For years I've owned a Logitech X-503 multimedia system that provides the sound for my main PC. At the time I purchased it, it was around US$70, which was quite a good price, considering that the system consisted of 10" small 1.7" drivers (two in each of the satellites) and a 4" driver in a gnat-sized vented box to provide bass duties. The satellites aren't too bad (nothing that can't be fixed with a bit of EQ), but the bass unit was definitely a study in compromises. The driver has a relatively high Q and the box is tuned to around 80 Hz, so the end result is a big peak around that frequency that makes everything sound "robust", until you notice that a lot of a low notes are actually missing. Interestingly enough, the output from the bass unit's amplifier is not rolled off (significantly) below 80 Hz, which means that the driver does end up getting signal below Fb. The amplifier must incorporate some sort of dynamic EQ though, because even when turned up, there's no sounds of significant distress from the driver when it's fed very low frequencies.
The image below shows the measured response of the X50's bass module with the vent sealed (when vented, it was even more peaky), both with and without EQ, and the black line in the graph shows the frequency response of the bass unit's amplifier. Yes, its response actually peaks at 60 Hz, a little below the bass unit's Fb when the vent is unplugged.
Anyway, with no very low frequencies to speak off, the "bass unit' had to go, and I decided to replace it with a subwoofer design based around the Dayton DCS205 8" subwoofer driver. For this particular design, I wanted a solution that had an Fb around 32 Hz, as my intent was to use EQ to address the low-frequency performance in-room, and the lowest band on the simple EQ included with the PC was centered at 32 Hz. So, I went to work on a new Excel workbook to describe the design, and I eventually came up with an MTL-looking design that was around 26.6 litres net and 45 litres gross, primarily due to the use of 21mm MDF for the build. The HornResp sim showed a response that gently slopes down from 100 Hz to just above 30 Hz, just right for what I wanted.
Here are the details of the box I built, copied from the workbook:
When put together, the internals of the box looked as diagrammed below. The red line is the path length as calculated by the workbook. This, along with other parameters derived by the workbook, were used to model the response of the subwoofer in Hornresp, a program designed to simulate horns, but can be used to model a wide variety of subwoofer alignments.
The workbook also works out the expansion of the "horn" (in this case, the pseudo-MLTL) and graphs it. For best results, we want a smooth reduction from the start of the path down to the vent. The minor "bumps" in the graph show where the "horn" is folded
The following images show the Hornresp parameters used to model the alignment. All of these were generated by the workbook, so it was just a matter of importing them into Hornresp. Note that in Hornresp I opted to include in the model the effect of puttling some polyester fiberfill in the first section of the alignment. According to the sim, this would drop the resonance frequency (Fb) a bit, and smooth the response in the passband. Real-world measurements of the built subwoofer confirm that the added filling achieved these goals. Note that the predicted frequency response is slightly optimistic, as Hornresp does not account for the impact of box losses. The rolloff from 100 Hz to 40 Hz is slightly steeper than predicted, and the "corner" at around 32 Hz is a bit shallower.
The following image shows the subwoofer's linearty (response at different input levels), which is pretty good as mentioned above. The slight variation around 100 Hz was actually caused by the soundcard used for the measurement. Note that this is NOT an accurate frequency response graph, though it is close. The rolloff from 100 Hz is actually due to the built-in lowpass filter in the amplifier that I used for the tests.
The following image shows what the distortion curve looks like at around 20W. Peak THD is pretty low at 5.22%, most of which is 2nd order, so a lot less noticeable and objectionable. This suggests that the subwoofer is going to sound "clean" in actual use.
After messing around with tapped horns for awhile, it was nice to return to relatively simple alignment, and this little subwoofer based around an 8" driver delivers all that I need for my multimedia system. If I was building this for another purpose, I might likely opt to flare the port's exit a bit, to reduce vent noise and compression effects at high volumes even further. The following image illustrates how this could be done.