by Chu Moy
Electrostatic headphones continue to capture the imaginations of audiophiles, although dynamic types comprise by far the largest portion of headphones sold. The sound of electrostatic headphones is often characterized as detailed, low distortion and spacious, owing to their large area, lightweight diaphragms driven over the entire surface. For all the mystique that surrounds them, electrostatic transducers are in many respects easier for the DIYer to make than dynamic ones. Although commercial electrostatic headphones are the product of sophisticated manufacturing processes, homemade versions are also capable of high performance.
From 1968 to 1979, the U.K. magazine Wireless World published three projects for DIY electrostatic headphones by J.P. Wilson, Philip D. Harvey and Neil Pollock. This article reviews the concepts of electrostatic headphone design with attention to the contributions of each of the above authors. Warning: the high voltages involved in these projects do pose a serious danger. Only advanced DIYers familiar with high voltage construction techniques should attempt to build electrostatic headphones. As the projects are over twenty years old, some of the materials and parts described may be obsolete. However, the resourceful DIYer may find some inspiration herein to use modern materials and parts.
PRINCIPLES OF ELECTROSTATIC HEADPHONE DESIGN
For linear operation, an electrostatic transducer should be push-pull, and operate with a constant charge on its diaphragm. Figure 1 shows a cross-section of the basic assembly of a push-pull electrostatic transducer. It consists of two plates, two sets of spacers and a diaphragm. In a push-pull configuration, the diaphragm is suspended between two conducting, acoustically transparent plates which are fed high voltage audio signals that are 180 degrees out of phase. The diaphragm, which maintains a constant charge from a DC bias voltage, moves as the electrostatic differential between it and the plates varies with the audio signal.
In general, the requirements of a high performance electrostatic transducer are:
- The diaphragm should be light and flexible. A lighter diaphragm will result in a transducer with a wider frequency response. Also, the thinner the diaphragm is, the easier it will be to damp.
- A large transducer area that covers the ear will produce a more planar wavefront with more accurate localization cues. It will also provide a low diaphragm resonance frequency without requiring accurate control of the diaphragm tension. If the resonance frequency is too low, the transducer may become sensitive to subsonic signals or suffer a loss in sensitivity, because the bias voltage may have to be reduced.
- The transducer area should not be so large that the interplate capacitance makes the unit difficult to drive.
- In order for the diaphragm to hold a constant charge at low frequencies (when parts of the diaphragm can become unstable), it should have a very high resistance coating.
- The rear of the transducer should be open to radiate the backwave from the diaphragm.
- The spacers should be flat, insulating and of uniform thickness.
- For maximum acoustic output, the spacer thickness should be as small as possible, but not restrict low-frequency movement.
- The plates must be rigid, at least 20% open with a perforation spacing much smaller than the shortest wavelength to be reproduced. If the plates flex or are uneven, there could be variations in the signal field strength.
- The transducer should have adequate acoustic damping to damp the diaphragm resonance and to prevent ringing on transients. The acoustic loading from the perforations in the plates provides some damping, but additional damping is usually necessary to even out irregularities in the frequency response.
The motion of the diaphragm is affected as follows: by the diaphragm tension at low frequencies, by the acoustic resistance of air at mid frequencies, and by the mass-per-unit area of the diaphragm at high frequencies. The resonance frequency of the transducer determines the lower frequency limit. If the resonance frequency is too low, it could limit the apparent sensitivity of the transducer.
To ensure that the diaphragm maintains a constant charge at low frequencies, no significant current should flow in less than half the time period of the lowest frequency to be reproduced. Given a diaphragm with perfect conductivity and a transducer having capacitance C farads, and low frequency response to 27Hz, then the diaphragm must be fed via a resistance R ohms, such that:
RC > 1/(2 x 27) (approx.)
If C = 150pF (C= eA/d)
then R > 1 x 108 ohms.
However, R cannot be so high as to prevent the diaphragm from charging.
The Transducer Frequency Response
Figure 2a shows the mechanical-equivalent circuit of the transducer. m is the mass-per-unit area of the diaphragm, S is the suspension of the diaphragm in the transverse direction, and 2Rm is the damping in the mid frequencies from the impedance of the air. Fo is the peak force-per-unit area on the diaphragm.
The electrical-equivalent circuit in figure 2b converts m to an inductance of M = jwm henries, the suspension S to a capacitance of S-1 farads, the damping to 2Rm ohms, and the force to a voltage Fosin(wt)V. The high frequency response of this circuit is constrained by the inductance M, which is directly proportional to the diaphragm’s mass-per-unit area. Therefore, the lighter the diaphragm, the smaller the inductance and the wider the frequency response.
