A closer examination of underlying principles leads to the conclusion that the electrostatic loudspeaker may well supersede the moving coil for high-quality sound reproduction. Designs recently developed have proved to be capable of reproducing the full audio-frequency range, with harmonic distortions no higher than those of the associated amplifier.

Every loudspeaker designer must, at some time or other, have looked longingly at the electrostatic principal of drive as a solution to his problems of improving quality of reproduction.

The movement of a diaphragm driven all over its surface is entirely predictable. The diaphragm can be as light as required. The impedances influencing performance can be predominantly acoustic and - since there are no shape restrictions - entirely under the control of the designer.

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• (1) First, the fact that in its generally known form it is intrinsically nonlinear and even in a push-pull construction linearity can only be approached for small amplitudes.
• (2) Secondly, in order to obtain adequate sensitivity the available gap is small; the diaphragm movement limited and largely stiffness controlled, both factors restricting its use to high frequencies.
• (3) Thirdly, that being essentially a capacitive electrical load, it is difficult to match to an amplifier.

The first of these objections, that of non-linearity, can be removed completely by an expedient which is spectacular in its effectiveness and simplicity.

The second and third difficulties will resolve themselves, as we shall see later, when the designer makes his choice of the interdependent mechanical, acoustical and electrical variables.
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Under conditions of no signal, Fig. 1 (b), and assuming the diaphragm to be central, there will be equal and opposite attractive forces on the diaphragm. If one fixed plate is now made positive and the other negative so that the diaphragm will be deflected to the right, the effective capacitance will increase, and to satisfy the relationship "Q=CE" the charge "Q" will also increase and will be supplied by a current "i" during the movement.

The force acting on the diaphragm per unit area will, however, be proportional to :

The relationship will be non-linear. Note that the charge "Q", although varying, does not enter directly into the relation.

Suppose that after having charged the diaphragm electrode the source of polarizing potential is disconnected (Fig. 1(d)). The diaphragm now carries a constant charge "Q" which experiences a force proportional to the product of the field intensity and the charge.

This force will be independent of the position of the diaphragm between the plates since both Q and the distance between plates are constants; the only variable is the applied voltage "e". Note that the difference between "dx" and "d2", although varying, does not enter into the relation.
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The above is perhaps an over-simplification, but it shows that distortion is not necessarily inherent in the electrostatic principle.

The "constant Q" method of operation has another very important advantage in that it reduces the risk of collapse, which occurs at large amplitudes with the conventional method of connection, when the negative stiffness resulting from electrical attraction exceeds the positive mechanical stiffness of the diaphragm.

As the diaphragm approaches one of the fixed plates the capacitance is increased, but as the charge "Q" has been assumed constant, "E" must fall since "E = Q/C".

Professor F. V. Hunt(†) of Harvard University has shown, that the criterion for dynamic stability under large excursions is that the time constant "RoCo" of the charging circuit (Fig. 1(e)) should be large compared with l/2f, the half-period of the applied frequency.

This also supplies the condition for low distortion and Professor Hunt gives the results of measurements (Fig. 6.14, p. 212, loc. cit.) showing the dependence of second harmonic distortion on both the degree of unbalance due to displacement of the central electrode (in terms of Deta C/C) and of the ratio of time constant to half period "2fRoCo".

Even when this latter parameter was reduced to unity, and the diaphragm displaced by a distance equivalent to a capacity unbalance of 25%, the second harmonic did not exceed 0.5%, when driven at 150 c/s by 780V r.m.s. (plate-to-plate) with a polarizing voltage of 500. Third and higher harmonics were always less than the second.

So much for the driving mechanism; it now remains to see how it fares when coupled to the air and to an amplifier.

" Electroacoustics " by F. V. Hunt, chapter 6. Published by John Wiley & Sons (Chapman & Hall).

It will help in understanding the broad principles involved if we start by considering a loudspeaker whose diaphragm is large compared with the longest wavelength of sound to be reproduced.

Under these conditions the mass reactance of the air load on both sides of the diaphragm can be neglected and the impedance per unit area "2pc" offered to the motion of the diaphragm is predominantly resistive (pc=42 mechanical ohms per cm2).

With constant voltage driving the diaphragm the force will be proportional to the applied signal voltage and independent of frequency.

If the load is resistive the velocity, and also the acoustic power output, will be independent of frequency.

At very high frequencies the mass reactance of the diaphragm can exceed the radiation resistance and will cause "a falling off" in velocity when the force remains constant; the acoustic output will then decline by 6db/octave, but, with suitable choice of diaphragm material, not until a frequency of 20 to 25 kc/s is reached.

