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Old 26th October 2010, 02:08 PM   #21
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Yup, my direct-driver amp was half-way between Brian Beck's glorious monster and a Sanders. Absolutely the way to go for a DIYer (if they have no children in the home) but not feasible for folks who sell ESLs (should be obvious who seems cool to the notion).

A lot of this discussion is over my head (and some comments are not coherent) but here are a few points which I believe to be true.

The spacing of the ESL parts is a mechanical choice driven, ideally, by the excursion you want which in turn is acoustic/mechanical at root. As spacing goes up, voltage requirements go up fast. But you want to be able to have high bias voltage which requires big spacing.

The bias voltage dramatically (square power?) increases the sensitivity of the speaker - a very good goal (good to have adjustable bias so you can crank it up in dry weather). Prolly also influences linearity - but a long time since I read the famous foundational book by Hunt, the guy from MIT. Bias voltage depends on spacing and air humidity.

We are talking about electrostatic forces (duh). You need hundreds of voltage of push-pull to traverse even millimeters of space to move the diaphragm with electrostatic forces.

So, aim for bigger spacing, very high bias (easy to make), and good signal voltage.
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Old 26th October 2010, 07:19 PM   #22
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Quote:
Originally Posted by Calvin View Post
Under near field conditions, Headphones e.g, linear response is achieved with voltage source


Calvin
Hello Calvin,

I'm quite interested in this statement. Do you have a reference for it ?
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Old 27th October 2010, 07:08 PM   #23
Calvin is offline Calvin  Germany
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Hi,

the references have been named...Walker Baxandall and v.d.Waal
Besides every microphone positioned in near field prooves the matter.

jauu
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Old 27th October 2010, 07:45 PM   #24
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Quote:
Originally Posted by Calvin View Post
Hi,


Besides every microphone positioned in near field prooves the matter.
Microphone.. how old fashioned

Why not try the ESL simulator and set the speaker-mic to 1cm.
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Old 27th October 2010, 09:12 PM   #25
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Originally Posted by arend-jan View Post
Microphone.. how old fashioned

Why not try the ESL simulator and set the speaker-mic to 1cm.
Actually I'm interested in how regular headphones (not electrostatic ones) behave.
If they have linear response when voltage driven, does that mean that they will have a non-linear one when current driven ?
Does that mean that a headphone amp for regular headphones cannot be a current drive ?
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Old 28th October 2010, 07:12 AM   #26
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Voltage vs. current drive of dynamic speakers has been discussed at great length several times on this site (albeit in a different subforum). Insofar as consensus was reached, I think the gist of it can be summarized as follows:

"Since dynamic speakers are designed to be driven by voltage sources, it is suboptimal to use them with current sources. Current drive works very well but only when the speaker was specifically designed for this mode of operation. In other words, you need to design the entire system for current drive"

and

"If current drive were really superior to voltage drive, we would have more current drive speaker/amp systems out there in the market."

Kenneth
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Old 28th October 2010, 07:23 AM   #27
Calvin is offline Calvin  Germany
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Hi,

a dynamic speaker or headphone behaves differently with current-drive. Basically the voltage drive curve is overlayed with the impedance plot.
This means that the voltage-driven response curve is a bit elevated where the impedance plot rises and lowered where the impedance plot is lowered.
Damping of the driver is omitted with. So especially at the resonance point Fs the driver´s response peaks. Current drive makes sense when You want to implement motional feedback because it easens the FB loop design.
Otherwise there´s typically nothing really gained from current-drive...the same as it is with ESLs.

