Hi all,
I have for some time now been contemplating a planar loudspeaker and from a SQ point of view I consider the ESL to likely be capable of delivering the "best" SQ (whatever that may be
) due to its design features.
However, in most all cases a transformer is inserted between the amplifier and the ESL thus reducing bandwidth (and more?) both top and bottom of the ESL. I am only considering a constant charge ESL design.
I would be interested in playing quite loud - i.e. in a very large (up to 400 square meters) room - and thus I reckon that either a very powerful amplifier is needed, or an efficient ESL design.
Considering an efficient ESL design I am aware of two options being open (there may be more):
A.: The bias voltage is set to be high, and/or
B: The D/S spacing is kept low. The latter may reduce the available diaphragm excursion but I am considering a diaphragm altogether with a couple of m2 size (~ 2.2 m2 - big, I know!). For a low D/S spacing a reliable way of stabilizing the diaphragm (so that it doesn't become excentered towards either of the stators) is assumed to be in place.
So - just to get an idea about what might be needed I calculated what the "moved" air volume would be of a 14" membrane, corresponding to an appr. ~15" woofer, moving 3 cms peak-to-peak. This corresponds to appr. 1000 cm2 woofer surface area and appr. 3000 cm3, or 3 dm3, moved at this 3 cm p-p excursion. Quite loud I reckon if such movement is assumed available throughout the audible range ... ?
Similarly, for a 2.2 m2 ESL membrane (22000 cm2) this corresponds to a peak-to-peak excursion of appr. 1.36 mms. That is 0.68 mms on either side of the membrane centerline ...
Which leads me to a question for those of you familiar with ESLs:
How much voltage/current is actually needed to drive a static charge ESL in practice? Here I am thinking about the voltage & current fed directly to the stators and not the voltage/current input to a transformer.
I hope some of you may be able to give some idea about this ... please when/if replying also state stator size, D/S spacing, diaphragm impedance, diaphragm bias voltage, or .. ?? that you consider relevant in order to realistically assess the voltage/current needed to drive an ESL ...
Hope this is accessible to reply to ... - & thanks for any feedback ...
Cheers,
Jesper
I have for some time now been contemplating a planar loudspeaker and from a SQ point of view I consider the ESL to likely be capable of delivering the "best" SQ (whatever that may be
) due to its design features. However, in most all cases a transformer is inserted between the amplifier and the ESL thus reducing bandwidth (and more?) both top and bottom of the ESL. I am only considering a constant charge ESL design.
I would be interested in playing quite loud - i.e. in a very large (up to 400 square meters) room - and thus I reckon that either a very powerful amplifier is needed, or an efficient ESL design.
Considering an efficient ESL design I am aware of two options being open (there may be more):
A.: The bias voltage is set to be high, and/or
B: The D/S spacing is kept low. The latter may reduce the available diaphragm excursion but I am considering a diaphragm altogether with a couple of m2 size (~ 2.2 m2 - big, I know!). For a low D/S spacing a reliable way of stabilizing the diaphragm (so that it doesn't become excentered towards either of the stators) is assumed to be in place.
So - just to get an idea about what might be needed I calculated what the "moved" air volume would be of a 14" membrane, corresponding to an appr. ~15" woofer, moving 3 cms peak-to-peak. This corresponds to appr. 1000 cm2 woofer surface area and appr. 3000 cm3, or 3 dm3, moved at this 3 cm p-p excursion. Quite loud I reckon if such movement is assumed available throughout the audible range ... ?
Similarly, for a 2.2 m2 ESL membrane (22000 cm2) this corresponds to a peak-to-peak excursion of appr. 1.36 mms. That is 0.68 mms on either side of the membrane centerline ...
Which leads me to a question for those of you familiar with ESLs:
How much voltage/current is actually needed to drive a static charge ESL in practice? Here I am thinking about the voltage & current fed directly to the stators and not the voltage/current input to a transformer.
I hope some of you may be able to give some idea about this ... please when/if replying also state stator size, D/S spacing, diaphragm impedance, diaphragm bias voltage, or .. ?? that you consider relevant in order to realistically assess the voltage/current needed to drive an ESL ...
Hope this is accessible to reply to ... - & thanks for any feedback ...
