Fishing for Bass: A Look at the Subwoofer Scene (March/April 1977, Vol. 1, No. 2)

Our initial haul consists of two somewhat flawed specimens that go very deep and an almost faultless one that doesn't.

For openers, we'll try to make you angry or at least frustrated. Did you know that the recipe for attaining ruler-flat loudspeaker bass down to 30 Hz and below, with high efficiency, low distortion and optimum transient response, in a large but still manageable enclosure, is available-and has been available for a good many years? And that it involves no special tricks, gimmicks, inventions or costly high technology shenanigans? And that no manufacturer has taken full advantage of it to this very day? Huh? Neville Thiele originally presented his brilliant paper, correlating filter synthesis with the equivalent circuits of speaker systems, to a convention of engineers in Australia 16 years ago. This highly practical, 100% usable information lay around neglected for ten years, after which it was miraculously rediscovered by the Audio Engineering Society and followed by the even more complete and rigorous studies of the redoubtable Richard Small. At about the same time, other researchers like Robert Ashley and Don Keele also made important contributions to this body of knowledge, which, taken together, just about completely defines the electromechanical operation of a speaker system, so that it no longer holds any mysteries or surprises or opportunities for "breakthroughs." This is especially true of the woofer.

The mathematical model of the woofer has been for some years now so complete and ac curate that one needs only to define the maximum tolerable box size and minimum accept able efficiency in order to obtain exact design parameters for the theoretically unexceedable frequency response, distortion and transient characteristics. The whole process is about as dependent on the personal "creativity" of the engineer as the zeroing in of a piece of artillery.

All it takes is homework. But, as we all know, homework is a pain the posterior, so hardly anyone is doing it. The exceptions are companies like Electro-Voice, where the emphasis is on optimizing PA-type sound rather than producing state-of-the-art speakers for the audiophile.

Editor's Note: In the accompanying article, our Consulting Engineer offers a qualitative explanation of the mathematical approach to woofer design. Being a basically gentle and scholarly person, he refrains from rubbing it in that nearly all of today's makers of $2000 and $3000 speaker systems are innocent of this discipline.

In view of the thoroughly documented, scientific information available on woofers and subwoofers (the two being conceptually the same except for the latter's relative freedom from restrictions on size), it depresses us greatly how the most vulgar, locker-room generalizations on the subject rule the minds of even advanced audio enthusiasts and of the manufacturers who cater to them. "Sealed enclosures are OK but they don't give you really low bass." Or "vented enclosures are more efficient but boomy." Or "if you want really tight bass you've got to use a transmission line." If there's one thing you get out of this report, we hope it's an understanding of how amateurish that kind of talk is. A speaker cone doesn't know about enclosure formats. All it knows is the combination of forces acting upon it. And that combination can be applied in a multitude of ways, none of them inherently good or bad. The important things are the damping (indicated by the Q of the total system), the 3-dB-down frequency, the linear excursion capability and other such purely performance-related data.

For example, if you ask about a sealed system what the Q is and the answer is 0.707, you already know that the frequency response is flat without a ripple, that the 3-dB-down point is the resonant frequency of the system, that an octave below that frequency the response is down 12 dB, and that the transient response is the best possible for these conditions. On the other hand, if you're told that the Q is 1, you already know that the response at the resonant frequency is now 3 dB better (0 dB down) but at the cost of a ripple just above that frequency and of slightly degraded transient response, which is nevertheless still quite adequate. For a vented system the numbers are again different. (See also the accompany article.) The point is that woofer design deals with the laws of nature, which in this case are completely known and will be the same in the year 2100 as they are today. Therefore, no one is going to come up with a triangular driver loaded by an elliptical slot in an L-shaped box that will give you a 115 dB level at 20 Hz with 10% efficiency in three cubic feet. Forget it. It's not going to happen. Whether the force that moves the driver is electrodynamic, electrostatic or copacetic. Nor can motional feedback accomplish anything that wasn't damn close to the desired end result in the first place, before the feedback was applied. You can't fool Mother Nature.

