Electrostatic speaker

Electrostatic speaker

The electrostatic loudspeaker ( ESL ) is a type of loudspeaker in which sound waves are generated by means of the electrostatic attraction force .

Physical basics

Electrostatic loudspeakers do not use the Lorentz force but the electrostatic attraction:

${\displaystyle |{\vec {F}}|=Q\cdot {\frac {U}{d}}}$.

Voltage control

The following applies to voltage control:

${\displaystyle |{\vec {F}}|=Q\cdot {\frac {U}{d}}}$with . ${\displaystyle Q=C\cdot U\quad \Rightarrow \quad |{\vec {F}}|=C\cdot {\frac {U^{2}}{d}}}$

The force is not linear to the current, but square to the voltage. A preload is necessary to achieve a usable reproduction.

Constant charge

For push-pull ESLs based on the constant charge principle, and that is almost all ESLs built today, the driving force is linear.

In the case of a constant charge ESL, the following applies to the force on the membrane (which carries the charge ):

A homogeneous electric field forms between the stators with the strength

${\displaystyle E={\frac {U_{b}}{2d}}}$

The force on the charge on the membrane is then

${\displaystyle F=Q\cdot E\quad \Rightarrow \quad F={\frac {Q\cdot U_{b}}{2d}}}$

In this equation is proportional to and therefore linear because and are constant. ${\displaystyle F}$ ${\displaystyle U_{b}}$ ${\displaystyle Q}$ ${\displaystyle 2d}$

This applies under the condition that the charge is small and has practically no field effect of its own. For great force to be effective, however, must be great. This leads to a constant deflection of the diaphragm from the zero position towards a stator, where a new zero point results together with the mechanical prestress of the diaphragm. But even under these conditions it can be proven mathematically that the force / voltage characteristic remains linear. ${\displaystyle Q}$ ${\displaystyle Q}$

Influence

The calculations given above assume that the charge distribution on the surfaces involved is homogeneous. This can only be achieved for one of the areas. This is carried out with a comparatively high resistance. A current must be able to flow on the other surface in order to reload them.

Freely displaceable charge carriers, however, tend towards the lowest potential. That is on the opposite surface. If the surface does not vibrate completely homogeneously, as assumed above, the disturbances tend to intensify themselves through influence - the instantaneous equilibrium is unstable (see also below, inverter principle). These partial vibrations are difficult to control on the surface. On the one hand, because the elasticity and mass of conventional foils are of great importance for the efficiency that can be achieved. On the other hand, for a sufficiently strong sound emission, membranes must be used which are large compared to the wavelengths of airborne sound and the transverse surface wave on the membrane. The system can behave chaotically. A sound emission then takes place like on a bending wave converter , variant DML.

construction

Single-stroke construction

Sketch of a single-ended setup

Single-ended solutions work stably. Here an attractive force is kept in equilibrium due to a constant electrical pre-tension and the mechanical membrane tension. The modulated audio signal ensures a corresponding force effect and thus deflection around this point of equilibrium. Due to the quadratic force / voltage characteristic, this system is low-distortion only for very small deflections. Single-ended ESL are used as tweeters, but are practically no longer found in new products.

Push-pull construction

Principle of an electrostatic loudspeaker, conventional control

In 1957, the first commercial electrostatic full-range flat-panel loudspeaker appeared on the loudspeaker market: it was the QUAD-ESL ® from the English hi-fi manufacturer Quad , which worked on the push-pull principle. Two solid, mechanically stable grid electrodes are used as stators, between which the vibrating membrane film is located. The stators are coated with polyester resin for electrical insulation. The stators are perforated to allow sound to escape. Force and field point in the same direction during operation.

The membrane is thin, oscillatable and electrically conductive (but with high sheet resistance ). The material for the membrane is u. a. Polyester and polydisulphenol used, which is provided with an electrically conductive layer. The membrane is extremely thin, about 2 to 20 micrometers thick.

Control

In contrast to dynamic loudspeakers, control does not require a high current (5 to 10 A), but rather a high voltage (1000 V to 4000 V).

This high voltage is either generated directly by high-voltage amplifiers ( tube amplifiers or MOSFET ) or is stepped up (e.g. to 1000 V) by means of a transformer from the usual power amplifier voltages (e.g. from 20 V).

Conventional

With conventional control, the audio frequency is applied to the stators in antiphase, while the polarization voltage is applied to the membrane:

• Stator 1: + U _tone
• Membrane: U _Pol
• Stator 2: −U _tone
• Differential voltage 1: U _Pol + U _Ton
• Differential voltage 2: U _Pol - U _Ton

The ESL, which can be found predominantly on the market, work according to the constant charge principle. Here the music signal is sent to the stators with different polarity and the membrane foil is charged to a constant charge by means of a voltage source. The membrane film usually has a high resistance due to an extremely weakly conductive coating. A homogeneous field forms between the stators, the force / voltage ratio of which is completely linear. For this reason, the distortion behavior of this type of ESL is the best of all principles used, as long as there is no disturbance of the fundamental symmetries.

