a 100 volt/0.001 inch voltage gradient on both speakers, R. J. Matthys writes: "A woofer has the same efficiency per unit area as a tweeter because the tweeter has a smaller air gap than a woofer, as the diaphragm amplitude is much less at high frequencies." I was trying to compare an ESL with a low voltage gradient and larger area (the large one) to an ESL with a larger voltage gradient and a smaller area (the small one).
I took some time off from DIY, so wasn't able to answer you earlier. I'm back now.
Near the beginning of this thread, you asked about the lobing I heard in my large ESLs. As I reconnected the wiring on one of them after using its electronics to test the small ESL, I had a chance to try some different things. Long story short, the lobing wasn't caused by one ESL. It was a result of the beaminess (hehe, Firefox says that's not a word) of both ESLs together. I was just moving in and out of the sweet spot and perceived it as a fault of the individual speakers.
Back to the efficiency of the small vs. large ESLs. Again it turned out to be something other than what I thought it was, it just took me a while to figure it why the small ESL played so much louder than the larger one. One of my large ESLs, the left one always had leakage problems. I had done everything I could to correct it and ended up lowering the bias voltage to stop the arcing. To balance the right ESL, I turned down its bias too. With a higher bias, the right ESL can play considerably louder than the left without arcing. I tested the small ESL on the right side electronics, biased as high as I could, and used the left large ESL without modification. At the time I thought the small ESL was much more efficient than the larger ESL. Now I know it was a flawed test.
I've been reading 'Telestar-Shaped Electrostatic Speaker' by R. J. Matthys and grabbed some math from it to help me understand what went wrong. The math agrees with yours, Few.
If we have two different speakers tested at the same frequency, then:
Efficiency = (Vb/d)sqrd x a
Where:
Vb = bias voltage
d = diaphragm-stator distance
a = diaphragm area
After assuming a 100 volt/0.001 inch voltage gradient on both speakers, R. J. Matthys writes: "A woofer has the same efficiency per unit area as a tweeter because the tweeter has a smaller air gap than a woofer, as the diaphragm amplitude is much less at high frequencies." I was trying to compare an ESL with a low voltage gradient and larger area (the large one) to an ESL with a larger voltage gradient and a smaller area (the small one).
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