Okay, but where does that leave us with subwoofers? What we must ask when evaluating a sub woofer, other than how good (i.e., accurate) it sounds, is whether the design is optimized for its particular size. Could the same size box, with different engineering, give you more cycles on the bottom? Or, if you're satisfied with its range, could it be more efficient (easier on the amplifier)? Or, if it's optimum on those counts, could it have lower distortion? The mathematical model referred to above provides the answer in each case. And, of course, one can push the inquiry a little further. Could a tolerable increase in size, at no additional cost, give you considerably better performance? In other words, has the designer explored all the available options in the light of present-day knowledge? We can state without hesitation that no subwoofer known to us, whether it's separately available or part of a system, can stand up under this kind of cross-examination unscathed.

We don't know of a single design about which a panel composed of Thiele, Small, Ashley, Keele and their peers could say: "This one incorporates everything we know." Please note that this is not the same as submitting, say, a preamplifier to the same kind of scrutiny. No one knows exactly how good a preamp ought to be with a given number of transistors, resistors, capacitors, etc. The sky, or rather a straight wire with gain, is the limit.

Not so with a subwoofer.

What about crossover networks? This is an extremely complex subject about which we'll have a lot more to say in the report on large, expensive speaker systems in our next issue. For the moment let's just summarize the basics.

Since subwoofers are intended to be crossed over to systems that presumably have decent upper-bass response, the crossover frequency is generally 100 Hz or lower. If the crossover is at low impedance, as in the typical passive network that goes between the power amplifier and the drivers, the coils required at those frequencies must be rather large and un wieldy, especially if they are wound on air cores. What's more, the subwoofer may drain too much power from a single amplifier that handles the full audio power. Although there are some valid exceptions to this generalization, we ordinarily prefer to biamp the sub woofer through an electronic crossover. If nothing else, IM distortion will certainly be lower.

Each of the subwoofers we tested comes with its own electronic crossover, although in principle others could also be used.

The main problem with electronic cross overs is the same as with preamps: they usually have a sound of their own. It's not easy to design a stage of gain that can be inserted between the preamp and the power amp without altering the sound at least to a slight degree.

If you're particular enough about preamps to use a Mark Levinson JC-2, for example, you may not want to plug it into just any old IC crossover thrown together by a speaker manufacturer. (You've probably noticed by now that we consider speaker people to be the least knowledgeable element in the audio industry, probably because it doesn't take a heavy technical background to put together a bad speaker.) One alternative is a passive crossover ahead of the two power amplifiers; nothing can be more transparent than that, especially if you stick with a 6-dB-per-octave network, which can be made out of a dollar's worth of resistors and capacitors. That's what we've been using until recently; now we find the ingenious new Dahlquist half-electronic, half passive crossover to be just as transparent and more practical.

The rule of thumb is: passive is more transparent than active; 6 dB per octave is better in transient response than either 12 dB or 18 dB per octave; 18 dB per octave louses up the phase response less than 12 dB per octave. Ultimately, however, the choice of network configuration depends on the acoustical characteristics of the speakers, not on electrical theory. For example, the only thing that would really help the Janis subwoofers in our opinion is a 36-dB-per-octave active network (see Janis W-1 review below).

To sum or not to sum.

Each of the subwoofers reviewed here can be used either singly or in pairs. Their net works have provisions for summed as well as left/right operation.

Summing the two stereo channels into a single bass channel anywhere below 100 Hz will not result in any appreciable loss of directional information. There's virtually no such information in that frequency range. There is, however, ambience information. The sense of the hall, what some audiophiles call the airy or breathy quality of the bass, has some very low-frequency components, and these are not necessarily identical in each channel. In quadraphonic reproduction this information ac quires even greater importance and should not be summed.

Another argument for using a separate subwoofer in each channel is that the kind of low-frequency "cheating" necessary to cut disc masters without insane amounts of groove modulation is based on the assumption that the listener has two complete bass channels.

The phase cancellations resulting from summed operation could easily negate the little engineering tricks used to create at least a semblance of deep bass at high modulation levels. And, of course, two bass channels will give you 3 dB more power than one, which in marginal situations could also come in handy. For all these reasons, we used two subwoofers for stereo listening.

The listening and laboratory tests.

We didn't find it necessary to A-B the subwoofers against one another. The differences were large enough to be retained even in the feeblest aural memory. Furthermore, we weren't really satisfied with any one of the subwoofers tested so far, and our reluctant choice among them was based on far more obvious considerations than subtle differences that only A-B-ing might have revealed.