Cheers,
Jesper
Hi Jesper
I would learn as much as you can from this reprint document written by Peter Walker
originally in Wireless World :May 1955
Wide Range Electrostatic Loudspeakers P.J.Walker Wireless World May 1955
Secondly get to hear a good set of ESL57's, noting the design requirement
for a curved panel and how that is going to be achieved
Thirdly assess amplifiers for them
The Quad ESL - Christian Steingruber
Another notable manufacturer of ESL panels and speakers is Martin Logan
similarly get to hear what they can do.
Hope that helps.
I would learn as much as you can from this reprint document written by Peter Walker
originally in Wireless World :May 1955
Wide Range Electrostatic Loudspeakers P.J.Walker Wireless World May 1955
Secondly get to hear a good set of ESL57's, noting the design requirement
for a curved panel and how that is going to be achieved
Thirdly assess amplifiers for them
The Quad ESL - Christian Steingruber
Another notable manufacturer of ESL panels and speakers is Martin Logan
similarly get to hear what they can do.
Hope that helps.
Hi Gentlevoice,
How did you you come to the conclusion that the step up trafo is limiting bandwidth ?
Like tube amps if trafo is well design, bandwidth is not compromise at all. Amp wise, I believe it's more to do with the design then anything else. I'm using a 100 watt AB amp
with my ML Odyssey which plays pretty loud.
Cheers
How did you you come to the conclusion that the step up trafo is limiting bandwidth ?
Like tube amps if trafo is well design, bandwidth is not compromise at all. Amp wise, I believe it's more to do with the design then anything else. I'm using a 100 watt AB amp
with my ML Odyssey which plays pretty loud.
Cheers
Hi
You really need to download a copy of Baxandall's paper on Electrostatic loudspeakers - I'm sure, like me, you will find it a revelation. there are several copies around on the WWW - see The wire electrostatic Loudspeaker page - Introduction for example.
The maximum OP from the ESL is almost entirely determined by the area and the low cutoff frequency - stator-membrane spacing is almost irrelevant - see Baxandall for detail.
Also, ESLs are a pressure source, conventional speakers are a volume-velocity source - the displaced volume on an ESL membrane will be quite different from a conventional cone.
For all practical purposes, the ESL behaves electrically like a capacitor. A large full range ESL of 1 m^2 has a capacitance typically about 1.5 nF, and the capacitive load is a serious difficulty. Consider a 1:100 transformer with 1 ohm primary resistance, the source impedance seen by the ESL is 10 k (100^2 x 1 ohm). Hence the RC filter formed by the resistor and ESL has a cutoff frequency of 10.6 kHz - hence problem. The problem gets much worse with higher step-up ratios. So the primary winding resistance (including speaker leads) must be very low.
Also, consider 3 uH output inductance from amplifier and speaker leads (e.g., 1 uH from the amp and 3 m of speaker leads at 0.7 uH/m) then the cutoff frequency of the LC filter is 24 kHz. To build a transformer for such an ESL is very difficult because there is so little headroom without reducing bandwidth below 20 kHz. With higher step-up ratios the transformer design is impossible.
So the problems are primarily with the capacitive load of the ESL, not the transformer per se. This can be fixed by using passive equalisation of the ESL. For a point-source ESL, the LC transmission line segmentation used by the QUAD ESL-63, converts the ESL impedance to a pure resistor - much friendlier load (Technically a difficult solution too - see Baxandall for detail). For a line source, the RC transmission line equalisation described by White (also on the wire esl site or pm me for a copy) reduces the capacitive load by a factor of 20 X, again a much friendlier load. This solution is easy for DIY, only requires resistors.
The bad reputation of ESLs for killing amplifiers comes from people trying to drive large capacitive ESLs directly through the transformer e.g., using active equalisation. The impedances have to be very low to avoid the bandwidth limiting effects, and the slightest problem will result in massive currents and a suicidal race between the fuse and the OP transistors.
regards
R
You really need to download a copy of Baxandall's paper on Electrostatic loudspeakers - I'm sure, like me, you will find it a revelation. there are several copies around on the WWW - see The wire electrostatic Loudspeaker page - Introduction for example.
The maximum OP from the ESL is almost entirely determined by the area and the low cutoff frequency - stator-membrane spacing is almost irrelevant - see Baxandall for detail.