The transducer acoustic output
The acoustic output of an electrostatic transducer is limited by the breakdown of air and diaphragm stability, but can be improved by coating the plates with insulation. At low frequencies, the output is constrained by the diaphragm touching the plates, and so is affected by the spacing between the diaphragm and the plates. The force acting on a diaphragm in a push-pull transducer is calculated as:
where e is the differential plate voltage, E is the polarizing potential on the diaphragm, A is the diaphragm area, and d is the spacer thickness. This equation suggests that output can be maximized by increasing e or E. However, the maximum value of E for diaphragm stability is
where T is the diaphragm tension. The maximum bias voltage, then, is limited by the plate spacing. The maximum voltage between the diaphragm and plate is limited by arcing in the airgap, which is also a function of d. Thus, the construction criteria for a high output electrostatic transducer are: a high diaphragm tension, a small diaphragm area with the highest acceptable diaphragm resonance frequency, the smallest plate spacing with good low frequency response.
CONSTRUCTION OF ELECTROSTATIC TRANSDUCERS
The following sections describe the electrostatic headphones built by J.P. Wilson, Philip D. Harvey and Neil Pollock. All three designs are similar and construction techniques for one can often be used with the others. When assembling the transducers, all drilled holes should be deburred, and all dirt or lint between the diaphragm and the plates should be carefully removed; otherwise, there might be arcing or a loss of sensitivity. All exposed high voltage areas on the transducers must be insulated to avoid shock.
Because the diaphragm bias supplies for all of the headphones have a high impedance (see the section on Electrostatic Headphone Amplifiers below), there is no danger of lethal shock – although DIY electrostatic headphones should be inspected periodically to ensure proper and safe operation. As a further precaution, Mark Rehorst recommends that bias supplies be built from low voltage DC step-up converters (available to 5000VDC or more), instead of using high-voltage AC transformers. These converters are sold in IC packages by companies such as Emco High Voltage Co.
The Wilson Electrostatic Headphone
J.P. Wilson built a pair of electrostatic headphones as an experiment to eliminate the “in-head” characteristic of headphone sound fields. He reasoned that normal hearing of sound involves the processing of head motion cues and the acoustic diffracting properties of the outer ear. The wavefront of a sound source arriving at the ear is nearly planar and could be simulated with large-area headphone transducers that covered the ears. The transducers had to be poor acoustic reflectors to prevent sound reflection between the transducer and the head and ears, and to be free-air mounted so as not to form a semi-enclosed resonant cavity with the ears.
Figure 3 is a detailed illustration of the Wilson transducer. The size of the plates was chosen to be large enough to overlap the ears and give the desired bass resonance frequency to the diaphragm. Wilson used paxolin boards (4.75″ x 4″) with holes that comprised at least 20% of the total area and spaced closer than the shortest wavelength to be reproduced. .
The smoother side of each plate was made conductive by first applying a stripe of high conductivity paint over the surface to the edge of the plate to be the connection point for the brass shims that carry the signal source (the shims could also contact the graphite directly, without the paint). Wilson then covered the perforated area of the plates with a thick coat of colloidal graphite (Aquadag), being careful that none of the paint or Aquadag would spill into the holes. Once dry, the surface was polished with a dry cloth and blown clean. A flame was applied to the surface just before assembly to remove any remaining dust or lint.
The spacer material should have uniform thickness and be an excellent insulator. Wilson used acetate sheeting with a 0.04″ thickness, which produced 90dB SPL (free field – the level is about 10dB higher in an artificial ear) from 30Hz onward. The output increased to nearly 100dB by reducing the thickness to 0.025″, but only above 60Hz due to restrictions on the diaphragm excursion. For each plate, Wilson cut four rectangular pieces of acetate that formed a frame with the same outer dimensions as the plate. After gluing the spacers to the plates (Evostick adhesive), he drilled the assembly holes around the spacers and applied a stripe of high conductivity paint to the inner edge of the spacers for connecting the bias supply.
The factors affecting the resonance frequency of the diaphragm are size, shape, mass and tension. Wilson’s diaphragm was formed from a sheet of 0.0005″ thick plastic foodwrap (Vitafilm), which gave the assembled transducer a free-air resonance of 50Hz (damped to about 30Hz). When the transducer was placed against the ear, the resonance frequency was further reduced due to the increased effective mass of the trapped air.
