Transmission Line Subwoofer Project

For a long time I had been resistant to the idea of using subwoofers. I seem to be less tolerant of crummy bass than the average joe. So long ago I adopted a "do it right or do without" philosophy for low bass.

It has been, and still is, my belief that it is difficult and expensive to do subwoofers right. I have heard far too many systems with poorly executed subwoofers. After a long wait I decided that I had enough understanding and funds to maybe get it right.


Background

My #1 priority for this project was low distortion. The vast majority of subwoofers I have heard, particularly the Home Theater types have lots of distortion. It was a revelation when I first heard Grant Gassman's massive horn subwoofer. It was unlike anything I had heard before. If you havn't heard really low distortion bass before you don't know what you are missing!

With Grant's subwoofer setting the bar high, I employed a number of ideas for reducing distortion.


Drivers

My primary criteria for driver selection was low distortion. Inexpensive drivers will produce distortion artifacts much higher in frequency than the crossover frequency. This results in distortion and smearing in the upper bass and midrange. This of course cannot be eliminated by using a steep crossover filter since the distortion originates in the driver.

Some time ago I helped a friend build subwoofers using inexpensive Polypropylene cone woofers. The bass was great but there was a muddyness in the midrange that I could never live with. We utilized a 4th order active crossover so it was clear that the problem was with the drivers. From that experience I was determined to only use top notch drivers for my subs.

I ended up with four outstanding 10" woofers from FRC Soundworks. These drivers feature carbon-fiber/paper cones, heavy cast basket and a low distortion motor design utilzing a copper Faraday ring. The quality and workmanship of these drivers is exceptional. They are extremely clean sounding without a trace of the midrange problems I was concerned about. I chose 10" drivers to avoid cone flexing and breakup problems that larger drivers would be more prone to.


Enclosure Design

My initial plans were to use low Q sealed enclosures with two drivers per enclosure in a push pull configuration. Wanting to experiment before cutting wood I put a pair of the drivers into some old AR-3a cabinets that these drivers just happened to fit into. The cabinets were about 15% bigger than my plans called for but close enough to get a feel for how they would sound. Not surprising the oversized cabinets resulted in a slightly over damped alignment and the bass was a bit too lean. The bass was very clean but not detailed. I know that that sounds contradictory but it's the best description I can come up with. There was nothing obviously wrong but the bass just was not very interesting.

A friend convinced me to try a transmission line enclosure. Experimenting with a t-line design ended up being ridiculously easy. I bought a 5 foot length of 10 inch sonotube from Home Depot and just duct taped a driver onto one end. Then it was just a matter of stuffing some dacron into the sonotube. With the tube just lying on the floor I did some listening. The results were stunning. Very deep, smooth and far more detailed bass than I had with the sealed boxes.

Once I decided that t-lines were the way to go I set out to design an enclosure. I liked the idea of using cylindrical components to build the t-line because of their inherent resistance to flexing. But sonotube is just too flimsy, especially with larger diameters. I found some sources for heavy cardboard and plywood cylinders but unfortunately the sizes were all wrong. After some searching I found a near ideal solution, 12 inch PVC sewer pipe. With a 0.38" wall thickness it is rigid, well damped, heavy and has a nice smooth exterior surface. I had to buy a 13 foot length for $81 but it was well worth it.

I used a push-pull mounting arrangement for the drivers. With the drivers mounted back to back the inertia from cone movment cancels resulting in a major reduction in cabinet vibration. To accomplish this I built a small box to fit onto the end of the PVC pipe with the drivers mounted on opposite sides. To take advantage of the cancellation effects the drivers need to rigidly connected to each other. I used solid maple crossbraces between the drivers to provide a simple but reasonably rigid connection. Even with the woofers really cooking the cabinets are dead still. I had always figured that cabinet vibrations were primarily excited by sound waves. This experience would suggest that the majority is actually from the inertia of the speaker cone.

A variation I almost didn't try was mounting one of the woofers backwards (with the magnet facing out) and then wire the drivers out of phase. The theory is that woofer cone movement is not perfectly linear. In response to a symetrical sine wave the outward motion of the cone does not match the inward movement. By mounting the drivers front to back and wiring out of phase the non-linearities cancel out. I figured that with a high quality driver and limited excursion that the cancelation effects would not be audible. Boy was I ever wrong! The bass was notably cleaner and controlled with lots of slam. Subjectively there seemed to be a little less bass which is a clear indication of less distortion. After hearing the difference I would never consider any other topology than out-of-phase push-pull. It is more than a little odd looking but it fits with my non-conventional theme.

