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Author: W.J.J. Hoge [Kustom Electronics, Inc., Chanute, Kans. 66720 ]
Two years ago the kindly editor talked me into writing a construction article about a subwoofer (1). Because a system with 1-percent efficiency and a low-frequency cutoff of 20 Hz must be rather large (600 liters or about 21 ft.3), I didn't expect too much reaction from the gentle readers. Boy, was I wrong! To date, I've gotten hundreds of letters and hundreds of phone calls about how to subwoof. So, at the end of this article I'll present a list of corrections and updated information to the original article. Also, an improved electronic crossover (with foil patterns for a set of PC boards) will be given. Meanwhile, I'll try to answer some of the most common questions provoked by the original article.
Several folks have written to ask if there isn't some way to miniaturize the subwoofer. One letter from Germany put it this way: "After I explained to my wife what 21 cubic feet meant, she explained to me what divorce meant." The answer to this question is "No, not if we wish to have both a low cutoff frequency and low distortion." Remember, cabinet volume, Vg, is probably the single most important specification of a loudspeaker system. To put this in mathematical terms:
is the system reference efficiency, f, is the system low frequency cutoff (-3 dB), and kn is the fudge factor based on the type of system. In the real world, efficiency and distortion are inversely related in well-designed systems.
[...] a living, you can call up one of the companies that builds loudspeaker drivers for original equipment manufacturers, give them a set of specifications, and have a driver developed for your particular application. Any of these companies will be happy to give you samples--if they think they have a chance to sell you several thousand more. If you are a hobbyist, you are stuck with using a readily available driver.
TABLE Typical Driver Parameters.
Note: The two coaxial loudspeakers have leaks around the treble drivers. This increases the effective enclosure losses and lowers the QL to about 3. The method outlined in this article will not yield good results with these drivers. Try using the QL=3 design chart given by Small (4). The QTs of the 18-in. driver is too high for use in most vented-box alignments. Try a very large closed-box design.
These parameters are typical values as measured by Prof. J. Robert Ashley of the University of Colorado. Individual drivers vary according to manufacturing tolerances.
Given a few bits of information about a driver, you can tell if it's useful for your proposed application. Since quite a few gentle readers have written in to ask me if I could design them a box to use a Brand X Model Y driver (yes, I can; I do it for a living and expect to get PAID for it), I will describe one method I use for vented-box woofer design. It was originally developed by Keele (2) and represents an approximation of the charts given by Small (3, 4) for systems with an enclosure loss factor of QL = 7. In order to use this method, we must have the following information about the driver: fs, the driver resonance frequency; ()Ts, the total Q of the driver, and VAs, the compliance equivalent volume of the driver. I won't attempt to define these terms in this article, but references 1,3, and 4 can provide background information. Armed with these data and the design flow chart in Fig. 2, we can check to see if a driver is useful. Let's try a couple of worked examples .... Suppose we want a system which is useful down to around 40 Hz and reasonably small, say, around 100-liters net volume. The two drivers available to us are a 38-cm unit designed for use in horns and a 25-cm (10-in.) high-compliance unit designed for closed-box systems. The parameters of the larger unit are fs=18 Hz, QTs=0.17, and VAs=1300 liters.
Plugging this data into the flow chart, we find that:
which is reasonably close to our goal. This is the enclosure volume which will come close to giving maximally-flat response. Continuing along, we find that:
which is too high. To lower the f,, we would have to increase VB. Thus, we must discard this driver.
Now let's try the 25-cm driver. Its parameters are f, = 22Hz, ()Ts = 0.30, and VAS = 230 liters. Running this through our Texas-Packard calculator gives us:
Thus f, is lower than we desire. Let's try a smaller box. For a 60-liter enclosure:
which is close to what we were looking for.
To find the frequency to which we tune the enclosure's Helmholtz resonance, we continue with:
Since we are not using the 110-liter box, which approximates maximally-flat response, we will have either a peak or sag in the frequency response. To determine the amount, we use
If this amount of peaking is tolerable, then we can use this driver. We can reduce the peaking and lower the f, by using a larger enclosure.
Our next step is to calculate the dimensions of the vent required to resonate the enclosure at 34 Hz. Figure 3 shows two forms which a vent may take. The first is a simple hole in the (12 front panel of the enclosure; the second is a pipe or tube. To calculate the required area of the first type of vent we use the formula:
Where dv is the diameter of the vent in cm, lv is the thickness of the front panel in cm, and VB is the enclosure volume in liters. For our 60-liter enclosure with a 1.9-cm (0.75 in.) thick front panel, we would have a 3.9-cm (1.5-in.) hole for an enclosure resonance of 34 Hz. High power output at low frequencies might cause a vent of such small diameter to whistle. This happens when the particle velocity in the vent becomes so great that the air flow is turbulent. We can solve this problem by making the vent larger in diameter, but simply increasing the vent diameter will mistune the enclosure. If we increase the diameter of the vent, we must also increase its length. Thus, we have the second type of vent. We may find the required length with
A vent 7.6 cm (3.0 in.) in diameter is probably adequately large for a 60-liter enclosure tuned to 34 Hz. In this case the required tube is 19.7 cm (7.75 in.) long. A vent of larger diameter would require a longer tube.
