The Subwoofer DIY Page v1.1 - Projects
"El Uglito" - a 4th order bandpass system
last updated: 1st February 1999

The system
This project is a 4th order bandpass isobaric systembased on two Pyramid W61 6.5" drivers. "Isobaric"basically means here that the drivers are mounted face to face with theconnections to one driver reversed, the idea being to reduce by half thevolumes required for the sealed and ported sections of the system.

Picture of two Pyramid W61 drivers

The driver
Why Pyramid W61 drivers? Well, basically I had two ofthem lying around the house, doing nothing. I'd pulled them from my cara few months ago, where they were doing a decent job of rear fill whenfree-air mounted on the rear package tray.

The W61, like most car audio drivers, is pretty solidlybuilt, but the cone is made of paper and is basically too soft to do anyserious thumping. Pyramid didn't provide any Xmax specifications for thedriver, but the cone does have about 0.5" of excursion before thesuspension brings it to a dead halt. For my calculations, I guestimatedan Xmax figure of 0.1 in. Pyramid DID provide figures for Vas (19 litres),Qts (0.47) and Fs (64.5 Hz), but a quick check of the drivers showed thatthe published specs were a bit off. Average Fs for the two drivers checkedin at 52Hz, quite a bit below the published spec, which is nice as it meansthat I should get a bit more bass out of it.

The average Qts for the pair of drivers checked in at0.50, and the average Vas at 'round 28 litres or so. No probs - the lowerFs and higher Qts suggested to me that the W61 could give decent resultsin a sealed or 4th order bandpass system. I'd expected the measured specsto be different anyway, as I'd quite recently replaced the original dustcovers for the drivers with some new ones that I'd purchased locally.


Choosing an alignment
Now the bad news.

The specs for a single W61 driver indicated that, fora sealed system with a Qtc of 0.71, the net box volume would have to beabout 28 litres (almost 1 cu.ft.), pretty big for a 6.5 incher. The F3would also be around 73Hz, which isn't so hot either. An isobaric systemusing two drivers would reduce the net volume to 15 litres, but the cutofffrequency would still be a bit too high for my tastes.

In steps the 4th order bandpass system!

My calculations showed that a single W61 used in a bandpasssystem could give a pretty decent response, but the resulting box wouldbe pretty big. My intuition also told me that the power handling wouldn'tbe so hot because of the driver's limited Xmax (rule #1 - bigger isNOT always better!).

An example of a 4th order bandpass alignment using oneW61 driver would be as follows:

    Vf = 13.9 litres    Vr = 27.2 litres    Fb = 74.3Hz    Fl = 45.7Hz    Fh = 120.7Hz    Gain = 0.00dB


The 4th order bandpass alignment above has a pretty goodcutoff point for a 6.5 incher, but the Xmax for this driver is pretty low,so I may not get decent output at that frequency. The box size is alsopretty big, at about 41 litres (1.4 cu.ft.) total.

Here's where the flexibility of the 4th order bandpassdesign steps in!

Say we use an isobaric system to decrease the volume requirements,then reducing the size of the rear volume even further by settling fora higher cutoff frequency? With this in mind, I fudged around with thecalculations again and came up with the following alignment:

    Vf = 7.0 litres    Vr = 9.9 litres    Fb = 81.2Hz    Fl = 52.0Hz    Fh = 126.9Hz    Gain = 1.56dB


The cutoff frequency of 52 Hz indicates that this 4th orderbandpass system can't be described as a proper subwoofer, but that's OKbecause the limited Xmax of the W61 indicates that it shouldn't be usedin a very low frequency application anyway. However, the cutoff frequenciesdo indicate that it'll make a good woofer element for a small three-piecesystem, so I decided to go ahead and give it a try to see what it soundedlike.

Designing the box
Designing the box for a 4th order bandpass isn't difficult,once you take certain precautions. First of all, you MUST account for thevolume occupied by the drivers, port, bracing and any other items thatare going to be enclosed in the box! This becomes even more critical whendesigning small enclosures, as the volume displaced by the drivers andthe port could have a significant effect on the final dimensions of theenclosure.

Designing the box - the vented section
Bandpass systems usually suffer from out of band noise,but the effects of this can be reduced by taking appropriate steps in thedesign of the vented section. The steps that have worked for me in thepast include:

  • Orienting the driver so that its magnet structure islocated in the vented section
  • Placing the driver asymmetrically within the enclosure
  • Placing the port so that the driver is not visible throughthe port
  • Line the ported section using fiberglass or similar dampingmaterial

There is one potential problem here - the damping materialmay increase the effective size of the vented section and lower Fb, theresonance frequency. I didn't foresee this being much of a problem, however,as I could reduce the effective volume by adding additional braces to bringthe resonance frequency back up to specification. I decided to opt fora vented volume that was slightly more than that required for the alignment.If necessary I could use bracing and/or damping material to make anyfurther adjustments.

