To assist with coming up with the best dimensions for the new tapped-horn, I put together a spreadsheet that would allow me to adjust the various dimensions until I came up with a smooth expansion curve. The spreadsheet then gave me the appropriate parameters to insert into HornResp to simulate what the results would be like. By varying the dimensions in the spreadsheet and updating the simulation accordingly, I was able to come with a decent-looking alignment in a reasonably-sized box.
The HornResp parameters are as follows:
The predicted performance is as follows:
The required panel dimensions are as follows:
Not included in the above list are the panels required to brace the enclosure properly.
The required layout is as follows:
I then proceeded to build the box (see images below). Ingredients: one sheet of 4 x 8 18mm ply, one sheet of 4 x 8 12mm ply, a box of drywall screws, wood-glue, a few bricks (to act a temporary table), some mounting screws for the driver and of course the driver. This time around I left no removable panels, as it's possible to mount the driver in the box without having to remove any panels. This build was a bit more difficult than my previous POC build due to the number of panels involved, the bracing, and the different thicknesses of ply used.
The image below shows the box partway though the build. You can see where I've inserted bracing in almost all sections of the horn. Not visible in the image is an additional bracing panel mounted right behind the panel that's facing the driver.
The image below shows what I did for the baffle, where I used two pieces of 12mm ply bonded together, and cut so that the driver is countersunk into the hole. Doing it this way ensures that the driver is properly positioned over the cutout, as any minor leaks in this area will result in a considerable loss in low-frequency output.
The image below shows what the built box looks like in my car. It's wider than my previous tapped-horn, but it is not as high not as deep. I can actually transport it now without having to put down the rear seats.
The impedance curve of the built system (see below) suggests that further bracing may not be required, as the three impedance peaks are well-formed (as compared to my previous build, where the third peak was almost non-existent until I properly braced the box).
The image below shows the measured frequency response (in red) , compared to the HornResp predictions (in brown). Also shown is the measured response with 48dB/oct filters applied at 30 Hz and 120 Hz (blue). The measured results suggest that Fb is between 38~39 Hz, an almost perfect match for the simulation. I suspect that it's slightly lower because the driver's structure is blocking the mouth a bit.
The images below shows one my "Blastorama" speakers on top of the box, which should give a good indication of its size. The second picture was taken after the subwoofer was painted flat black and the mouth was reinforced with a few metal brackets.
The response of a tapped-horn can be cleaned up significantly with the use of DSP, and I strongly suggest that if you plan on building one, you consider including a DSP solution in the signal path to get the most out of it.
For example, here's the raw response of the POC#3:
...here's the response with DSP used to flatten the response between 40 Hz to 200 Hz:
...here's the final response with DSP used to apply a 48dB/oct filter at the low end (to control excursion below the resonance frequency of the tapped-horn) and at around 100 Hz (to blend in with the main drivers):
.The combination of the EQ and X-OVER results in a much smoother response and easier blending with the main speakers. The DSP requirements to accomplish this could be met by using something like the Behringer iNuke 3000DSP amplifier to power the tapped-horn.
Finally, here's an image comparing the raw vs. DSP'd output, with a HP filter @ 38 Hz and a LP filter @ 200 Hz. This measurement was done at a "moderate" volume, and includes distortion measurement. The distortion curve looks really good, with no peaks in the system's passband.