There are two alignments that exert significant control over the driver excursion at low frequencies - sealed and 4th order bandpass. Other alignments such as vented and 6th order bandpass do exert control within the passband of the alignment, but things get very ugly pretty quickly at lower frequencies outside of the pass-band.
I took the opportunity to remeasure the T/S parameters for my INF10 driver, and they are as follows:
The published Xmax for the INF10 is 8 mm, and the published power handling capability is 100 Watts. From previous tests, I deduced that the cone could move about one inch peak-peak, which suggests an Xmech of 12 mm.
The following table demonstrates the relation between Qtc, Vb, Fb, F3 and peak excursion at 100W, based on the driver's measured T/S parameters:
Moving Qtc up to 0.85 looked interesting. F3 moved up slightly to 48 Hz (still unappetizing), but this time the excursion of the driver at Pe was kept well within Xmech.
So, how can we get a lower F3 without running into over-excursion problems?
Well, how about a 4th order bandpass alignment?
A 4th order bandpass alignment are like a cross between a sealed alignment and a vented alignment, with the advantages of both appearing in the results. Not only can you achieve a lower F3 than a sealed alignment using the same driver, excursion outside of the pass-band is controlled just as it is for a sealed alignment. Not only that, but excursion within the pass-band is reduced, which should result in lower distortion and better power-handling capability.
The disadvantages of 4th order bandpass alignment are (1) transient response that is inferior to sealed alignments (but comparable to vented alignments), (2) no audible warning of a driver being pushed past its limits, and (3) out of band noise, which has to be dealt with via some means of filtering (active or otherwise).
In my view, all of those disadvantages are outweighed by the lower F3 and increased powerhandling capability afforded by the use of a 4th order bandpass alignment for the INF10, so I started to design one.
A simple bandpass alignment that I came up with is as follows:
Here, Qbp (the Qtc for the sealed section of the enclosure) is kept around 0.85, the best choice for Qtc from the previous table. An Fb of 58 Hz is *not* the suggested Fb for this alignment - Fb should match the predicted Fb for a sealed enclosure where Qbp=Qtc, in this case, 55.7 Hz. Well, there is a method to the madness - I plan to use this alignment with an active 12dB/octave filter with an Fc of 100 Hz. The use of the higher Fb will ensure that the pass-band remains flat when the active filtering is taken into consideration.
This is the predicted frequency response without the the active filter:
...and this is the predicted frequency response, with (1) the active filter (12dB/octave @ 100 Hz):
After running a few simulations on my spreadsheet, the internal enclosure dimensions that I finally settled on were 12.5" x 15" x 17.5", split into two sections with a 0.75" separator that will be holding the driver. This gives just over 0.9 cu.ft. per side, which should drop to 0.71 cu.ft. per side once the volume displaced by the driver, the ports and the braces are taken into consideration. If not, the dimensions give me enough "play" to adjust the tuning of the enclosure accordingly. 4th order bandpass enclosures provide quite a few options if you want to adjust the response, e.g.
The following should also work, just in case you want to try this:
It just depends where you want the seams to show up. In my case, I wanted only two seams to show on the front panel. Also, if I go with positioning the ports to face downwards, the "top" panel will have no visible seams - ideal for the subwoofer-posing-as-end-table look.
Here's a picture taken partway through the construction process, showing the box before the top and bottom panels were added and the cutouts made for the vents:
You'll notice that the box strongly resembles an 'H' baffle for a dipole woofer alignment. I noticed that too, so I stopped construction here - once the glue has dried, I intend to do some tests with the INF10 mounted in the box, to see if the actual frequency response of this "dipole" matches what the equations predict. The results will be covered on the INF10 dipole subwoofer page.
Here's another picture taken further into the construction. This one shows the two holes cut for the Madisound 3" flared ports. My "hole-cutting" tools are a jig-saw, a drill with a big bit (to drill the pilot hole for the jig saw's blade) and some rough sand-paper wrapped around 2" PVC (to sand down the rough edges) - so many boxes built, and I'm still unable to cut a good circle :-).
The image below shows one side of the box where one of the two remaining panels is to be mounted. Also shown is the front flange for one of the Madisound 3" flanged ports. Note that I've added a 3/4" edge around the inside of the box - the panel shown will be screwed down onto this, and glued into place to complete construction. Note: that step won't be done until (1) a similar edge has been added to the other side of the box for the other panel, and the fit tested, and (2) basic testing has been done to ensure that we're hitting the target Fb.
A change of plans
Below is another view, this time showing the end panel that's going to be fitted to the sealed section of the enclosure. Note the additional bracing added to the end panel.
Below is a view of the sealed section, with the driver screwed into place for testing. I wanted to ensure that I was on target for Qbp (0.85).
