Electrostatic Loudspeaker Design
Neil S. McKean
This is article has been written for inclusion in the DIY Loudspeakers homepage, with the intention of addressing the main issues in the design and construction of an electrostatic loudspeaker .
There have been many excellent articles written over the years regarding ESL design and construction and a bibliography is included at the end of this text. I will avoid a formal treatment of the wave equation for stretched membranes of various shapes and the operation of the speaker in terms of the internal forces applied, as these have been well covered in the literature. The bibliography will enable the constructor to gather as complete a resource guide as possible.
The four main categories to be covered in the text are :
- Design constraints
- Materials technology
- Speaker topology
- Construction details
The basis of the electrostatic speaker is that of a planar panel of either circular, square , rectangular or even triangular shape. The main characteristics of such a planar panel are :-
- The driven plate mass (diaphragm) has a very low value and is approx. the mass of a few mms of air.
- The motion of such a diaphragm is essentially linear.
- The design must be push-pull for low distortion.
- The reactance of the air mass presented to the motion of the diaphragm is different to that of a cone loudspeaker.
- The nature of the load impedance presented to the driving amplifier is essentially capacitive.
Some definitions of the basic characteristics involved in ESL operation are given below as these will be referred to in the text and it is useful to be able calculate these quantities in the design of speaker panels which may depart in dimensions from the ones to be described later.
C = k A / d
C is the capacity of the speaker in Farads
A is the panel area in sq.meters
d is the diaphragm / plate distance
k is a constant (8.85 X 10^-12)
E is the field strength in volts/mil.(0.001 in)
V is plate to diaphragm voltage
d is plate to diaphragm distance in mils.
For constant Q (charge) the force on the diaphragm is independent of the its position between the plates and is essentially linear. The only non-linear parameter is due to the compliance of the diaphragm, and since its magnitude is small, is not a significant influence on the diaphragm motion.
For a diaphragm whose diameter is large compared to the longest wavelength to be reproduced, the mass reactance of the air load on the diaphragm can be ignored and the impedance seen by the diaphragm is essentially resistive. When the load is resistive , the diaphragm velocity and acoustic power are independent of frequency. Not until the reactance, as result of the diaphragm stiffness, exceeds the resistive air load does the output drop at a rate of 6dB/oct. At the top end of the spectrum, the reactive effects are due to the mass of the diaphragm and have no part to play below about 20KHz, as long as the mass of the diaphragm is small.
The characteristics of ESL panels in respect of air load / diaphragm interactions have implications for the size, frequency range and topology of a practical ESL speaker.
Suitable construction materials:
Styrene ( plastic)
Copper clad epoxy laminate
The panel materials listed above are all suitable for use as driven plates in an esl speakers. The important features of each are discussed below:
- Needs to be perforated to 50 - 60% of the panel area and must not be thick, so as to avoid restriction of air from the diaphragm movement and any apparent "breathing" characteristics through the panel.Typically the maximum thickness would be about 1.6mm and be uniformly flat to avoid irregularities in field strength across the plate to the diaphragm. Burrs from perforations if any must be away from the diaphragm. (During preparation for the anodising process most burrs would be removed by chemical etching).
- Anodising must be carried out after perforation. It would be possible to drill all holes in aluminium panels after first making a panel template (to save costs), however the time required will be considerable. The anodising could be replaced with high voltage insulating varnish but these chemicals do not adhere very well to Al. and in any event the anodising gives the desired colour and hence pleasing appearance.
- Anodising insulates the plates well from the high driving voltage and renders them safe. A small area of anodising must be scraped away on the bottom of the panel for electrical connection.
- Decorative anodised mesh is often available at a moderate cost and can be a suitable material as long as the previously stated requirements of thickness, openness and rigidity are met.
- This group includes high-impact and ABS types.
- This material is a good, cheap option, comes in a number of colours (including black) and requires little or no preparation.
- The styrene must be perforated and kept flat as with the aluminium.
- The surface is first roughened with 220 grade oxide paper and then made conductive by applying Electrolube nickel loaded spray. In this case 0.002" thick gives a low resistivity. The base fluids are xylene and acetone, which provide a good key in the plastic for the metal. The cost of this preparation is about $55AUS ( $40 US) per 500ml can and will cover many panels.
- The connection is made from the inside surface of the to panel bottom outside corner by a piece of very thin copper shim, window alarm tape or similar, to allow electrical connection. If the tape or shim is applied first the nickel is sprayed over the join to consolidate the connection.
- The cost of a 4x3' sheet of styrene is about $10 AUS ($7 US).
- Any burrs should be positioned away from the diaphragm.
- The outside of the panel requires no further treatment for electrical safety.
