Acoustically small enclosure = harmonic distorion?

[Bill F.]

I've recently been mulling over two methodologies of bass reproduction: boxless dipole (which I have the pieces for and am going to build) and ELF (which I am designing a transducer for).

With both of these very different approaches in mind, I began wondering about something they share in common--the air they move.

I have heard it said that air, like any compressible medium, is single-ended. That is, its behavior under compression is different from its behavior when rarified.

Common sense has it that a good loudspeaker begins with a linear transducer whose suspension applies constant centering force against both directions of displacement in mirror-image fashion. I'm assuming that all conscientious transducer designers strive for this goal.

However, take that beautifully linear driver and mount it in a box. Now it's compressing and rarifying your room (very compliant, highly damping) on one side, and the enclosure volume (much less compliant, less damping) on the other. Now you've got a nonlinear sum of forces acting on your diaphragm over its excursion. Presto! You're creating even-order harmonic distortion.

For a given diaphragm displacement, the greater the difference between the compliance of your box and your room, the more pronounced the distortion. As I pondered ELF subwoofers, with their tiny, highly pressurized enclosures, this truth sent me off on a tangent to design a *nonlinear* suspension to compensate.

When you're designing a driver for a defined enclosure, it's probably possible to regain decent force symetry with good design. But what about all other OEM drivers, destined for enclosures unknown? It got me wondering if correction could also be applied to the audio signal.

Aside from intentional correction, either mechanical or electronic, it seems to me that only open-baffle dipole or large infinite baffle approaches avoid inherent harmonic distortion.

Your thoughts, flames?

Bill

 

[CHRIS8]

Though dipole/infinite baffle systems exhibit minimal signal overshoot(ringing) as compared to other alignments, and dipole woofers almost eliminate room modes, these are the only significant advantages. The same transient decay behaviour can be obtained in a sealed box with a LT circtuit also. IMO, the disadvantages to dipole/infinite baffle far outweigh the advantages. The reduced efficiency and considerable excursion rates required at low frequencies, causes severe non-linear(and hormonic) distortions unless you have very large, or many mulitple woofers. In this case, a servo feedback system can be implemented to somewhat increase linearity at higher excursions. Fortunately, most good woofers have very low distortions at moderate and low amplitudes. The phenomena that you describe about unequal damping on oppostie sides of cone, simply is not relevant to real world application. The resonated enclosure provides equal damping in both directions, it is an oscillator..not a rectifier . Also, how would you propose(if this was a real issue)providing a different level of damping in one direction as opposed to the other, as a property of the driver itself? The REAL issue is linear motor power and a stiff cone, if you want low distortion LF output. Most aspects of distortions can be easily analyzed with your favorite software package, using tone bursts and distortion:signal comparing. I recommend you perform some tests for yourself before you try to create a 'non-linaear' suspension.

-Chris

 

[Bill F.]

Thanks for the reply, Chris.

Though I haven't thought it completely through, I could buy your argument that the nonlinear damping characteristics of boxed vs. room air isn't important. What I was more concerned about, especially in long-excursion ELF alignments where Vd is a significant portion of Vb, was how the different compliances would affect inward excursion vs. outward.

Since room air contributes more damping than springiness, we'll discount it for a moment and just consider the enclosure air spring. Below FB (where ELFs live), the boxed air controls diaphragm motion by its springiness, not its mass. At very low frequency, the diaphragm's inward stroke compresses the enclosed volume and sees counterforce that rises geometrically with excursion, right? On its outward journey, the diaphragm rarifies the enclosed volume. Trouble is, rarification doesn't cause geometrically rising counterforce. The force curve rate starts steep and then tapers. Playing a sine wave, the net result would be a forward displacement of the excursion midpoint, right? So, in that way, I guess you could say the driver self-corrects for the nonlinear forces by effectively loading its suspension to compensate. Of course, the resultant shrinking of Xmax isn't good. That's why I was wondering if boosting the negative portion of the wavform a tad would be a good thing. Like I said, I really haven't thought it all through yet. I appreciate any correction.