The main speaker system above the crossover frequency was in each case the Dahlquist DQ-10. For our rationale in sticking with this old standby, see our power amplifier survey in this issue. It might turn out to be a little repetitious to track through our reasons once again. Besides, the DQ-10 needs a subwoofer.

Both the DQ-10 and the subwoofer under test were driven by the Quatre DG-250 Gain Cell power amp, a separate one on each. The rest of the reference system was the same as described in the power amp survey, except that the electronic crossover supplied with each subwoofer was used between the preamp output and the two power amps.

Measurement of each subwoofer was by means of the "near-field" technique described by D. B. Keele, Jr. in the April 1974 Journal of the Audio Engineering Society. This method corresponds very closely to anechoic measurement in the accuracy of the results obtained.

The calibrated microphone used was the Bruel & Kjaer 4133, the measuring device the Hewlett-Packard 3580A spectrum analyzer.

Here are the results.

Dahlquist DQ-1W with DQ-LP1

Dahlquist, Inc., 27 Hanse Avenue, Freeport, NY 11520.

DQ-1W Low Bass Module, 3275. Tested #0023 and #0024, owned by The Audio Critic. DQ-LPI Variable Low-Pass Filter, 3250. Tested unnumbered sample, on loan from manufacturer.

Editor's Note: The DQ-1W was reviewed in the last issue in conjunction with the DQ-10 speaker system. This is a follow-up report with new data and an evaluation of the new electronic crossover.

Last time we said that the DQ-1W wasn't really a subwoofer but simply a very high quality woofer. Our measurements bear that out, in spades.

Guess what the lowest frequency is at which the DQ-1W is still dead flat. You're wrong. It's 78 Hz. It rolls off very gently below that and its 3-dB-down point (what Thiele calls its f3) is 42 or 43 Hz. From the response profile our guess would be that the system has a Q of just over 0.6 (not 0.707 as we reported last time), meaning that it's heavily damped.

Nothing wrong with that; the curve is beautifully smooth, including the upper range. It's the kind of curve that can be equalized just a touch at the bottom end without any ill effect (to pick up a few more Hz) and rolled off at the top without any great hurry for an inaudible crossover. And you can do both with the new DQ-LPI, as we shall see.

But a rip-roaring, subterranean, four-foot bass-drum-in-the-solar-plexus monster it isn't.

Instead, it's a very smooth, quick and accurate speaker for the second octave from the bottom. Ed Villchur's AR-1W of more than twenty years ago wasn't all that different. The DQ-1W (is the name an unintentional reminiscence?) is a little larger and probably somewhat more efficient. Since there's hardly ever any bottom-octave information on records and in FM broadcasts, the DQ-1W will in most cases give you an excellent replica of the signal going into it. And, as we pointed out in our first report, it sounds right with the DQ-10.

But it most emphatically isn't the subwoofer for organ buffs and other bass addicts.

Room replacement can, of course, either beef up or cut down the response of the DQ-1W and also change its damping characteristics.

That's true of any woofer; however, it's least critical with a completely sealed direct-radiator system such as the DQ-1W. By definition. Any one who tells you that this woofer is especially sensitive to room placement doesn't know what he is talking about. Even so, you'll do well to experiment. And remember that the lower the crossover frequency, the less critical the distance of the woofer from the rest of the system.

Which brings us to the DQ-LP1 crossover network. What an elegant little box, both in visual styling and in engineering concept! Crossover design, like politics, is the art of the possible, and to our mind the DQ-LP1 represents the most intelligent trade-off to date between the conflicting requirements of frequency-response shaping and transient performance.

Above the crossover frequency, which is variable (by means of two neat little dials) from 40 to 400 Hz, the network is passive, so that it can't possibly introduce any electronic veiling. Once you've selected the crossover frequency, the input impedance of your high amplifier determines the adjustment that must be made inside the box (soldering in one or two little components per channel, to raised terminals available for this purpose). This will create a 6-dB-per-octave roll-off below crossover in the passive section of the network.

If your midrange or high-bass driver has to be stopped dead below the crossover point, this isn't the network for you. For the DQ-10, it's ideal.

