Isobaric 4th order Bandpass Subwoofer

This is not a constructional article as such as this design relies heavily on the parameters of the drive unit. I used surplus drive units and accurately measured their Theile/Small parameters.

Requirement: 

The very fact that one considers the need for a subwoofer implies that there is something lacking in the performace of the main speakers.
This is not surprising since speakers, unfortunately have to co-exist with families, wives and girlfriends, leading to the inevitable compact, stand mounted loudspeaker.  Modern, compact loudspeakers can perform extremely well but there is no getting away from the laws of physics, small box=poor bass.
So modern loudspeakers are designed to have a limited bass response ?
Yes, they certainly are and my A/V speaker design was no exception to this.  I knew before I cut the first panel what the lower frequency response was going to be.  If you find your speakers to be adequate, then all well and good.

If not.....well you could replace both speakers with something bigger and better... or... you could use a subwoofer.

Enter the subwoofer:

The word subwoofer is a bit of a misnomer. It implies sub-audio which of course you cannot hear.  We really mean Low-audio.  That is not to say that we cannot "perceive" sub-audio frequencies.  The body can percieve sub-audio frequencies as vibrations and this can enhance the reality of the listening experience.  There is not generally much low audio content below 20Hz in most music. The only (non electronic) instrument capable of producing anything below this is the church organ at 16.67Hz.  Even if the organ is fitted with this massive pipe, it is usually stuffed with something to prevent the building falling down around it !
For practical purposes, we can settle on 20Hz as the lowest audio frequency that we want to reproduce, any lower than this, boxes tend to get a bit big.
OK. so that determines the lowest frequency that we want our subwoofer to handle, but what about the highest frequency ?
This is easy, it has to match the response of the existing speakers.  In my case, my A/V speakers are -3dB at 47Hz. This actually much better than most small speakers, -3dB at 70-80Hz is fairly typical. Ideally the subwoofer should also be falling to -3dB at the same frequency.  This is readily acheivable by an electronic low-pass filter. These can easily be made adjustable to integrate with almost any existing speakers.
The answer to this one relies on how the human ear perceives direction.  The brain very accurately compares the phase of the sounds from the left and right ears and makes a decision based on this.  At high frequencies the spacing between the ears is a significant portion of a wavelength and the phase difference is large.  As the frequency is lowered, the spacing between the ears becomes small compared with the wavelength. The phase difference is reduced making it more and more difficult for the brain to calculate the direction of the sound.  This is not by any means the whole story, the ears also use the difference in level and slight head movements to further determine direction. Below 200Hz, the human hearing system is almost totally incapable of determining direction, so it doesn't matter if the bass is in stereo, mono or even where in the room it is generated. Thus, one subwoofer is all that is required.   It is normal to sum the left and right channels within the subwoofer so no information is lost.  Joint stereo is often used as part of the MP3 coding system.  Low frequencies are encoded in mono, higher frequencies in stereo.

Types of Subwoofer: 
  1. Large speaker, large ported box.
  2. Electronically equalised sealed box below resonance.
  3. Bandpass coupled box.
These are the main types, the ported box being the most common.

For my purposes, I chose option 3, the Fourth order Bandpass coupled design:
4th order bandpass design

The drive unit is mounted on a baffle forming a front and rear cavity. The port is the only opening.

I had already obtained several cheap 180mm drive units and carefully measured thier parameters. This is critical in this type of design as even small errors will affect the frequency response quite drastically.
I used WinISD  and added my speaker to the database to plot the response and calculate the box size.  Some compromise is neccessary in this type of design. You can have good efficiency and a very narrow bandwidth or poor efficiency and a wider bandwidth.  What is actually acheivable depends totally on the characteristics of the drive unit.  I was lucky in that my £3 driver produced a  -3dB bandwidth from 29-76Hz.  This, I couldn't change but I could filter the high end to match my existing speakers.
I decided to use an Isobarik configuration, with two drive units back to back. This has the advantage of halving the required volume of the two halves of the bandpass enclosure.