Regarding IBs, they are actually VERY efficient at very low frequency since their Fs is essentially their Fb. and their air load is very compliant. Just a few watts can drive them to full excursion, ergo their reduced power handling.

As to dipole woofers, you're right about the inefficiency. That's why I'm building mine with 4 15s per channel in a folded baffle.

Bill

 

[CHRIS8]

Sorry, I was not considering ELF alignments. Maybe you do have valid reason to be concerned, maybe not. I have not tested and/or analyzed behaviour on ELF alignments. Primarily due to my distinterest in them because of severe inefficiency, and high non-linear distortions at higher ampliltudes, at least with almost any existing woofer available. Again, I would first perform analysis of a converntional woofer in an ELF before offering any suggestions on this issue. Thus, I certainly can not help with ELF issues.

-Chris

 

[Bill F.]

ELF alignments, especially extreme ones like Bob Carver's "True Subwoofer" place harsh demands on the driver (giant Xmax, power handling, and motor strength, low Fs). I hardly know of any available raw driver that would be up to the challenge. Stress almost any driver like that and you end up with bad distortion and, pretty soon, smoke.

Your comment about low efficiency brings up an interesting point. If you T/S model an ELF, the highly rolled-off response curve looks quite discouraging, calling for up to maybe 12 or 15dB of boost to restore a low flat response. For any kind of SPL, this directly equates to kilowatts.

As stressful as those numbers sound for the driver/amp, there is a sort of loophole, if you maximize back-EMF and make the highest demands of the sub at/near its resonance impedance peak. Check out Bob Carver's True Sub whitepaper. http://www.nortek.net/learning_center/audio-video/sunfire_sunwoofer_white_paper.htm
He basically maximizes the motor strength and the avg. VC velocity to induce the highest back-EMF he can. This creates a high impedence for a portion of the waveform, effectively resting the amp/VC at low current throughput during moments of high VC velocity. That's how he gets away with a 2,700-watt amplifer "the size of a large candybar." The high number speaks to the amp's instantaneous voltage/current capability through the driver's Re, not what it can sustain. The truth becomes clear when he mentions that the amp pulls its 115 AC volts of wall power through a 6A fuse. That's only 690 watts, max.

Operating the driver motor at high velocity as far from stall mode as possible basically creates a voltage-drive situation that is much less stressfull on the amp/VC. It also results in large efficiency dividends. He claims a 115dB warble tone centered on 28Hz draws only 360 watts from the wall. I read a review of this sub in which the reviewers tried to blow the fuse with loud sub-bass sine waves. The fuse held until they turned up the frequency, thus moving the sub out of its band of efficiency.

With these thoughts in mind, I have been doodling on an extreme ELF system for large-venue sub bass (<50Hz). I envision dual concentric motors driving 24" diaphragms in a force-cancelling bipole config.

To maximize avg. VC velocity, I hope to attain a relatively linear (2-way) excursion of 6 inches or so. Pretty extreme, I know. To this end, I spec 2.5" deep NdFeB magnetic gaps in circuits similar to Aura's 18-8 NRT motor, only larger diameter, of course. To get 6" of excursion from 2.5" of gap height, I plan to use three evenly-spaced underhung voice coils. As excursion causes the middle coil to exit the magnetic gap, an outer coil enters the gap. A positional sensor within the driver triggers amp output to hop from inner to outer coil, and excursion continues until the outer coil begins to exit the gap. Suspension will be spiderless, a combination of linear bearing, air bag, and air spring of the enclosed volume. Displacement should be around 3 cubic feet per cycle--roughly equivalent to 40 typical 15" drivers. All this in a tidy roll-away <3-foot cube.

In case you're wondering, no, I haven't built it yet! The Devil is hiding in the details, I'm sure.

Bill

 

[CHRIS8]

Thank you very much for that link. I had not before read that white paper. It was extremely interesting! Sheds a new light on old technology.

As for ELF alignments, still too inefficient IMO, considering the potentail efficiency of any given driver. That was not an ELF alignment, but a PR. Not wasteful.

-Chris

 

[dice45]

Bill,

1st, what is an ELF alignemnt subwoofer?