Below the crossover frequency, the DQ LPI is an electronic low-pass filter, with a very clever response profile. The roll-off starts at 6 dB per octave, for the best possible transient characteristics in the crossover region.

Then it accelerates to 12 dB per octave and finally ends up with an 18 dB per octave slope to kill the totally unwanted frequencies higher up. It makes you very nearly able to eat your cake (i.e., fast slope) and have it too (i.e., transient fidelity).

In addition to level controls for the low pass section, the network also provides equalization controls (0 dB to +5 dB) for the bottom end. With an almost overdamped woofer like the DW-1W, that's very useful, making it possible to lower the fs slightly, without hell to pay. But careful-with an underdamped woofer the Q just goes to pot. Woof, boom and slop.

The highest praise we can give the DQ-LP1 is that it introduces no more coloration than a purely passive, 6-dB-per-octave crossover, while being infinitely more versatile and effective in controlling the level and dumping the unwanted upper range of a woofer.

Our conclusion (only about the crossover, mind you, not the subwoofer): Every American family should own one.

Janis W-1 with B4SL-C Janis Audio Associates, 2889 Roebling Avenue, Bronx, NY 10461. Model W-1 Subwoofer System, 3650. Model B4SL-C Electronic Crossover, $240. Tested samples on loan from manufacturer.

We have this fantasy that John Marovskis, the founder of Janis Audio and designer of the Janis woofer, made a pact with the devil.

"Do you really want ruler-flat bass all the way down to 30 Hz?" asked the Evil One.

"Maybe 2 dB down at 25 Hz?"

"More than anything in the world," said John fervently.

"With really high efficiency?" teased the Devil. "Say an SPL of 85 dB with only about one watt going in?"

"Yeah, yeah!" cried John.

"From a moderate-sized commode, say 22 inches square and about 'a foot and a half high?' chuckled the Tempter of Mankind, moving in for the kill.

"That does it!" exclaimed John. "I'll do anything!"

"There's a price to pay," warned the Prince of Darkness.

"My soul?' asked John, well prepared for the demand.

"We'll talk about that later," smiled the Devil. "For the moment all you pay is a rising response above 100 Hz, about 6 dB per octave- and the biggest peak at 460 Hz you'll ever see in your life."

"How big?" asked John, knowing deep down it no longer made a difference.

"Fourteen dB up above your flat range," replied the Devil, himself amazed at the poor bargains struck by men.

"I'll take it, I'll take it!" cried John.

"I'll get rid of the rise with an 18-dB-per octave crossover. Tell me what to do, Satan." The Devil held out his hand and John grasped it eagerly. A sulfurous puff of smoke exploded from their handshake. Then the Devil whispered in John's ear:

"Put a 15-inch driver in a sealed enclosure.

Give it a system Q of 1. Then load the front of the cone with this magic slot I'm about to show you. And just ignore all the bad things you've heard about slot loading." And that's the way it happened. John made the subwoofer, calling it the W-1. And he told everybody the truth about it. That it was dead flat below his chosen crossover point of 100 Hz, down to the system resonant frequency of 30 Hz, where the response was still 0 dB. We've verified that. That it had oh-point-something percent harmonic distortion at any frequency down to 30 Hz, never even as much as 1%, at an SPL of 85 dB. Also true. That it could shake the plaster off your walls with a 60-watt amplifier. You better believe it.

But there was one thing he didn't tell any one. That even with the cute little 18-dB-per octave electronic crossover he had signed for his subwoofer, the response at 200 Hz was down less than 12 dB below the flat range on account of the inherently rising characteristic of the slot, and the peak at 460 Hz was only 22 dB below the crossover point. That's with the B4SL-C network in. Since the woofer is pluperfect in every other way we could deter mine, that has just got to be the reason why we didn't like the sound. Because we didn't like it at all. The upper bass and the mid range, in combination with the Dahlquist DQ-10, were thick, opaque, incoherent and un pleasant. "No, no, it just doesn't sound right!" was the reaction of our staff members.

The lower bass is, of course, astonishing.

The W-1 laughs at 32-foot organ stops, massed double basses and the Moog synthesizer. "Is that the hardest you can hit?" it seems to ask them. As a matter of fact, when the output of the woofer into our room was adjusted with the B4SL-C network's level controls for measured flat response above and below the crossover point, the bass was much too heavy and had to be turned down. Quite regardless of its overall fidelity, a 25-Hz woofer is another breed of audio component and requires very different feeding and care. You have to tame it before you can use it.

