What I Wanted Most of what I play is older classic rock (Stones, Beatles, Cream, Zeppelin, early Neil Young) or blues. I don’t quite get to jazz, or to metal. At present, I get the tone I want from an Orange Tiny Terror after it was modified by Juleamps to stabilize its power supply, separate the preamp power from power tubes, and fix a few cheap manufacturing issues. This is a 15 watt tube amp, but it is pretty loud when combined with an efficient speaker. I’ve been struggling for the past year to upgrade my speaker cabinet to something with 1) good efficiency, 2) good bass, 3) clear midranges with enough treble for articulation, 4) nice dispersion of sound, 5) light weight, 6) low cost. I am inclined towards speakers without too much coloration of their own, and I don’t expect any speaker breakup with a 15 watt amp (which is usually run at 7 watts when I am indoors). I tried 2x12 speaker cabinets that have great sound, but were heavy and sometimes expensive. I suppose I can compromise a bit on the price, but the weight is a real issue. I load and unload everything into my car twice a week, and at my house I have only myself to do it. The weight issue led me to a 1x12 cabinet, but how can I get decent bass response with a 1x12 cabinet? I ended up with a tuned port enclosure, and this is the story of how I tuned the port. There is some interesting physics here, at least I think so. This turns off a lot of folks, though, so you may prefer the pictures, and they tell much of the story. About Loudspeaker Enclosures You may already know that an unenclosed speaker driver in free air has lousy bass because the sound from the back cancels precisely the sound from the front. Sound waves from the back are precisely 180 degrees out of phase with waves from the front. The simplest solution is a sealed box, where the back radiation from the speaker is dissipated and kept away from the front radiation. You also know that open back enclosures have a wonderful dispersion of their midrange and treble. The midrange from the open back can also bounce off the back walls of the room, giving a big full sound. Unfortunately, for open back cabinets the bass is suppressed because at bass frequencies, some of the back radiation from the speaker cancels some of the forward sound waves. I mention this well-known stuff because it helps to understand my approach to a bass reflex design. The way a bass reflex speaker works is by designing around three resonances. All can be understood approximately as masses on springs: 1) The speaker itself has its own resonance in free air. You can look these up from the manufacturer’s site, although I found that the resonance frequency of my own speaker was a bit lower, maybe because it is well broken-in. The mass is the moving cone and voice coil, and the spring is from the suspension (the cone surround and the spider). 2) The air in a sealed speaker box acts mostly like a spring, since it is not very heavy. The force required to compress the air in a sealed box can be thought to increase the spring stiffness felt by the speaker cone. It raises the resonance frequency above the free air resonance. 3) With a tuned port you also make a Helmholtz resonator. Think of blowing across the top of a bottle. This resonance does not depend on the speaker driver. A typical analysis is to use the stiffness of the air in the box (the same as for 2) plus a “mass” associated with the air in the port (the neck of the bottle restricts the air motion, and makes it seem heavier). With tubes for tuned ports this is fairly predictable, but for open holes in the side of a box filled with fiberglass it gets hard to assign the correct “mass” to the air in the port. It is not too hard to combine the effects of 1 and 2, and predict the performance of a speaker in a closed back, sealed box. This is really easy is when the speaker manufacturer gives you the “volume equivalent compliance”, the number of cubic feet of air that have the same stiffness of the speaker driver itself. I think that sealed box performance can be predicted pretty well just by calculation alone. What you will find is that you need a really big box for good bass response, unless your driver has a rather small volume equivalent compliance plus a low resonance frequency in free air. Guitar speakers have neither, unfortunately, and even getting good performance at 84 Hz of the E string in standard tuning is a challenge (and I was aiming for drop D). An exception seems to be Electro-Voice EVM 12L, which should do really well in a box of 3 cu ft. (At 19 lbs it doesn’t pass my weight test, though.) Other “55 Hz” drivers might also do well in sealed boxes of volumes of 3 cu ft. or less. Bigger boxes get too heavy for me to lift, even for a 1x12, unless compromises are made as they usually are. My Own Bass Reflex Design So here was my plan. I wanted to use my Eminence Tonker, which has high efficiency (102 dB at 1 kHz 1 W 1 m from specs) and a nice midrange (to my ears, you may disagree). The Eminence specs say it has a resonance of 89 Hz, and a compliance equivalent volume of 1.2 cu ft. That means a box of 2-3 