Speaker Asylum: Re: Subwoofer Design by MrJ

I'm a tourist, and I've had my evening Vodka-tonic (well, the second pour skipped the tonic), so take my rambling lightly. Here's my take on your inquiry.

You have the general idea. Multiple drivers increase the total swept volume of the bass driving system, which drops overall excursion for a particular SPL.

Some inherent problems:

Cabinet size - two drivers require twice the cabinet room to perform as well as a single driver of the same model. Without this doubling, the two speaker unit will note have as good a bass presence (i.e. earlier rolloff) as a design with a single driver of the same model, although the smaller dual design will have a potential higher SPL. With four driver designs (not popular in Hi-Fi these days) it's even worse.

Phase incoherence - your ear's position will undoubtedly be a slightly different distance from one driver than the other. This is particularly noticable at higher frequencies, because potential cancellation effects depend on the length of the waveform (smaller waveforms have increased chances for interference). This problem even occurs on single large drivers at high frequencies (the sound from one edge may reach you before the sound from the opposite edge does). Since the issue usually applies to bass design, it's negligable. Note, though, it may limit your design's crossover point, and it's the reason drivers are arranged vertically in MTM designs.

More labor - more holes, more wire.

Impedence issues - this is double edged. Depending on the target impedence of your system, you have be forced to choose 4 ohm drivers for wiring in series, or accept a 4 ohm design if wiring 8 ohm drivers in parallel (suggesting, for example, 4 ohm tweeters if it concerns you).

Damping - some designers are concerned about the damping factor of the Amp/Speaker system. If so, two drivers generally need twice the damping of one.

Symmetry - Cabinet symmetry (acoustic symmetry in particular) dictates some of the design. Although some have ignored this point (Bose 901 has 9 drivers, all with slightly different distances from each of the sides of the interior), the goal of a multiple driver system is, usually, to cause the drivers to function in perfect unison. Slanted front faces, for example, are difficult to select while keeping vertical arrangement and internal symmetry.

There are no truely inherent advantages, except in price performance options. For example, I know of a single 12 inch that costs $60, and another that costs about $22 if I buy the latter 4 at a time. The $60 woofer has a much better Xmax, but otherwise the math predicting both bandpass and reflex designs indicates that in the same size cabinet these designs have remarkably similar characteristics. I could choose to build a dual design with the cheaper drivers for $88 in drivers, or a single driver design for $120 using the more expensive driver. Power handling, max SPL at 25Hz and the overall response curve is very similar - even the cabinet size (surprisingly) turns out to be the same. If the $32 is the greater issue, this is a time to choose two drivers. This doesn't usually happen, though. The dual design cabinets are usually much larger, and choosing a better single driver with sufficient swept volume for the target Max SPL at 25Hz (or some other frequency target) will be more practicle.

There's a unique approach to multiple driver design you may find surprising, called "isobarik" mounting. One driver is mounting behind the other, effectively coupling the two cones as a single unit. Imagine a short tube with one driver mounted at each end, where the air between them is sealed, and only one driver faces the listener, while the rear of the other faces the cabinet interior. Only 1 driver pushes air, and thus only 1 driver contributes to the overall swept volume (a considerable waste). However, this has the effect of dropping the VAS in half, which in turn drops the optimum cabinet size for a given design by nearly the same. The primary advantage is a "large cabinet rolloff in a small box." Max SPL at a given frequency is the same as with a single driver.

Recent thought in driver design tends to create drivers with large Xmax and thus high swept volume so as to obviate the need for multiple drivers. As frequency decreases excursion must increase dramatically to maintain a flat response. At one point, for all drivers, there is a maximum excursion (and thus a minimum frequency for the target MAX SPL) beyond which you will require multiple drivers.

