Miscellaneous Ramblings on Subwoofer Crossover Frequencies September, 2002 (updated May, 2004) Colin Miller and Brian Florian

 

Many die-hard conservative audiophiles at first eschewed the use of a subwoofer as a novelty trick of home theater, unsuitable for music reproduction.  As the frequency extension benefits of a dedicated subwoofer became more and more undeniable, many shifted to the policy of running every loudspeaker �full-range� with a �pure� signal, and then setting the subwoofer to simply �fill in� where the other speakers left off.  As knowledge moved on, the position has retreated to recommending lower crossover frequencies for larger, floor-standing loudspeakers, such as between 30-50Hz, as opposed to higher crossover frequencies in the 80-100 Hz range.

Higher crossover points for subwoofer integration, regardless of the range of your main or surround speakers, have some potential advantages. The higher the crossover frequency�

� With a greater range of the bass content handled by the subwoofer, a component with usually greater placement flexibility than the other speakers, such as in corners, out of corners, under coffee tables, or even right next to your �main� speakers, you may be able to get a better room lock over more of the low frequency range, where standing waves can be extremely problematic. In fact, Floyd E. Toole goes into this with great depth and clarity in his paper located at

www.harman.com/wp/pdf/Loudspeakers&RoomsPt3.pdf

If you haven�t read this already, you really should.

� Less output is demanded at the same SPL, both from the amplifiers driving the front and surround speakers, but also from the front and surround loudspeakers themselves, resulting in lower distortion, and less compression in the most audible spectrum, and greater dynamic range from the system. Subjectively speaking, the sound may become clearer, more open, and more realistic. This does assume that your subwoofer is similarly or more competent handling low frequency content than your other speakers, but if the sub�s truly a good�n, that�s pretty much a given.
(Side note: I noticed that according to Consumer�s Report�s latest issue, all subwoofers are pretty good, and that for a couple hundred bucks, you should be fine. I strongly disagree, as in my experience, although a subwoofer is the most cost-effective means to get your hands on the bottom octave, you should start your shopping at about three times that if you expect to get anything that even remotely qualifies as a subwoofer, as opposed to simply an extra woofer in another box.)

� �Faster� bass. I know that �fast� bass is an oxymoron, and if you really care about transient response, assuming a competent subwoofer design, you�re best off spending your energy addressing room interaction to obtain the flattest frequency response, and the transient response will follow. However, if you really want to nitpic, the fact is that aside from subwoofers that have peaky frequency responses themselves, and are doomed from the beginning, the greatest limitation of transient response is usually at the low-frequency limit of the subwoofer (and if it�s low enough so that you can�t hear it, who cares) and at the high-frequency limit, imposed by the low-pass crossover slope. Given any particular alignment (in the case of our THX spec, 4th order Linkwitz/Riley) the actual group delay imposed by the filter will be inversely proportional to the frequency at which the filter is implemented. I.e., the group delay for a 40 Hz crossover frequency will be twice that of an 80 Hz crossover frequency, and four times that of a 160 Hz crossover frequency.

� LFE Channel integrity.  When it comes to the "subwoofer jack" on the back of the surround sound decoder, most everyone assumes that bass is taken from channels set to "Small", combined with the LFE channel and bang, you have a subwoofer output.

In the majority of surround sound processors and receivers, FULL RANGE copies of all channels set to "Small" are combined together with the LFE channel, and the sum is low-passed.  Think about that.  Strictly speaking, any* such processor with a sub/sat crossover frequency set lower than 120 Hz is "discarding" the upper end of the LFE channel.  THX units are NOT exempt from this.  With the standard THX 80 Hz 4th order crossover, the top of the LFE channel gets chucked.

Don't panic. This has been going on since day one, and virtually nobody has noticed . . . with good reason. I've said many times before, and I will say it again:  THX did not pull their crossover out of thin air.  It is the product of much development, and, when used in concert with THX speakers (or others which exhibit the correct roll-off), represents the best overall compromise of minimizing localization, extending dynamic range, and as it turns out, minimizing LFE truncation.  When Dolby Digital was coming to the consumer marketplace, THX looked at an inordinate number of modern 5.1 soundtracks and guess what they found in the LFE channel:  not much at all in the region of 80 Hz - 120 Hz, making their original choice of 80Hz rather fortuitous.  Dolby Digital's LFE channel has a digital brick wall at 120 Hz, not a roll-off, so content creators almost always roll-off their stuff, usually somewhere around 80 Hz.  Therefore, chucking the top band of the LFE is no big deal but the argument here is that a standard SSP crossover set much lower than 80Hz or so may actually be costing you bass content.

