Small sealed subs - harmonic distortion

[Brian Steele]

Hi Everyone:

I'm just wondering if anyone here has taken a closer look at harmonic distortion and the resulting effect on tonality that happens when you use a driver with high Vd in a small sealed enclosure as a subwoofer.

I've done some preliminary measurements of an old Shiva driver in a 1.1 cu.ft. sealed cabinet, and the results are pretty interesting. For example, at 30 Hz, 2nd HD is already over 25% at a drive level of 16.15V (coils in parallel). The Shiva is nowhere its rated Xmax at this point. I'm doing some other similar tests with another "high-excursion" 12" driver, and the results are looking quite similar.

This may be of interest to those who use or are considering using LR alignments to get the best from big drivers squeezed into small sealed cabinets. While the predicted F3 might look impressive, what about the HD?

[WmAx]

Hi Everyone:

I'm just wondering if anyone here has taken a closer look at harmonic distortion and the resulting effect on tonality that happens when you use a driver with high Vd in a small sealed enclosure as a subwoofer.

I've done some preliminary measurements of an old Shiva driver in a 1.1 cu.ft. sealed cabinet, and the results are pretty interesting. For example, at 30 Hz, 2nd HD is already over 25% at a drive level of 16.15V (coils in parallel). The Shiva is nowhere its rated Xmax at this point. I'm doing some other similar tests with another "high-excursion" 12" driver, and the results are looking quite similar.

This may be of interest to those who use or are considering using LR alignments to get the best from big drivers squeezed into small sealed cabinets. While the predicted F3 might look impressive, what about the HD?

Most woofers have **** poor motors. Linearity is non-existent after about 5mm one way on most. Then have the drivers with good linearity, but only at lmited excursions, which won't cut in the sealed application you are discussing. For example, the Dayton 12" RS has a 1st class motor in terms of linearity in conventional stroke range woofers. But it won't do much down low in a small sealed cabinet at all without high THD. The very few that can be used for any substantial LF SPL with very low distortion in small sealed boxes are rather costly. JL Audio W7 woofers work superbly in tiny cabinets like this whilst providing high SPL and extremely low THD. Some of the middle level to high level TC Sounds/Audio Pulse drivers will do as good or even better than the W7 drivers, if you get a depending on the specific TC motor you end up with. There a few more makes/models than can do it well, but they are far and few between. Some might chime in and claim the Shiva-X, as this is a new popular driver, and they may claim it do well - but I have not seen any measurements to confirm it really can provide the same level as say a JL W7 in your desired application. It would be pretty amazing if it could match the W7 in this application.

-Chris

[JRT]

Hi Everyone:

I'm just wondering if anyone here has taken a closer look at harmonic distortion and the resulting effect on tonality that happens when you use a driver with high Vd in a small sealed enclosure as a subwoofer.

I've done some preliminary measurements of an old Shiva driver in a 1.1 cu.ft. sealed cabinet, and the results are pretty interesting. For example, at 30 Hz, 2nd HD is already over 25% at a drive level of 16.15V (coils in parallel). The Shiva is nowhere its rated Xmax at this point. I'm doing some other similar tests with another "high-excursion" 12" driver, and the results are looking quite similar.

This may be of interest to those who use or are considering using LR alignments to get the best from big drivers squeezed into small sealed cabinets. While the predicted F3 might look impressive, what about the HD?

I'd leave the EQ out of consideration in this.

I think I recall you, I, and others talking about this years ago in reference to the example provided by Linkwitz's use of the Peerless 12" XLS 830500. Distortion was lower in open baffle dipole application (a Phoenix dipole woofer variant) than it was in his Thor sealed woofer application, the latter he added to his Orion because dipole is poorly suited to low freqs.

At the links below, note the increase in odd order distortion, especially 5th order, with the enclosed woofer in the meaurements taken with 30_Hz fundamental at 0.5" peak to peak excursion:
Phoenix--- http://www.linkwitzlab.com/woofer3.htm
Thor--- http://www.linkwitzlab.com/thor-measmt.htm

IB would be larger but would provide a more nearly constant spring rate from the enclosed air volume.

George Short's MAPD alignment might more advantageous, if suitable drivers are available. But it is going to take up more space, total net enclosed volume 4/3 Vas.

http://www.northcreekmusic.com/MAPD1.htm



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[Brian Steele]

At the links below, note the increase in odd order distortion, especially 5th order, with the enclosed woofer in the meaurements taken with 30_Hz fundamental at 0.5" peak to peak excursion:
Phoenix--- http://www.linkwitzlab.com/woofer3.htm
Thor--- http://www.linkwitzlab.com/thor-measmt.htm

Actually, I thought that the distortion caused by the use of a small sealed box should be more of the even order variety. It takes a bit more force to compress the air in the box (inward stroke) than to rarify it (outward stroke).