Also, ESLs are a pressure source, conventional speakers are a volume-velocity source - the displaced volume on an ESL membrane will be quite different from a conventional cone.
For all practical purposes, the ESL behaves electrically like a capacitor. A large full range ESL of 1 m^2 has a capacitance typically about 1.5 nF, and the capacitive load is a serious difficulty. Consider a 1:100 transformer with 1 ohm primary resistance, the source impedance seen by the ESL is 10 k (100^2 x 1 ohm). Hence the RC filter formed by the resistor and ESL has a cutoff frequency of 10.6 kHz - hence problem. The problem gets much worse with higher step-up ratios. So the primary winding resistance (including speaker leads) must be very low.
Also, consider 3 uH output inductance from amplifier and speaker leads (e.g., 1 uH from the amp and 3 m of speaker leads at 0.7 uH/m) then the cutoff frequency of the LC filter is 24 kHz. To build a transformer for such an ESL is very difficult because there is so little headroom without reducing bandwidth below 20 kHz. With higher step-up ratios the transformer design is impossible.
So the problems are primarily with the capacitive load of the ESL, not the transformer per se. This can be fixed by using passive equalisation of the ESL. For a point-source ESL, the LC transmission line segmentation used by the QUAD ESL-63, converts the ESL impedance to a pure resistor - much friendlier load (Technically a difficult solution too - see Baxandall for detail). For a line source, the RC transmission line equalisation described by White (also on the wire esl site or pm me for a copy) reduces the capacitive load by a factor of 20 X, again a much friendlier load. This solution is easy for DIY, only requires resistors.
The bad reputation of ESLs for killing amplifiers comes from people trying to drive large capacitive ESLs directly through the transformer e.g., using active equalisation. The impedances have to be very low to avoid the bandwidth limiting effects, and the slightest problem will result in massive currents and a suicidal race between the fuse and the OP transistors.
regards
R
Hi all ... & many thanks for your feedbacks ;-)
... BTW before replying ... I notice that both Chris & golfnut are from New Zealand ... maybe there's some interest in electrostatics there ... ?
@Chris Daly: As it is I actually have a copy of the Peter Walker article and have read it a couple of times. It is a quite interesting paper, however, besides detailing some of the theory of electrostatics (like e.g. the bandwidth vs efficiency correlation) I didn't remember it being specific about ESL efficiency (could be, though, that my memory lacks here).
In any case I was hoping that someone had actually measured the voltages going to their panels (together with some information on the design) so that I could get an idea about the actual requirements for driving an ESL.
@golfnut: Thanks for outlining some practical technical aspects of ESL design - and some of the work-arounds for compensating for the capacitance of the ESL assembly ;-)
Regarding the Baxandall paper I will just consider ordering the book from the library - I think it is available here in Denmark.
And then I'd like to "re-phrase" from #1 that my main reason for asking this question - what is actually needed to drive an ESL - is that I am curious as to if it is at all feasible to direct drive an ESL - i.e. build a (superb!) dedicated amplifier to drive the ESL without the transformer in-between. Thus omitting the band limiting of the transformer etc. ...
I realize there may indeed be challenges in designing such an amplifier but knowing what the approximate required voltage/currents needed are may give an idea about the magnitude of such challenges. Again, I will need to play loud so SPLs around 115 dBs are likely ...
Anyone knowing about this?
@sumotan: Hi & thank you also for your input. But as I write above I would like to omit the transformer, if possible.
Cheers,
Jesper
... BTW before replying ... I notice that both Chris & golfnut are from New Zealand ... maybe there's some interest in electrostatics there ... ?
@Chris Daly: As it is I actually have a copy of the Peter Walker article and have read it a couple of times. It is a quite interesting paper, however, besides detailing some of the theory of electrostatics (like e.g. the bandwidth vs efficiency correlation) I didn't remember it being specific about ESL efficiency (could be, though, that my memory lacks here).
In any case I was hoping that someone had actually measured the voltages going to their panels (together with some information on the design) so that I could get an idea about the actual requirements for driving an ESL.
@golfnut: Thanks for outlining some practical technical aspects of ESL design - and some of the work-arounds for compensating for the capacitance of the ESL assembly ;-)
Regarding the Baxandall paper I will just consider ordering the book from the library - I think it is available here in Denmark.