We weren't quite able to decide whether the low bass quality of the W-1 had anything to do with what we didn't like about it. The Q, as we said, is 1 and that's not the ideal damping characteristic for a sealed system, 0.707 being the classic trade-off between pressure amplitude and transient response. With the latter Q, the W-1 would measure -3 dB at 30 Hz instead of 0 dB. On the other hand it wouldn't be up almost 1.5 dB at 40 Hz, which is the characteristic ripple of a Q = 1 system and the W-1I's greatest deviation from absolutely flat response. Whether this makes the Janis sound less "fast" than the Dahlquist, for example, was difficult to judge on account of the more disturbing qualities that intruded.

John Marovskis has been going around saying that a Q of 1 makes his woofer "critically damped," which is simply an error. We managed to prove to him that critical damping in a sealed system means Q = 0.5, which of course no one is advocating as it would mean that the amplitude response had to be down 6 dB at resonance.

A friendly technical controversy then ensued, on which we have some correspondence that would be much too unwieldy and confusing to reproduce here. Basically the position taken by Marovskis is that he considers 0 dB at 30 Hz to be nonnegotiable (i.e., that -3 dB at 30 Hz would not be acceptable to him) and that, given that unyielding condition, Q = 1 provides still the best transient response. To us the whole thing seems less important in the case of the Janis woofer than the basic issue of slot loading and the resulting perturbations in response above the crossover point.

We understand that Janis also has a design for a 36-dB-per-octave electronic crossover, which hasn't been marketed so far. Although that type of network (sixth-order) has its own problems, it would be interesting to hear what it could do for the W-1 above 100 Hz, since 18 dB per octave just doesn't seem to be enough.

Let's not forget that the very concept of a crossover network assumes reasonably flat and smooth response in both directions immediately above and below the crossover point.

Just to make sure we weren't listening to colorations in the B4SL-C, we also tried our purely passive network as well as the Dahlquist DQ-LP1 on the Janis, both set for cross over at 60 Hz. As you can guess, they didn't do any good, but you can't blame us for trying desperately. The Janis is much too tantalizing to turn your back on.

Somebody down there knew that all along.

Janis W-2 with B4SL-C Janis Audio Associates, 2889 Roebling Avenue, Bronx, NY 10461. Model W-2 Subwoofer System, $450. Model B4SL-C Electronic Crossover, $240. Tested samples on loan from manufacturer.

The W-2 is offered by Janis as virtually identical in performance to the W-1, at a $200 saving. Like everything else these people say, it's true-and that's just the problem.

The rising response of the W-2 is virtually identical to that of the W-1; if anything it's a little worse. Measured through the B4SL-C network, the W-2 at 200 Hz is down only 10 dB below its flat range. It doesn't have the Matter horn peak of the W-1 at 460 Hz, but it has even more elevated average response just below that.

Between 350 Hz and 420 Hz, the average level is only 21 dB below the crossover point. To our ears, the sound of the W-2 is also virtually identical to that of the W-1 in the upper bass and midrange.

The bottom end is slightly different. For one thing, the W-2 appears to have a slightly lower (and to our mind better) Q. The ripple just above the knee of the curve is much smaller. Does the W-2 sound better damped than the W-1? We aren't sure. Its entire bass quality is somewhat lighter, most probably on account of the 4 dB lower output at 30 Hz and 2 dB lower at 50 Hz (when the 100 Hz outputs are matched). If we call the W-1 a 25-Hz woofer, we can probably call the W-2 a 33-Hz woofer, as there appears to be a distance of about 8 Hz between the bottom-end slopes of their superimposed curves.

Would you pay $50 per dB at 30 Hz for otherwise virtually identical sound? How about $25 per hertz? We wouldn't, but then it isn't a Janis enthusiast who's talking.

Recommendations These have been slim pickings and certainly no occasion for definitive conclusions in boldface type. The Janis W-1 and W-2 are spectacular but faulty subwoofers, and the Dahlquist DQ-1W is no subwoofer, although excellent as far down as it goes and highly recommended if you don't expect too much of it. Only the little DQ-LP1 crossover is a jewel, but what would you do with it without a sub woofer?

