Jon Dahlquist on Loudspeaker Design: Of Speaker Design, Theory and the Recorded Truth

--This is a 1973 article which has, perhaps, greater relevance in today’s age of a multiplicity of speaker designs and radiation patterns than it did in 1973, when quadriphonic sound seemed a real possibility.--

It still seems fashionable in hi fi circles to blame the loudspeaker for the great disparity between the live musical experience and its reproduction in the home. Yet, the truth of the matter is that for the last 15 years or so this has not been the case. The real blame for lack of realism must be placed on the incompleteness of the cur rent process of recording and reproduction.

In the absence of a “record”-”reproduce” process that is inherently reversible (governed by the physical laws of reciprocity), it can be shown that the accurate reproduction of a spatial sound field is not possible and that the concept of a correct, or perfect, reproducer has no meaning. That is, a perfect speaker can be defined only if there is a perfect recording scheme.

The appreciation of this interdependence between the recording and the reproduction process is essential before one defines what a loudspeaker should and should not do, particularly with respect to directionality. Therefore, it is not sufficient, as has been customary, to state that a loudspeaker should radiate constant energy in all directions at all frequencies (point source omnidirectional). One must first examine how the program material has been recorded, how the speaker radiation interacts with the listening environment, and then prescribe what directivity is appropriate to achieve the best reconstruction of the original sound field.

The advent of discrete four-channel sound recording makes it seem that the high fidelity industry has been moving toward facsimile reproduction; that is, reproduction that is indistinguishable from the live experience. While the attainment of this goal is perhaps remote, it is useful to idealize a “perfect” process that will illustrate the required relationship between the processes of recording and the process of reproduction.

As an example, consider the problem of recording and reproducing a real sound field wherein sound waves impinge upon the body from all directions. If an imaginary spherical surface is constructed about the listener that excludes the source of sound, all perceived radiation must pass through the surface from the outside. In order to record this sound field for facsimile reproduction, it will be necessary to set up a multichannel microphone array that defines an acoustically transparent spherical surface. The microphone elements must be responsive only to sound waves passing through the surface from the outside. The array is situated within the sound field to be recorded and the elements are connected to a multichannel tape recorder.

In like manner, the loudspeaker must also consist of an acoustically transparent, but pressure tight, surface with the same number of elements and of the same diameter as the microphone array. A segmented electrostatic spherical shell would serve the function well. Playback is accomplished by placing the loudspeaker within a free-field environment and energizing the various speaker elements with their respective channels. The listener, within the speaker sphere, would experience a close approximation to what he would have heard had he been present within the microphone cluster during the recording. The degree of approximation would naturally increase with the number of channels, but I suspect that any more than 16 channels would produce only marginal improvement for most common sound fields.

Other useful properties of this scheme include a bass response that extends to DC, a constant resistance air load (independent of frequency) and a reverberant field that is zero everywhere. In fact, such a device could readily be built, using known techniques that would have so little distortion, such a wide bandwidth, and such high efficiency that it might be a problem finding auxiliary equipment good enough to drive it. The problem is that this device would not be very useful at the moment because it is incompatible with current recording techniques, and its use necessitates a rather impractical listening environment.

What has all this to do with omnidirectional speakers? The fact is that the omni directional speaker (pulsating sphere or practical approximations thereof) can in no way be considered an ideal speaker because the sound field it propagates is incongruous with a spatially accurate recording process. Facsimile reproduction requires a speaker that radiates from all directions rather than in all directions.

Despite the disqualification of the omnidirectional speaker from the “perfect” category, the “omni” approach does have certain useful attributes with respect to the reproduction of two-channel recordings in a normal listening room. The most important of these is that the total sound pressure level is much more uniform over a wider listening space with the omni than with conventional semi-directional speakers (speakers such as the bookshelf, which are omnidirectional only at low frequencies). This occurs because the sound field from an omni consists almost entirely of reverberant energy whose sound pressure level does not depend significantly on the distance from the speaker. There fore, the attenuation of direct field components via the inverse square law has only a slight effect upon the total sound pressure level. This is the reason why omni’s sound quite good from an adjacent room compared with directional speakers.

Another advantage is that the omni tends to sound smoother than a semi directional speaker (assuming equally smooth drivers) where both speakers have a flat on-axis frequency response.

This is because the omni would possess a constant mean spherical radiation where as the semidirectional unit would have a discontinuity in its mean spherical response (direct plus reverberant), with an attendant hardening of the sound. It should be pointed out that with most suit able listening rooms there is a substantial selective absorption of higher frequencies from the reverberant field energy, which tends to aggravate the problem of perceived balance with the omni. (The effect also explains why the addition of wide dispersion tweeters to conventional speakers tends to smooth the response.) In fact, the problem of selective absorption is so great with the omni that they often require equalizers to maintain proper balance.** Another advantage sometimes claimed for the omnidirectional speaker is that, since the direct field is audible over a much wider listening space than with the semidirectional speaker, the area of stereophonic perception is thereby increased. This point requires us to consider the substantial shortcomings of omnidirectional speakers.