Styrene is the author's choice as it does not dull tooling and when used as the spacer, the material bonds easily to the driven panel. Many adhesives are suitable for styrene and most bond well to this material. Various forms of epoxy resins have been used in the past for construction, but the author finds them brittle and only marginally satisfactory.
- Dulls tooling easily and does not perforate readily.
- This material is reasonably costly.
- Can be painted, but best results are with epoxy paint which is expensive.
- Not the preferred material but is effective and requires no external insulation.
- Material is heavy but stable.
- Can be perforated but must be insulated on the outer surface.
- Steel is of moderate cost.
- Use only if other materials unavailable or a surplus is at hand.
There are other materials available but most of the materials that are suitable (most are metals and plastics) and available are either more costly or less suitable and less common than those listed above.
The critical factor for selection of the spacer material is the dielectric constant, as this parameter determines in part the capacitance of the speaker. Any energy that used in driving the frame capacitance is wasted and should be kept to a minimum. This is achieved by a low value of dielectric and minimisation of the spacer area. The frame capacitance is proportional to spacer area. The table below details some common plastics suitable as insulating materials. Plexiglas and polycarbonate can be used but are more expensive although they have suitable D.C of about 3-3.5.
Dielectric constants of some common plastics suitable for use as insulating spacers for ESL panels.
High Impact Styrene
From a cost point of view styrene is about the best and has a low dielectric constant and still maintains a high dielectric strength, so resisting breakdown and arcing. As stated earlier the styrene bonds well and can be chemically welded with the appropriate solvent, in this case xylene or toluene. Alternatively, less toxic plastic adhesives and contact adhesives give satisfactory bonds as there is relatively little stress on these bonds.
Bonding aluminium or other metals to styrene is best achieved with good quality contact adhesive. There may be a query with the longevity of the bond in certain climatic conditions with contact adhesives but the latest high quality types promise upwards of 25 years without problems and strength can be added by clamping the panels to a rigid frame (made from MDF) at least along the largest panel dimension with an appropriate gasket between the surfaces for acoustic isolation.
The only suitable material I have found is Mylar. The mass of 500 sq.cms of 12 micron Mylar < 1gm, so that the response of the panel is unaffected below about 20Khz. The 12 micron film is a little more robust than 6 micron film but any thickness of this order is satisfactory.
The diaphragm must remain stable under both static and dynamic conditions.
For practical speakers this leads to a large value of R = 50-200 Mohms or so and because the diaphragm forms a curved surface during its motion due to the interaction of forces ( the diaphragm is fixed at the sides and is not a true piston), this resistance must be uniformly distributed on the diaphragm surface to achieve constant charge and prevent charge migration due to the diaphragm motion.
The diaphragm must be tensioned to obtain static stability as well as the desired fundamental resonance. At this stage the method which I am suggesting for the size panels suitable for a practical speaker is detailed in the diagram below. Four lengths of wooden dowel approx. of 1 - 2" (2-5cm) are located on a table or piece board ( MDF is suitable ) as shown. The pieces can be fixed together at the corners if desired. A piece of clean, flat MDF, slightly larger than the speaker by 2-5 cms, is placed centrally in the frame so that top surface of the board is almost level with the height of the dowels. The mylar is then placed across the frame and 4 masses of between 100-500gms, depending on the desired resonance, taped to each edge of the molar ( support each pair of opposite weights) the supports are then removed in pairs and the tension is applied to the diaphragm. The panel with its adhesive may then be applied to the molar. This procedure will be further described in the construction section.
There are other techniques available see references at the end of the article. I will at a later time include a somewhat more complex stretching frame made from MDF and having the tension applied by adjustable threaded rods, but this a time consuming device to make and isn't actually necessary to achieve accurate results. Although if making a large number of panels would construction would be a worthwhile exercise. I do not recommend heat to shrink the mylar, at least in Hostaphan the film the author uses, as the elongation factor is quite low, and is not the same in both dimensions and most importantly the applied tension is not easily controllable. Heat, however may be useful in adjusting small differences in tension to enable the matching of the Fo of a particular panel. If the Fo of a particular panel is too low hot air from hair drier or heat gun can be used to increase tension slightly and bring the Fo up to the other value. The procedure must be carried out with care and the tension increased gradually until the desired Fo is reached.
With the two preferred methods, fundamental resonances of panels within 5 -10Hz of each other is achievable
The diaphragm tension T is proportional to fundamental resonance Fo and depends on the mass of the diaphragm, the shape, spacer thickness and the dimensions of the panel . This leads to a number of interacting parameters to give the desired Fo for a given shape. Higher tensions result in higher fundamental frequencies. The panel would be used in a range a little higher than the Fo of the panel e.g Fo=150Hz then use at ~200Hz and above.
