The Subwoofer DIY Page
Bandpass Systems
 26 October, 2018

Bandpass subwoofer systems are basically systems where the driver's output is subjected to one or more "acoustic filters" in the form of an additional vented section added in front of the driver. The two most common type of bandpass subwoofer systems are the 4th order bandpass system and the 6th order bandpass system (which can be be "parallel-tuned" or "series-tuned").  There are other higher-order bandpass systems of course, but they are more difficult to design and construct, and it might be more practical to choose a design and build a simpler system using a better driver.

As all of the output of a bandpass system is via its vent(s), careful attention needs to be placed on the design of the vent or vents in order to get the best results. For example, the largest port diameter possible for the enclosure should be used in order to minimize vent compression effects, and the ports should be flared whenever possible, for the same reasons.

Bandpass systems rarely exhibit a perfect bandpass response - there is usually some out-of-band noise present in its output. A low-pass filter can be used to reduce this out of band noise if it is audible, but the impact of this low-pass filter on the overall output of the bandpass system needs to be taken into consideration when designing it. Careful choice of enclosure dimensions, the driver's location within the enclosure and the use of lining or stuffing within the sections can also be used to minimize out of band noise.

 
4th Order Bandpass System
The 4th order or sealed rear chamber bandpass system is basically a sealed enclosure system with the addition of an acoustic filter in front of the driver in the form of an additional chamber that is vented. The resulting system usually provides a lower cutoff frequency, the tradeoff being a larger enclosure, usually approximately the same size as a vented system using the same driver. 4th order bandpass systems usually demonstrate better power handling characteristics than the other main systems considered here, and its transient response is second only to the sealed enclosure systems, making it a good choice for subwoofer applications.
6th Order "parallel-tuned" Bandpass System
The 6th order bandpass system is similar to the 4th order bandpass system, except in this case both the front and the rear sections are are vented. In the "parallel-tuned" variant, both sections are vented to the outside. The power handling of the 6th order bandpass system ranges from excellent within its passband to poor for frequencies lower than its passband (like vented systems, the driver becomes unloaded at frequencies below the system's resonance frequency), and its transient performance is usually worse than the other subwoofer systems, making it more suitable for sound reinforcement, multimedia and other less critical applications, rather than high-end audio.
6th Order "series-tuned" Bandpass System
In the "series-tuned" variant of the 6th order bandpass system, the vent from one section leads into the other section, which provides two advantages - shorter vent length requirement (for one section) and better acoustic filtering (as the output from "series" vent is subjected to the acoustic filtering of both sections).

Designing a Bandpass System
There are several software tools available that can be used to design a bandpass system. My favourite at the moment is Hornresp, as it allows quite a degree of flexibility in the design stages, and it Hornresp is able to model not only the passband response, but the out of band "noise" - which will give you a pretty good idea of what to expect in that regard, and peak particle velocity in the vents, which can use to ensure that you don't design a system with too-small vents. Hornresp can also use the "semi-inductance" model to simulate the output of the system, and the "semi-inductance" model will give more accurate results than the basic t/s parameter model.

Pictured below are (1) the input screen for a 4th order bandpass system in Hornresp. The driver in question is the Dayton Audio PA310-8, and the semi-inductance option is enabled.  The model includes a simulated sealed section that is 32 litres in volume and 51 cm deep, and the vented section is 17.2 litres in volume and vented with a vent that is 27.5 cm long with 200 sq.cm. of cross sectional area.

..and this is what the simulated response of this 4th order bandpass system looks like:

As you can see from the simulation, the out of band noise starts from around 350 Hz, and the predicted level peaks at around 3dB below the passband level.  This out of band noise will be very audible, unless it is dealt with using one of the techniques previously described. Pictured below is what the impact on the response would be if a 200 Hz 12dB/octave line-level filter was used with this particular system.  The vent has been trimmed slightly to minimize the effect of the filter on the response in the passband.

 

Pictured below is the Hornresp input screen for a series-tuned 6th order bandpass system using the same driver.  In this case the rear section is 30.5 litres in volume and tuned with a vent 49.1 cm long with a cross-sectional area of 150 sq.cm. that connects to the front section, and the front section is 40 litres in volume and tuned with a vent 12.5 cm long with a cross-sectional area of 200 sq.cm.  The resulting passband is wider than that of the 4th order bandpass system that was previously simulated with the same driver.  However the resulting box size is also quite a bit bigger.

 

...and this is what the simulated response of this 6th order bandpass looks like:

Apart from a very narrow spike at 300 Hz which will very likely not appear in a built version of this design (Hornresp does not include the impact of box losses in its simulations), the out of band noise appears much further up in the frequency range, above 600 Hz, making it a lot easier to deal with with a simple low-pass filter that does not impact the response in the passband.

Bandpass Subwoofer projects on the Internet