sbhattac@rnd.gba.nyu.edu (Shankar Bhattacharyya) (09/18/90)
This is part 2 of my effort at filling requests for information on how to put together sub-$200 woofers. This is not aimed at experienced builders, who don't need my opinions anyway, so pardon detail you consider unnecessary. CLOSED BOXES AS A DESIGN CHOICE: Closed boxes are relatively insensitive to the exact volume. This also means that they are relatively insensitive to the Vas parameter, possibly the parameter most likely to vary wildly from the nominal value. The only real variable in choosing a design, given a driver, is the net box volume. So the design process is easy. Afterwards, there is damping and bracing to be done, and so on, but the minimal design exercise is easy for anyone. For those who don't already know, system Q goes down as box volume goes up. An infinitely large box, i.e. the defining infinite baffle, will produce Qtc=Qts. For any real box, Qtc > Qts. A system Q (Qtc) of 0.5 to just over 1.0 seems to work quite well. The cutoff frequency (F3) does not change dramatically as you cover this range, perhaps about 1/5 octave for most drivers. The transient response freaks say Qtc = 0.5 is best (no ringing). The bass extension freaks say larger is better, but that is simple-minded. For most drivers, Qtc = 0.707 ( actually, 1/sqrt(2) ) provides lowest F3. The flat frequency response freaks say 0.7 is best (maximally flat, and no response peak). For Qtc <= 0.5 there is no oscillatory behaviour. For Qtc > 0.5 there is. For Qtc <= 0.707 there is no response peak. For Qtc > 0.707 there is. At Qtc = 1.3 the response peak is about 3 db. The response peak tends to occur in the midbass. Rock enthusiasts are alleged to prefer this, since it provides mid-bass punch. However, high Q woofers lack deep bass. Now that synthesizer tracks in popular music do put a substantial amount of low bass on recordings, perhaps that preference will change. It used to be that non-classical music had almost no real bass. Classical music enthusiasts are alleged to prefer lower Q, flatter woofers. Orchestral music sounds thin without the bass foundations. At Qtc = 0.7 you get a nice, well balanced, rather flat system, with the best F3, and the ringing is very slight indeed. I lean towards this quite strongly, but am not married to the idea. My attitude is that all this simply means that we have some leeway. If we mess up, it will probably still sound good, even if the Q is a bit away from what we planned. ON GETTING REAL: Assuming a closed box system: We need about 1800 cc of peak to peak volume displacement to produce 100 db at 30 hz at 1 m into free space. Two longish throw 12 inch woofers may just be able to do that. Since we don't radiate into free space (i.e. 4 * pi) in our listening rooms, it may be just barely feasible to get 100 db at 30 hz at 1 m in a room, taking advantage of boundaries, etc., using one 12 inch woofer, but I think that is pushing things. Even if the levels are achievable, at the extremes of excursion one can reasonably expect fairly high distortion. The effective diameter of a woofer is significantly less than the nominal diameter. A 12" woofer usually has a 12" frame. The piston diameter is usually about 10". Since this fake diameter gets more serious for smaller drivers, they have even less capacity to move air than their nominal diameters suggest. With reasonable assumptions, other things being equal, as a very rough approximation: nominal woofer diameter 12" 10" 8" real piston diameter (approx) 10" 8" 6" (Deff, say) relative air moving capacity 100 60 40 (varies as Deff**2) Of course, other things are not always equal. In particular, the linear excursion capability varies widely. And some manufacturers specify it as the amplitude, which is how it should be done, and some as the peak-to-peak excursion, or twice the amplitude. Dynaudio uses a peak-to-peak number. What is worse, the excursion capability almost never comes with an estimate of the distortion at that excursion. So there is almost no way to compare this number across drivers. Undistorted bass requires that the driver have a long voice coil, with sufficient overhang in the magnet gap that the same length of coil remains in the gap even during large excursions. Usually, the maximum excursion is specified to define the maximum excursion that maintains constant voice-coil length in the magnet gap. The item of real interest, of course, is the peak-to-peak volume displacement for linear excursions. Further, the compliance of the surround needs to remain linear with excursion. Finally, the displaced volume needs to be small compared to the net box volume. Small suggests that it be a "small percentage". Real-life systems that I know of appear to have a displacement of 1-4% of the box volume. This is based entirely on knowledge of the driver used, and an estimate of the size of the enclosure. Don't ask me to document this. It is just my memory of a not necessarily representative sample of guestimates I have made over the years, most of them probably wrong. At the same time, I gather that the ear is relatively insensitive to low frequency distortion. So this sort of hand waving may well be less important than we builders tend to think. I would appreciate informed comment on this. Getting deep bass at high spl is expensive. However, if one maintains some perspective on the problem, quite satisfactory woofers are possible. Many people who want 20 hz bass have no idea what bass sounds like, and base their desire on reading, or hearsay, or some arbitrary criterion. A good 40 hz is quite respectable. A good, flat 30 hz is as good as a a woofer needs to be for almost anyone. Lower bass is nice, but not having it is not a good reason to shoot oneself. Since we are talking about bass on a budget, this is a good time to think about this sort of thing. Even so, within the $200 budget, it is possible to make a woofer which would be happy with a pair of Spicas. You just won't get enough output to blow you through the rear wall of your room. But there is, indeed, some perspective to be maintained. On a budget you have to compromise quantity of bass, in F3 and/or in spl, but you need not compromise quality seriously. I have a pair of Quad esl's (old ones), and a single woofer good down to about 30 hz, with a little equalization. I'm quite happy with that. I have no idea how loudly it can play, since I would get thrown out of my apartment long before I found that out. But it does suggest that, to my ear, it is possible to make a woofer at home which is happy with a speaker of extraordinary resolution, even if that speaker cannot shout. Old Quads are not high output speakers. BIAMPING Accept that you are probably going to biamp. If not now, tomorrow. It is quite easy to build a good woofer, which, as a standalone device, measures and performs very well. It is quite another to integrate it into a system which has satellites already in existence. Designing passive crossovers is nontrivial, and it gets even more messy if you want to use a single woofer. I would predict that most people who try passive crossovers will eventually decide that active crossovers and biamping are the way to go. So the $100-200 cost is likely to be only a start. Doing a good job of tying things together will cost more money. It need not cost a lot of money up front. Initially, drive the woofer with a cheap amp. It won't be perfect, but it will add bass. (And ignore those who exclaim, "You mean you don't use a Krell? How disgusting!") Improve things as and when it becomes possible. Loss of perspective will get extremely expensive. Stay sensible. If you want to use passive crossovers, you are on your own. I don't know anything about them, certainly not enough to do anyone any good. Obviously, there are many people on the net who do. More later ..... ---------------------------------------------------------------------- Shankar Bhattacharyya, Information Systems, New York University sbhattac@rnd.gba.nyu.edu ----------------------------------------------------------------------