And then I'd like to "re-phrase" from #1 that my main reason for asking this question - what is actually needed to drive an ESL - is that I am curious as to if it is at all feasible to direct drive an ESL - i.e. build a (superb!) dedicated amplifier to drive the ESL without the transformer in-between. Thus omitting the band limiting of the transformer etc. ...
I realize there may indeed be challenges in designing such an amplifier but knowing what the approximate required voltage/currents needed are may give an idea about the magnitude of such challenges. Again, I will need to play loud so SPLs around 115 dBs are likely ...
Anyone knowing about this?
@sumotan: Hi & thank you also for your input. But as I write above I would like to omit the transformer, if possible.
Cheers,
Jesper
Hi gentlevoice, if your goal is a couple of m2s in a large room, you may go for many smaller sections, like 8 x 0.25 m2 each. A transformer will be needed for impedance matching, but not the transformer will limit upper and lower corner frequency. Lower is limited by the dipole principle (front-to-rear cancellation) and higher by the diphragm thickness. If you use e.g. 8 sections each 0.25 m2, it will be 2 m2. Then you can have 8 transformers, one for each section, and combine the primaries series/parallel for better matching. Study how Acoustat achieved large surface using several smaller panels (2+2).
As for omitting the transformer, there are serious arguments against it: you are dealing with lethal voltages. The driving audio voltage is several hundred volts (yes it could be easily delivered by a tube amplifier, but then you would need huge coupling capacitors in terms of capacity and voltage, at the end the size and cost won't be less than using transformers), and there is the bias voltage of several kilovolts. If you use 8 x 50W transformers, their size could be really small.
As for omitting the transformer, there are serious arguments against it: you are dealing with lethal voltages. The driving audio voltage is several hundred volts (yes it could be easily delivered by a tube amplifier, but then you would need huge coupling capacitors in terms of capacity and voltage, at the end the size and cost won't be less than using transformers), and there is the bias voltage of several kilovolts. If you use 8 x 50W transformers, their size could be really small.
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I suppose there is no theoretical obstacle to any extension of ESL powers. But like with cone drivers, the trade-offs are challenging: size, movement, corona discharge, beaming.......... I'd guess dreams of low freq extension and loudness have to be eased.
Dayton-Wright ESLs were capable of great loudness, maybe KLH 9s some too. The Dayton-Wrights cells were enclosed in a heavy gas in an acoustically (almost) transparent box, that brought important benefits of various sorts.
I kind of don't like transformers with their idiosyncrasies. I built and used a direct-drive amp for a few decades. Certainly the best sound I've ever heard.
B.
Dayton-Wright ESLs were capable of great loudness, maybe KLH 9s some too. The Dayton-Wrights cells were enclosed in a heavy gas in an acoustically (almost) transparent box, that brought important benefits of various sorts.
I kind of don't like transformers with their idiosyncrasies. I built and used a direct-drive amp for a few decades. Certainly the best sound I've ever heard.
B.
Hi again ... Icsaszar & bentoronto - thank you both for your replies.
@bentoronto:
However, I've searched some more in other diyaudio threads and noticed that Calvin in this thread & post mostly answered my question:
http://www.diyaudio.com/forums/plan...ive-esl-amp-projects-share-6.html#post5066713
So it seems that the voltage & current demands are quite substantial. Things to ponder ...
Thanks again for replying ... I think I now know what I need to know.
Cheers,
Jesper
@bentoronto:
... This is along my line of thinking and the reason why I asked my question in #1.
However, I've searched some more in other diyaudio threads and noticed that Calvin in this thread & post mostly answered my question:
http://www.diyaudio.com/forums/plan...ive-esl-amp-projects-share-6.html#post5066713
So it seems that the voltage & current demands are quite substantial. Things to ponder ...
Thanks again for replying ... I think I now know what I need to know.
Cheers,
Jesper
My colleague Frank Verwaal studied the theory of electrostatic loudspeakers before building his own and also made his own Matlab scripts for simulating the SPL, see Elektrostatic Loudspeakers
By the way, with his ESL design 2 kV peak was not enough for an ordinary living room.
By the way, with his ESL design 2 kV peak was not enough for an ordinary living room.