It has been known for some time that two-channel stereo reproduction is unable to provide the spatial sound components necessary to reproduce the ambience experienced at a live recording session or in a concert hall. It is my opinion that this limitation is directly responsible for the recent interest in speakers branded as omnidirectional and direct/reflecting. Both speaker types attempt to provide wider areas of stereophonic perception than is normal, and both introduce spatial components that, it is claimed, lie hidden in the recording. However artificial these devices may be in absolute terms, they have gained wide acceptance by surprisingly large portions of the lay public that have become increasingly disenchanted with conventional two-channel stereo reproduced via semidirectional loudspeakers. The problem inherent to both speaker types is that the additional spatial components that the listener perceives are generated within the listening room, and have nothing whatsoever to do with the spatial components that existed during the recording. But for many typical recordings that are made today that contain too much direct sound (close miked), the addition of spatial components, artificially or other wise, does increase the “sense of realism.” But it is characteristic of things artificial that sooner or later they are recognized by the human ear; and what was initially labeled as realistic becomes repugnant.

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** The subject of required equalization of the reverberant field is sufficiently complex to require further elaboration. It turns Out that while a sufficiently selective frequency equalizer can restore the reverberant field energy balance under steady state (sine wave) or quasi steady state (stationary random noise) conditions, the equalization process can never be complete even for the reverberant field due to the aperiodic nature of musical waveforms coupled with the fact that some of the room energy fluctuations are the result of varying decay time/frequency characteristics and other fluctuations are the result of normal room modes (resonances). It is further noted that the equalization of the reverberant field involves a corresponding do-equalization of the direct field, and while this may not be much of a problem with omnidirectional speakers that contain so little direct field any way, it seems to be serious enough with semi- directional speakers and doublets. What appears to be necessary is a separate means of dealing with the reverberant field response without altering the direct response.

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In order to maintain a semblance of correct stereo imaging, the omnidirectional and direct/reflecting speakers rely heavily on the precedence effect of the small amount of direct sound that reaches the listener ahead of the reverberation. The direct/reflecting approach is surely much better in this respect because there is pro vision for more direct sound than would exist with an omni mounted in the same relative position, and the reflections are mostly confined to the horizontal plane.

However, both systems are highly dependent on room acoustics, which is hardly surprising since at least 95 percent of the sound you hear from them comes off the walls, floor, and ceiling. But by far the most obvious defect with the omni, and to a lesser extent with the direct/reflect unit, is the diffusion of the stereo-imaging components recorded in all two-channel program material. The ability of an omnidirectional loudspeaker to establish a meaningful stereo image is generally the poorest of any principal loudspeaker type. This is true despite the fact that the direct field components are audible over a wider listening space. Furthermore, the performance of an omni is highly sensitive to room volume. Omnis work best in small (less than 2500 cubic feet), highly damped rooms with short reverberation times, and they generally work poorly in large rooms. In fact, when dealing with omnis, anything done that reduces the reflectivity of the room improves their performance. Another often-overlooked hazard with omnis is that at a given location in a room, they excite more room resonances than any other speaker; a problem that, as noted earlier, is not correctable.

Given the choice between the omnidirectional speaker and the direct/reflector types, one would find the direct/reflector would surely be the lesser of two evils. This is true because the direct/reflector has a better defined speaker/room relationship. The ratio of direct to reflected sound is greater than with the omni, and therefore the sound field is more accurate. The direct/reflector also tends to confine its reflections primarily to the horizontal plane. The idea of a “magic” ratio of reflected to direct sound (9:1) is nonsense. The ratio of reflected to direct sound is one of the most common variables of the recording process, and there is simply no fixed acoustic ratio which could correspond with all recorded environments. The fact that a 9:1 ratio may be correct for a concert hall is interesting in itself, but I suggest that the recording engineer place his microphones wherever this ratio exists if he wants it reproduced.

It is not the function of a loudspeaker to compensate for recording defects or limitations, because with good recordings (few of which exist) the process will be inverted. Most of today’s recordings are not made in concert halls anyway, so in the majority of cases, the magic ratio of 9:1 is wrong. It is also pertinent that recording studios use as monitors speakers with for ward-directed radiation patterns. It follows that virtually all recorded material has been “mixed down” for reproduction through speakers more or less conventional in their radiation patterns. Despite their interim popularity, the real Waterloo for the omnis and direct/reflectors will be four-channel. If anything, it will require speakers with even narrower radiation patterns than has been customary for two- channel in order to achieve the best results. The lack of spatiality in two-channel recordings which precipitated interest in the omnis will no longer exist, and in all likelihood neither will the omnis.

Clearly, the most satisfactory method of dealing with the problem of room coloration is to design the loudspeaker to interact with the room as little as possible, consistent with satisfactory coverage of the listening area. While it may seem disadvantageous to purposely restrict the listening area in the interests of minimizing room effects, it must be remembered that no matter what the radiating characteristics or the acoustic ratio are, the best place to listen to stereo is in front of the two speakers, equidistant from each. The stereo effect depends on the perception of temporal, intensity, and informational differences between the two channels, which can be experienced properly only in the direct field midway between the sources. The “stereo everywhere” approach means, “correct stereo nowhere.”

