PX30 design - subwoofer

Very soon after completing the SP18M the need for a superior subwoofer was immediately apparent. The SP18 proved better than the $17k Piega in the midrange through the treble, though its small size and modest budget couldn't measure up in the low end of the spectrum. High quality low bass is hard to come by unless you're willing to spend a lot of money. Even keeping cost as tightly under control as possible, a pair of the PX30 subs ended up costing almost as much as a pair of the SP18M.

Application

A subwoofer specifically designed to complete the SP18M, providing the low end extension with the power necessary for the most demanding music and movies.

Design Parameters

The design goal : A 12" acoustic suspension, low frequency unit with a bandwidth from 20 – 160 Hz, +0/-6 dB or better, peak output of 105 dB, low distortion, in a reasonably small enclosure and footprint. (While subs can be built with drivers as small as 8”, or as large as 18”, larger drivers would bust the size requirements, and smaller 8” or 10” would make it difficult to get adequate SPL at 20 Hz without the aid of a port, passive radiator, or massive amounts of EQ, power, and likely distortion. A 12” driver was deemed the best choice to meet these goals.)

III

Research & Development

It's said that building a subwoofer is the easiest speaker project to tackle, and a good place to start for DIY. On the surface it appears true, but look a little deeper. Very low frequencies require the alternate compression and rarefaction of large amounts of air and lots of power for doing it. (You often hear someone talking about "moving air" in reference to producing low frequencies. Moving air is a current. Wind is moving air—you can't hear wind unless something disturbs the flow to create vibrations or pressure variants. Sound is a pressure wave—the wave moves, not the air.) Each octave lower requires the twice the air volume to get the same SPL. To do this, and to do it with low distortion is not an easy task unless you're willing to have a sub the size of a refrigerator. A large driver with a low resonance frequency needs a large enclosure. Smaller enclosures raise the resonance frequency, and the power requirement. Large enclosures are bulky and obtrusive. Ported or passive radiator allows for greater efficiency and lower F3 from a given enclosure size, but increases distortion and sacrifices transient response. It is a difficult balancing act. Finding a driver good for sealed enclosures is also more difficult. Most subs are ported bass reflex or passive radiator, and therefore most drivers are made for that usage. Achieving a good, strong 40 Hz is not too difficult, 30 Hz is more challenging, and every few Hz lower gets progressively more and more difficult to obtain while keeping the response flat. It may be easy to cobble together a box, screw in a driver, drop in a panel amp, and there you have it, a bam-bam woof-woof sub. But, a good, powerful, low distortion subwoofer that doesn't have a camel hump frequency response is a real tough nut to crack. It's much more difficult than it appears superficially, and it's guaranteed to require some equalization.

There are hundreds of commercially made subs. Prices range from a couple of hundred for a pseudo-sub to several thousand or more for a digital servo-controlled monster sub with multiple drivers that's as big as a steamer trunk. Subs that are capable of a flat 20 Hz with reasonably low distortion cost at the very least $1500-$3000. And don't trust specs without the +/- dB numbers. Too many brag about how low they play, not telling you that the low figure they claim is likely to be 12 dB or more below the average output, and consequently useless. Two or three thousand dollars is a lot to spend on a single speaker just to get the bottom octave of audible bandwidth. In many cases the cost is more than the main speakers. As with spending thousands on surrounds, I can't justify a high expenditure on a single speaker that does one tenth of the bandwidth and might be working for less than that fraction of time. With music, very few instruments play below C1, 32.7 Hz, and if capable, rarely do. It's absolute madness. But many recordings have information below 40 Hz, and no matter how you look at it, the importance of the bottom octave must not be discounted. Once you've experienced music with all of the lowest frequencies in balance, you'll never be satisfied with less. It is necessary for getting the full impact of live music, and the full theater experience on movies. It's disproportionately difficult to reproduce, and it's disproportionately costly. The goal is to bring that cost down to a reasonable disproportion. (Don't let this fool you into thinking subs have to be way expensive. Manufacturers love selling subs, because just like SUVs, they have a much larger markup on them adding yet more to the disproportion.)

I strongly wanted to keep the visual design the same as the other speakers, using a PVC pipe for the enclosure, a felt jacket, and external amplifier, however, a tube reduces internal volume compared to a cubical enclosure of approximately the same external dimensions and footprint. For instance, to get an internal volume of 56.63 liters (2 cu.ft.) a 12” diameter tube would need to be 31” long. Add end caps and feet, and the total length/height would be almost a yard—that's taller than the height of the woofer section on the SP18M. Trimming it a couple of inches really wouldn't make a significant difference, but an 18” cube has the same volume. Being on the lookout for possibilities, I started checking out standard ready-made cubical MDF subwoofer cabinets and 12” drivers by various manufacturers. Found a few 12” drivers that should work well in a small 56L sealed enclosure. Ran across an amp specifically designed for subwoofers that looked particularly promising. It has a very useful notch filter for taming the mid-bass hump, and features some equalization abilities to level out the lowest half octave. It all pointed to a combination of elements quite possible of producing the high quality bass needed for music with the high SPL punch necessary for home theater LFE tracks, a blend of accuracy and power. Could this be the Shangri-La of subwoofers? The only disadvantage of a cubical cabinet is the probability of panel resonances, which is not the case with the inherent rigidity of a cylinder.