[billfitzmaurice]

Actually, I thought that the distortion caused by the use of a small sealed box should be more of the even order variety. It takes a bit more force to compress the air in the box (inward stroke) than to rarify it (outward stroke).

Harmonic distortion, ie., the creation of harmonics not present in the original signal, is closely related to excursion and sensitivity. The further the cone must move relative to a given SPL output the more distortion it will create. Since small sealed subs have a poor excursion versus SPL ratio they also have poor distortion characteristics. The worst distortion is found in small autosound subs, but since they are usually trunk mounted much of that distortion is effectively filtered out by the back seat, which lets the lows through but acoustically filters the harmonics.

[JRT]

Since small sealed subs have a poor excursion versus SPL ratio they also have poor distortion characteristics.

Not sure I buy into that, your implied assertion that the additional nonlinear distortion is tied closely to the increased current in the coil, the increased force. Something beyond that imposed by dynamic compression? What is the underlying cause, is there an increase in Le variation?

I can see an issue with the air spring, since [ delta volume / delta stroke ] is increased with smaller enclosed volumes, increases the variation in the spring constant of that air spring. And I would expect that increased intracycle variation of applied forces to increase nonlinear distortion.

Sorry if this comes off as too argumentative, I just want to better understand your thoughts in this.



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[JRT]

Actually, I thought that the distortion caused by the use of a small sealed box should be more of the even order variety. It takes a bit more force to compress the air in the box (inward stroke) than to rarify it (outward stroke).

I think what you describe is what is happening in larger sealed enclosures, where there is little variation in spring rate. The spring rate increases as the air is compressed, and the smaller the enclosure the bigger that variation in spring rate. I do not yet have clear understanding as to whether odd order or even order would be affected by that variation in spring rate, but in the example mentioned earlier (Linkwitz's Phoenix and Thor), odd orders (esp 5th) were increased by enclosing the Peerless 830500.



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[JRT]

in the example mentioned earlier (Linkwitz's Phoenix and Thor), odd orders (esp 5th) were increased by enclosing the Peerless 830500.

Taking a closer look, 4th order took a big jump also.

And thinking about this a little more, SL may not have used the same sample woofer in both tests, so perhaps comparisons are not all that valid.


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[djarchow]

Here is an example in the differences in distortion for the same driver going from a relativly small sealed enclosure (100 liters) to a 200 liter enclosure with passive radiators. Note the huge spike in distortion in both systems below the boz tuning (~27 Hz for the sealed and about 16 Hz for the 200l PR system.)

Please note that this sub uses the TC Sounds LMS-18, probably the lowest distortion subwoofer driver ever made.

Sealed 100 l http://www.hometheatershack.com/foru...0l-lt-new.html

Passive Radiator 200 l: http://www.hometheatershack.com/foru...-200l-new.html

Regards,

Dennis

[Brian Steele]

I do not yet have clear understanding as to whether odd order or even order would be affected by that variation in spring rate

As I understand it, any factor that affects one half of the waveform more than the other will tend to increase even order distortion.

It will be great if someone can try duplicating my test (not necessarily with a Shiva, but with another high-excursion driver mounted in a small sealed box). I'm making the assumption that my measuring equipment isn't adding gross amounts to the distortion, but who knows...


Method: Insert driver in box, make sure there are no air leaks, feed it a 30 Hz tone, and monitor its output with a mike (close-miked) and RTA at -70dB minimum (I used TrueRTA). Adjust the volume level until 3rd HD just registers at -70dB, and record input voltage, fundamental level and 2nd level at this point. Then, continue increasing the volume in 3dB increments of the fundamental, recording the input voltage to the speaker and the levels of 2nd and 3rd HD at each point. You can calculate the distortion level from the differences between the fundamental and the overtones - if you need the equation to do so, let me know.

[JRT]

Here is an example in the differences in distortion for the same driver going from a relativly small sealed enclosure (100 liters) to a 200 liter enclosure with passive radiators. Note the huge spike in distortion in both systems below the boz tuning (~27 Hz for the sealed and about 16 Hz for the 200l PR system.)

Please note that this sub uses the TC Sounds LMS-18, probably the lowest distortion subwoofer driver ever made.

Sealed 100 l http://www.hometheatershack.com/foru...0l-lt-new.html

Passive Radiator 200 l: http://www.hometheatershack.com/foru...-200l-new.html

Regards,

Dennis

It is not surprising that nonlinear distortion might increase toward the excursion extremes, at low frequencies.

But it is interesting how the PR loaded woofer exhibits increased nonlinear distortion well above tuning, 30_Hz - 50_Hz range at 105_dB.