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Hi Marcel ... Thank you also for considering my question and replying.
Incidentally I actually found this webpage of yours yesterday evening while searching for information about ESL power requirements. As it is, however, I am not familiar with Matlab so I would not be able to use his simulation ...
Ok, very useful information, thanks! ... that really is my worry ... that ESLs are so power hungry that driving them is quite a challenge. A DD amplifier is my best guess but can e.g. the PSU be made sufficiently stable at such high voltages - and will it be able to deliver sufficient current while keeping the voltage stable ...
Anyway, I might just ponder this ... and otherwise consider my question replied.
Cheers
Jesper
Incidentally I actually found this webpage of yours yesterday evening while searching for information about ESL power requirements. As it is, however, I am not familiar with Matlab so I would not be able to use his simulation ...
Ok, very useful information, thanks! ... that really is my worry ... that ESLs are so power hungry that driving them is quite a challenge. A DD amplifier is my best guess but can e.g. the PSU be made sufficiently stable at such high voltages - and will it be able to deliver sufficient current while keeping the voltage stable ...
Anyway, I might just ponder this ... and otherwise consider my question replied.
Cheers
Jesper
I always thought that an 833 triode could directly drive any electrostatic speaker element.
The 833 is rated for up to 3kV B+, and with a proper choke (multi chokes, or multi sectioned choke) could have enough inductance and low enough distributed capacitance to work with the 833 medium plate impedance. RF chokes were built this way, but can be applied to audio too. They need to be floating (no capacitance from the magnetic cores to ground).
The 833 could then swing from a couple hundred volts, to almost 6kV. The 833 is an RF tube, u = 38, and can swing to 2X B+ without arcing over. That is plenty to drive any electrostatic element I know of.
You need a very high voltage capacitor from the junction of the choke and 833 plate, to a resistor to ground (RC coupling from the junction of the 833 plate-and-choke, to the resistor and membrane).
You have to have one stator at + HV, and the other stator at - HV in order to make the membrane move properly. Then you have to have very high voltage insulation outside of the stators.
This is not for anybody that can not safely design, build, and operate one (and safe for all who come near such a high voltage device). All voltages have to be completely inaccessible.
The 833 is rated for up to 3kV B+, and with a proper choke (multi chokes, or multi sectioned choke) could have enough inductance and low enough distributed capacitance to work with the 833 medium plate impedance. RF chokes were built this way, but can be applied to audio too. They need to be floating (no capacitance from the magnetic cores to ground).
The 833 could then swing from a couple hundred volts, to almost 6kV. The 833 is an RF tube, u = 38, and can swing to 2X B+ without arcing over. That is plenty to drive any electrostatic element I know of.
You need a very high voltage capacitor from the junction of the choke and 833 plate, to a resistor to ground (RC coupling from the junction of the 833 plate-and-choke, to the resistor and membrane).
You have to have one stator at + HV, and the other stator at - HV in order to make the membrane move properly. Then you have to have very high voltage insulation outside of the stators.
This is not for anybody that can not safely design, build, and operate one (and safe for all who come near such a high voltage device). All voltages have to be completely inaccessible.
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The 833 may not be worth it, since as far as I know, nobody has even tried this approach.
The essence of the design seems logical to me, just more than anybody wants to do, or even thought of.
I would love to build an SE 845 amp, but even that tube requires more work, expense, and weight than I want to deal with.
My friend built a pair of Western Electric 212E SE mono blocks.
Yes, special safety design considerations must be taken, and properly implemented for any of these high voltage beasts.
It amazes me how many tube amplifier schematics I see without any B+ bleeder resistors.
And some that do have bleeders, have such long time constants that it takes a minute or more to discharge to a safe Voltage.
For such high voltages as used in an 845 amp, I would have more than 1 set of bleeder resistors.
What if one failed?
Even for my lower voltage amplifiers, I use a DMM to test the B+ at all capacitors, in case the bleeder fails, or one of the resistors from one filter cap to the next filter cap failed.
Even many types of test equipment are subject to the safety rule of 42V maximum for exposed connections.
The essence of the design seems logical to me, just more than anybody wants to do, or even thought of.
I would love to build an SE 845 amp, but even that tube requires more work, expense, and weight than I want to deal with.