For a rectangular diaphragm the Fo is proportional to
1/A × sqrt T/m
where A is the diaphragm area
T is the tension in the diaphragm
m is the diaphragm mass
The desired resonance is most easily determined by selecting a weight or setting near the required value and adjusting the value accordingly. See construction section.
The value of the peak diaphragm amplitudes are in the literature but a few common values are given below:
500Hz - ~ 0.015"
250Hz - ~ 0.03"
100Hz- ~ 0.06"
50Hz ~ 0.125"
These are somewhat conservative values and depend on the field strength.
Various coatings may be applied to the mylar to give the required high resistance coating.
This topic is most likely to be the most contentious in regard to the following speaker characteristics:-
- Low frequency characteristics
- Maximum reproducible sound levels
- Room interactions and positioning
- Dispersion relations
- Frequency and impulse response
I do not wish to canvass all the possibilities but rather the topologies that produce the most cost effective speaker in keeping with reasonable efficiencies, size and most importantly accuracy. The author's preferred panel dimension is one that is narrow and long compared to lambda / 3 at the lowest required frequency (lambda= wavelength).The width should be small compared to lambda / 3 at the highest frequency of interest. The strip can be assumed to be of infinite length providing the length of the strip together with the floor image is » lambda /3, when assessing the load on the strip with all pressures along the strip length equal. This gives rise to the following summary:
- The air resistance R is proportional to freq. F and couples reasonably well to low frequencies.
- The panel will have a good dispersion relation until the frequency attains lambda /3.( To extend the response to 3 -7 ocatves, the rear of the panel must be treated resistively and sealed so that the front air load resistance is maintained across the passband ).
- Where the panels are crossed over to other panels they are placed close so that they couple at a distance less than lambda / 4 at the cross-over frequency.
The recommended module sizes in the practical panel element to be covered in the construction section are:
2.25" x 18" (5.7cm x 45.7cm) _ spacer 1.6mm :- mid-range and treble
5.5" x 18" ( 11.5cm x 45.7cm) _spacer 3 - 4mm :- bass ( depends on lowest Fo)
Both dimensions are the effective diaphragm size and best meet the previous requirements of stability, sensitivity and dispersion when used in a practical loudspeaker.
The author does not recommend doublet configurations for the following reasons:
The main disadvantage of not using the rear output of the panels is offset by being able to:
Suitable low frequency panels with spacer distances to allow large excursions can be loaded adequately by rear enclosures just as with moving coil loudspeakers and the panels can be used above the resonant frequency or the fundamental resonance can be damped and output used below resonance to the required cut-off. Details of some such enclosures will be given after the construction section of this article. Such speakers may also be combined with moving coil units used in sub-bass configurations.
Several options are available for the bias voltage circuits are mentioned below:
Various EHT voltages may be attained by either varying the transformer secondary voltage or the number of sections in the multiplier or any combination. Note the output voltage shown here is negative with respect to ground. The current required from the transformer is only a few mA or less.
The EHT level can best be gauged by increasing the HV supply output ( if made variable) until the diaphragm starts to pull away from its static postion and oscillates back and forth. This sounds somewhat like the diaphram flapping and when this occurs the voltage should be backed of about 5-10% or until stable. This reduction makes only a very slight difference to the efficiency. Also if the speaker arcs over at any point due to the break down of insulation, the bias must be reduced and when thought to be set correctly should be tested again with reasonably high level of program material. If arcing occurs the bias must be further reduced or the panel re-made if requiring significantly different bias to other panels.
The Fo of the speaker should be tested by applying a sine wave to the amp input to only a moderate level and observing the speaker output on an oscilloscope. The frequency is varied until a maximum amplitude is apparent and this point is the Fo of the speaker.This resonance can also be readily identified audibly.
A satisfactory but more approximate way of detecting Fo if frequency generator and CRO are unavailable, is to place the panel with the 2 shortest edges on supports and then to tap the panel lightly with a pen, pencil or even finger. A characteristic resonance can be heard and panels can be approximately matched this way. An electronic tuning fork or musical instrument can be used to establish the resonant panel frequency. This is a static test and expect the Fo to drop by ~10-15% when the bias voltage is applied. All panels should drop by about the same amount so uniformity will not be a problem.
Once experience is gained with the diaphragm stretching technique and the required Fo is established, proceed to stretch and assemble the number of panels that are required for the entire speaker.
