Impedance Corrections for ESLs

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Some friends of mine and I are in the midst of an electrostatic speaker project. They work great, and now we're in the post-build process of setting up; getting them prepared for everyday duty.

After some experimentation, we ran them on an impedance analyser, and got this god-aweful plot that peaks around 170 ohms at 700hz, and drops to less than .4 ohms around 20khz. The phase shift swings more than 70 deg around 20 hz, and -80 deg around 5khz. This is dangerous to our amps, so we're looking for methods of cleaning up the complex impedance that the amp (or crossover) sees.

For those unfamiliar, the electrostatic speaker consists of a stepup transformer, and two parallel plates with a charged membrane suspended between them. The amp plugs into the the transformer, the transformer powers the plates, and the membrane gets pulled back and forth. So the impedance the amp sees is some combination of capacitive and inductive impedance.

SPICE seems to have trouble realistically representing a transformer, so my efforts of computer modeling the system have hit a roadblock. If anyone can provide some assistance in this aspect, that'd be great. . .

I'd heard mention of a Zobel network for smoothing inductive impedance for regular magnetic coil speakers. I was wondering if a similar configuration would work for the ESLs. RIght now, we've just got a big, honker 2ohm power resistor in series with the transformer on the amplifier side, so that helps boost the resistance a bit (though of course we're dissipating a lot of wasted power as heat). But that doesn't help with the wild phase shift swings, which could induce all kinds of crazy destructive oscillations in our amps. If anyone could give me some help, or point me in the right direction, it'd be most appreciated. Thanks.

The resistor in series with the transformer will help tame the impedence somewhat and help the bass, but it can sometimes shut the highs down. I have found that bypassing this resistor with a good quality film cap can help.
You will have to experiment with values, try starting with 1uf.


P.S. What is the turns raito of yuor transformer?

[Edited by jam on 10-03-2001 at 11:38 AM]
With the current setup, the turns ratio of our step-up transformer is around 50:1. They're the transformers that are for sale at the Electrosatic Speaker Exchange. There's little to no documentation on these things, so I'm a bit uneasy about them. I DID pump them with white noise, and took the 100-second average of the output power vs. frequency plot. It wasnt very linear . . . but then I dont really have anything to compare it to. If anyone can tell me what I should expect, I'd be happy to try that again.

I don't quite understand how a simple resistor could affect frequency response, other than shifting the whole plot up two ohms, but I'll take your word for it. One interesting thing is that what you're describing with the capacitor is starting to resemble what I've seen of a zobel network, for instance here . It'd be nice to flatten out the resistance component of the impedance, but what im really worried about is the phase shift. We've blown 3 amps so far, and while my compatriot Dan doesn't agree, I think it was from excessive phase shift at the low and high audible ends. So right now we're using an equalizer to heavily deaden the lows and highs - needless to say it sounds less than full. Thanks for the help, we'll try the shunted capacitor and see what happens. Thanks again.
- Jonathan
The first blown amp was my friend Dan's Aiwa shelf system, i dont rememeber the model or power rating. The second amp was a Yamaha receiver, rated at 100 wpc, I dont remember the model. The third blown amp was a Yamaha R-9, I think rated around 150 wpc. The R-9 has since been repaired, and we dont run it abouve -34db, along with the heavily damped equalizer I described before.

Dan believes all three amps were blown because we turned them up too far. Opening them revealed blackened output stage transistors in all three cases. Oddly enough, the Yamaha website recommends not turning up any of their amps beyond the halfway mark on the volume knob. But surely with a normal commercial set of speakers, its not this easy to blow an amplifier.

We're both planning to use different amps in the final setup; Dan recently bought a Yamaha MX-830 power amp rated at 190 wpc. We have no desire to blow more amplifiers, but we also dont want to have to limit our sound as severely as we have in order to be safe. The goal as I see it is to make these speakers as safe to drive as a commercial set of speakers (or at least as close as possible). Any help you can provide is of course, greatly appreciated. Thanks.
- Jonathan

Yamaha amplifiers are not particularly great on driving reactive loads, I should know because I used to repair them.
I would suggest a Hafler, Adcom or Aragon as a better choice.
The main problem that you are facing is the low dc resistance of the transformer. The solution would be to use two large back to back elactrolytics, about 1000uf 50v, bypassed with a film capacitor in series with the transformer. Remember that capacitors in series are half the value of one capacitor. This should prevent your amplifier from blowing up, though I do not recomend using anything built by Yamaha to drive electrostatics.