The type of speaker radiation pattern that best meets the requirements of mini mal room coloration is the dipole, which is alternately referred to as the “figure of eight” or “acoustic doublet.” This type of speaker operation is typical of the full-range electrostatics and the best explanation of its advantages that I know of was given in 1955 by P.J. Walker in his famous Wireless World articles on electrostatic speakers:

We now come to consideration of the doublet as a sound source and we shall see that it possesses properties of considerable significance in improving loud speaker/room relationships. By a doublet we mean a diaphragm, radiating on both sides.

If we assume a 12”-15” unit, (moving coil or electrostatic) mounted in a 4’-5’ baffle, we find that the acoustic system has three main faults: (1) The acoustic air load falls to very low values at wavelengths larger than the baffle size; (2) the acoustic load is very irregular at low frequencies, and (3) reflections from the baffle edge occur at higher frequencies. The second and third faults can be mitigated by adopting peculiar shapes.

If, instead of a baffle, we construct a composite electrostatic unit of the same area, the position is completely altered. The resistance per unit area and the total working area are both increased so that the air load is many times that of the baffle case. The load, and consequently the performance, is regular and predictable.

The construction is that of strip units progressively increasing in plate spacing and area from the center line. Due to the air load resistance involved for each strip, the permissible bandwidth is reduced over that which could be obtained if the back radiation were sealed off, and it is necessary to split the frequency range into three to obtain the efficiency comparable to a two-way ‘sealed’ system.

Any unloaded strip considered alone will have a resonant frequency when the diaphragm stiffness reactance equals the air load mass reactance. This is, however, placed below the frequency range of the strip, so that the mutual radiation of the adjacent strip carrying a lower frequency range increases the radiating area and prevents the application of any effective mass.

The complete system is therefore entirely free of resonance except at one low frequency (usually placed at 30-35 cps). The 0 of this resonance is adjusted to maintain response to this frequency.

The complete loudspeaker has a cosine characteristic, and this is substantially maintained through the range. It can not radiate sound in the direction of its surface, horizontally or vertically, so that it cannot excite room modes in two of the three room dimensions. It will only excite modes in the remaining dimension when placed at a region of maximum velocity for that mode. (The impedance looking into the loudspeaker is low.)

Having a ‘cosine’ polar characteristic the mean spherical radiation is reduced by a factor of three at all frequencies, so that quite apart from freedom of mode excitations any color due to the room is reduced by a factor of three. This is exactly analogous to a ‘velocity’ microphone. In the same way that a ‘velocity’ microphone is used in place of a ‘pressure’ microphone to reduce studio color, this ‘velocity’ speaker will reduce color due to the listening room, and ‘velocity’ speakers of otherwise similar characteristics.

Listening tests comparing ‘pressure’ characteristics indicate that a velocity characteristic may well have important features for high-quality reproduction. An electrostatic speaker of this type correctly positioned in the room meets all the requirements, as did the ‘wall’ form previously described, with the addition of an even better loudspeaker/room relation ship. The fact that it is required to be free standing within a room may or may not be advantageous.

The more the acoustic ratio is reduced (provided always that it is reduced equally at all frequencies), the more one approaches the state of affairs that the pressure at the ears is a replica of the pressure at the position of the microphone in the concert halt or studio (ideal headphone conditions).

The problems of using doublets properly are not always easily solved in home listening situations, a factor that has seriously restricted their use for most people. Furthermore, there is much evidence that doublet operation at all frequencies is not as desirable as the theory would indicate. One well-known engineer recommends doublet operation above about 250 cycles with the bass remaining. However, it would seem that most of the real benefits of doublet operation in eliminating room coloration in the range where it is most apparent (below 500 cycles) are lost in this approach. It is my belief that the range most problematical with doublet operation is between 500 and 5000 cycles, where the wavelengths are similar to the distance required between the wall and the speaker to get good bass response. The best solution for the audiophile who chooses the doublet radiator is to spend time and money in providing acoustical treatment to his listening room.

The absorbing of a certain percentage of the speaker’s rear radiation above about 500 cycles should allow a more practical speaker placement than would otherwise be possible.

Despite the proliferation of speaker designs that generate “acoustical multi-path” under the guise of greater realism, I think that the attention given to the speaker has caused a lot of people, myself included, to reexamine the room/speaker relationship together with the methods of recording and the process of hearing, If the only long-term effect of the omni’s and the direct/reflectors has been to speed the inevitable introduction of additional recording channels as a means of properly pro viding greater realism, then I think their rediscovery may have been worthwhile. In the meantime, there appears to be growing evidence that speaker coloration is even less tolerable in four-channel than it was in two-channel, and this fact in itself should redirect speaker design back to its proper direction of exploring more accurate methods of changing electrical signals into sound, and of perfecting those techniques we have. The room problem will still exist, and it may be even worse in four- channel, but if we can better coordinate the process of recording with speaker radiation patterns, it shouldn’t be insurmountable.

—Jon Dahiquist

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ALSO SEE: Wiki article (German)

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