I think the point Brian was pointing out in starting this thread was that a smaller enclosure increases distortion at the same excursion, same SPL and frequency.

[billfitzmaurice]

Not sure I buy into that, your implied assertion that the additional nonlinear distortion is tied closely to the increased current in the coil, the increased force.


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Most harmonic distortion is mechanically sourced, not electrically. If, using the same driver, cab A requires an excursion of 10mm at, for instance, 50 Hz to reach an SPL of 100dB, while cab B only requires 5mm excursion for the same SPL, then cab B will generate a far lower percentage level of harmonics of the 50 Hz tone.

[JRT]

Most harmonic distortion is mechanically sourced, not electrically. If, using the same driver, cab A requires an excursion of 10mm at, for instance, 50 Hz to reach an SPL of 100dB, while cab B only requires 5mm excursion for the same SPL, then cab B will generate a far lower percentage level of harmonics of the 50 Hz tone.

For the same driver in two different sized sealed enclosures, only difference being the enclosed air volume, SPL would be the same function of excursion and frequency. EQ'd to the same SPL output, RMS mechanical excursion would be the same, but the smaller enclosed air volume would impose a more varied spring rate from that air spring.



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[spasticteapot]

Hmm. I was thinking of building a small sealed sub, but now I'm worried that this is not such a good idea.

Perhaps a transmission line would be better? While a T-line is usually quite big, the fact that you can build them 12" wide, 12" deep, and 60" high means that they take up relatively little space in a small room.

[JRT]

Hmm. I was thinking of building a small sealed sub, but now I'm worried that this is not such a good idea.

Perhaps a transmission line would be better? While a T-line is usually quite big, the fact that you can build them 12" wide, 12" deep, and 60" high means that they take up relatively little space in a small room.

Its not wrong to use a sealed alignment. Smaller size comes with some tradeoffs. There is no free lunch.

The argument has come up in the past when someone advocated acoustic suspension, sealed with an enclosed air volume = ~1/3 Vas.




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[Brian Steele]

Hmm. I was thinking of building a small sealed sub, but now I'm worried that this is not such a good idea.

Perhaps a transmission line would be better? While a T-line is usually quite big, the fact that you can build them 12" wide, 12" deep, and 60" high means that they take up relatively little space in a small room.

I think you should be fine, once Vb isn't too small (I've seen 20*Vd mentioned as one rule of thumb for minimum box size - my test box is about double that size).

FWIW I went back and repeated my measurements, this time measuring the Shiva in free-air as well. For a given excursion, the even-order distortion was at almost the same as when it was mounted in the box. Grrrr....

In fact, I could visibly tell when the even-order distortion was going to rise significantly - the center position for the cone started creeping forward. Something I didn't notice when the driver was mounted in the box, as it's much easier to see if you're viewing the driver edge-on.

Odd-order distortion increased though, when the driver was mounted in the box. Around 6dB 3rd HD for example.

I should mention that this is an old driver, that used to be one of my car audio subs until my mechanic wrote the car off (hitting a tree head-on would do that), so what I'm measuring may not be a characteristic of Shivas in general. I intend to redo the same tests for the other driver this weekend.

[rone]

I'm just wondering if anyone here has taken a closer look at harmonic distortion and the resulting effect on tonality that happens when you use a driver with high Vd in a small sealed enclosure as a subwoofer.

John K wrote a spreadsheet.
http://www.musicanddesign.com/driver_box.html

regards,
Ron E

[Texan]

Thanks’ John & thanks for posting the link
This work book is very impressive. I have looked at John’s sight before but never noticed this.

[WmAx]

Hmm. I was thinking of building a small sealed sub, but now I'm worried that this is not such a good idea.

Perhaps a transmission line would be better? While a T-line is usually quite big, the fact that you can build them 12" wide, 12" deep, and 60" high means that they take up relatively little space in a small room.

I guess this depends on the driver you planned on using. Obviously a W7 works superbly, and with low distortion, in this capacity. But it was specifically designed for this application, and is costly. What reasonably priced driver will work well in this application?

-Chris

[Dennis H]

Most harmonic distortion is mechanically sourced, not electrically. If, using the same driver, cab A requires an excursion of 10mm at, for instance, 50 Hz to reach an SPL of 100dB, while cab B only requires 5mm excursion for the same SPL, then cab B will generate a far lower percentage level of harmonics of the 50 Hz tone.

If we're talking sealed boxes, not horns or ported boxes, SPL is ALWAYS a direct function of excursion. Power required, distortion, etc. may change with box size but not SPL/excursion.

About the (mostly 2nd order) distortion of a small box, the formula in one of SL's spreadsheets with some unit swapping is:

Box air-spring distortion % = 140 * (one-way driver swept volume) / (box volume)

Double the box size, air-spring distortion gets cut in half.