cubic feet could be sensible for a closed back enclosure. From the measurements below, though, I found my own speaker to be much more compliant, with a 2.45 cu ft compliance equivalent volume. I assume this is because it is rather broken-in now. The measured resonance was also lower at 85 Hz. Anyhow, based on the Eminence specs (before I made my own measurements) I bought an unloaded cabinet from AB Custom Audio: http://www.abcustomaudio.net/index.htm I wanted a larger cabinet than the usual 1x12, so I bought a 2x12, and got it with vertical orientation. I am delighted with the construction, delivery, and price of barely over $100 with the convertible back. It has a 2.1 cubic feet internal volume, which is only a little smaller than ideal for my speaker, according to the reference by Badmaieff and Davis below. I installed a stiff plywood plate over the second speaker opening, and tried it out in open back and closed back configuration. Actually, it wasn’t bad this way. I quite liked it with the open back. I played it this way for a while, and was mostly happy. I could hear, though, that it was deficient in bass for the lower frets on the E string. So here is the conceptual design of my bass reflex speaker. The design has two ports, a tube port in the front, which accounts for part of the Helmholtz resonance, and a large open port in the back, which drops the Helmholtz resonance frequency even more. My big idea, which seems to have worked out, is that the open back port lets the midrange escape to give a nice dispersion of sound, like for an open back cabinet. Measurements Needed to Tune a Cabinet, and the Physics Behind Them To get this all to work, I had to measure resonance frequencies and how they changes with port openings. I have an old book that gave the key hint (How to Build Speaker Enclosures, Alexis Badmaieff and Don Davis, H.W Sams, 1970. I see you can get it used through amazon for about $13, a fine value). If you drive the 8 ohm speaker through a large resistor of, say 1.3 k ohms, the driving amplifier will be unable to damp the speaker, and you can measure electrical impedance of the speaker rather well. The acoustic resonances of the speaker and its cabinet show up nicely in the electrical impedance versus frequency, and electrical measurements are much easier than measuring the sound pressures from the speaker. The test circuit is simple: A typical digital voltmeter is plenty accurate for measurement of AC voltage across the speaker. Here is a photo of the oscillator that I used (I bought it used for $50 a few years ago for my day job, and brought it home for a few days for these measurements). It has a stable output voltage, and I calibrated its dial against my Seiko electronic tuner. I measured the free air resonance right away, and compared it to the Eminence impedance curve for the Tonker. My measured points are the red dots, and the only adjustment was a vertical scaling so that the peaks were the same height. (Later I found that the absolute impedance was pretty good, too.) The agreement is good, but my speaker has a lower resonance frequency than the published curve (the red points are shifted to the left). I was a bit surprised that the measured resonance was so sharp in frequency, and had to remind myself that a real amplifier will damp it because a real amplifier has a low output impedance. To get the compliance of my Tonker loudspeaker, here is the important comparison of the resonance curves for free air and for a closed, sealed cabinet. You can see the big increase in resonance frequency when the cabinet is closed. From this fractional frequency shift you can calculate the compliance equivalent volume of the speaker. In this case the increase in frequency is roughly sqrt(2), so the speaker’s compliance equivalent volume is nearly equal to that of the box itself, 2.1 cu. ft. Certainly it is more compliant than listed on the Eminence spec sheet. You can find some web sites with port tuning calculators. I liked this one, for example: http://www.ajdesigner.com/fl_subwoofer/subwoofer.php and this one is good, too: http://www.carstereo.com/help/Articles.cfm?id=31 These results were generally in agreement with the curves I found in my old book on building speaker enclosures. Now for the physics of port tuning. In a bass reflex enclosure, the back radiation from the speaker cone, 180 degrees out of phase with the forward radiation, drives the Helmholtz resonator. The trick is to tune the Helmholtz resonance to a low frequency. Whenever you drive an oscillator with a frequency above its resonance, it responds with a phase lag of up to 180 degrees (when you are well above resonance). The net effect is that the Helmholtz resonance is up to 360 degrees out of phase with the forward radiation, which means it is back in phase again. Actually, so long as you are more than 240 degrees out of phase, you are doing pretty well. You can get all sorts of port openings for Helmholtz resonators from tubes to holes in a box, but the optimal area of a simple hole equals the active piston area of the speaker cone itself. Ideally (but not likely), you can