Wilson put a conductive coat of colloidal graphite to both sides of the diaphragm, so that it would hold a charge. The resistance of the coating had to be in the range of 100M to 10G ohms (as measured between two parallel electrodes 1″ long and separated by 1″). Too low a resistance would result in charge migration during signal movements and a loss of linearity.
To apply the graphite, Wilson first pressed the plastic sheet onto moistened glass with a rubber roller. When the top of the plastic surface was dry, he used a piece of cotton to rub on colloidal graphite, rubbing until nearly all of the graphite was removed. When the coating reached the proper resistance, he turned over the plastic sheet and coated the other side (rubbing carefully to avoid damage to the first coat).
The diaphragm was then glued to the spacers (Evostick adhesive) on one of the plates and was pressed between two flat surfaces to dry (the glue should not touch the connection between the diaphragm and the conducting stripes on the spacers). Wilson put the diaphragm assembly under a hot grill for a few seconds to tension the plastic (a fan heater with restricted air flow would also work). The Vitafilm tensioned in a consistent manner, so Wilson concluded that the resonance frequency was constant for same size diaphragms.
The two halves of the transducer were joined together with 6BA nylon nuts and bolts and brass shims inserted to make contact with the conducting stripes. Note: both sides of the diaphragm are charged by the bias voltage. Wilson used a single brass shim for bias supply by “nicking” the edge of each diaphragm so that the conducting stripes on both sides were in contact.
Acoustic Damping and Final Assembly
Without foam acoustic damping, the frequency response of the Wilson transducer was not very flat (figure 4). Wilson sandwiched the transducers between two layers of 4mm foam, which served as acoustic damping and were held in place with rubber bands. Adding additional layers of foam did not improve the response. He fashioned a 12″ x 0.5″ strip of 16-gauge aluminum into the headband with a slight twist at each end to hold the transducers flat against the ears.
Wilson set the bias voltage for each transducer, so that when he blew the diaphragm in the direction of one of the plates, it returned to the central position. The source of the bias voltage was from the high voltage power supply of a 15W tube amplifier (375V), which had been converted to drive the electrostatic headphones directly (see below more details about the amplifier connections). Note: to avoid excessive capacitance, Wilson bundled the transducer wires neatly in parallel, not twisted. The capacitance of each transducer is about 80pF.
The Harvey Electrostatic Headphone
Philip D. Harvey designed an electrostatic headphone that featured a small frame around the transducer to extend the low frequency response (figure 5). He called the frame a “transmission tunnel,” which was bolted to the transducer with plastic screws. The tunnel was molded from polystyrene plastic and lined with latex rubber foam for acoustic damping.
The plates are made from singled-sided copper-plated fiberglass board. Harvey drilled 3mm holes, spaced 5mm apart, in the plates, such that the holes comprised 30% of the total plate area (figure 6). He removed a 2mm copper border around the edge of each plate and the bolt holes to prevent charge leakage if the diaphragm tore.
To form tags on the plates for making safer high voltage connections, Harvey clipped a corner on each plate (an alternate corner on the second plate) and both corresponding corners on the spacers (figure 7). When the spacers and plates were stacked, each plate had an exposed corner for soldering a connection. The connections were insulated with Plasticine.
The spacers are cut in a single piece from a sheet of 0.37mm thick polyvinyl acetate (see figure 7). Harvey experimented with different spacer thicknesses. With thinner spacers (0.18mm and 0.25mm), the acoustic output increased, but the airgap tended to ionize on humid days (the ionization manifested itself as low frequency clicks).
The Transmission Tunnel
The transmission tunnel is a type of earcup for mounting the transducer assembly (figure 8). Harvey cast the tunnel from polystyrene with a two-part wooden mold that was overwaxed for easy removal. Tunnels made from colored polystyrene turned out to be more sturdy than the clear polystyrene versions. He did not specify the depth of the tunnel, but denoted it as “short.”
For the diaphragm, Harvey selected a thin, light film made by the Borden Chemical Co. (15u thick p.v.c. sheeting with a resistivity of 109 ohms). To prepare the diaphragm, he constructed a wood frame (200mm x 250mm) over which he stretched and taped the plastic film (smoothing any creases). The frame was placed over a slightly thicker piece of glass (240mm x 190mm) to support the film. Harvey rubbed colloidal graphite (Aquadag) over the plastic surface until it had a resistivity of 108 ohms – (he used the same method as Wilson for measuring resistivity). Unlike the Wilson diaphragm, the Harvey diaphragm appears to be coated with graphite only on one side.