My friend built a pair of Western Electric 212E SE mono blocks.
Yes, special safety design considerations must be taken, and properly implemented for any of these high voltage beasts.
It amazes me how many tube amplifier schematics I see without any B+ bleeder resistors.
And some that do have bleeders, have such long time constants that it takes a minute or more to discharge to a safe Voltage.
For such high voltages as used in an 845 amp, I would have more than 1 set of bleeder resistors.
What if one failed?
Even for my lower voltage amplifiers, I use a DMM to test the B+ at all capacitors, in case the bleeder fails, or one of the resistors from one filter cap to the next filter cap failed.
Even many types of test equipment are subject to the safety rule of 42V maximum for exposed connections.
Building a large surface area is a good trade-off to get loudness at lower frequencies.*
Big spacing and pushing bias to the "humid air" limit of maybe 12kv also feasible (no risk with very large series resistors in the bias supply).
I lived with DD for a long time. The system is spatially contained and user can picture the danger zone and always pull the mains plug before going near the zone.** But whenever I mention DD esp to tout benefits, I try to always point to the risk.
B.
*among the many "theories" of Dayton-Wright speakers was putting the 8 cells forming each speaker on the surface of a sphere thereby making a curved radiator, with the sphere origin like 10 feet behind.
*in one house, I had the amp in the basement with the wires coming up through the floor. Parts of the speaker assembly were still lethal, but the amp lived happily and cooly in the basement.
Big spacing and pushing bias to the "humid air" limit of maybe 12kv also feasible (no risk with very large series resistors in the bias supply).
I lived with DD for a long time. The system is spatially contained and user can picture the danger zone and always pull the mains plug before going near the zone.** But whenever I mention DD esp to tout benefits, I try to always point to the risk.
B.
*among the many "theories" of Dayton-Wright speakers was putting the 8 cells forming each speaker on the surface of a sphere thereby making a curved radiator, with the sphere origin like 10 feet behind.
*in one house, I had the amp in the basement with the wires coming up through the floor. Parts of the speaker assembly were still lethal, but the amp lived happily and cooly in the basement.
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I should have read more of the literature, I guess Direct Drive has been much used for a long time, I just never saw anybody use an 833 for that.
Decades ago, another fellow and I had a special woofer negative feedback scheme. It did not use current sense or voltage sense negative feed back, and did not use an accelerometer.
We built a rudimentary prototype to prove the concept, but we never developed it into a product. Modern materials might or might not negate the need for the method we developed.
Decades ago, another fellow and I had a special woofer negative feedback scheme. It did not use current sense or voltage sense negative feed back, and did not use an accelerometer.
We built a rudimentary prototype to prove the concept, but we never developed it into a product. Modern materials might or might not negate the need for the method we developed.
Hi,
if I were tempted to build a DD Tueb amp, the 833 would be high in my favourites list.
It certainly is a beefy tube, able to cope with the complex currents of the load.
Besides it´s power capabilities and lowish plate impedance it might be interesting feature that a suitable bias point is at Vg=0V or close to 0V.
One needs of course a driver that can deal with asymmetric loading, as a positive signal swing at the tube´s gate will draw some gate current/gate power.
jauu
Calvin
if I were tempted to build a DD Tueb amp, the 833 would be high in my favourites list.
It certainly is a beefy tube, able to cope with the complex currents of the load.
Besides it´s power capabilities and lowish plate impedance it might be interesting feature that a suitable bias point is at Vg=0V or close to 0V.
One needs of course a driver that can deal with asymmetric loading, as a positive signal swing at the tube´s gate will draw some gate current/gate power.
jauu
Calvin
If you can estimate the equivalent sound pressure in the free field, and assuming that the loudspeaker will be designed for a flat far-field response, then you could use Walker's equation to find the required current.
You already know the required sound pressure level at the listening distance. If that distance is within the reverberation radius (see http://journal.telfor.rs/Published/Vol2No2/Vol2No2_A6.pdf ), you can take the listening distance as the equivalent distance for free field listening, otherwise you can take the reverberation radius as the equivalent distance for free field listening. Maybe you have to correct for floor reflections - does anyone here know how to do that?