Ben, Your assumption that an increase of d/s is positive is wrong.
It is correct that the polarizing Voltage Vpol should be as high as possible, close to the limiting flashover level of air, since the Force acting upon the membrane rises with rising Vpol. But how do other parameters influence the Force, like membrane Area and the d/s?
The Force acting on the diaphragm consists of two parts, a static part and a dynamic part.
The static part simply leads to an offset x of the diaphragm from its middle position between the stators. We all know the effect from seeing the membrane flex when the polarizing voltage is switched on.
The dynamic part of the Force is the one that moves the membrane after the music signal.
Both parts add up independantely, because the superposition principle applies here.
After P.Baxandall the Force calculates to:
F= Eps0*A*[2*Vpol˛*x/dł + Vpol*Vsig/d˛] with Eps0=8.854exp-12, A=diaphragm area, Vpol=polarzing Voltage, Vsig=signal Voltage, d=d/s-value and x=Offset of the diaphragm from its middle position.
We can rearrange the above equation in that Vpol/d is substituted by Epol, the polarizing field strength and a constant in this calculation, which is limited by the flashover level of air of approx. 2kV/mm
The formula then reads:
F=Eps0*A*[2*x*Epol˛*(1/d) + Vsig*Epol*(1/d)] introducing the constant M=Eps0*A and the variables N=2*x*Epol˛ and P=Vsig*Epol, the formula reads easier.
F=M*[N*(1/d) + P*(1/d)]
This shows the 1/d-relationship of the Force in both, the static as well as the dynamic part.
So one should not aim for bigger spacing but just the opposite!
When designing a panel one needs to specify the dynamic range and the lower bandwidth limit. From this set of values one can estimate which volume of air is needed to fulfill the requirement.
This leads to a set of area-values A and excursion-values d. One should always choose the largest area allowed or possible and the smallest d. This increases the Force acting upon the diaphragm the most.
It is not that You choose a value of polarising Voltage first and adjust d accordingly, but quite the opposite. A chosen d-value allows for a certain maximum Vpol.
Besides the voltage levels quickly becoming unpractical and more dangerous to handle with rising d-values, the power requirements also rise proportional to d˛.
Since we are free in the design of the panel shape and since it is easy to design larger membrane areas than with comparably sized dynamic drivers the option should always be: "larger in A, smaller in d"

jauu
Calvin

Last edited by Calvin; 28th October 2010 at 07:48 AM.
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Old 28th October 2010, 08:40 AM   #28
Elias is offline Elias  Finland
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Hi,

I think current source can be used to drive a capacitor, but since it acts as an integrator you need to first calculate derivative of the input signal in order to reproduce the original waveform across the capacitor.


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Old 28th October 2010, 09:28 PM   #29
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Quote:
Originally Posted by Calvin View Post
Ben, Your assumption that an increase of d/s is positive is wrong.
It is correct that the polarizing Voltage Vpol should be as high as possible, close to the limiting flashover level of air, since the Force acting upon the membrane rises with rising Vpol. But how do other parameters influence the Force, like membrane Area and the d/s?
The Force acting on the diaphragm consists of two parts, a static part and a dynamic part.
The static part simply leads to an offset x of the diaphragm from its middle position between the stators. We all know the effect from seeing the membrane flex when the polarizing voltage is switched on.
The dynamic part of the Force is the one that moves the membrane after the music signal.
Both parts add up independantely, because the superposition principle applies here.
After P.Baxandall the Force calculates to:
F= Eps0*A*[2*Vpol˛*x/dł + Vpol*Vsig/d˛] with Eps0=8.854exp-12, A=diaphragm area, Vpol=polarzing Voltage, Vsig=signal Voltage, d=d/s-value and x=Offset of the diaphragm from its middle position.
We can rearrange the above equation in that Vpol/d is substituted by Epol, the polarizing field strength and a constant in this calculation, which is limited by the flashover level of air of approx. 2kV/mm
The formula then reads:
F=Eps0*A*[2*x*Epol˛*(1/d) + Vsig*Epol*(1/d)] introducing the constant M=Eps0*A and the variables N=2*x*Epol˛ and P=Vsig*Epol, the formula reads easier.
F=M*[N*(1/d) + P*(1/d)]
This shows the 1/d-relationship of the Force in both, the static as well as the dynamic part.
So one should not aim for bigger spacing but just the opposite!
When designing a panel one needs to specify the dynamic range and the lower bandwidth limit. From this set of values one can estimate which volume of air is needed to fulfill the requirement.
This leads to a set of area-values A and excursion-values d. One should always choose the largest area allowed or possible and the smallest d. This increases the Force acting upon the diaphragm the most.
It is not that You choose a value of polarising Voltage first and adjust d accordingly, but quite the opposite. A chosen d-value allows for a certain maximum Vpol.
Besides the voltage levels quickly becoming unpractical and more dangerous to handle with rising d-values, the power requirements also rise proportional to d˛.
Since we are free in the design of the panel shape and since it is easy to design larger membrane areas than with comparably sized dynamic drivers the option should always be: "larger in A, smaller in d"
Hello Calvin,

I agree that for practical reasons it is desirable to use large A with smaller d.
However, the “static” + “dynamic” force formula you rearranged does not support the conclusion that smaller spacing results in larger obtainable forces on the diaphragm. The spacing, d , is not actually involved in defining the obtainable force per unit area. Only the flashover field strength of air is involved.

Starting from your intermediate step where you had substituted Epol for Vpol/d:
F=Eps0*A*[2*x*Epol˛*(1/d) + Vsig*Epol*(1/d)]

Looking at just the “dynamic” portion of the Force:
F = Eps0*A*Vsig*Epol*(1/d)

Substituting Esig for Vsig/d and solving for Force per unit area gives….
F/A = Eps0*Epol*Esig

So, the Force per unit area is proportional to the product of the Signal field strength and the Polarizing field strength. The spacing, d, only defines the signal voltage and polarizing voltage required to reach a given field strength . For the practical reason of minimizing the transformer step-up ratio it is desirable to select the minimum spacing required to handle the diaphragm excursions at the lower bandwidth limit.