Before my compadre Jon gives any false ideas, let me describe what happened to these amps, as they belong to me. The Aiwa system was rated at 30 wpc, a meager amount when trying to drive electrostatics. To its credit the music was barely audible at the maximum volume of the unit very shortly before its smoking demise. The second amp blown was a Yamaha A-27. It was playing a softly recorded tape when it blew. The soft recording demanded that the volume be turned past its dreaded halfway point. However, it had put in almost a week of demonstrations prior without any problems. The third amp blown was a 150 wpc yamaha that was purchased off of ebay. In an attempt to hook the speakers up to the the B+C setting (3 Ohms), I, through ignorance, shorted the terminals. Amps do not like this. Obviously the electrostatic load did not have any impact. The 100wpc amplifier was repaired and sounds as solid as ever on the electrostatics. Of course, I'm playing CD's which don't carry as much sound covering static as the softly recorded tape. I find that the volume knob at around -34dB (one fourth) is loud enough as I need it. At this level the wattage indicators only peak in the "red zone" once in a while.
It seems to me that the problem with the electrostatics is human error rather than a mechanical problem. Of course with a larger more robust amplifier I feel more comfortable. Hence, the MX-830 with a 190wpc safety net and impedances as low as 2 Ohms.
Hope that this will shed some light on a possible problem and/or solution.

PS If any one is in the market for a less than perfect R-9 let me know! :)
Putting a 2 ohms resistor in series with the transformer, while preventing the amp from seeing 0.4 ohms at 20kHz (it now sees 2+ 0.4 = 2.4 ohms) will also attenuate the sound level by over 15dB at 20khz, 7dB at 10kHz, 3.5dB at 5kHz etc, so no wonder you now don't hear any highs from the speaker. Kind of defeats the purpose of having a low mass diaphragm, doesn't it !! Basically, you have to much diaphragm area /too small plate speacing / too high transformer turns ratio, take your pick. The resultant capacitance is too high so the reactive impedance is too low at high frequencies.
As for the low frequencies, the impedance is partly governed by the value of bias voltage you are using, as this cuases a negative compliance in series with the positive compliance due to diaphragm tension. Electrostatics are very complex beasts, despite the apparent simplicity of their construction. They do have wild impedance swings and demand very capable amplifiers to drive them. If you are interested in reading the most comprehensive and thorough treatment ever published on electrostaic speakers, look at he book "Loudspeaker and Headphone Handbook" edited by John Borwick, Focal Press, ISBN 0 240 51371 1. It is excellent though very complex.
A very good reference, I've read it several times but still I don't understand it fully.
My experience with the low (and complex) impedance of an ESL turns out most transformers are the pain in the ***. Many transformers are rather poor, with a too big secondary capacitance and leak inductance.
An example: 1:100 ratio, Cs=1nF will give 0.8ohm at 20kHz. These numbers are are not uncommon!
If you hook up an ESL (1nF), this number will halve!
To check the influence of the transformer, do an impedance measurement without an ESL hooked on. This will make a lot clear.

I don't like series resistors in the primary winding, though sometimes it's the last way to go. The best way it to try to get a better transformer.

I ahve done some spice simulations with an ESL and transformer, using microcap. I generated a spice listing, mayby you can use it...:
CESL 4 0 {1.2N*100*100}
CMYLAR 5 4 {C(CESL)*2.5}
CP 1 0 20P
CS 4 0 {1N*100*100}
LAIR 6 0 450M
LP 0 2 0.2
LS 3 4 5U
RAIR 5 6 44
RLOSS 0 2 220
RP 1 2 0.2
RSEC 2 3 0.1
VGEN 1 0 AC 1 PULSE (0 1 0 1e-006 1e-006 0.000499 0.001)

.AC DEC 171 1 1e+006
.PLOT AC (V(VGEN)/I(VGEN)) 0.3,300
.PLOT AC VDB(5) -80,20
.PLOT AC VP(5) -180,180

success with it...
Thank you very much for the info. I agree completely that a series resistor is pretty crappy, even if the frequency dependant attenuation wasn't a factor, you're still losing power for no other use but heating the room. Any method of helping our impedance that doesnt resort to power resistors would be ideal.

Also, thanks for the netlist, that did help a lot. And on that topic I've got some questions. First of all, given a physical transformer, what sort of calculations must be prepared to represent it in the model you've proposed? Are the values for R,L,C primary/secondary just the raw measurements of the transformer? I assume Rloss is just an efficiency estimate. Is this model of a transformer really accurate? If it is, damn, why dont they use that in most spice models . . .