Before I ordered the parts for the sub, I had to carefully review the T/S parameters of the three drivers that looked good for the chosen enclosure. Driver A had qualities somewhat in between drivers B & C. A's T/S parameters seemed to be the best compromise. Ran its numbers through my spreadsheet calculator for sealed enclosures. A looked good, Fc just over 37 Hz, Q of .71, but not impressive. Driver B has a longer Xmax, slightly lower Fs, and lower Vas. It has a couple of other mechanical/electrical differences, and uses a different cone material, paper instead of aluminum. Running the numbers through the spreadsheet, the results looked even better, 3 Hz lower Fc, lower Qtc, and greater volume displacement. My only concern was with the longer throw. Woofers with longer excursion may be able to pump out more SPL, but usually at the cost of higher distortion. The third driver C is identical to driver A in most ways, same aluminum cone, basket, magnet. The differences are a stiffer suspension, much lower Vas, and a marginally higher Fs. Checking it out with the spreadsheet, the Fc came out almost 1.5 Hz lower (than A, despite the higher Fs), and it has the lowest Q of all three. It calculated out as an infinite baffle rather than an acoustic suspension because the Vas was less than the enclosure volume. I decided the driver C with the stiffer suspension would be the most appropriate for the small 56L box, thus making, for its size, an unheard of infinite baffle subwoofer with a low Q of 0.55. So with that, I went to order the parts. What I had worked out was very close to one of the supplier's kits, but with two minor differences. So, I called to request making these substitutions and still get the kit price. “No,” was their answer. I asked if they would give me a package deal on the parts I wanted. “No,” was the answer to that too. And “No,” was my answer to them. I went back to the drawing board.

And, back to the original plan for using a PVC pipe for the enclosure. Carefully reconsidered drivers, again only three looked promising. One from the previous group, and the other two from a couple different suppliers I hadn't previously searched. One stood out from the other two. Its Fs is lower, its Qs are much lower, and in the desired enclosure size, its Fc (34.3) and Qtc (0.39) were the lowest of all the other drivers. Its cost is more, yet the entire system will be only marginally more than the kit price from the inflexible supplier. Because the amp and crossover will not be integrated within the enclosure, this necessitated buying a more sophisticated crossover with 3-way operation, and very importantly, equalization for the sub output. In addition, the 3-way digital crossover is capable of equalizing other bandwidths. This would allow for leveling out some of the slight nonlinearities of the SP18M, providing added benefits that will more than justify the small increase in cost. I even decided to plunge into building a pair of subs instead of only one.

The Qtc for a 30” tube is so low (0.39) that I considered making it smaller and raising the Q to 0.5. I was also debating up or down firing. Down firing would hide the driver. Up firing would eliminate the need for feet. Smaller would be nice, although, raising the Q also raises the F3, resonance frequency, power requirements, equalization needs, and stress on the driver. Checking the calculations, showed that with 3” less height, to allow elevation for a down firing configuration, only increased the Q to 0.43, the Fc to 36.5. Other changes would be equally small. Only significant drawback would be the increased cost by adding feet or casters. If the height were reduced more, say to 27”, it would raise the Q to .46 and the Fc to 39.2. That's getting into changes little greater than I wanted to make.

After carefully considering the pros and cons, I decided the down firing configuration with neoprene leveler glides would be the best option. I left the total height at 32”, and reduced the tube length by 2” to allow for the elevation of the levelers. Anything smaller would be too compromised. The Qtc only rose to 0.42, and the Fc to 35.6 Hz. The levelers added $32 to the cost and a couple of extra steps in the assembly. For such a simple design, the cost is still much more than I had hoped, and not any less than other kits, or some ready-made. But the advantages out weigh the cost. No other kit brings together a lower Q driver, with a lower Q acoustic suspension configuration, in a more rigid and resonance-free enclosure. No other commercially made sub puts this all together either. Plans were revised, parts were ordered, construction and testing began.