Designing the box - the sealed section
Designing the sealed section was even easier. Using fiberglassor another damping material in the sealed section leaves me with some leewayin the design, as the effective size of the section can be varied by addingor removing damping material. I opted for a sealed section equivalent tothe calculated value for Vr. The bracing and the volume displaced by thedriver would reduce the volume, but damping material could be used to counteractthe reduction.

Designing the box - response variations
After thinking about it for awhile, I worked outthat the conditions listed below may occur in the design and affect theoutput as indicated. I put together an action plan for each scenario. It'salways best to work out all of these details BEFORE you actually startcutting wood, and save yourself unncessessary headache afterwards!

  • Vented section too large.
    • Result: narrow bandwidth; higher cutoff frequency.
    • Action: reduce Vf by adding bracing in the ventedsection.
  • Vented section too small.
    • Result: wider bandwidth, non-flat bandpass characteristic,degraded transients.
    • Action: add damping material to vented section.
  • Sealed section too large.
    • Result: lower efficiency, response peak in upperfrequencies.
    • Action: remove damping; add bracing to sealedsection.
  • Sealed section too small.
    • Result: higher cutoff point; response peak atlower frequencies.
    • Action: add damping material to sealed section.

Designing the box - the final plan
My final battle plan for the project was as follows:

    Determine Lv, the length of port of diameter Dv, requiredto tune Vf, the vented section of the enclosure, to Fb.

    Build the enclosure such that Vf', the gross volume ofthe vented section, is slightly more than Vf, the net volume predictedby the calculations. Also, Vr' the gross volume of the sealed section,will be equal to, if not slightly less than, Vr, the net volume predictedby the calculations.

    Add a port of length Lv and diameter Dv to the ventedsection. As Vf' is more than Vf, the tuned frequency of the vented sectionshould be lower than that called for by the calculations.

    Add bracing/damping to the vented section until the tuningfrequency is equal to Fb, the tuning frequency predicted by the calculations.

    Add bracing/damping to the sealed section until a flatbandpass characteristic is obtained.

At this point, the 4th order bandpass system should havea frequency response that is as close to ideal as I can get.

Building the box
And now the hard work began!

Basically, a cross-section of my final design looked somethinglike the following:

      +---------------------+| Vf          +-------+|   /----\    |  Port | |  /      \   +-------++---------------------+|  \      / Drivers   ||   \----/            || Vr                  |+---------------------+      removable panel       

And this is what the finished product looked like, frombelow (with the bottom removed):

Inside view of El Uglito

The drivers were mounted from below, in the sealed sectionof the enclosure. The bottom of the sealed section was made removeable,so that the drivers could be accessed at any time. The bottom of the enclosurewould be facing the floor when the system is in its normal position, sono screws are visible. Vf is 7.5 litres, and Vr about 10 litres. 3/4 marineply, butt joints and aliphatic resin (wood glue) was used throughout. Drywallscrews were used to hold the sections together while the aliphatic resindried, then they were removed and the holes filled with wood filler. Theenclosure was then sanded and painted with a white laquer (basically tostop the ply from splintering along the edges!). Tuning was done as outlinedin the previous sections.

This is what it looks like from the front:

Front view of El Uglito

Final Results
The final results are pretty good, if I do say so myself.The passband is very close to the predicted 52 Hz-126 Hz, and the noiseband is pretty low in level - the highest point is 11dB below the passband,and the noise is virtually inaudible when the system is used along withtwo Mordaunt-Short 3.2's that I employed temporarily as satellites. A fullfrequency response check on the system shows that there's a very slightpeak in the lower section of the passband ('round 60Hz or so) but thatcan easily be fixed by adding a bit of bracing to the front chamber toincrease the tuning frequency. So far it isn't bothersome, so I haven'tbothered to add the bracing.

Frequency Response - 22nd June 1997
Recently, I had the opportunity to measure thefrequency response of the system again, using a technique I've been experimentingwith over the past few weeks. The results are shown in graphical formatbelow:

Frequency response

Notes:

  1. The peak at 1 kHz is the port resonance (a "feature" ofalmost all bandpass systems), and can be cured by a simple notch filter.So far I haven't found it bothersome (probably because I'm driving thesystem using an active filter in the amplifier).
  2. The small ripple at 450 Hz is caused by reflections fromwithin the box, probably from the back panel, which is parallel to theport openings. The peak was reduced considerably by the addition of dampingmaterial in the front section - which in turn is probably causing the slightpeak in output at 60 Hz, because the tuning of the front section has nowbeen altered!. However, the slight bump at 60 Hz is a lot less objectionablethan a huge peak at 450 Hz...
  3. The slight ripple at 27 Hz I believe was causedby a small leak in the sealed section of the system, which I subsequentlyfixed.
  4. The 2nd and 3rd harmonic distortion readings were takenat a drive level of 2.83 volts to each driver in the system, and the resultswere measured relative to the output level of the fundemental frequencyat this drive level. At this level, the system was generating over 120dB at the port in the middle of the passband. The rapid rise in 3rd harmonicdistortion below 50 Hz is caused by the drivers exceeding their Xmax atthis volume level.