Next, i see you have plot defined as V/I of the voltage source. Is this a plot of the impedance that the amp would see in the real world?

And finally, Im a bit confused about your esl model, as shown. What are Cesl and Cmylar, and why are they in parallel? What are R(air) and L(air), and what do they relate to in the real world, and why are they in series with Cmylar? And lastly, you're plots refer to the phase and voltage at point 5, between Cmyl and Rair. Whats the physical significance of that point? Why is it important? I realize these questions are going to seem pretty elementary, I've got a lot of holes in my electronics experience. Thanks for any help you can offer, and for the help you've already given me.

- Jonathan
Hi Jonathan,

The model of the transformer I got from an ESL building friend of mine, I'm not an expert on this topic, but I'll try to answer your questions.
RLC prim/sec are just the values of the corresponding variables of a transformer. Rloss is, I think, the loss of the core. This is not a very accurate model, is doeas not include the core for example, but can be used for most cases. The simulation I, among others, did correspond very well with the actual measurements.
I think other models are around.....

V/I of the generator is indeed the impedance of the total schematic, so this is what the amp will see.

The ESL model I used is from "Loudspeaker and Headphone handbook", chapter 2. This describes in a lot of detail an ESL.
Cesl is just the capacitance between the two plates,
Cmylar has to do with the stretch-strength of the mylar, the force which pushes the mylar in it's middle position,
Rair and Lair is a model of the accoustical resistance of the air, so the actual sound is the power from these. This last point is my personal interpretation of the theory, but it looks ok, I think. The values of Rair and Lair are just chosen to give a nice plot, I don't really know what to put there.

By the way, all secondary values are transformed to primary values, so divided by 100*100, for a 1:100 turn ratio.
My friend Dan, as mentioned above, has built a working set of ESLs and using this god-aweful huge 'inpedance analyser' we have in the lab, I generated the below impedance data. This is the impedance across the entire load circuit (across what would attach to the amplifier speaker terminals). Shown vs. frequency are the magnitude and phase plots of the transformer by itself, and also the transformer attached to the esl (but without the bias supply activated).

The project now, as stated before, is to try to even out the impedance the amplifier is driving. The peak around 500 hz isn't too troublesome, nor is the corresponding phase shift there (34.5 deg.). What bothers us is the low ends of the peak; 0.4 ohms at its worst. Also, the phase shift extremes approach 85 degrees at either end. This, I've been told, could do bad things to amplifier stability, sending it into ultrasonic oscillation.

When constructing a crossover circuit for regular magnetic drivers, there's a correcting device called a Zobel Network, that fits between the speakers and the crossover. Basically, its a filter of some sort (or so I gather). I've seen plots of before / after input impedances, and it seems to be doing what I would like to do here. I've mentioned it before, but here it is again: this site talks about this zobel network . The problem, of course, is that this is not a simple mostly-inductive load like most magnetic drivers.

What would anyone suggest here, to even out the impedance curve, keep the impedance away from dangerously low values, moderate the phase shift extremes, and do all this without loosing too much power to resistive heating? As mentioned above, sticking a resistor in series with the transformer is not the best option. Thanks for any help.
- Jonathan

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what I did not mention before, a well known way to improve the impedence and performence of an ESL is to place series resistors between the secondary of the transformer and the ESL, so one on each side. This will lower the Q of Lsec and Cesl, which improves impedence, phase (I prefer to talk about groupdelay), and amplitude around the top end of the audio spectrum. Due to Csec you hav some limits, and the resistors must be choosen carfully, but with this the dip can be made almost the same as without an ESL attached.

I have with a Cesl of 500pF the best result with two resistors of 10k each.
Try a 10 OHM Power Resistor in Parallel with the transformer

I am using the same kinds of transformers on my ESL panels and they have been running for almost a year on a Crown DC-300A power amp. I spoke with Barry at the ESL info exchange, and he put me in contact with a friend of his who suggested that for a passive crossover you should put a ten ohm power resistor in parallel with the transformer's primary. This will produce a smoother curve when using passive high-pass crossovers (and also gives the amp a resistive load to drive). This suggestion works, just remember to use a 50Watt power resistor mounted on a heatsink.

My ESLs use a 47uF solen cap in series with the primary, and the 10 ohm resistor in parallel(after the capacitors). This rolls mine off at around 500 hz. Then I use a conventional woofer.

See my website for more details:
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