Inverter principle

When controlling according to the inverter principle, the polarization voltage is applied to the stators in antiphase, while the audio frequency is applied to the membrane:

• Stator 1: + U _Pol
• Membrane: U _tone
• Stator 2: −U _Pol
• Differential voltage 1: U _Ton + U _Pol
• Differential voltage 2: U _Ton - U _Pol

The membrane still has to be mechanically pretensioned, since the rest position is unstable (with magnetostats it is indifferent ).

The inverter principle is patented.

Activation with two DC voltages of different polarity on the stators (the grid electrodes) is only one option that is rarely used. A highly conductive membrane is required to which the music signal is sent. This is a constant voltage ESL that is subject to the quadratic force / voltage ratio and therefore does not have a linear drive. The system is low-distortion only for small deflections.

Force on the electrode in the rest position

Voltage control

• Preload: ${\displaystyle U}$
• AF voltage: ${\displaystyle U_{b}}$
• Distance between a GE and membrane: ${\displaystyle d}$
• Voltage between GE1 and membrane: ${\displaystyle U_{1}=U+U_{b}}$
• Voltage between GE2 and membrane: ${\displaystyle U_{2}=U-U_{b}}$
• Capacity between a GE and membrane: ${\displaystyle C=\varepsilon \cdot {\frac {A}{d}}}$
• Force between GE1 and membrane: ${\displaystyle F_{1}=\varepsilon \cdot {\frac {A}{d^{2}}}\cdot (U+U_{b})^{2}}$
• Force between GE2 and membrane: ${\displaystyle F_{2}=\varepsilon \cdot {\frac {A}{d^{2}}}\cdot (U-U_{b})^{2}}$
• Resulting force on the membrane: ${\displaystyle F=4\cdot U\cdot U_{b}\cdot \varepsilon \cdot {\frac {A}{d^{2}}}}$

The resulting forces are very small compared to electrodynamic loudspeakers (in which values ​​of up to 50 N are normal at full modulation). Values ​​of 2 kV, 1 kV, 4 mm, 1.5 m 0.4 m = 0.6 m² result in 2.6 N. However, since the mass to be driven is also significantly lower, a direct comparison is not useful. ${\displaystyle U=}$ ${\displaystyle U_{b}=}$ ${\displaystyle d=}$ ${\displaystyle A=}$ ${\displaystyle \times }$ ${\displaystyle F=}$

advantages

An electrostatic loudspeaker as a lampshade

Electrostatic loudspeaker as headphones (in the picture a Stax SRS model with amplifier)

Electrostatic loudspeakers allow a lot of design freedom, as they can be made very thin.

disadvantage

Despite push-pull control, larger oscillation amplitudes generate audible distortion (the two distances to the fixed electrodes are no longer identical, so square components no longer stand out as in the calculation above). The design problem is that for larger oscillation amplitudes, the larger distances between the electrodes required, drastically reducing the characteristic sound pressure.

The movement of the membrane in turn generates a charge shift on the surface ( influence ). Irregularities tend to reinforce themselves. If this results in a chaotic membrane movement, this in turn can improve the radiation behavior without noticeably increasing harmonic distortion, as is the case with distributed mode loudspeaker.

Another problem in the bass area is that the pressure equalization between the front and back leads to an acoustic short circuit , which further reduces the bass reproduction and further increases the vibration amplitude.

In electrostats, the sound is emitted in a relatively strongly directional manner. H. A stereo setup creates a very narrow area for optimal hearing (also known as the “sweet spot”).

An attempt is made to counter this phenomenon by means of appropriate constructions:

• Curvature of the surface of the electrostat
• Segmentation of the radiating surface
• Use of acoustic lenses in front

Bass reproduction requires a disproportionately large electrostatic surface, which is why this converter principle is not particularly suitable for bass reproduction and is often supported in the bass by additional electrodynamic converters.

swell

1. ↑ see Baxandall
2. ↑ ^{a b c} Technology Review March 2010, page 8, "Thin and Loud"
3. ↑ Archive link ( Memento of the original dated December 30, 2015 in the Internet Archive ) Info: The archive link was inserted automatically and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.  
4. ↑ http://www.patent-de.com/19980520/DE19641503A1.html
5. ↑ US patents US 3668335, 7054456 and others

literature

• Wolfgang-Josef Tenbusch: Basics of the loudspeakers. 1st edition, Michael E. Brieden Verlag, Oberhausen, 1989, ISBN 3-9801851-0-9 .
• Helmut Röder, Heinz Ruckriegel, Heinz Häberle: Electronics 3rd part, communications electronics. 5th edition, Verlag Europa-Lehrmittel, Wuppertal, 1980, ISBN 3-8085-3225-4 .
• Technology Review March 2010, page 8, "Thin and Loud" (Online also on Spiegel Online Loudspeakers: Transparency thanks to the electrostatic membrane )

Web links

Commons : Electrostatic Speakers  - Collection of pictures, videos and audio files