� More consistent frequency response between channels. If the bass from all channels is routed to the subwoofer, the frequency response over the range that the subwoofer produces will be identical between channels. The greater the range of the subwoofer, the greater this benefit. In contrast, any low frequency information produced by separate loudspeakers will not only have different responses in the room due to different physical locations, but there will be cancellations between channels due to distance between them. For instance, the bass response of the right front loudspeaker may be different from the bass response of the left front loudspeaker, which will be dramatically different than the bass response from the left and right front channels combined, and very much NOT an average of the two, but a haphazard mix, most likely a boost at extremely low frequencies, and a dip at frequencies just slightly higher, such as a rise 20 Hz and below and a dip at 50 Hz for a pair of speakers separated by 10 feet.

As always in this ying and yang world, some downsides...

� As higher frequencies are more audible than lower frequencies (in the range of a potential subwoofer crossover) higher crossover frequencies put the crossover transition in a more audible position, so that the same degree of screw up in implementation will be easier to detect. If you don�t do it right, it�ll bite you. If you�re afraid or ambivalent about using an SPL meter to get an even channel balance between all loudspeakers, you may be best of keeping the crossover frequency at 50 Hz or lower, regardless of potential benefits of higher settings.

� Less �stereo� bass. This is far less valid a concern than most would think, but it may be a valid gripe IF you�ve got some media content with real �stereo� low frequency information, most likely phase difference between channels as opposed to level differences. However, unless a particular source was recorded with substantially spaced microphones (10-20 feet, for example) and the recording engineer actually took efforts to keep that low-frequency information discrete (not summed to a single channel, which is itself a common practice for low bass) all the way through the mixing, and then the mastering process, those phase differences will be lost, and simply result in amplitude changes. For the few recordings that may actually have directional low-frequency content, such as fringe audiophile labels like Chesky, you can conceivably benefit from �stereo� bass IF you put subwoofers or your full-range speakers on different sides of a large room, allowing the phase differences from different directions to lend a sense of space reflecting the size of the original venue, which may be of use if 1.) there was a real venue, meaning it wasn�t recorded in a recording studio, and 2.) the venue was large enough to benefit from a sense of space, for instance a large concert hall or cathedral. Then again, simply having the full extent of low frequency content, stereo or not, can impart much of the same sensation. For those of whom for which this rare scenario makes stereo bass worth it, the scenario of a subwoofer for each channel might be worthwhile, despite the inevitable, and in my opinion, more substantial drawbacks.

� Some subwoofers can�t cut a higher crossover frequency. While even large �full-range� speakers will usually perform substantially better when alleviated from low bass duty, some subwoofers aren�t suited to higher crossover frequencies, for two reasons.

1. Their crossovers (or the low-pass slopes in the surround processor or receiver) aren�t fast (sharp) enough in their transition. It�s not that 100 Hz is really that easy to localize, but that frequencies a bit above it are. Keep in mind that the shape of the low-pass filter is an issue, and in reality a curve which varies from crossover to crossover in how quickly it transitions from no slope to it�s steepest slope, the rate specified, such as 12 dB/octave or 24 dB/octave. Still, consider a theoretical impossibility, for the sake of illustration- the immediate crossover that goes from completely flat to a straight angle down exactly at the stated crossover frequency.

Take 400 Hz and 800 Hz tones as content to be filtered out by our subwoofer crossover as an example of localizable content. A crossover at 50 Hz, 12 dB/octave will be �
-12 dB @ 100 Hz
-24 dB @ 200 Hz
-36 dB @ 400 Hz
-48 dB @ 800 Hz

Contrast that with the same 12 dB/octave slope kicking in at 100 Hz, and you get�
-0 dB @ 100 Hz
-12 dB @ 200 Hz
-24 dB @ 400 Hz
-36 dB @ 800 Hz

In such a case, the 100 Hz crossover point is certainly worse than the 50 Hz crossover point, and very likely problematic.

On the other hand, consider a 24dB/octave crossover slope implemented at 100 Hz, and the results show�
-0 dB @ 100 Hz
-24 dB @ 200 Hz
-48 dB @ 400 Hz
-72 dB @ 800 Hz

As you can easily see, a subwoofer with a 12 dB/octave crossover would not be suitable for a remotely higher crossover frequency. However, that would not preclude 100 Hz as a crossover frequency, as the sharper filter slope that started at 100 Hz would have less content above 200 Hz than the first, shallower filter that started at 50 Hz.

