I always wanted to ask...why Bias voltage on ESL?

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#41
Hi Bondsan

Just double checking...

3"x14" = 3 x 2.54 x 14 x 2.54 = 271 cm^2 stator area.

with 1.6 mm spacers between membrane and stators (3.2 mm total)=> 67 pF. 🙂

with 67 pF, the lowest frequency where the 20M resistor provides some distortion reduction is 1/4/pi/R/C=60Hz. The distortion reduction (due to the charge movement only) is in proportion to frequency above this - reduced a factor of 2 at 120 Hz, a factor of 3 at 180 Hz etc.

It doesn't matter if the 3x14" area is sectioned - what matters is the total capacitance of the area connected to the HT resistor.

You are also correct that the distortion increases with volume. This particular distortion increases as volume ^3, i.e. double the volume, the distortion is eight times greater. (The percentage distortion increases by 8/2 = 4 times)

Most distortion mechanisms in ESLs depend on the membrane displacement. Second order effects (which are not very audible) increase as vol^2, third-order effects increase as vol^3, etc , etc. The highest order distortion effects tend to be more audible because they are not masked by harmonics in the music. The worst effects are independent of volume because they become most apparent at low volumes - quiet passages lose definition and sound like crap. Crossover effects in amps are like this.

Note too that the membrane displacement also decreases with increasing frequency, so most ESL distortion already decreases with increasing frequency anyway - the resistor just makes things better.

BTW - I thought there were 10 kinds of people, those who understand binary and those who don't. 😀

In a similar vein - what goes "pieces of seven! pieces of seven!"

Ans - a parrotty error :Pirate:

BW,R
 
#42
Hi Golfnut,

golfnut said:
Just double checking...

3"x14" = 3 x 2.54 x 14 x 2.54 = 271 cm^2 stator area.

with 1.6 mm spacers between membrane and stators (3.2 mm total)=> 67 pF. 🙂

Yes that is correct. I got a little ahead of myself. With the help of a Google converter, 3" x 14" = 7.62cm x 35.56cm which resulted in actually 270.96 square cm. Divided by 1/8" = 3.175cm = 85.34cm x.8= 68.27 pF. I guess that is somewhat close.

But egads, I sure ruined my math debut, didn't I.😱

Bondsan
Click to expand...
 
#43
I read the whole tread and thought I finally understood the whole CV CC difference but still:


so its clear for CV that the voltage remains the same on the whole foil as it has a low resistance compared to the capacitor value to the stators.



But if you look as CC: the signal to the 2 stators will have opposit voltages (stator1 =-stator2) this means the foil also stays at the same voltage as both stator capacitors pull equally in opposite direction isn't is?


This would mean the foil remains at its initial rest voltage independent of the signal, which is exactly what happens with CV... So I am confused.. Can someone help me understand my thinking error?
 
#44
You may have missed one of the key points here in post #8.

I always wanted to ask...why Bias voltage on ESL?
This charge/voltage relationship has the following consequence:
1) For constant voltage diaphragm, as the diaphragm is moved towards a stator the charge on it increases.
2) For constant charge diaphragm, as the diaphragm is moved towards a stator the voltage on it decreases.

Also in post #9
I always wanted to ask...why Bias voltage on ESL?
The large value resistor does keep the total charge on the diaphragm constant, but does not keep the charge on the diaphragm from moving around to areas closest to stators.
 
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#46
Further to Mattstat #44

The use of the high resistivity coating on the membrane in addition to the high series resistance, rather than a metalised coating, stops the charge on the membrane from moving about and makes the electrostatic motor linear.
 
#48
Hi Wout31

The full explanation is given in the chapter on ESLs by Baxandall.

Constant voltage mode: Without the series resistance and high resistivity coating on the membrane, the ESL operates in a mode where the voltage on the membrane is fixed by the HT supply.

When the membrane is displaced from the central position between the two stators, as it is at low frequencies, the capacitance between the membrane and one stator increases, while the capacitance to the other stator decreases, with the combined effect being that the total capacitance increases.