double the bass power output by getting all of the back radiation out of a large port of this size. (If you go larger, the speaker starts to become unenclosed, like an open back cabinet.) The rule of thumb, then, is to tune the Helmholtz resonance to a frequency of the free-air resonance of the speaker itself, or somewhat below it in my case. I could have done this by putting one big port in the back of the speaker, but I was worried about the speaker becoming unenclosed because the port is just behind the loudspeaker. I wanted some opening in the back for dispersion, but I found some problems in the resonance curves when the port was too big. (I measured about 30 different resonance curves, as described below.) So anyhow, I bought a piece of PVC pipe at the hardware store to make a front port that was a smaller than optimal so I could have most of the port in the back to get dispersion of the midrange and high frequencies. The port and its installation are shown below. Okay, now for the tedious part. I found that the AB cabinet back was very nicely sealed, and the back plate would stick in place when I pressed it in at an angle. It also made a pretty good seal at the bottom, so I was able to change the opening at the top and re-measure resonance curves. Here is how the speaker looked as I slid the backing board up and down to tune the port. And here is only about half of the data I collected on the resonance tuning. Don’t expect to figure this out, I can’t sort it out myself without decrypting all my notes at the time. Over several hours, I made a bit of a journey as I tried all sorts of openings at the top of the speaker enclosure as shown above, but also at the bottom. The choices seemed logical at the time, but I cannot really explain the reasons for all measurements. Anyhow, my goal was to keep the low frequency Helmholtz resonance below 84 Hz as far as possible, while still having a large opening in the back of the box. Another big change came at the very end. I stuffed the enclosure with fiberglass. This is not just to damp reflections off the walls, although this helps. There is another curious effect where the fiberglass helps keep the air at a constant temperature as it compresses and expands in a sound wave. Effectively, this serves to enlarge the volume of the box, maybe by 10 or 15 percent. My final port tunings had to be redone, but the good news was that I got an even larger port opening in the back. Here is the fiberglass. And here is the final tuning curve How It All Turned Out Here it is I have been loading this into my car a couple of times per week for over a month now. It is heavier than I would like, but I can carry it and load it myself without undue stress. It does not seem to be getting heavier each time I carry it, which is a good thing. I don’t enjoy carrying it up and down a flight of stairs, though. It does have great bass. Really, this part was a real success. I am pleased. Also, the midrange dispersion from the port in the back is good. This depends on where I place the speaker near walls, though, and I am still learning how to do this best. On the other hand, it is really loud. The speaker has 102 dB efficiency, and the new enclosure is particularly efficient by couple more dB in the bass. I’d give it a 6 dB advantage over many typical speaker cabinets, equivalent to a factor of 4 in power. My 15 watt amp is therefore equivalent to maybe 50 watts into a more typical speaker. This is just way too loud to crank in the indoor places where I play with my bandmates. I have learned a lot about attenuators. I hope to do another post on attenuators soon. Lessons Learned If I did it again, I wouldn’t put in the front port. Using the open port in the back gives a nice dispersion of midranges plus enhanced bass. The best of both worlds, IMHO, and getting rid of the front port would have let me make a larger port in the back, although not by much. You have to tune the port yourself. This is work, unfortunately. Use the web service calculators to get close enough to buy the speaker and the box, but afterwards you have to work at it. Your design work will be easier if you can buy a speaker with a lower free air resonance, but with a small volume compliance equivalent. (Unfortunately, this works against speaker efficiency and weight.) Also, it is easier to make a good design if you can lift a larger box. (You can get a box that is too large for a good bass reflex design, though.) I think the speaker parameters change with the speaker break-in. I can’t prove this because I did not do any measurements on the Tonker when it was new, but it is now quite different from the Eminence specs. Mine is more compliant (less stiff as a spring) and has a lower resonance frequency. Finally, I hope I convinced you that you can’t put any speaker into any tuned cabinet. Speaker and cabinet have to be matched with care. I don’t think it is possible to get by with much less work than I have done if you want to do your own tuned port enclosure. I am doubtful about any cabinet builder who will put the speaker of your choice in a ported cabinet of a standard design.