2. Some subwoofers aren�t suitable for higher crossover frequencies because of distortion. Harmonic distortion components are multiples of the original content, be it an original fundamental or harmonic itself. For example, harmonic distortion of a 20 Hz tone will generate energy @ 40 Hz, 60 Hz, 80 Hz, 100 Hz, etc., usually with the lower components higher in amplitude in the case of loudspeakers. In fact, many less experienced listeners, even some experienced musicians, will actually PREFER the distorted low frequency reproduction, as it provides MORE low bass, with the added spectrum in the more audible range. It sounds louder, and richer. When these subwoofers are allowed to run at higher frequencies via higher crossover settings, their harmonic distortion components reach a higher spectrum as well. It�s not that they necessarily produce more distortion than at lower crossover settings, but that the distortion is easier to hear, and easier to locate, and unlike the original content that fed the subwoofer, impervious the attenuation by the crossover, as the distortion is generated after the filter circuit by the power amplifier or the driver itself. In such a case, many may blame the crossover frequency for the increased localization problem, when in fact it�s just making the distortion problem more obvious. While I mention this in the context of subwoofers that have problems with higher crossover points, for those looking for any measure of fidelity, I would go so far as to offer this as an indication of a subwoofer unsuitable for use, period.

Mixing high and low frequency crossovers in a multi-channel set up

Once you wrap your head around the fact that in most products you are setting a high-pass on each main channel and a single low-pass on the sub, the use of a different setting for each speaker (or pairs of speakers) no longer sounds like such a good idea (pun most definitely intended).  Lets take an extreme scenario, just to illustrate the point.

We set the high-pass on the main left and right to 35 Hz because we think its in the best interest of our massive tower speakers.  We set our center channel high-pass to 100 Hz because it isn't very big.  What is the subwoofer low-pass in the processor going to be?

If set at 35 Hz to complement the main speakers, the center channel signal will have a huge hole from 35 Hz - 100 Hz.  Whoa!  Lots of bass on that channel we don't want to miss out on.  So let's try setting the subwoofer low-pass to 100 Hz.  Oops!  Now we have IN-ROOM 6 dB too much from 35 Hz - 100 Hz on the main channels because BOTH the main speaker and the subwoofer are voicing it.  You CANNOT correct for this.  If you lower the subwoofer level, you lower it for everything, and now you don't have enough bass from the center channel.

By now some of you are thinking, "Why not low-pass a copy of each main channel at the various frequencies I want and sum that with the full LFE channel?".  Possible, yes, and if fact there are some SSP models which do this, but at a price: doing so inherently results in frequency response aberrations due to phase issues.  Bass is often common to the front three channels and even more often common between the LFE channel and the fronts.  Summing different low-passed copies of the same material would by definition result in a messy frequency response. Take the ubiquitous 4th order low pass as an example:  At the crossover frequency its phase has come around to 180deg, absolutely inverted (compared to material it is being summed with).  Granted the relative amplitude of that low pass at the crossover frequency is down 6dB but is still enough to create the aberration.

The THX design manual references the Dolby Digital licensing manual which mandates that the subwoofer output be arrived at the way it does for these reasons.  If there was a better way to do this, without adding a lot of cost and/or making the product overly complex, I think Dolby would tell us.

One alternative found in some decoders is to take a low-pass copy from the center (in our extreme example, at 100 Hz), add that to the front left/right and still high-pass those at 35 Hz, the balance going to the subwoofer (though you still waste 35 Hz - 120 Hz off the LFE channel).  This can be both good and bad, depending on the rest of the design:

- Unless proactively addressed, you can still have the phase issues described above.

- When mixing channels digitally, S/N is lost (approximately 6 dB when two channels are added for example), because after the summing, the combined level has to be attenuated to the original level.  Might not sound (pardon the pun) like much but its something a designer has to consider when weighing the pros and cons of doing something.

We acknowledge that a different crossover point for each speaker is a desirable thing from the point of view of real world acoustics and dynamics. The different positions of the speakers in the room virtually dictate it, and the various members of a mismatched speaker set will each have different points of intersection for increasing dynamic range and maximizing bass performance.  But without also having a selection of slopes in the SSP and some VERY expensive measuring equipment, one is likely to end up further behind than ahead.

If you want consistent bass response from each channel of your 5.1 system, in our opinion, you're best to set all speakers to "Small", set them all to the same crossover point, and set that point no lower than what you are comfortable throwing away from the LFE channel.  If your main left and right speakers are genuinely full range (be honest now!), then you are better off running them full range as opposed to high-passing them at a ridiculously low frequency.  Short of that, high passing floor-standing speakers at 70 Hz is not "wasting" them in any way shape or form and in fact will more than likely extend their dynamic range thanks to the relief they'll be getting from the high-pass.  Alternatively, setting center and surrounds as "Small", the mains as "Large", subwoofer as "None", and implementing an external two channel crossover to the subwoofer is a valid, and in some situations an advantageous way to go.

- Colin Miller & Brian Florian -

* there are a few units which add the LFE channel to subwoofer output without low-pass.  Electrical summing of low-passed and not low-passed material results in phase issues and so this method of handling the LFE channel is not advised.

 

Related to the article above, we recommend the following:
IEEE 1394	Nature of Equipment Reviews
The Digital Link	What we Hear
High Fidelity	Accuracy, Distortion, and the Audiophile

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