Why does enclosure volume determine distortion for low frequencies?

[lowerFE]

If we look at the CEA-2010 burst output of the various DIY 18'' in the 4 cu ft box, we see that below 25Hz, all of the high end drivers produce almost exactly the same output. 108-109dB is the maximum for 20Hz, 101-102dB for 16Hz, 95-96dB for 12.5Hz, 90-92dB for 10Hz.

 

What's particular is the 10 and 12.5Hz numbers. All drivers aren't even close to their Xmax at those output numbers. But, by 40Hz most woofers are capable of exceeding their Xmax and still pass the THD thresholds. 

 

Earlier I cited a possible reason from a book stating significant distortion arises from more than 5% compression of air. However, this doesn't hold as several subs are compressing air close to 10% during burst output at "higher" frequencies such as 31.5Hz or 40Hz and still putting out minimal THD.

 

What do you gents think is the reason for this lower limit on distortion at very low frequencies?

[shadyJ]

It is not all distortion from just the subwoofer. The CEA-2010 software consider any noise not part of the original signal distortion, and remember that distortion is being reported here as a percentage. It can be difficult to get a passing reading at 10 hz and 12.5 Hz, because the subwoofer has to have a strong enough fundamental to raise the thresholds above the noise floor, but not be pushed too hard that it exceeds the distortion thresholds itself. The fundamental has to be 40 dB above the noise floor for a passing measurement, and consider that on a quiet day in a nice neighborhood the noise floor can still hover around 50 dB or so. 

[Mfusick]

When a motor in a sub is used the force or control it has on the cone diminishes the farther away from dead center because the magnetic force is weaker farther away and stronger closer.

 

That's why distortion shoots up when you push a driver.

 

Some motors like LMS have some advantages over a more traditional motor but generally all subwoofers will exhibit and increase in distortion as output is expanded or frequency lowers its just kind of how it is. Many sub makers have battled these realities so if you can solve it you can make some cash

[Funk Audio]

It is not all distortion from just the subwoofer. The CEA-2010 software consider any noise not part of the original signal distortion, and remember that distortion is being reported here as a percentage. It can be difficult to get a passing reading at 10 hz and 12.5 Hz, because the subwoofer has to have a strong enough fundamental to raise the thresholds above the noise floor, but not be pushed too hard that it exceeds the distortion thresholds itself. The fundamental has to be 40 dB above the noise floor for a passing measurement, and consider that on a quiet day in a nice neighborhood the noise floor can still hover around 50 dB or so. 

And once you get some room gain helping out even with systems that have a large difference in output between "max pass" and "No THD limit" you can often get much closer to the "no THD limit" output from the sub while passing, the SB13 ultra is a good example, in ground plane it had nearly 6db more output at 10hz than its passing level, but in Josh's room it got within a db of the "no limit" level and passed in room, and even the "no limit" output TDH was massively lower. Because the room boosts the low end fundamentals more than the harmonics. Everyone's room will be different though.

[Ricci]

I'm not sure I put too much stock into air spring distortion. By that I don't mean that it doesn't exist but it doesn't seem to be a very big factor when compared against the general suspension and motor distortion in the driver itself and mechanical operation noises when a driver is pushed hard. ASD causes primarily 2nd harmonic THD according to the equation. The general question is why do larger boxes have less distortion in the deep bass and in that case one component even if perhaps relatively small is ASD.

 

Another factor is that in a smaller air volume general low frequency efficiency is decreased and the impedance peaks(areas of high efficiency) will be shifted up higher in frequency. This requires more current and power be put into the voice coil to produce the same low frequency output as the larger system. There are distortions that occur in the coil/motor systems that increase as the current through the system becomes larger.

 

Also there is the natural response shape of the system. If the output at 10Hz is down 18dB compared to 30Hz with the same voltage input and the impedance peak (maximum efficiency) of the system is also near 30Hz, the system naturally gravitates towards producing 30Hz much more than 10Hz and any 3rd harmonic of 10Hz is amplified by the systems natural response at 30hz.

 

The larger airspace has less ASD, has greater low end efficiency relative to the systems maximum efficiency and requires less current or power for the same output, the area of maximum efficiency drops to a lower frequency also. Add all of those factors up and the result is a drop in overall THD at low frequencies. Which of these is the biggest factor is a good question but I believe that they are all inter related to some extent.

 

Generally sealed systems that do not produce a passing result at 10Hz or 12.5Hz cannot get above the background noise floor while also having passing 3rd harmonic distortion. IOW the output is very low and THD is high. The sealed systems I've tested are nearly always limited by 3rd order distortion at the 10 and 12.5Hz bands. Drivers which have stronger motors and thus a much lower system qtc in the standard sealed cabs generally have less distortion in the deep bass.

 

A good point was made about in room versus outdoor GP. Low frequency reinforcement in room dramatically lowers overall deep bass THD in every room or vehicle I've ever measured in. What is 40% outdoors GP may turn into 10% in room quite easily. Other frequencies that may be very clean naturally outdoors may be reinforced badly by a room resonance and increase the THD of a certain harmonic or multiple ones by a large amount. Usually these are more narrowband.

[SME]

What do you gents think is the reason for this lower limit on distortion at very low frequencies?

 

There are a few reasons, but I believe the primary reason is the difference in response at the fundamental frequency vs. harmonics of the driver's output to motor force when measuring the lowest frequencies.

 

It's helpful to think about how this works by analogy to a signal chain.  If a component of your signal chain introduces harmonic distortion, then the harmonics will be passed down along with the signal to each successive component in the chain.  Any signal shaping done downstream will alter the level of fundamental disproportionately to the harmonics.

