Rapture Audio System
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Electrostatic Loudspeaker Theory
ESL Basics
Electrostatic Loudspeakers (ESL) became a commercial reality in the late 1950s. However, due to the nature of electrostatic loudspeakers, not many have been produced commercially and the ones that exist today are very expensive. However, the basic theory behind electrostatic loudspeakers is not new or complex. As the name implies the ESL operates by the force due to static charges. Like electrical charges repel and different charges attract. An ESL is created when a charged membrane or diaphragm is suspended between two perforated conductive plates called stators. The diaphragm is held between the stators by insulating spacers. Depending on the charges on the stators, the diaphragm will be attracted to one stator and repelled from the other. The perforations in the stators allow the diaphragm to couple its motion to the air in the surrounding environment. If the charge on the stators is modulated by an audio signal, with the polarity of one stator opposite to the other, the motion of the diaphragm will track the audio signal and the motion will be coupled to the air as sound waves.
The diaphragm must be an extremely thin and lightweight plastic material. It also must be slightly conductive to hold a distributed charge. This charge is due to a very high applied voltage called a polarizing or bias voltage. The most common application involves a thin layer of graphite impressed into the surface of Mylar. The resistance is very high, but as the theory is for current not to flow the surface gets an even surface charge that doesn't move, hence electrostatic operation. A high voltage is needed because the force due to electrostatic force is very small.
The stators must be very strong and ridged, but also acoustically transparent. They must also have a very uniform inside surface to apply a very uniform electric field to the diaphragm. There are three main styles of stators: perforated metal, wire grid, and conductive plastic. Each has its own specific pros and cons. However, perforated metal and wire grid are the most common.
The spacers are as important as the diaphragm and the stators. The spacers hold the membrane centered between the stators uniformly. Uniformity is very important as changes in distance will result in differing forces and therefore non-uniform diaphragm movement. Also, the spacers must perfectly insulate, even in humid weather, as the resistance in the diaphragm may be upwards of 1Gohm and the voltages may rise above 10kV. Any leakage represents a loss of output and possibly a dangerous situation depending on drive characteristics.
Many factors influence the output of ESLs, including (but not limited to): Bias voltage, spacer radio, diaphragm to stator distance, uniformity of construction, drive voltage, and dimensions. For more information and possibly the best resource for electrostatic loudspeaker design, please refer to The Electrostatic Loudspeaker Design Cookbook by Roger R. Sanders (ISBN 1-882580-00-1).
Benefits of Electrostatic over Dynamic Loudspeakers
Electrostatic Loudspeakers have many advantages over standard dynamic loudspeakers. Dynamic loudspeakers create sound by using an electromagnet mechanically coupled to a ridged diaphragm (usually a cone or dome structure) suspended in a strong magnetic field. The electromagnet is driven with an amplified audio signal and the time-varying magnetic field that results causes a force applied to the diaphragm due to interaction with the static magnetic field. The motion of the diaphragm couples to the air just like an ESL to produce sound waves. The cone and the electromagnet have mass and therefore an inertia. Although the diaphragm in theory should have a position in direct relation to the input electrical signal, the inertia causes the cone to over and undershoot coloring or muddying the sound. The magnetic field is non uniform outside the small gap and as the heat builds up due to power dissipation, the characteristics change. Furthermore, the diaphragm itself is not uniformly ridged and causes distortion through the intense forces at work on it.
ESLs fix all of these problems. At around 1 mil thick, the diaphragm is about the same mass as a slab of air 1/4" thick of equal area. When compared to the mass of the air volume of the listening area, the diaphragm is essentially mass less. This completely eliminates distortion caused by overshoot or undershoot. Also, the electrical field is uniform between two parallel plates, and the motion of the diaphragm is therefore theoretically perfectly linear until the mechanical limit of the diaphragm is reached. The bias voltage creates a constant force in one direction that causes the diaphragm to bow slightly towards one stator. However, this is very small when tension is proper. What is important is due to the uniform electrical field, the diaphragm responds as a moving plane to the input drive signal. Since the entire surface is being driven, there are no losses or distortions caused by mechanical coupling. Only a very thin area around the perimeter is restricted from movement due to the proximity to the spacers, and this is usually around 1/4" insignificant to the size of the ESL diaphragm. As a bonus, the ESL does not have any resistance theoretically and therefore does not dissipate any power as it is a voltage dependent device as opposed to current. Of course the ESL has resistance and acts like a giant capacitor, so dissipation in the amplifier can be quite large.
Design Issues with Electrostatic Loudspeakers
Like any system, ESLs have a very complex set of tradeoffs that occur depending on design parameters. However, there are some issues that cause electrostatic loudspeaker construction and design to be very challenging and even dangerous. The ESL does not dissipate power because it is a capacitor, but it stores charge. Therefore, although the amplifier doesn't theoretically supply power, it must sink the energy it sources which causes drive problems that cause most standard consumer amplifiers to oscillate in the ultrasonic range or just self destruct. Also, the voltages involved range from 1 to 10kV. Although the current for the bias supply may be in the micro amps, the current in the high voltage audio section can be significantly higher due to the capacitive loading effects of the ESL. Aside from the electrical properties, the ESL represents a challenge acoustically too. It must be operated as a dipole, which means both sides must be open to then environment. This can cause sound to cancel out by interaction from the front and back waves, which therefore requires acoustic baffles or wave guides. Room placement in critical because the sound is very directional. The diaphragm motion is very very small, and this requires very large surface area to reproduce standard listening levels. Below its resonance point, an ESL output is virtually non-existent, but unlike dynamic speakers in standard enclosures, there is usually no resonance peaks or dips. Also, because the ESL is incapable of producing sound below its resonance point, bass extension is virtually non-existent for most systems.
Biasing and Supply
The standard setup involves connecting the stators to the terminals of a step up transformer with the diaphragm biased with reference to the center tap of the transformer. An amplifier drives the step up transformer, which causes the stators to be driven perfectly opposite to each other. This is a simplified representation of such a connection using the step-up transformer.
Design
The ESL design parameters were for a single panel approximately 18"x40" using the techniques from Roger Sanders's book. DuPont donated a few square meters of their melinex type 442 film (92 gauge) for the project. I purchased some perforated steel panels from a local company, but they were too warped to really use.