Acoustic Damping and Final Assembly
To connect the bias supply to the diaphragm, he enlarged a bolt hole in one of the plates and the corresponding hole in one spacer (the lower plate and spacer) to accommodate a brass bush, which when inserted into the plate-spacer, made electrical contact with the diaphragm (figure 9). Harvey assembled the transducer by first taping the diaphragm (graphite side up) over the the upper spacer with double-sided tape. The lower spacer and plate with the brass bush went over the diaphragm. Then, he positioned the transmission tunnel over the lower plate, clamping the bias supply wire in between and in contact with the brass bush.
Nylon nuts and bolts completed the assembly. The diaphragm was tensioned with warm air and the tunnel’s inside walls lined were with latex foam rubber (polyurethane foam) to dampen cavity resonances and insulate the ear. Harvey constructed two amplifiers (tube and solid state versions – see the section on electrostatic headphone amplifiers) for driving his headphones. Harvey tried bias voltages from 200V to 600V, which gave increasing acoustic output, leveling off above 600V. The finished units had a bias voltage of 300-350V.
The Pollock Electrostatic Headphone
Neil Pollock sought to make an electrostatic headphone that could produce more realistic sound pressure levels. Most electrostatic headphones of that time (1979) had a bias voltage of 400V or less and a minimum spacer thickness of 0.5mm. These could generate a maximum free field r.m.s. sound pressure of about 93dB, whereas some musical recordings sounded best when the headphones could reach 100dB or more. Pollock designed a transducer with a bias voltage of 800V to 1300V (as well as a matching amplifier, discussed below) that could output over 100dB SPL.
The four plates (figure 11) are cut from a sheet of 3mm thick Perspex acrylic. Pollock stacked the plates and drilled a matrix of 3mm holes through all four plates. He drilled a countersunk hole in one corner of each plate so that a M2.5 or M2 brass screw would lie slightly below the surface. All of the holes were deburred and the plates were masked before applying the Aquadag. The brass screws were attached with connecting tags and then the resistance between the tag and any point on the plate measured. If the resistance was more than 10K ohms, he applied additional coats of Aquadag. Finally, he covered the Aquadag with a coat of clear polyurethane varnish to prevent ionization in the airgap during periods of high humidity. The dry varnish was sanded slightly to reduce the surface gloss, which tended to stick to the diaphragm.
The spacers (figure 12) were built by layering sheets of drafting film, laminated to a 0.8mm thickness with rubber cement. After cementing the spacers to the Aquadag side of the plates, Pollock drilled countersunk holes for the diaphragm. Each pair of plate-spacers was positioned face-to-face, and the assembly holes drilled. He painted the spacers with Aquadag to the inner edge of the spacer and into the countersunk hole to provide electrical contact with the diaphragm (taking care that no Aquadag should spill into the assembly holes). After installing the diaphragm contact screws, Pollock checked that there was a resistance from the connecting tags to all points on the Aquadag.
Unlike the other diaphragm designs, the Pollock diaphragm is not coated with graphite, but is used without any coating. The diaphragm material is 0.0127mm thick food wrap film, similar to Vitafilm. So long as the diaphragm contacts are made as shown, the film’s own high surface resistance is adequate to hold a charge.
Pollock began assembling the transducer by stretching and taping the plastic film (smoothing out any wrinkles) over a piece of rigid cardboard that had a cutout larger than the plates. Then he pressed the diaphragm between the two plate-spacer assemblies and bolted the plates together with nylon nuts and bolts. The excess film around the plates was trimmed with a razor blade.
Acoustic Damping and Final Assembly
To test the transducers, Pollock connected the bias supply (set to the minimum of 800V) to the diaphragms, and checked them for centering. If a diaphragm moved to one side or oscillated, he heated it with a light bulb to tension it. The transducers were then wired into headphones, and silicone rubber applied to insulate the exposed contacts. He made acoustic dampers from 6mm foam plastic, glued (or sewn) into pouches that enclosed the transducers. With the dampers, the frequency response of the transducer is 30Hz to 40kHz ± 5dB and down to 20Hz when measured in an artificial ear (figure 13).
The headband came from an old pair of headphones. Pollock attached an acrylic bridge between two of the assembly screws that protruded from the foam damper of each transducer to mount the headband. Each transducer has an approximate capacitance of 100pF. To minimize capacitance, he loosely bundled the wires between the headphone and amplifier (as opposed to twisting them together) and kept the resulting cable less than 1.5m in length.
Once the headphones are assembled and connected to the amplifer, the bias voltage is increased to the point just before the diaphragm collapses or the airgap ionizes. Pollock was able to set a maximum bias voltage of 1,300V on his units.