Said another way:
For ESLs, maxSPL is NOT dependent on diaphragm to stator spacing, although the required Vsig & Vpol required to achieve it increase linearly with D/S. Note that this does not mean that you can use whatever spacing you want to go as low as you want. The spacing still must be defined to allow the required diaphragm motion for maxSPL at the LF breakpoint.


Looking at just the “static” portion of the Force:
F = Eps0*A*2*x*Epol˛*(1/d)

Solving for Force per unit area and rearranging gives….
F/A = 2*Eps0*Epol˛*(x/d) = (constant)*(x/d)

This is the linear negative stiffness term that results in a force proportional to the diaphragm displacement in the gap away from the central resting position x=0. For a given spacing, d, the larger the polarizing voltage, the larger the negative stiffness coefficent and the lower the fundamental resonance of the diaphragm.

See this thread for plots of resonance trends vs Vpol I posted before I had read the Baxandall paper.
Diaphragm Resonance change with HV bias

Since this thread is about current drive, I will add that Baxandall mentions in Section 3.3.2 that if the stators are fed from a current source the linear negative stiffness term drops out of the Force equation. This means that varying the polarizing voltage would have no affect on the fundamental resonance of a current source driven ESL. I haven’t verified this experimentally yet, but plan to in the near future.

Concerning Vpol selection:
It is true that for a given Vsig, increasing Vpol will increase the force on the diaphragm and increase the voltage sensitivity of the ESL. However, this does not neccessarily produce the maximum possible Force on the diaphragm and thus the maximum possible SPL peaks. From Section 3.2.9 of the Baxandall paper, for a given diaphragm spacing d, the optimum Vpol and Vsig(stator-stator) for maximum SPL are:
Vbias = Emax * d / 2
V(stator-stator) = Vbias * 2

where Emax = the flashover voltage for air usually taken to be 2kV/mm - 4kV/mm.

The reasons this is so is because the force is proportional to the product of the two voltages, but the break down is based on the sum of the two voltages. For example, suppose the airgap can sustain 10kV, and Force(for illustrative purposes) is just the product of the Vpol and Vstator.

Vpol...Vstator..Force
0........10.........0
1.........9.........9
2.........8........16
3.........7........21
4.........6........24
5.........5........25
6.........4........24
7.........3........21
8.........2........16
9.........1.........9
10........0.........0

You can see that if we are limited by 10kV across the airgap, we get maximum force(peak SPL) before breakdown in the airgap when we set Vpol= 5kV and apply 5kV of audio signal to each stator.(out of phase of course, so Vsig=10kV from stator to stator) This is consistant with the Baxandall equations.

In practice what you will find is that:

1) If your step up transformer can generate the optimum stator voltages, turning up your bias beyond the optimum Vpol value will result in higher sensitivity but reduce maximum SPL.

2) If your transformer generates less than optimum stator voltages, turning up your bias beyond the optimum Vpol value will result in higher sensitivity and increased maximum SPL.
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Old 28th October 2010, 10:37 PM   #30
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Thanks for that in-depth treatment.

"2)"... right. Like Mike Wright said.

Seems to me there's not much doubt that big spacing and proportionally smaller diaphragm movement leads to cleaner results. A loafing big cone driver will outperform a stressed small driver and likewise for an ESL for similar reasons.

Calvin - while your math looked superficially impressive (at least until I read bolserst incisive critique), it would be far more helpful (or to use the current cliche, "inclusive") if you could put into plain language words what you are doing, finding, and concluding. Then the rest of us could judge what made sense and what didn't and how it relates to Hunt.

About current vs voltage, I've fooled some with motional feedback for cones and that is a matter of juggling positive and negative and voltage and current sourcing. In order to create an amp with a negative output impedance equal to the driver (no kidding). The dirty little secret (at least with cones) is that it is all a matter of balance between cone diameter and the radiation resistance of the air and some other acoustic parameters and there just isn't a "right" way to drive. By convention (and because of the need/convenience for negative voltage feedback around amps), the audio world universally agrees to market the kind of speakers that sound kind of flat in kind of ordinary homes and room when driven with constant voltage drive. By convention. Secondarily, you need various tricky and changing EQ with current drive and Rice-Kellogg drivers.
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Last edited by bentoronto; 28th October 2010 at 10:49 PM.
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