Initially I was reluctant to do a t-line design because it seemed that there was too much dissagreement and even vodoo in working out the design. I had helped a friend with some t-line experiments that worked poorly so I didn't have a lot of confidence in the suggested design process. Well that all changed when I read John Risch's excellent design guidelines. It is a slightly more complex process than what I had used before, but It seems much more logical. But most important, John's formulas accurately predicted the poor results with my friends failed t-line experiment.

I will not attempt to repeat John Risch's design guidelines here but rather show the results of my calculations. First of all John suggests that the cross sectional area of the t-line should be 100-125% of the driver cone area (SD). With my drivers the combined SD was 108 sq in. The 12 inch PVC pipe has a cross sectional area of about 107 sq in. Not quite perfect but I figured that it was close enough.

With a somewhat iterative process I came up with an equivalent volume of 103 liters and t-line length of 54.5 inches. This yields an empty t-line tuning of 62hz and a fully stuffed tuning of 31hz. Computing the driver resonant frequency in an equivelent sealed volume I came up with 35 hz stuffed and 32hz empty. The objective was to have the t-line tuning and the driver resonance ranges fully overlap. So far I have only tuned the t-line stuffing by measuring the speaker impedance. I should follow this up with some by ear tuning, but it sounds so good as it is...

The final cabinets stand 56 inches tall and certainly have an unorthodox appearance. I finished the cabinets with a latex primer followed with a semi-gloss black latex paint. Sanding the surface of the PVC pipe seems to have provided good surface for paint adhesion. With the drivers installed the cabinets weigh in at 88 pounds each.


Crossover

I believe that bi-amping with an active crossover is essential for good subwoofer results. For me it was of parmount importance to not have distortion products from the subwoofers mucking up the midrange. To accomplish this I believe that you have to use low distortion drivers and a steep 3rd or 4th order active low pass filter.

The crossover design started with analyzing the acoustic roll-off of the Ariels. According to the charts that Lynn Olson provided on the Ariel web page the Ariels have a well behaved 2nd order rolloff starting at about 85hz. Using a Radio Shack SPL meter this was confirmed. Add to this a simple 1st order RC filter and you get a nice 3rd order combined response.

I wanted to avoid adding anything to the signal path for the Ariels so I came up with a simple way to add the 1st order filter. My preamp has been modified so that the output coupling cap serves as the 1st order RC filter. The filter is formed by a small coupling cap loaded with a resistor at the RCA jack and also the grid resistor in the power amp. My preamp now has two outputs. One full range and one with an 85hz high pass filter. Adding this filter made a notable improvemnt in the upper frequencies. This is probably due primarily to making life a lot easier for the amps by not having to deal with the lower octaves. I suspect that the smaller capacitor also contributed to the improvement.

For the low pass filter I used a pair of XM1 24db active crossover boards from Marchand Electronics. These are easy to build, inexpensive but high quality crossovers. Just add a case and a simple +-15v supply and you are in business. You could also buy a complete crossover such as the XM9 rather than rolling your own. The Marchand crossovers have both high and low pass outputs but I am only utilizing the low pass.

I am rather proud of the box I made for the crossover. I made a three sided box of of a nice hardwood (can't remember what kind!) and epoxied 3/16" aluminum plates to the front and back. I used a router with a flush trimmer to trim the aluminum so that it matched up with the wood. It's a simple technique for making a nice looking enclosure.

You observant souls may have noted that my slopes do not match, 3rd order high pass and 4th order low pass. With steep slopes this is relatively unimportant. I was able to get the crossover region quite flat in spite of the mis-match. However, I am considering using smaller coupling cap between the driver and output tubes in my power amps to get a 4th order high pass. My motivation for this would primarily be to further reduce the amount of low frequencies that the amps and Ariels have to deal with.


