Electrostatic speakers have been around for a while – in fact, the earliest ones apparently date back to the 1920s and were built using pig intestine covered with gold leaf. The image they conjure up is one of a large thin sheet which looks esoteric and sounds great, but is delicate and cumbersome to carry around. What if you had an electrostatic speaker that you could not just carry around with one hand but actually insert into your ear? That is what researchers Qin Zhou and A. Zettl at the University of California at Berkeley and the Lawrence Berkeley National Laboratory tried to prove could be possible. Their work was published in Applied Physics Letters , Vol. 102, Issue 22, June 2013.

Electrostatic speakers 101

The principle of operation is quite simple and is based on the fact that unlike charges attract and like ones repel. An electrostatic transducer has for its diaphragm a plastic film, coated or impregnated with an electrically conductive material such as graphite. The impregnation is done in a way that results in a very high surface resistivity though, because the intent is to distribute a static charge on this diaphragm that can stay evenly distributed as the diaphragm vibrates in the electric field. This diaphragm stands between two stators, which are perforated steel sheets coated with an insulator (to make sure the diaphragm does not discharge by touching it). The diaphragm is charged by connecting it to a fixed positive voltage (typically a few kilovolts) and the AC audio signal (again amplified to a few kilovolts) is applied to the stators. Because like charges repel and opposite charges attract, the diaphragm's positive charge will force it to move forward or backward depending on the polarity of the high voltage AC on the stator. One advantage of electrostatic speakers is the fact that since the damping force is almost entirely from the very air that is being driven, the efficiency is much higher than conventional drivers.

One key reason that electrostatic speakers are large is that they operate on the principle that air should provide the primary damping force for the diaphragm. The per-area air damping coefficient significantly decreases when the size of the diaphragm falls below the sound wavelength, and that is why, for sufficient low frequency response you need a large diaphragm with traditional materials such as metalized Mylar. The only way to make them smaller is to make the diaphragm thinner and lighter, and you cannot do that beyond a point because the material will simply break apart. A bit of math helps understand exactly what forces are responsible for SPL behavior. In the equation on the left below, the left side represents the velocity of the diaphragm. On the right side, F is the driving force, ζ is the damping force, k the spring (restoring) force of the diaphragm, and m the mass of the diaphragm. In the equation on the right, c is the sound velocity and ρ the air density.

and

What this tells you is that the SPL is constant with frequency if k and m are small enough so that ζ is the only significant parameter. Of course that is an idealization but it gives you the sense. The thinner the diaphragm, the smaller become k as well as m .

Enter graphene

Graphene is a recently discovered material that can be described as a one-atom thick layer of graphite. This material has exceptional mechanical strength, with a breaking strength over a hundred times greater than a hypothetical steel film of the same thickness. It would take an elephant, balanced on a pencil, to break through a sheet of graphene the thickness of cling film! The Wikipedia article on this miracle material lists a large number of uses for it. What is interesting is that a graphene diaphragm of the same size and thickness as a diaphragm made of Mylar has a very high spring constant – something that is not obvious from the paper. What graphene allows you to do is to build the diaphragm enormously thin and therefore reduce k as well as m, because k is proportional to thickness. This is what made Zhou and Zettl reason that it should work well as a small diaphragm for an electrostatic transducer. Let us see what they found.

The researchers fabricated a graphene diaphragm no larger than 7mm in diameter and a mere 30nm in thickness. The details of the fabrication process are described in their paper. Graphene is an excellent conductor of electricity, so we do not need a further impregnation or coating of conductive material on the diaphragm. The conducting graphene diaphragm was biased at a fixed DC voltage of 100V (which is substantially lower than the kilovolts voltages used with typical electrostatic transducers), and the diaphragm was positioned between two fixed silicon electrodes onto which the AC signal of about 10V was applied. This is illustrated in the diagram above taken from their paper.

Performance

They compared the performance of this earphone with a commercially available, non-electrostatic device. As the graph from their paper shows, the performance is rather good for what is essentially a crude laboratory prototype with no special acoustic design. What is also very interesting is that the efficiency of this transducer, operating at a few nanoamperes, was close to 100%, in stark contrast to conventional earphones that operate at less than 1% efficiency.

Conclusion

If you are not in the habit of reading research journals, don't be misled by the fact that this work was published in a journal that goes by the name Letters . This is cutting edge physics, immediately applicable to the real world. Even with no further progress on fidelity enhancement, one can immediately foresee the use of this technology in the design of a new generation of super-efficient hearing aids that are powered by, say, motion, or ambient light.

As I see it, one of the aspects that would make for some interesting future research is whether one could get better fidelity with an insulating film reinforced with graphene in such a manner as to make a diaphragm with high surface resistivity as with current electrostatic speakers, but much thinner and stronger (therefore making a smaller size possible) rather than a pure graphene diaphragm which is highly conductive.

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