Speaker Topologies :-
1. The easiest design involves coupling a conventional moving coil unit as a bass driver. Typically the well known NHT 1259 would be a driver of choice, but there are many other units suitable. I would suggest that the moving coil type would need to be one of very low coloration in order to compliment the ESL panel array. Various bass enclosure types are suitable for coupling with ESL panels and many designs and ideas may be found in the Basslist and associated web pages. Several suitable panel designs are included below :-
- Open baffle monopole design : - This configuration suits mid / high panel from about 75Hz upwards with an Fo of between 60- 350Hz. The figure below shows the array, the dimensions of which may be varied to suit individual needs. The panels must be sealed at the rear and treated resistively with fibreglas wool or other suitable acoustic material. As previously indicated, the dispersion horizontally is that of a line source with the correct air load on the strip and the vertical coverage is good due to the height of the panel array. Any electronics , amplifiers and electronic xovers, etc may be mounted at the bottom of the array and at the same time the weight of these items provides a counter balance to speaker. N.B. More panels may be used than that shown and the supporting structure varied to accomodate them. A 3dB increase in sound level will occur with every doubling of the number of panels.
- Cylindrical bass enclosure :- The next configuration is designed to be full range with the option of crossing to a sub woofer for the very lowest frequencies, especially if very high acoustic levels are required at these frequencies. A 2 octave bandpass design may appeal, covering the range of ~20-40Hz. It should be noted that the panels are again enclosed and the rear of the panels are resistively treated as before. The enclosure is open at one end at the point where its length is 1/4 lambda, and the enclosure will radiate through this aperture at resonance. Above this frequency, if the cross-section of the enclosure is small compared to the wavelength, the enclosure volume behaves essentially as a capacitance. The enclosure Q can be controlled by the resistance of the material loading the rear of the ESL panel and part of this may be distributed through the enclosure volume if necessary. The enclosure walls should be 3/4 - 1" thick and possibilities for materials are thick cardboard tube, two concentric PVC tubes filled with sand and sealed top and bottom with pieces cut from a PVC sheet. One further possibility is that concrete pipe, where a 1/2" wall thickness would be suitable. The diameter of the pipe will be 15- 18", and a length of 6' giving full frequency reinforcement and radiating from the aperture at ~ 45Hz, and gradually falling below this. The fundamental panel frequency required for this speaker is 35-40Hz and a spacer thickness of 0.2" to accomodate the diaphragm excursion. The HV bias will in this case be of the order of 6KV. If difficulty is experienced in obtaining a low tension for this Fo, then the length of the panel may be inceased from 18" to around 24" which will lower the Fo for the same diaphragm tension, as the Fo is proportional to 1/A ( A=area of diaphram ). In order to mount the ESL panels a section must cut away to within an inch or so (2.5 - 3cms) of the top and bottom to facilitate mounting of the panels. If the wall material is concrete then a mounting strip of MDF may fixed to edges of the cutaway for mounting. In the case of PVC, a flat strip of PVC may be glued to seal the annulus on both sides and a strip at right angles top to bottom on both sides for mounting. In all cases the panels should be sealed to the enclosure with a thin foam waether sealing strip about 1/4" wide.
The base of this speaker can enclose any associated electronics, and should be weighted for stability.
Full range ESL
The enclosure height may be varied from 5 to 6' depending on the size and number of panels. For instance in the case of the 6' enclosure :- 3 panels 6.25" by 24" or 4 panels 6.25 by 18". Less panels may be used for smaller versions of this enclosure and the reader may wish to experiment with smaller diameter versions, perhaps with narower panels to a lower frequency for mid/high use. As a guide 3" width panels in a 6-9" diameter tube for operation to 150Hz with the column either full height or reduced height placed on a floor stand.
In all of the topologies above, panels are wired in parallel with each side of a set of driven plates in phase with each other. Similarly, all the diaphrams requiring the same bias voltage may be wired together in parallel.
Two more versions currently under development may be tried. the first of these is a telstar shaped system with a radius of about 1/2 metre, horizontal coverage of 180 degrees and vertical coverage of about 120 degrees. the unit is suspended at the top of a cylindrical bass enclosure based on a 6.5" to 8" drive unit. The small individual ESL panels are in this case triangular in shape and when forming the entire speaker are intended to approximate a point source, with near spherical dispersion characteristics.
The second, is a wall unit proposed in the literature by Peter Walker of QUAD. In this unit two of the 3 element panels are mounted in an enclosure enclosed within a wall and the cabinet treated internally so that it appears deep compared with the lowest wavelength of interest. The high frequency dispersion is controlled by the usual resistive treatment. Details of these designs will appear in a further update of this page. It should be noted that these two last designs would be suitable for advanced constructors.
This page will remain under construction for a time, while sections on complete speakers based on different topologies are added.
Neil S. McKean.