Amplification

To drive the subwoofers I am using a highly modified Hafler 220. This amp is a relic from my pre tube days and was just the ticket for driving the subwoofers. The Hafler has upgraded parts and wiring throughout but most important it has two 15 amp regulators in the power supply. With power supply regulation the damping factor is increased, providing better control of the woofers. Adding the regulators reduced the maximum power output by about 10% but I still get about 150 watts/channel into 4 ohms. The regulated power supplies produce the kind of control and authority that you typically will only find with much more expensive amps.

I don't have a feel for how much power is required to drive the subs. Probably more than 150 watts would be required to comfortably drive them to their maximum excursion. However, the Hafler is capable of producing bass at ridiculous levels in my room. At these ridculous levels where anything loose rattles and buzzes the speaker excursion appears to be less than half of the 1-1/4" maximum.


Placement

From the perspective of frequency response I found that placement of the subwoofers was not critical. There were some small changes in measured response but but I never noted anything that was audible. Placing the subwoofers closer to the corners increased the amplitude, as expected, but this was easily compensated for by adjusting the crossover level control.

However, I did find that correct phase alignment was clearly audible. When properly aligned kick drums came into focus and there was better sense of rythmn and drive. After blindly moving the subwoofers back and forth it was was apparent that the best sound was with the subwoofers the same distance from the listener as the main speakers (duh!). It was interesting however, that the worst sound was with the subs back about 18 inches from the ideal. For purely cosmetic reasons I had the subs oriented with the drivers front and back. I rotated the boxes so that the drivers were on the sides and lined up with the drivers in the main speakers. Wow! That was the ticket. More snap and detail. It looks more peculiar with this arrangement but the sound is well worth it. No surprise that my wife wanted them back in the corner. But she reluctantly agreed that it was worth it to phase align them.

With the subs moved so far forward I was concerned that it would foul up imaging. But the imaging was slightly better. The round surface of the subs evidently disperses sound waves nicely. An unexpected benefit from building a round enclosure!


Measurements

I found it useful to be able to measure the frequency response during the experimentation phase and also to fine tune the final design. I generally don't put a lot of stock in measurements but for this project it was invaluable. On a couple of occasions I though that everything sounded right, but then after making some adjustments based on measurements things sounded better. In my opinion some method for frequency response measurements is essential for this type of project.

My measurement tools were decidedly low tech but adequate. A Radio Shack SPL meter, a Stereophile test CD with warble tones and a sine wave signal generator.

The frequency response of the finished subwoofers is quite good. There is a small dip at 50hz that I found was somewhat sensitive to where to subwoofers were placed. Note that the dip is far more pronounced with the left subwoofer. The subwoofers measured almost identical when they were in the same position so this a room interaction issue. Other than the 50hz dip the response is very flat to 40hz at then rolls off gently. With room lift the in room response is most likely flat down to about 20hz.

The combined response shows a small bump in the crossover region and the same dip at 50hz. Raising the frequency of the high pass filter a little should take care of the 100hz bump. Note that the Ariel response also dips a little at 63 and 50hz.


Summary

From the beginning the design goals for this project were quality over quantity. However, It seems that to get good quality you need quantity. During the project I had the opportunity to listen with 1, 2 and 4, 10" woofers. Each time woofers were added to the mix there was a notable reduction in distortion. More woofers mean less excursion to produce the same sound level. A single 10" woofer was, in my opinion, unsatisfactory. With one woofer the quantity was fine but the quality was not. Using two woofers was a considerable improvement. With four woofers there was an improvement but it was not as significant.

It was interesting that there was a small imaging advantage with stereo vs. mono subwoofers. In theory sound is completely non-directional at the frequencies involved so it should not matter. I can pass on what I hear but can't explain why. But if I had to choose, stereo subs with one driver each or a single subwoofer fitted with push-pull, out-of-phase woofers the single subwoofer would be a no brainer.

So how do they sound? Pardon me while I gush! They are superbly detailed, and clean. Kick drums have a viceral slam that is stunning. Even at SPL's far beyond what I ever listen to they still have clean transients and lots of snap. Did I mention deep! They reach way down and reproduce those low pipe organ notes with bone shaking realism. My description probably makes me sound like one of those weirdos driving around with thumping, obnoxious bass that makes your license plate rattle. Believe me these subwoofers, thankfully, don't sound anything like the typical autosound or home-theater subwoofers.

I think that I got it right :)