Results

First thing to note is that building a subwoofer is physically more difficult than smaller speakers. Everything is bigger, heavier, and more cumbersome. Second, testing & measuring low frequencies is quite different than mid to upper frequencies. The initial set of measurements and settings were made by placing the meter on the floor at the edge of the baffle. Nearfield measurements are customary in order to mask the room's effect. With a little EQ, this gave a beautifully flat response and more output than I expected. It was all too easy. When I set them up for listening. It immediately became apparent that the level with music at listening position was too low. Several hours of adjusting, readjusting, and frustration followed. Very low frequencies don't behave so predictably, especially in-room. The EQ ended up being greater than expected, but the output stayed at the initial setting. Starting without any EQ, I checked the response from 160 Hz down to 20. After peaking at 100 Hz, there was a steady roll off. A low pass filter was selected with a 12 dB gain at 12 dB per octave. This brought the lowest octave up to near flat while balancing with the 80-160 octave. The transition from the sub to the midrange is very smooth. Final measurements put 20 Hz at -4.5 dB, center room, flat in near wall position, with 80 Hz, the crossover point, at 0 dB. Concerns about the power requirements were quickly dispelled. Watching the output from the amps indicated relatively little power was being drawn most of the time, and less than the midrange amps. However, a 20 Hz sine wave draws considerable power, almost to clipping at 96 dB, but I never turned it up enough to clip. There is enough power to get the concrete slab under the carpet to resonate at 25 Hz. 120 watts per channel is good.

Distortion is low, below audibility at good listening levels. When listening to 20-40 Hz sine waves I can't hear any harmonics unless I turn up the volume very high and then only a just audible 2nd harmonic of 20 & 25 Hz. Many subwoofers create a large amount of 2nd harmonic distortion, which is audible, overpowering the fundamental. I doubt that 105 dB of output down to 20 Hz is possible for the PX30 without distortion or bottoming out (or shaking the house apart), but otherwise it meets the design specifications, and since volume in the upper 90s is pretty loud, I'm satisfied.

The addition of the sub does less than one might imagine, that is until something comes along with very low bass, then the difference is appreciable. My room mode at around 50 Hz is obvious. It can be tamed with EQ. My main concern was to get a flat response without taking the room into consideration. I can't say with certainty that the in-room measurements haven't had an effect to some extent, as noted in the difference between center room and speaker position measurements. Perhaps the very lowest frequencies are exhibiting some gain center room. Only anechoic measurements can tell if they are.

(II) UPDATE 01-09-09 : Stereo bass is often challenged on the assumption that low frequencies are non-directional, that we can't hear the source location. Some people debate the importance of stereo subwoofers on the basis that the phase difference between channels is insignificant. This ignores the volume difference that does exist in stereo recordings of orchestral music and many other types of recordings. Most recordings may not have any signal difference below 80 Hz, but we must be prepared for those that do. Each channel of low frequency information should be kept separate and produced from the original location in the recording. However, there is another reason for more than one subwoofer, and this reason is not controversial. A single subwoofer creates very strong room modes that are impossible to cure. Multiple subs radiating from different points within a room make substantial improvements in the linearity of the low bass response. See Floyd Toole's book Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms.

Observations & Comparisons

I made no comparison to the commercial sub I had been using. There wasn't any reason. The PX30 unquestionably outperformed it—flatter response, lower extension, and much cleaner, much more authoritative output.

Organ music shows off the added bass extension as well as most orchestral music. The resonance of the lowest notes on the piano sounds beautiful. And jazz, rock, electronica put the sub to work. Its crucial place in delivering everything that's on a recording is undeniable. With the full bass extension and its authoritative presentation, my previous 17 thousand dollar speakers can no longer pose a challenge to this system.

Now when I compare this system to the Orion+ the differences are extremely small. The Orion, with its open baffle configuration, still seems to have a trifle more openness, dynamics, transients, headroom, and maybe lower distortion at very high SPLs, yet it takes twice the cost to achieve this modest improvement. As I listen to the same recordings on both systems I'm wondering, how much of the difference is due to the room? The Orion is in a smaller room, 16'x18' with an 8' ceiling, the SP18 in a 22'x26' room with a 12' ceiling. Could the different rooms be making the perceived difference in the sound? In the past, differences between speakers were clearly noted, even between the two rooms. When the same speakers were setup in both rooms, I've always preferred the smaller room. It's quieter and less reverberant. So, do I prefer the Orion, or do I prefer the room? It seems the room difference may be a greater factor when two systems are close in their characteristics and capabilities. Yet there is one more factor to consider. The reverberation distance, i.e., the distance at which the reverberant field volume is equal to the direct volume. The Orion's dipole radiation reduces the reverberant field level relative to the direct. It is surprising to see how high the reverberant sound can be at listening position. It contributes a great amount to the total sound we hear. This empirically illustrates the importance of the off-axis polar response.

For an explanation of the reverberant field read the following link : http://www.linkwitzlab.com/rooms.htm#Reverberation%20distance.

The Orion is without a doubt an exceptional value relative to any commercial speaker—the SP18M system sacrifices very little, if anything, in comparison. I am thrilled to listen to any recording with either. Now I have two serious listening systems.

Conclusions

The PX30 subwoofers completes the SP18M making it a solid full range system capable of the entire audible bandwidth with low distortion while reaching peaks around 100 dB. If you want rock concert SPLs (over 110 dB), you need to look into professional studio monitors. The Project has gone well past the original goal of building a good home theater system. It’s a complete audio system that delivers high performance in a highly cost effective way.

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