2nd,
methinks your considerations about nonlinear sum of forces acting on the diaphragm over its excursion are intriguing and quite an eye opener to me concerning listening experiences with open baffle speakers in general and woofers in particular.

I am not on your theoretical levels with speakers, folks, i just can contribute some fresh practical experineces.
Since a few days my Fertins are running and before I made long-term listening tests with both unequalized and equalized woofers used as fullrange speakers (to try out whether i am compatible to this sort of sound .. .. yes, i am!!)
With each speaker i subjectively experienced a detail resolution and tone colour saturation in the low end which was only avaiable in the the mid and treble range before. I never was coming close to this level of resolution this with a conventional vented or closed woofer.
And the Fertin beats every other speaker driver in that respect, even the Altec 414.

True, it was preliminary and not designed thru and most of the time i was listening to unequalized speakers. True, one always gets fantastic low end resolution with brick-size 2-way speakers as room resonances are not that much excited as with adult speakers.

I feel right on my way using the Fertin as open baffle fullrange speaker from 100Hz to 20kHz and to have a pair of 18" Beyma paper cone woofers mounted in a size-minmized folded open baflle and equalized to run linearly from 20Hz to 100Hz and then drop out. Considering i use 2x 100dB/W/m woofers per channel, i should get along with 100W of amplifier power output even if EQ is taken into account.

Very pleased to read that dipole woofers do not tend to excite room resonances that ecstatically , so atleast a considerable fraction of that fancy low end resolution should be maintainable.

Don't want to crusade, folks, but from what my ears tell so far, i feel urged to recommend open baffle subwoofers.

I keep you informed how my open baffle subwoofer merges with room and open baffle fullrange speaker as soon as i have the thing up and running.

 

[CHRIS8]

1st, what is an ELF alignemnt subwoofer?

Sure, I'm not Bill...but i am BORED, so I'll answer your questions whether you want me to or not.

An ELF (Extended Low Frequency?)design is somwehat similar to a Linkitiz Transform alignment. An ELF alignment tunes the box resonance completely above the bandwidth the woofer will be reproducing. Now, an EQ boost curve is applied at signal level to achieve whatever response you wish. Since below resonance the box no longer acts as a resonator, you have low effieciency..typically requiring massive excursion capability and power handling from the woofer to achieve the same outupt as a low powered standard resonant alignment. Transient decay response(ringing/overshoot) is controlled by the slope of low frequency cutoff you specify in the EQ. So if the woofer has the excursion/power ability, a transient perfect response is easily possible in a very tiny box. However, you will never acheive the SPL levels possible with the same woofer in a traditional resonant alignment.



With each speaker i subjectively experienced a detail resolution and tone colour saturation in the low end which was only avaiable in the the mid and treble range before. I never was coming close to this level of resolution this with a conventional vented or closed woofer.

Purely a function of environment. The ONLY actual output difference from a box implementing a resonator to gain efficiency, is very slight(INAUDIBLE) group delay(s) approaching resonance(s) and a minor transient decay overshoot. Of course, in MOST eviroments not implementing significant bass correction treatments, a dipole woofer will sound better...but only because of fewer excited room modes.

i feel urged to recommend open baffle subwoofers.

I ALMOST feel urged to use them. However I do not wish to sacrifice the space for enough of them to compensate for their deficiency. Bass traps for Chris.

I keep you informed how my open baffle subwoofer merges with room and open baffle fullrange speaker as soon as i have the thing up and running.

Please do. I like to read about personal experiences. Also, be sure to describe the room and positioning.

-Chris

 

[CHRIS8]

Bill...

If you are planning on developing driver similar to Carver's, then why use an ELF alignment? That design uses a resonant system, thus no potentail pressurization/rarification issues are at hand. The compliance and q of the driver is so low, providing for such a small box, that an ELF would seem to be actually be counterproductive. A 4th order alignment, or 2nd order with LT circuit would seem the best solution IMO.