Pick a target SPL (at a given typical listening distance) and target low end frequency (I like 25Hz at 100db at 3 meters). Using typical software (or math) you can calculate the SPL at that frequency and distance you'll receive from a driver at it's Xmax. In a given box design, you can determine if that point requires more power than the voice coil withstands. If so, the driver is limited by power, otherwise it will be limited by Xmax. If the target SPL can be reached then you don't need multiple drivers of that model. Otherwise, try the calculation with two drivers. For home audio you should probably stop there (distances of 3 to 5 meters are typical in such cases). Skip from 2 to 4 drivers if you're filling a large studio, and keep to two colums of even numbered drivers as you ramp up quantity. You may, for example, attempt to create 100db at 25 meters at 20hz, which you'll find exceedingly expensive.

You also touched upon the point of transient response, but that has some practicle points upon which many disagree. Even with "drum kicks" and other percussive sounds, low frequency audio does not usually have a fast ramp up or down. The "slew" of low frequency musical content is most often within the realm of performance of modern large diameter drivers, given appropriate upper frequency cutoff. That's the real key, in my thinking, about whether this is an issue. As long as the driver is limited to low frequencies (say below 60Hz), the maximum real-world transient attack is probably not much faster than a typical sine wave (save for artificial sound sources).

If the low frequency driver is also required to extend beyond 100Hz, then transient response becomes a serious issue. However, when bass drivers do reach beyond 100Hz, the loud low frequencies require so much more excursion that "doppler" distortion may appear. That is, the higher frequencies are produced as if on a moving surface, which undulates to a fro. Here, again, the wavelength is the governing constraint. If the excursion required to produce low frequencies approaches 1/4 of the wavelength of the upper frequencies, there is probably some audible contribution. This is a strong case for low bass crossover frequencies (and against single driver theoretical designs), and causes us to spend considerable money for a midrange driver that covers the most sensitive range of the system.

If you're really considering an 18" driver, then you do indeed have grand expectations. To meet them, the larger driver should be limited to the very low end in order to curb your concern over transient response. However, as you probably realized, even 12" drivers are large enough to have massive cones that can impact transient performance. In this case three factors counter this problem somewhat. Magnet power (not just size, but actual flux), damping and wattage. Without a sufficient magnetic base, no driver can be controlled. If the cone is massive, and the magnet has enough power to counter it, all you need is wattage (with damping sufficient to control the cone well).

However, as cone mass increases the corresponding magnet size must increase dramatically to keep control. This corresponds to a grand increase in cost. There are 18" drivers for about $80 to $100 that otherwise kick out power, but have sloppy and ringy response. In contrast, some 12" drivers at the same price can actually outpower this 18" at most low frequencies. Conversly, it can take about $400 to make an 18" perform well enough to qualify as "good." The massive cone doesn't just have a transient attack problem (which is most often negligable at very low frequencies), but it has a ring problem (which can't be ignored at any frequency). Like in cars, brakes are at least as important as the engine. Powerful magnets provide part of the brake. From a price/performance standpoint, it appears that 12" drivers are about the best you can do for home audio (in designs with Xmax beyond 12mm) if you accept about 25hz as the low end max SPL target. For targets as low as 18hz, even a 15" driver with Xmax beyond 12mm isn't quite enough to reach 100db at 3 meters. At the risk of cost overrun and ringing, the 18" or 21" driver is required to hit 15hz at high db at 3 meters, or you must employ multiple drivers.

Consider, for example, a $400 18" (Xmax around 9mm) with just enough magnet power to keep the cone in control (perhaps 100oz). At 15hz I can get nearly 97db at 3 meters at Xmax (even though that's more than my Amp produces at 8 ohms). However, there's a 12" that's about $100 in qty of 4 with an Xmax of 15mm. With 4 of them I can hit nearly 99db at 3 meters at Xmax, with much better control of the cone (that is better transients, less ringing and overshoot). If I choose an $800 18" (Xmax around 14mm), plenty of magnet power, very good cone control, I get about 99db at 3 meters at Xmax. The 18" does require a much smaller cabinet, but the 12 inch array seems to sound better (and costs less). In some cases, it turns out, the driver itself (given a particular design) has a "sweet" quality you may prefer, at the expense of multiple drivers.