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A Rational Approach to Low-Frequency Speaker Design

By Bruce Zayde

Editor's Note: Engineers who have a thorough grasp of the mathematics of speaker system analysis can probably be counted on two hands and maybe a foot (which is how the others probably count them). The name of Bruce Zayde, our Consulting Engineer, generally comes up somewhere between the seventh and the ninth finger.

Before we can understand why nearly all speaker systems miserably fail to reproduce the bottom octave of music, we must examine the very essence of a loudspeaker. We have to ask --and answer-what is a loudspeaker? How does it work? And we must ask whether our demands for the '"'perfect" loudspeaker are realizable.

All right, then, what is a loud speaker? It is an oscillator. It has mass (voice coil and cone), it has a suspension (spider and surround), and it be haves exactly as a ball would when attached to the end of a spring suspended from the ceiling. The oscillator has resistance in the suspension, which tends to damp oscillations to a greater or lesser extent. This resistance is proportional to the velocity of motion.

This is wonderful news, since the mathematical form for the oscillator is a second-order ordinary differential equation with constant coefficients. The solution for this kind of equation is straightforward and yields extremely useful results. They tie in and link the variations of mass and spring stiffness so that resonant frequency can be accurately predicted. The degree of resistance in the system can be analyzed to provide data on how this resistance will affect the resonant behavior of the oscillator. That is, will the system only respond by oscillating at its resonant frequency, or will it be able to oscillate at frequencies closely, or more distantly, neighboring its resonant point? The manner in which this resistance alters the oscillator's behavior is handled by the concept of the "Q" of the oscillator.

The Q, or quality factor, of the oscillator is inversely related to the resistance, or damping, of the system. I.e., the higher the relative resistance in our oscillator, the higher the damping and the lower the Q.

It must be cautioned that in dealing with the Q of an oscillator one doesn't interpret ''quality factor" as meaning relative goodness. That is, a high quality factor, or Q, does not suggest a good system, nor does a low quality factor (and high damping) imply a poor or not so-good oscillator. The Q is merely a good way of illustrating the relative resonant behavior of an oscillator.

The solution of the differential equation, furthermore, gives us details regarding the excursion of the oscillator, the velocity of the oscillator, and the acceleration and deceleration of the system during excitation and after a driving force (whatever it may be) is removed.

Perhaps, at this point, we should modify our definition of a loudspeaker as a simple oscillator by considering the fact that it is driven by a linear motor. The magnetic field with a voice coil seated within it comprises a motor whose power is determined by the strength of the field and the amount of voice-coil wire saturated within the field.

This motor has control over the oscillator that has been described above.

The motor serves to accelerate and decelerate the oscillator, and, in general, keep the oscillator under control.

But, we might ask, 'what drives the motor that drives the oscillator?" Well, how about an electrical oscillator? A power amplifier connected to a loud speaker provides current oscillations which, in turn, cause the motor to oscillate in accordance with the current commands, and this linear motor is then attached to the cone which oscillates the air in contact with it to follow the original electrical signal from the power amplifier. That's quite a lot of stuff going on. Our simple oscillator now becomes quite formidable, and must be entitled an electro-mechanico-acoustical oscillator.

Unlike the simple damping pro vided by the internal resistance of the original ball and spring model, there is damping provided by the power amplifier, which is brought about by the resistance ratio of the loudspeaker input to the power amplifier output. Especially where a goodly amount of negative feed back around the output stage of the amplifier is present, the output impedance of the stage can be extremely low (less than 0.5. ohm). The amplifier then greatly assists in the overall damping and, in fact, in the ideal case, is largely responsible for it. (Low TIM amplifiers with reduced overall negative feedback have low output impedances, too, and provide ample loudspeaker damping.) So, for example, where the loudspeaker has an impedance of 8 ohms, and the amplifier has an output impedance of 0.5 ohm, the overall damping, neglecting all other (mechanical) damping, is 16.