Isobarik loading: 

This is not a new concept, having been originally introduced by Harry Olson in the early 1950's. Technically, "isobarik" is not really an enclosure type; it is a loading method. This loading method involves the coupling of two drivers to work together as one unit. This is typically accomplished either by placing two drivers face to face or by coupling them with a small chamber. The result of coupling the two speakers is that the coupled pair (iso-group) can now produce the same frequency response in half the box volume as a single speaker of the same type would require. For example, if a speaker is optimized for performance in a 40l. enclosure, one iso-group of the same speakers can achieve the same low frequency extension and overall response characteristics in a 20l. enclosure.

Isobarik loading

Two drive units are mounted in a clam-shell configuration. They are driven in anti-phase so that the pressure of the trapped air remains constant.

The design:

The data below shows the plotted response and the design information from WinISD. All I had to do was translate the data into a physical enclosure. The two drivers were mounted back to back on the divider between the front and rear cavities. A large round hole was cut using a router to connect the two drivers. Neoprene sealing tape was used between the two drivers and the baffle to make the isobaric pair air-tight.

As the port is the only source of energy from this kind of design, it is very important to note the speed of the air in the port. WinISD specifies this in "mach" where "mach 1 " is the speed of sound.  If you make the port too small in cross section, the speed of air in the port will create turbulance which will be audible as a "chuffing" sound.  I chose 60mm square rain water drain pipe as this was available and the speed worked out to mach 0.02.  WinISD warns you to choose a larger diameter port if the speed exceeds mach 0.18.

Rsponse as plotted by WinISD

The subwoofer response using my £3 drivers as plotted by WinIsd.




Number of drivers
2 (used as isobarik installation)
Box type          
 4th Order Bandpass
Box size         
Front chamber 11.0 l

Rear Chamber 24.5 l
Port tuning frequency 
46.56 Hz
Vent              
 1 vent  -> Front Chamber

0.401 m length

0.060 x 0.060 m square

The design parameters from WinISD.


One effect of the Isobarik loading is the halving of the required volumes as opposed to if just one driver was used.  Another is that the port tuning remains the same but in half the volume, which equates to doubling the port length.   Note in the above table, the port is 401mm long.  There is no room for this in the 11 litre front cavity so a bit of latteral thinking was required to accommodate it.  Some designs fail at this point if the port cannot physically be made to fit.  In this instance, I solved this problem with the design below.

bandpass box design sketch

Bandpass subwoofer box and port design.

Note how the port passes from the front cavity, through the rear cavity and exits through the right hand side. The RH cavity is sealed where the port passes through. It is important to take into consideration, the volume occupied by the drive units and the port in each of the cavities.

Power amplifier and active filter:

The end compartment houses the 100w amplifier and active Low-pass filter.  The amplifier in this case was a kit comprising of a pair of VMOS power FETs. Its heatsink protrudes through the outside of the box.   An active Low-pass filter feeds the power amp. This is preceded by a virtual earth mixer which sums the line level signals from the left and right channels. A volume control sets the subwoofer level and is adjusted by trial and error to get the balance right.

Measured response and results:

Measured response
Measured frequency response with no low pass filtering.
The above graph shows the measured response of the subwoofer.  This was measured in the garden with my measurement microphone pushed just inside the port.  The graph indicates a -3db response of 24-79Hz which compares very favourably with the design specification. (29-79Hz).

Used in conjunction with my A/V speakers, the subwoofer has certainly brought back the missing bass.  It took quite a while to balance the volume of the sub with the rest of the system. In fact, I started with the volume far too high and over several periods of listening, brought it down in stages until I was happy.

I have now repalced the A/V speakers with my 3 way active system.  I have still retained the subwoofer though, but now it is connected to the LFE channel of my Dolby Pro-logic decoder.  I have a small, centre speaker (BBC LS3/5a) which benefits enormously from the extended bass that the subwoofer provides. As a pure fluke, the unfiltered response of my sub, virtually maches that of the LS3/5a.... lucky or what ??

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