To maintain the same voltage on an increased capacitance requires current to flow from the HT to the membrane.

At the same time, the increased capacitance at constant voltage means there is an additional force of attraction between the membrane and the close stator, and less force between the membrane and the distant stator - the change in force on the membrane is not proportional to the membrane displacement - it is non-linear. That leads to distortion.

Constant charge mode: With the series resistor in place, the current flow from the HT to the membrane is slowed - if the membrane moves fast enough (at high enough frequencies), for all practical purposes, the charge on the stator-membrane capacitance stays constant.

If the charge is constant - the force on the membrane depends only on stator voltage - no matter where in the gap the membrane is located - the electrostatic motor is linear - no distortion.

If the membrane moves slow enough (very low frequencies) then the charge has time to move about causing distortion.

The transition between these two modes is at the frequency given by the formula.


Notes:
  • The series resistance also stops the membrane sticking to the stators. In constant voltage mode, it is possible for the membrane to get so close to a stator that the force of attraction between stator and membrane increases enough to overcome the membrane tension and stick.
  • The high resistivity coating on the membrane stops charge from moving about on the membrane. If one part of the membrane gets closer to a stator than another part, the charge will try to move to that point, increasing the force of attraction between the stator, causing increase displacement, causing increased capacitance, causing increased charge movement, etc, etc. Result is increased distortion and tendency for the membrane to stick.
  • ESLs that use metallic membranes have these problems. I recall seeing a published test report on ESL with metalised membrane - distortion at low frequencies and full power was about 8%.


Hope this helps
 
#51
Hmm, have to look at Baxandall to be sure, but the usual formula for the cutoff frequency for an RC filter is 1/(2.pi.R.C).

I'm guessing that the 4 comes about because the membrane-stator capacitance is twice the stator-stator capacitance.
 
#52
bolserst said:
Inverted Push-Pull ESL

Attachment #1 provides a comparison of the basic setup for an Inverted Push-Pull ESL and the Standard Push-Pull ESL. As AcoustatAnswerMan pointed out, the Inverted ESL must be operated in CV mode to work properly over the whole audio band, so we will stick with CV mode for the comparison.

Using the same method as in Post#4 for plotting up relative levels of Force on the diaphragm, we can get an understanding of why the Inverted ESL produces 6dB more output for the same input. Sticking with a bias voltage of 5kV, lets suppose the step-up ratio of the transformer is 1:200. So, if we had a 200W amplifier, it would swing maximum peak voltages of about +/-50V resulting in the +/-5000V on the stators. Attachment #2 provides tabulated values for the diaphragm and stator voltages along with the relative Force vs Input voltage plot for the Standard CV push-pull ESL.

Now, if we switched out the transformer for one with a 1:100 step-up ratio and used it to power an Inverted ESL with +/-5kV bias voltages on the stators, you would get the voltages and relative Forces shown in Attachment #3. Notice that at each input voltage level the voltage difference between the diaphragm and each stator match that of the Standard arrangement from Attachment #1. If you kept the 1:200 ratio transformer you would double the voltage swing on the diaphragm, which would double the total Force resulting in the 6dB higher output as shown in Attachment #4

The "extra" output is coming from the fact that having the 2nd equal but opposite biased stator allows us to leverage the entire output voltage from the step-up transformer against that bias voltage value twice rather than having it split in half and fed to the stators before leveraging against the diaphragm voltage. Compare the +/-50V input lines in the table from Attachment #2 with the +/-25V input lines from the table in Attachment #4

One other thing to notice in Attachment #4 is that even though the diaphragm voltage swings higher than the bias voltage on the stators the total force on the diaphragm from the push-pull configuration is still linear as long as the diaphragm is centered in the gap. This is the case for the standard configuration as well. However, with a single ended ESL your signal voltage needs to be limited to something less than the bias voltage to avoid gross distortion.
Click to expand...
Hej Bolserst,
for me still remains the question: is the Inverted ESL in CV mode
linear or not?
Maybe you have the " Forces on Diaphragm vs Diaphragm Position "
for the inverted ESL in CV mode available?
Many thanks
Burkhard
 
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