Therefore, in a very real way, the output stage of a power amplifier must be considered as a part of the loud speaker system. Now, what happens if the output impedance of the amplifier is not especially low with respect to the loudspeaker. Let's say, for example, that the output impedance of the amplifier is the same as that of the loudspeaker. Damping is greatly reduced, and as a result the Q of the loud speaker plus amplifier is greatly in creased. In this case, if the overall response with high damping between amplifier and loudspeaker is maximally flat, equal impedance between loud speaker and amplifier will render a hump of 6 dB in the bass. (This is a Q of 2.) Note also that connecting a lot of wire between amplifier and loudspeaker will not only waste power (the lesser of the evils) but, more significantly, will spoil the damping relationship between loudspeaker and amplifier, and render a totally unsatisfactory response.

So far, we've only concerned our selves with a loudspeaker and power amplifier. It should also be pointed out that the entire discussion restricts it self to the piston range of a loudspeaker (generated wavelength greater than the circumference of the cone). What hap pens when we put our electro-mechanico acoustical oscillator in a box? Well, if the box is large enough to be an infinite baffle, essentially nothing. Except for restricting front-to-back cancellation due to dipole radiation, the infinite baffle does nothing to alter a loud speaker's output. The variables already discussed (mass of moving system, suspension stiffness, mechanical resistance and resultant mechanical damping, power amplifier interaction and electrical damping) are all preserved. But what about a small box? When a loudspeaker is placed in a box whose air volume is less than the equivalent air volume of the driver's suspension stiffness, the box then acts as an added stiffness, and raises the resonant frequency of the overall sys tem. This is the principle behind the air or acoustic suspension system. It is essentially the same as substituting a stiffer spring in place of the original one in our ball and spring analogy. As a result, the overall mechanical damping in the system is reduced and the system Q is raised. This can be beneficial if the loudspeaker damping is too great to begin with, but if it results in insufficient damping, the response will be ruined. A logical remedy is a larger motor to increase electrical damping and restore correct frequency balance.

But what if the resulting resonant frequency is higher than desired? A reasonable solution is to increase the mass of the moving system, and establish a new resonant frequency lower than the previous one. However, this procedure will also diminish the damping in the system and raise the overall system Q. Again, remedial action could be to increase the motor even more (increased electrical damping), or to add some heat-absorbing material in the box (tuflex, kapok or fiberglass) and in crease acoustical damping. The latter approach works by essentially changing a roughly adiabatic response to iso thermal and results in increased damping in the area where needed. It should be understood that this approach works only where the required increase in damping is minimal.

We may also increase the box size, thereby reducing the air stiffness within the enclosed space, and thus lower the resonant frequency of the system, but this would increase the overall damping and could suppress bass response despite the lower system resonance.

Notice that when a box is introduced, the overall complexity increases rather sharply. But it looks like the worst is over, doesn't it? No, not by a long shot. We must contend with the vented design, now reaching new levels in audiophile interest, and rightly so.

The vented design format introduces a further level of complexity by adding a Helmholtz resonator to our electro-mechanico-acoustical oscillator, with much further-reaching interactions.

A vented system makes use of the rear radiation from a loudspeaker, and since this is the case, boasts greater efficiency than the sealed systems mentioned above. For a moment, let's examine the enclosure of a vented system.

It consists of the box itself and a hole, possibly with a tube behind it, to which nothing is mounted. The hole and tube define an air mass that is contained within them. This air mass reacts with the volume of the box to create a new oscillator. (The stiffness of the air contained within the box is the "spring" and the mass of the air within the tube or duct is the "ball."') The rear of the loudspeaker, or driver, drives the acoustical oscillator just described, and all driver parameters mentioned earlier now become interlocked with the box plus vent.

The loudspeaker now is responsible for not only its own damping, but it must damp the box plus vent too. This requires, as might be suspected, a higher damping than that required for an equivalent sealed system.

The case for the vented system approach is a good one, since higher efficiency for similar bass response is welcome. But there is an additional advantage. Lower distortion. This is true because the oscillator defined by the enclosure plus vent relieves the driver of considerable cone excursion that would occur near the box resonant frequency were it not for the venting.

In a sealed system, for equal out put, driver cone excursion has to quadruple for every halving of frequency down to system resonance. This is also true for the vented system, except near the box resonant frequency. As the box resonance is approached, the excursion actually becomes less (and along with it the distortion) and at the box resonance the excursion is at a minimum because, at this point, the air mass contained within the vent reaches maximum excursion. This is actual motional energy transfer, in that the vent assumes a greater role in movement as the box resonance is approached. The energy is derived from the rear of the loudspeaker cone. In actual practice, the vented system is about 4 dB more efficient than a sealed system of the same size with the same 3-dB-down point in the bass.