-Chris

 

[GRollins]

I haven't read all of the above in detail, as I'm short on time. With luck, I'll have time to go back over it later.
Assume that you have a cone approaching Xmax in the forward direction, i.e. the pressure in the cabinet (I'm assuming sealed) is decreasing. The rarefaction in the cabinet acts as a braking force on the cone.
Assume that the cone is approaching Xmax in the rear direction, traveling into the cabinet and pressure is increasing. The back pressure acts as a braking force on the cone.
I'm not sure I see where the asymmetry is. Air is asymmetric in the sense that you cannot go below 0 PSI, yet you can compress to many, many PSI, but I don't know that the pressure/rarefaction in a speaker cabinet is extreme enough to make this a large effect.
If you feel that there is a sufficient discrepancy to be worth working with, incorporate a NFB loop to include the driver. This will take care of any and all nonlinearities, regardless of origin.
I'll try to slay a dragon or two (I'm at work) and get back to this with more time later. Perhaps I missed the thrust of the argument.

Grey

 

[Bill F.]

Chris,

Just to clarify my terms, I think of all subs whose passband is below Fb as ELF alignments, 4th-order resonant or not. Maybe the definition of ELF is strictly sealed, I don't know. Let me know if I need to correct my terminology.

There's plenty of attraction to Carver's PR design. What worries me is that the quasi-opposed motion of the two diaphragms doesn't cancel all the net force on the cabinet, as he admits in the FAQ. With the extreme excursion numbers I'd like to see, bad vibration could result unless there is balanced bipolar movement. I'm counting on the underhung switched coils to add efficiency and the huge back EMF and 1/3 duty cycle per coil to increase power handling.

Grey,

All I am pointing out is that for a given box volume, static counterforce on a low-frequency diaphragm at, say, 1" incursion will be higher than the counterforce on the same diaphragm at 1" excursion. This is because the compressibility graph of air is not a line, it is a curve tending toward vacuum at one end (1 atm. or 14.7 psi of return pressure on our hypothetical diaphragm) and infinite pressure at the other (infinite counterforce). The compressibility curve's rate of change for a given diaphragm displacement increases as Vb decreases.

It seems to me that this nonlinearity is inherent to any closed baffle alignment, except where room volume = enclosure volume, i.e, an infinite baffle. (It just occured to me that horns might be less effected as well.) Granted, it's manifestation would be small in alignments where Vd is minor compared to Vb (and at higher altitudes ). That's why I'm really just worried about it in connection with my extreme excursion ELF idea. Feedback would help, I'm sure. I was wondering if the dynamics were predictable enough to simply correct for it on the signal level.

Does it make sense to you as it does to me that the net effect of this nonlinearity would be a forward displacement of the diaphragm's excursion midpoint? Maybe such a phenomenon is already well known, I don't know.

By the way, my concept of a feedback-triggered coil-hopping amp isn't too far fetched, is it? It's something I've been thinking about for autosound SPL, etc. For slightly less extreme two-coil permutations, I also was thinking of a class B amp with two half-wave outputs.

Bill

 

[GRollins]

Warning: Unorthodox idea...
Use a small DC offset to push the voice coil off center, thus pre-loading the suspension.

Grey

 

[CHRIS8]

Bill:

Yes, an ELF is an alignment that operates below a resonant system. However, Carver's design is not an ELF, as I can tell from the white paper you specified. Accordingly, the passive driver would NOT work in an opposing direction to the active, if it was operated under resonace. Below resonance, behaviour changes on a spring and it moves with the source of energy, not in opposition. It appears this is simply a very low Q, low compliance woofer with extraordinary excursion capabality. Becuase of the low compliance, a very small box is possible, and with Carver's method for efficiently operating the woofer motor, it is now a practical design. Since you goal is to create a similar woofer operating principle for a woofer anyways, simply implement the same low compliance characteristics.

GRollins:

It seems that IF their is significant effect below resonance, as Bill suggests, then this would need to be accounted for in proportion to the input signal, and calibrated to the actual physical excursion of the woofer since the compression/rarefication effects are logarithmic, as actual incursion/excursion is increased. A static DC offest would not be effective, or at least it would seem from my perspective.

-Chris