To use the driver in the proposed 60-liter system, all we now need to do is select a set of dimensions which will give us the appropriate net volume and allow the driver and vent to mechanically fit into the system.
Of course, in order to use this method, the designer must know the required driver parameters. Any manufacturer should be able to provide you with this data. If you can't get it that way, you will have to measure it yourself. Ashley and Swan (5) and Hoge (6) describe methods for making these measurements. (Author's Note: My AES pre-print is available from the Audio Engineering Society, 60 East 42nd Street, New York, N.Y. 10017. It costs $2.00.)
Another question asked by many of the gentle readers concerned the design of a passive crossover for the subwoofer.
Neville Thiele has eloquently covered crossover design in another article in this issue, so there is little need for me to comment on this subject, except to say that I feel 18dB/octave crossovers should be used with subwoofers and that I agree with Ashley (7) that in high-power systems such crossovers are better realized with active crossovers.
Table II Filter Values
The original crossover schematic published with the article contained two errors. First, the 0.01-µF capacitors should be 0.1 µF. Second, the 0.33 µF capacitors should be 0.033 µF. built my original crossover on perforated board using push-in terminals and had no problem with it. However, some folks did. They got oscillators instead of filters. Oscillations in the filter can usually be solved by installing a 1000-ohm resistor in series with the base of the first transistor in each of the Darlington pairs. If the power supply oscillates, try installing a 47-ohm resistor in series with the base of the regulator transistor. In the past two years I have worked up a better set of crossover filters. Each filter section is on a separate card. This allows some versatility in their use. For example, I own a preamp with a center-channel (mono) output. By connecting the filters as shown in Fig. 4, I save having to use a second low-pass filter as in Fig. 5. These newer circuits are really the same filter type as the older one but with improvements.
Complementary devices are used in the emitter-follower amplifiers. This tends to reduce distortion. Also, the transistors used are quieter and allow for higher output voltage and current swings. The new filters have input impedances of over 200 kilohms and will drive a 10-kilohm load. To answer another specific question: Both the old and new crossovers will work very well with the amplifier circuit published in Audio by Leach (8,9). Both the old and new crossovers are low distortion devices. On the new unit the distortion is typically below the residual reading on most distortion analyzers. Using the DIM 30 (10) test for transient intermodulation distortion, no distortion products were visible on the analyzer above the 0.01 per cent level.
When building the new crossover, use 1-percent metal-film resistors in the tuning network and in the bias networks of the amplifier stages. This will improve the stability of the unit.
Otherwise, 10-percent composition resistors may be used.
The capacitors in the tuning network should be 5-percent (or better) polycarbonate or polystyrene. Parts values for the tuning network for several different frequencies are given in Table II. Because the physical dimensions of the capacitors required vary, some of the installation points for tuning capacitors on the circuit boards have two sets of solder holes.
For best results use the transistors specified; however, if the MPSA18 is not available, the 2N5210 can be used to replace it with some degradation in performance.
The filters require a ± 15 V power supply. Each board draws slightly less than 25 mA. No power supply details are given here--I'm not sure how many circuit boards any given home project might use. The National Semiconductor Audio Handbook (11) contains a good section on power supplies. I recommend that it be consulted. Also read the comments on ground loops and how to avoid them.
Finally, some comments on drivers for the subwoofer. The correct driver for the 20-Hz version is the CTS 15W38C. For a while this driver was out of production, but it is now being produced again by CTS of Brownsville, Inc., in Brownsville, Texas. The driver for the 12-Hz version is no longer in production. This is no great loss. There is no musical reason to build such a subwoofer anyway as 20 Hz is low enough.
(Editor's Note: Mr. Hoge is ordinarily quite free with helpful advice, but understandably tends to be annoyed by having to pay postage when gentle readers forget to send him self-addressed, stamped envelopes with their questions.
Specific information on complete kits or the PC boards for the crossover filters is available from W.J.J. Hoge, P.O. Box 127, Chanute, Kansas 66720.)
1) W.J.J. Hoge, "Switched on Bass," Audio, Vol. 60, No. 8, August, 1976, pg. 34.
2) D.B. Keele Jr., private communication.
3) R.H. Small, Direct-Radiator Electrodynamic Loudspeaker Systems, Ph.D. thesis, Univ. of Sydney, 1972.
4) R.H. Small, "Vented-Box Loudspeaker Systems, Part Ill: Synthesis," I. Audio Eng. Soc., Vol. 21, September, 1973.
5) J.R. Ashley & M.D. Swan, "Improved Measurement of Loudspeaker Parameters," AES pre-print No. 803.
6) W.J.J. Hoge, "The Measurement of Loudspeaker Driver Parameters," AES pre-print No. 1287.
7) J.R. Ashley, private communication.
8) W.M. Leach, "Build a Low TIM Amplifier," Audio, Vol. 60, No. 2, February, 1976, pg. 30.
9) W.M. Leach, "Construct a Wide-Band Preamp," Audio, Vol. 61, No. 2, February, 1977, pg. 38.
10) E. Leinonen, et al., "A Method for Measuring Transient Intermodulation Distortion," 1. Audio Eng. Soc., Vol. 25, April, 1977.
11) D. Bohn, ed., Audio Handbook, National Semiconductor, Santa Clara, California, 1976.
Parts List--Author's Crossover
(Source: Audio magazine, Aug. 1978)
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