 

You can think of the driver itself contributing a few more "components" to this signal chain:  A fluctuating voltage signal from the amp is transformed to a fluctuating current signal in the coil, I=V/Z where Z is the impedance.  The current signal is transformed to a fluctuating motor force on the cone, F = BL*I.  The motor force, in turn, is further transformed into actual driver output (equation omitted here as it is more complicated).  A lot of signal shaping is happening in this last transformation.  It is where the 12 dB/octave roll-off, observed in all sealed systems if you play low enough, is introduced.

 

For the lowest frequencies in the CEA testing, the response of output vs. motor force is greatly diminished for the fundamental compared to the harmonics, so any distortion introduced in the transformation of current to motor force will be amplified relative to the fundamental.  At resonance, on the other hand, the driver output is *very sensitive* to motor force because of the energy storing property of the mechanical system, so the opposite scenario occurs in which the response of driver output to motor force suppresses the harmonics relative to the fundamental.  Many drivers can be driven well past Xmax at resonance while keeping measured distortion low, because of this.

 

To minimize distortion in the lowest frequencies in a sealed box, you want a balance of low in-box resonance frequency (Fb) and low Qtc.  A lower Fb lowers the frequency where the transition in response from flat to 12 dB/octave is centered.  A low Qtc broadens the transition region.  Decreasing either Fb or Qtc alone generally raises the response of low frequencies relative to higher frequencies.  Unfortunately, small boxes are the enemy of both Fb and Qtc.  Additional mass on the woofer can lower Fb for a given box size, but it will increase Qtc.  Thus, adding mass is mostly a wash with regard to improving low frequency distortion performance of a driver.  The one thing that does help, other than just having a driver with very low distortion to begin with, is more BL.  With more BL, you decrease Qtc without changing Fb.  The greater BL also improves efficiency, which in turn reduces amp power requirements and distortion due to flux modulation.  So more BL a double win for low distortion of ultra low frequencies in small boxes because it helps to both reduce distortion in the transformation of current to motor force and it reduces the relative amplification of that distortion in the process of transforming motor force to driver output.  Note that BL influences the latter transformation as well because of its influence on back EMF.

 

You can extend the signal chain analogy just a bit further by treating the listening room as the final "component" in the chain.  For outdoor measurements, the response of the "room component" is essentially flat, but in a more typical listening room, there is room gain that increases the level of very low frequencies relative to higher frequencies.  The room gain effect may counteract much of the distortion amplification that occurs in the transformation of motor force to driver output, but the effect is more variable, both between different frequencies and between different rooms.  There may be some frequencies whose third harmonic coincides with a strong room mode, and it's not unusual to see a strong distortion peak in the in-room measurements at that frequency.

[Ricci]

All of the above is what makes me curious about the M-Force system despite relatively modest displacement relative to the huge cone size. They offer a 30" cone with  effective Qts below 0.17 and normalized motor force of 2200-3000. Not to mention the DPC feedback circuit which is also said to help with THD and signal tracking. It all points to an extremely over damped, high efficiency, low distortion, feedback controlled system which should be brutally loud as well. I really want to hear someone's finished product variation on it in an outdoor setting even if it only gets down to 25Hz.

[MemX]

 

The one thing that does help, other than just having a driver with very low distortion to begin with, is more BL.  With more BL, you decrease Qtc without changing Fb.  The greater BL also improves efficiency, which in turn reduces amp power requirements and distortion due to flux modulation.  So more BL a double win for low distortion of ultra low frequencies in small boxes because it helps to both reduce distortion in the transformation of current to motor force and it reduces the relative amplification of that distortion in the process of transforming motor force to driver output.  Note that BL influences the latter transformation as well because of its influence on back EMF.

.

 

Am I correct in thinking that the strong (and flat) BL curve of the LMS Ultra (I think that's the name?  The discontinued expensive ones!) is therefore the reason why it is lauded as being a very 'clean' driver?

[SME]

Am I correct in thinking that the strong (and flat) BL curve of the LMS Ultra (I think that's the name?  The discontinued expensive ones!) is therefore the reason why it is lauded as being a very 'clean' driver?

 

Probably.  The LMS Ultra had extraordinarily linear motor and suspension.  The trouble is that it didn't adequately restrain the driver and so was very easy to damage by over-driving it.

[Kyle]

All of the above is what makes me curious about the M-Force system despite relatively modest displacement relative to the huge cone size. They offer a 30" cone with  effective Qts below 0.17 and normalized motor force of 2200-3000. Not to mention the DPC feedback circuit which is also said to help with THD and signal tracking. It all points to an extremely over damped, high efficiency, low distortion, feedback controlled system which should be brutally loud as well. I really want to hear someone's finished product variation on it in an outdoor setting even if it only gets down to 25Hz.

 

That's a super powerful motor. I did a fair bit  of moving magnet chasing a number of years ago. Nothing really worked that well due to friction so I'm really curious how M-Force works in practical  applications. 

[Ricci]

That's a super powerful motor. I did a fair bit  of moving magnet chasing a number of years ago. Nothing really worked that well due to friction so I'm really curious how M-Force works in practical  applications. 

 

 

Friction? As in actual material on material contact?

The magnet assembly cannot physically contact the coil assembly in their design.  

[Kyle]

Friction? As in actual material on material contact?

The magnet assembly cannot physically contact the coil assembly in their design.  

 

Yep! that's probably why this design is a lot better