By David Gatti

Bass management in a home theatre surround sound system has become much of a headache for even the most dedicated enthusiasts.

Most home-theatre users have an elementary knowledge of loudspeakers, crossover design, the physics of sound, and room acoustics.
Furthermore, the standards and approaches used by equipment manufactures vary widely in regard to bass-management crossover frequencies, levels,
overload margins, how & when bass is routed between small/large/subwoofer speakers, different DVD / Blu-ray / HTPC / SACD / DVD-A requirements, etc, etc, etc.
Its so complex, with so little clear information provided to the user, that it all usually ends up being a guessing game. It's not surprising then, that the results will almost certainly be less than optimum.

Basically,, the whole system needs to be simplified, and I believe the best way to achieve that (in a high end system) is to use -:

- bi-amped, full-range main speakers (requiring no bass management).

- centre and surrounds big enough that they can be set to "large" (no bass management)

- 2 x dedicated LFE subwoofers (no filtering)

- sealed enclosures for all channels. for minimal group delay and excursion limiting.

Note : "Bass management" refers to the process of filtering the low frequencies from a loudspeaker, and routing those frequencies to a subwoofer.

Now, with some new speaker designs in the works, I'll attempt to explain how subwoofers and main speakers interact, and the simplest (not necessarily cheapest)
way to get the best low frequency performance. I refer you to Rob Elliots articles on phase & group delay for some background reading.

To begin with, lets compare the frequency response, and group delay for a variety of configurations.

Below is the response of a sealed main speaker with a natural 2nd order rolloff below 80Hz.

Notice the 12dB/octave rolloff (left graph), smooth phase-transition from +180 to 0 degrees (dotted line), and in the 2nd graph, peak 4mS group delay at 50Hz..

Compare this to a vented main speaker (below), with a 4th order Butterworth rolloff below 80Hz.
The response falls at 24dB/octave below 80Hz, the phase wraps through 360 degrees, and the group delay more than doubles to 8ms.

Now lets add a subwoofer to the above main speakers with a few different filters, and see what the result is.

Assume the subwoofer has -3dB at 20Hz, whether it's sealed or vented.

First, a vented subwoofer with 4th order lowpass at 80Hz. Mains are vented with an additional 2nd order highpass filter, giving it a 6th order rolloff below 80Hz.

Nice flat frequency response, although the phase wraps through 630 degrees and the group delay skyrockets to 36mS

How bad is 36mS? Sound travels at 330m/s. distance = velocity x time = 330m/s x 36mS = 12 metres!

That right, low bass frequencies will be effectively 12 metres further away! Now you know why vented subs are sometimes characterised as slow.

Lets try to improve on it and use sealed main speakers. The rolloff of the mains is now 4th order, effectively creating a 4th order Linkwitz-Riley crossover at 80Hz.

Not much change. Slightly less output in the 50-150Hz region, and virtually identical group delay.

Lets seal the subwoofer enclosure and see what happens.

Nice flat frequency response, and the phase shift is now improved 20% from 630 to 500 degrees (but stil poor), and group delay almost halved to 19mS.

This is probably the most commonly used setup in the marketplace because it has a good balance of compromises. The steep subwoofer rollof allows a lot of flexibility in regard to it's placement, and most speakers have a poor phase-response anyway.

Perhaps we could improve the phase/group delay performance.

How about using 2nd order crossover at 80Hz. In other worlds, a sealed main enclosure with no high-pass filter, and a 2nd order lowpass filter on the subwoofer.

Uh-oh, very bad cancellation around 80 Hz due to the sub and mains being almost 180 degrees out of phase.

Lets invert the subwoofer in the above scenario, to put both the sub and mains back in phase.

Getting better, with phase still shifting through 315 degrees, group delay at 17mS, but the 12dB dip replaced with a 3 dB hump. That could be improved by reducing the sub gain by 3dB, and applying boost of 3 dB at 20 Hz .

Now, the optimum (theoretical) response. This is achieved by using no high-pass filter on the main (sealed) speakers, and a 1st order lowpass filter on the subwoofer.
The active subwoofer also has 2dB of gain applied. Reponse is +/- 0.75 dB, phase-shift an excellent 135 degrees, and group delay only 15mS.

There's always a catch though, and here the slow rolloff of the subwoofer means that 2 are preferred and placement is more critical to prevent localisation.

To increase power handling, I would like to protect my mains bass-mid driver a bit more by giving it a 1st order lowpass filter at 80Hz and see what happens (below).

Very bad dip. However, that can be corrected by overlapping the responses more.

Finally, what I think is the optimum compromise for frequency response, phase and group delay in a specific real-world situation.

It is achieved using 1st order lowpass on the subwoofer, subwoofer gain and overlapping the sub and main speaker responses.

The main speakers are sealed (with a -3dB at 65hz), and a further 6dB/octave filter is applied at 65Hz with a simple, series, line-level capacitor between pre & power amps.

The subwoofer has 2dB gain and a 1st order filter at 150Hz. Note: Due to baffle-step diffraction (i.e. 4 - 6dB rising output from 100-400Hz) , the actual filtering may be 12dB electrical to achieve an approximate 6dB acoustic lowpass response.

The result - response +/- 1dB, phase shift only 135 degrees and group delay below 15mS, almost identical to the "optimum" setup above.