It is of course essential in a vented system that the free-air resonance of the driver and the box resonance frequency be carefully related. The driver damping and box size are also closely tied together, as are the mass of the moving system of the driver and the 3-dB-down point of the system bass response.

Somebody will probably have asked about transmission-line enclosures by now. Transmission lines (formerly called acoustical labyrinths) are non-optimal designs that use excessive amounts of damping material to suppress resonances within the cavities that comprise the enclosure. Generally, a better approach to producing low bass response with minimal parasitic energy dissipation is to stick with the sealed or vented direct-radiator format. (Horns, of course, are another matter altogether, and their virtues and shortcomings re quire a separate analysis.)

And now, what about how loud things get?

All of the above discussion can be called 'small-signal' considerations. We certainly are concerned with the amount of sound we desire to have a system reproduce. We cannot expect an 8-inch driver to produce a 32 Hz tone at 120 dB. It simply cannot move enough air to generate that sound pres sure level. With a 15-inch or 18-inch unit, that capability may be within the realm of possibility, provided that the suspension has been carefully designed to permit gross linear movement, and that the voice coil is long enough to guarantee full electromagnetic coupling during this extreme movement.

The size of the vent in a vented system undergoes the same considerations. A small tube diameter can tune a box to a lower frequency than a larger tube diameter, but the air within the smaller tube must move farther than within the larger one for the same sound pressure to be generated. This introduces the very unpleasant rushing wind noises created by the smaller duct. In order to increase the diameter of the vent, the length of the duct must also be increased for correct tuning and this could result in a tube of unrealistic length. One way around this is to intro duce the vent substitute, whose sole function is to have sufficient mass to tune the box to the desired frequency, while at the same time not having any length associated with it. The most popular vent substitute is a cone with the appropriate mass, whose appearance resembles that of a conventional loudspeaker driver. Increasing the cone diameter requires an increase in mass in order to tune the box to a specific frequency. The larger the cone, the greater sound pressure level it can pro duce, but the greater mass it must have.

All these variables have one extremely unpleasant aspect associated with them. They are all interrelated.

More specifically, all the parameters introduced from the beginning of this article are tied together, and changing any one of them requires a prescribed alteration in the balance in order to maintain correct relation.

One method of dealing with this situation is to treat a loudspeaker system as a giant soup. The cook adds a little mass here, a little volume there.

Oops, some more duct needed here. Oh, and we just must have some magnet over there. Ah, but now we reduce the volume just a smidge. Oh no, now we need a smack of wire just over there. Method you say-rubbish I say.

Gratefully, there is a splendid method of dealing with all these variables in a predictable and orderly manner. As first realized by the Australian researcher, A. N. Thiele, and greatly expanded and elaborated upon by Dr. R. H. Small, also from Australia, a loudspeaker and a loudspeaker en closure behave exactly as a high-pass filter, and all the glorious techniques of filter synthesis can be used to predict the performance of a proposed loudspeaker system accurately.

Through the use of dynamical analogies (comparing the mathematical form of electrical components and relating them to mechanical components with the identical form), a master circuit can be drawn up with all electrical, mechanical and acoustical elements accounted for, and then this circuit solved in the traditional manner (typically by the use of the Laplace transform) to yield all the critical interrelationships cited earlier. The solution is in the form of a high-pass filter (allowing all frequencies above a certain point to be passed, and all frequencies below that point to be increasingly attenuated), and accounts for all the linkages between the parameters of importance. This approach can be programmed into a minicomputer (or a large mainframe if so desired) and the correct design relationships can be almost immediately forthcoming.

In other words, achieving flat, boom-free, smooth bass response need not be a black art, but something de rived from the thorough discipline of filter synthesis borrowed from the practices of electrical engineering.

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[adapted from TAC, Vol.1, No.2]

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Also see:

Know Your Audio Critic: A Continued Discussion of Our Philosophy, By Peter Aczel, Editor and Publisher

Various audio and high-fidelity magazines