According to Walker's equation,
p_rms = (Vp/d) (i_rms/r) (1/(2 pi c))
with p_rms the RMS sound pressure, Vp the polarizing voltage, d the diaphragm to stator spacing, i_rms the RMS current through the loudspeaker, r the free-field listening distance, pi the ratio of the circumference and diameter of a circle and c the speed of sound.
Taking Baxandal's recommendation for the polarizing voltage, Vp will be half the product of the breakthrough field strength of air and the diaphragm to stator spacing, so Vp/d will be half the breakthrough field strength of air. That one half of 3.1 kV/mm to 4 kV/mm for spacings between 2 mm and 10 mm. Let's call this (1/2) E_breakthrough.
i_rms then follows from
i_rms = r p_rms (2/E_breakthrough) 2 pi c
For example, with r = 2 m, p_rms = 10^(115/20) * 20E-6 Pa, E_breakthrough = 3.1E6 V/m, c = 340 m/s:
i_rms ~= 31.00181202 mA
In practice you will have some losses, taking safety margins, charging up cable capacitances and so on, so maybe 40 mA to 50 mA RMS. This is assuming that a single loudspeaker has to reach 115 dB SPL, if you have two of them and they add in power it gets sqrt(2) times smaller, so in the 25 mA to 35 mA ballpark.
The voltage required to get this current to flow through a capacitive loudspeaker is inversely proportional to frequency. That's why it helps to restrict the bass response.
Walker's equation neglects diaphragm mass and diaphragm resonances. If you would manage to get the diaphragm resonance close to the lowest frequency you want to reproduce and if you could damp its Q to (for example) 2, you could get away with half the current at the lowest frequency of interest. That's one of the tricks Walker himself used in the ESL-63 to get a decent sensitivity. It does mean that you basically have a third-order Chebyshev alignment for the bass.
Mind you, all of this is assuming that the listener is in the far field. Practically that means that the hight and width of the diaphragm area that radiates treble needs to be made small enough. You will need some sort of cross-over to have a large diaphragm area available for bass and only a small one for treble. Loudspeakers designed as line sources are not meant for far-field listening, they are somewhere in between near field and far field. Anyway, you can find all about that on Frank's website.
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@MarcelvdG: Wow! ... thanks for detailing how to calculate the current in an ESL
As it is I'm still pondering what may be feasible to do. If it is possible to make a superb DD amp for an ESL panel my guess is that the sound may be second to none (i.e. if the ESL is also very good, of course).
However, over the years I have experimented with setting the bias currents in various amplifiers and given that increasing the OPS bias current did not cause the amplifier to either experience some kind of thermal run-away or go into oscillation I cannot remember even once where sensibly increasing the current did not bring about a (often significantly) improved sound ... I am saying this because due to power dissipation considerations the bias current in a DD amp would have to be rather low, so maybe what is gained by direct drive is lost elsewhere ... ?
Additionally, e.g. 8 kV DD voltages and essentially no current limitation likely would be lethal ... so some kind of very solid screen would have to be around the ESL - a screen that is at the same time entirely acoustically transparent ...
So, I must admit that I am a bit reluctant in this ... intrigued by the ESL driver itself, yet maybe altogether e.g. a magnetostat is a more feasible solution in practice.
Cheers & thanks again Marcel,
Jesper
As it is I'm still pondering what may be feasible to do. If it is possible to make a superb DD amp for an ESL panel my guess is that the sound may be second to none (i.e. if the ESL is also very good, of course).
However, over the years I have experimented with setting the bias currents in various amplifiers and given that increasing the OPS bias current did not cause the amplifier to either experience some kind of thermal run-away or go into oscillation I cannot remember even once where sensibly increasing the current did not bring about a (often significantly) improved sound ... I am saying this because due to power dissipation considerations the bias current in a DD amp would have to be rather low, so maybe what is gained by direct drive is lost elsewhere ... ?
Additionally, e.g. 8 kV DD voltages and essentially no current limitation likely would be lethal ... so some kind of very solid screen would have to be around the ESL - a screen that is at the same time entirely acoustically transparent ...
So, I must admit that I am a bit reluctant in this ... intrigued by the ESL driver itself, yet maybe altogether e.g. a magnetostat is a more feasible solution in practice.
Cheers & thanks again Marcel,
Jesper
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