Using test tones and checking current flow through the driver, I measured Fb to be about 56 Hz, almost exactly as predicted for a sealed enclosure of this size. I still went ahead and added a little polyester fiberfill at the bottom of the box (to reduce box resonances) - this dropped Fb to 55 Hz - just below the target, but I can live with the 1 Hz difference - I doubt anyone would hear it :-).
Below is a picture of the box, with one end-panel remaining to be installed. The two 3" flared vents have been cut to size and installed. Note: I shortened the vent lengths to 14" each. The flare adds 1" to the calculated lengths - but if I went along with the calculated lengths, the opening for each vent would be too close to the rear wall of the enclosure. Shortening them by 1" should not result in any significant problems - Fb will probably rise by 1 or 2 Hz, but this can be taken care of in the x-over, if necessary.
Below is a picture of the unfinished box, with vents installed. Looks pretty good so far. I'm considering flush-mounting the vents, but that will take quite a bit of work with a chisel and a sander, seeing that I don't have a router! As I haven't put in a terminal cup yet, I simply passed the speaker cable through one of the ports, to allow me to test the "raw" response of the system.
Below is the measured response of the raw system, without any damping material in the vented section:
Two things are of interest here - the extended upper cutoff point (over 100Hz, vs. the 92Hz predicted by the worksheet), and the large peak at 400Hz. This peak was clearly audible, and made the system sound quite horrible.
Below is the measured response of the system, this time with some damping material (polyester fiberfill) added to the vented section:
As can be seen from the graph, the huge peak at 400Hz has been significantly reduced (by about 10dB), with negligible effect on the system's pass-band - a clear indication that damping should be used in the vented section of 4th order bandpass systems whenever it is possible to do so. The "stuffed" system sounded quite a bit better than the "raw" system - and I plan to experiment with the stuffing a bit more.
At the moment I have no explanation for the extension in the upper cutoff point. Perhaps it's due to box losses, which will tend to widen the pass-band at the expense of efficiency.
Here's another graph, showing the fairly significant difference between the predicted response of the system (blue), and the measured response (red):
An impedance plot of the system proved to be even more intriguing:
The impedance plot suggests that the resonance frequency of the vented section is closer to 48 Hz than the target of 58 Hz! What could be causing the difference? And remodeling the enclosure with Fb adjusted downwards to 48 Hz still doesn't produce the extended upper pass-band response that I've measured. Quite unusual.
I decided to modify the design a bit, to see if I could bring Fb back to the target of 58 Hz, or even the lower 55.7 Hz if possible, as 48 Hz was way too low, and the likely result of having Fb so far below the target would be reduced gain.
First, I prepared the vented section for the inclusion of more stuffing. No, the stuffing isn't going to help Fb, unless I REALLY stuffed the stuffing into the box. However it will help reduce out of band noise (as the previous measurements show), so I decided to add a bit more. To ensure that stuffing was kept away from the driver, I made up a basic grill, as indicated in the image below:
Then I packed in stuffing and added the ports as indicated below:
Note that the stuffing is kept away from the mouths of the vents inside the box. Any stuffing placed there is likely to find itself ripped away and ejected out of the box if the system tries to play a loud bass note. I also shortened the ports by 1.75". This reduced the length of each vent to 12.25" (around 88% of their original length), which, according to Madisound's vent calculations, is supposed to result in an Fb of just above 63 Hz for this size volume. However, as has already been demonstrated, there's probably going to be quite a difference between the predicted Fb and the actual Fb.
And there was. The graph below shows that the the Fb has shifted upwards yes, but only to about 51.5 Hz. However, the midpoint between the two peaks works out to about 55.9 Hz, which is close enough to my lower target for Fb.
I decided to halt here for the moment, to do some more frequency response checks.
Below is the current impedance response of the subwoofer. The midpoint between the peaks works out to 55.3 Hz, but the minimum impedance of 7.5 ohms occurs at 50.8 Hz.
..and this is the current frequency response (driven by my HT amplifier with its 12dB/octave @100 Hz lowpass filter):
This is actually a pretty good pass-band response, with -3dB points @35 Hz and 100 Hz, and -24dB down @ 200 Hz. The measured Fb and the upper F3 are quite a bit off of the predictions for this alignment, but not in a bad way, and the low-frequency extension is quite close to what was predicted by the model. Out of band noise is also virtually non-existent. Efficiency is a bit low. The ports can probably be shortened just slightly again to flatten the pass-band a bit more and gain a little efficiency in the process.
Below is what the final system looks like. In the background you can see one of my "Mini-Me" speakers. The INF10 is a decent match for them, extended upper cutoff point and all (the Mini-Me speakers are designed for and fed via a passive 6dB/octave filter that results in a response that starts rolling off just above 100 Hz).