ELECTROSTATIC HEADPHONE AMPLIFIERS
The impedance of an electrostatic headphone is primarily capacitive. Step-up transformers that can provide sufficient voltage to a capacitive load are difficult to manufacture to manufacture and to find. Direct-drive amplifiers may be a more practical solution, if they can handle capacitive loads and have high voltage gain. Although the following electrostatic amplifier designs are more complex than those for dynamic headphone amplifiers, they are not exceedingly so – the requirement of high voltage power supplies notwithstanding.
Wilson drove his headphone with a commercial 15W push-pull tube amplifier (a Radford STA 15) that had been converted for electrostatic headphones (figure 14). The audio signals for the plates were taken from the anodes of the amplifier output stage. The Radford had a power supply of 375V, which Wilson tapped with a 10M resistor for the bias supply. It ran without a load connected to the output transformer for maximum voltage swing, but adding an output load may be preferable in some cases for amplifier stability. Further, some tube amps may balk at providing maximum output continuously to an electrostatic load in this manner. Harvey tried the circuit with his electrostatic headphone and could not eliminate the intermodulation distortion, which was audible even at low levels.
Instead, Harvey built two dedicated amplifiers to drive his headphones, one tube-based and the other solid state. The spacer thickness used in his transducers was 0.37mm, which limited the voltage between the diaphragm and either plate to about 1000V. With a diaphragm bias voltage of 300V, the plate voltage could go as high as 500V and still have a safety margin against ionization on humid days or from signal surges.
The amps are designed to output between 300V to 400V peak and have a similar topology: a differential input stage feeding a push-pull output stage. The tube version (figure 15) can generate a 400V peak signal; the transistor version (figure 16) a 300V peak signal. The transistors in the differential stage (Q1/Q2) are matched (they can be any NPN silicon unit with an hfe > 50 at 1 ma. and a VCE > 35V). P1 is adjusted to match the base voltages of Q1/Q2. The collector voltages of Q3/Q4 are set to an average of 115V using P3. Then the collector voltages are balanced with P2 and the process repeated until the collector voltages of Q3/Q4 are at 155V.
Pollock devised two electrostatic headphone amplifiers based on the National Semiconductor LM3900N current-input opamp. The standard bias version (figure 17) is for an earlier electrostatic headphone that he built based on the Wilson transducer and can be driven to full power from the standard headphone outputs of a stereo receiver or preamp. It produces a 300V peak-to-peak signal with 1.0% harmonic distortion at 1kHz. The amp has a frequency response of 10Hz-40kHz (-3dB) and a power bandwidth of 10Hz-15kHz.
The output stages are class A. IC1a is an inverting stage to produce an opposite phase output. R1 compensates for the small signal resistance of a diode in the non-inverting input of IC1b. If the headphone capacitance is greater than 150pF, R2 and R3 should be reduced to maintain the power bandwidth and the transistors should be heatsinked. The value of Rx is missing in the original schematic, but is estimated to be about 2.4K ohms from the similar topology of the high-bias version of the amplifier. P1 and P2 are adjusted so V1 and V2 are at one-half the supply voltage.
The high-bias version of the Pollock amplifier (figure 18) can generate 1400V peak-to-peak at 5kHz with an input sensitivity of 2.8Vrms for maximum output. The circuit topology is virtually identical to the standard-bias amplifier. Of special note are the output transistors, which must have VCE ratings in excess of 1000V. Pollock chose transistors that are used in television horizontal deflection circuits. These have peak VCEs in the range of 1.5kV. The specified device is a Matsushita 2SD200. Substitutes include the BU206, BU209A, MJ105, PTC146-RT and SK3115-RT.
Pollock built the high and low voltage sections on separate circuit boards to reduce the risk of instability and damage from building errors. Q1 and Q2 were heatsinked. The signal ground was taken from the source to avoid ground loops. If the amplifier shows instability, C1 can be increased to compensate. The power supply was installed in a ventilated, grounded, metal case. The high voltage section employes a half-wave voltage doubler (figure 19). The low voltage supply is decoupled at the amplifier with 0.1uF ceramic capacitors next to each opamp.
9/10/99: Added new figure 17. Also made various corrections and additions to text.
Harvey, Philip D., “Electrostatic Headphone Design,” Wireless World, Nov. 1971, p. 527.
Pollock, Neil, “Electrostatic Headphone Amplifier,” Wireless World, July 1976, p. 35.
Pollock, Neil, “Electrostatic Headphones,” Wireless World, Nov. 1979, p. 51.
Wilson, J.P., “High Quality Electrostatic Headphones,” Wireless World, Dec. 1968, p. 440.
c. 1999, Chu Moy.