(How different from the average moving coil in which the cut-off starts at about 1,000 c/s and must be sustained by focusing of high frequencies along the axis or by juggling with cone " break-up.")

The choice of stiffness will be dictated by the necessity of constraining the diaphragm against the forces associated with the polarizing voltage.

Under "static" conditions (2fRoCo less than unity) these forces can increase as the diaphragm approaches the fixed plates and must be limited by a suitable choice of stiffness, polarizing voltage and plate spacing.

The plate spacing also determines the electrical capacitance of the loudspeaker, and the impedance offered to the amplifier at the frequency chosen for " matching."

Thus the bandwidth available for constant output, under the acoustic conditions postulated, is limited at low frequencies by the diaphragm stiffness required for stability and at high frequencies by the conditions of matching to the amplifier. (The inertia cut-off will always be well above the matching frequency and can be ignored.)

The true efficiency of an electrostatic loudspeaker is very high indeed, but it is difficult to realize because of the large wattless current which has to be provided due to the electrical capacity of the loudspeaker unit.

Thus it is necessary to waste watts in the amplifier or in resistances associated with crossover networks of which the loudspeaker may be part.

For purposes of simplification, therefore, it is convenient to use the term "apparent efficiency" the meaning of which is the ratio of the acoustic power output of the loudspeaker to the amplifier volt-ampere output necessary to provide the required voltage across the loudspeaker capacity.

Since very high efficiencies are not a pre-requisite of high-quality reproduction, it is convenient to arrange the apparent efficiency to be similar to the efficiency obtained from present-day commercial moving-coil speakers.

Setting the efficiency at this level and applying polarizing voltages permissible in the given air gap, we find that the available bandwidth for level response is about four to five octaves.

Below the low-frequency cut-off we have the stiffness of the diaphragm controlling response, a large proportion of it under conditions where the "apparent efficiency" is high and wasted. (At low frequencies the impedance is high, and less power is required to maintain constant voltage.)

Thus, by a progressive change of "matching" in this area, one can compensate to extend the level response below the mechanical cut-off. The effect of this mechanical stiffness is best considered when we deal with possible forms of loading, since it can be lumped in with the acoustical circuit loading the loudspeaker.

A high polarizing voltage is desirable in order to place a high value of charge "Q" on the diaphragm. Each small unit area of the diaphragm can be fed with a high voltage at very high impedance, thus charging up that part of the diaphragm in relation to the fixed plates.

In this arrangement of the loudspeaker, where the signal is applied to the fixed plates only, there are no signal currents due to the wanted signal in the diaphragm itself, so that this arrangement of high-impedance charging of each unit area of the diaphragm is permissible, and is essential for linearity in any practical construction.

Any tendency for the air to conduct between the diaphragm and the fixed plate at any point in the loudspeaker merely causes a slight drop in the voltage at that area of the diaphragm, so that in this way high voltages can be applied without any danger of sparking.

Since the charge on the diaphragm is unvarying, it follows that the force on the diaphragm is completely independent of the position of the diaphragm in the space between these electrodes and the system in linear.

With this arrangement, then, it is no longer necessary to restrict the allowable motion of the diaphragm to a small percentage of the available gap. Again, there is no restriction to the ratio of signal voltage to polarizing voltage.

The only non-linear element entering the system at all is that due to the compliance of the diaphragm, and since in most designs this is not a controlling factor in the motion of the diaphragm its importance is small. There is no difficulty in producing units on this principle, the distortion content of which is even lower than that of present-day amplifiers, and many times better than a moving-coil loudspeaker of normal efficiency.

In a future article it is proposed to discuss the operation of such loudspeakers, i.e., when size is no longer large compared to wavelength, and to show the basis of design approach for the whole frequency range.

Distortion measurements on these units gave figures well below 1%. Measurements were made out of doors, and noise, wind, and other restrictions due to imperfect conditions made it difficult to get reliable figures below 1%. Inspection of the residual waveform indicates that the distortion due to the units is considerably lower than this figure.

Similar remarks apply to frequency response, due to the fact that it is virtually impossible to achieve perfect loading conditions. Measurements produce responses which are within 2db of the predicted curves, but the major part of these small discrepancies may be attributed to the approximations assumed in the structures used for loading.

Since 1953, electrostatic loudspeakers have been the subject of joint development between "Ferranti, Ltd., of Edinburgh", and "The Acoustical Manufacturing Co., Ltd., of Huntingdon". Some of the techniques involved in the design of these loudspeakers are the subject of joint patent applications by P. J. Walker and D. T. N. Williamson.

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