How can small low Xmax drivers produce bass at all?

[johninCR]

Out of curiosity I was plugging some of the smaller Fostex very low Xmax drivers into Linkwitz's SPLmax spreadsheet. The results show that drivers such as the FE126E with an Xmax of 0.35mm and the FE108EZ with an Xmax of 0.28mm can't break 90db at 300hz, much less 100hz or lower.

I've used these drivers and I know for a fact that these predicted results are not correct, but where is the error? Do these types of drivers have linear operation far past Xmax? Visaton, eg, claims linear operation for the B200 up to +/-3mm, yet the Xmax is only 2mm, as determined by the VC dimensions. How can we determine the true performance limitations of such drivers?

[pjanda1]

They are very dynamically limited. Horns help quite a lot. But this sort of thing puzzled me too.

I asked awhile ago what sorts of bass energy one could expect whith different types of prgram material at various listening levels. Nobody knew, and instead of doing a decent experiment, I played some various music at 90-95db A weighted at the listening seat (radio shack meter), and measured my drivers (8" with 2mm xmax) excursion in both sealed and vented enclosures. In sims, neither of my enclosures approaches 90db at 80hz without hitting xmax. However, with all of the program material I tried (everything from chamber music to rock), 95db in either enclosure didn't exceed .5mm of excursion (P-P) as measured at the whizzer edge with a ruler. On the contrary, an 80hz since wave at 90db get's 'em shakin'.

Outside of special effects (HT) there just isn't that much energy down there. Music is not linear. It's my opinion that the sims are telling the truth, but playing music and sine waves at 90db are completely different things.

Paul

[MJK]

John,

This is something I posted on the Madisound forum back in 2002 that attempted to explain why I am not that concerned about Xmax when music is being played.

OK, here is my explanation and thinking on Xmax.
Suppose I have a driver with an Xmax = 1 mm. I want to know what kind of input it can take at 20 Hz without exceeding this value. Lets assume that the standard Xmax plot, as a function of frequency from a T/S based computer simulation, shows that 1 watt of input will yield a displacement of 1 mm at 20 Hz. So 1 watt at 20 Hz corresponds to Xmax for a pure sine wave input signal.

Sinusoidal Input :
--------------------
If I excite this driver with a single frequency sine wave at 20 Hz so that the maximum displacement is 1 mm, then the maximum input power is 1 watt as shown in the computer simulation plot. The driver is limited to 1 watt of input at 20 Hz before Xmax is exceeded.

Square Wave Input :
-------------------------
If I excite the driver with a 20 Hz square wave that produces a displacement magnitude of 1 mm, then the input power at 20 Hz can be greater than 1 watt before Xmax is exceeded. Hopefully, the following over simplified derivation will adequately demonstate my reasoning.

Definition of a square wave at 20 Hz :
Time = 0.000 to 0.025 sec the magnitude is +1 mm
Time = 0.025+ to 0.050 sec the magnitude is -1 mm

Using the Fourier Series to represent this wave shape yields the following sine waves that are added to reconstruct the required square wave. Plase recognize that this is an infinite series and I am only showing the first 3 terms.

1st harmonic at 20 Hz = magnitude is 1.273 mm
2nd harmonic at 40 Hz = magnitude is 0.424 mm
3rd harmonic at 60 Hz = magnitude is 0.255 mm
.
.
.
.
Look at the magnitude of the first harmonic at 20 Hz, it exceeds Xmax. But the sum of all harmonics equals Xmax.

Conclusion :
--------------
If I have done my math correctly (maybe I screwed up and hopefully somebody can correct it NICELY!) then a 1 mm square wave would have a component that exceeds Xmax at 20 Hz. Recorded music is much more complicated then a simple square wave, it is made up of many different sine waves all adding together to generate displacement of a driver as a function of time. I do look at the driver displacement plot, calculated in my T/S based MathCad models, and track the input power that will cause Xmax to be exceeded, but I do not consider it to be a rigid limitation in a TL (or bass reflex) design.

In my audio system, I listen primarily to acoustic jazz. I do not use my speakers in a HT set-up and I only play the 1812 cannon shots when demonstrating my speakers to uninitiated guests needing a big "WOW!" to understand why I take building speakers so seriously.

I probably do not exceed Xmax at the listening levels typically being played. I can play loud enough to simulate the live event in the room and still allow my family to go about normal activities, like sleeping.

I am sure that I have exceeded Xmax on occasions and I have even managed to bottom out my 10" Focal woofers against the stops a couple of times during 1812 cannon shots. Got a big "WOW!" on those occasions. HT, or other types of music, may force a designer to stick closer to the Xmax specified if signals with strong low frequency content are commonly being reproduced (cannon shots, walking dinosaurs, helicoptors, ....). Each application is unique so you can decide how rigid a limit Xmax really is in your design.

One last thought, when using a bass reflex or a TL the situation with Xmax gets even better because the driver motion is significantly attenuated at the tuning frrequency. For an OB the situation is as described above. I have been running Fostex and Lowther full range drivers in ML style of enclosures for the past few years and have not had any real problems with a driver exceeding the 1 mm Xmax value specified by the manufacturer and producing audible problems or even worse damage to the driver.

Hope that helps,

Martin

[johninCR]

Paul,

I'm not really even thinking about bass. I see the little drivers exceeding Xmax with bass content in music. I'm talking about 200-300hz or more where the alignment isn't helping, and we're left with the driver only output. If my little 108's are Xmax limited to 84db at 300hz at 1m, how can I possibly play any semblence of good music from only a pair of them at 95db+ at my listening position? Yet I'm able to do so. We're looking at 1/4 the surface area and 1/7 the Xmax of your 8's.


Martin,

Thanks, I need let your explanation soak in.

[TerryO]

Just a quick note. The term Xmax has different interpretations. Some manufacturers spec Xmax as excursion in one direction only while others reference the total positive and negative throw of the driver. This can present problems when modelling, and for all I know, different software may assume one convention or the other. There needs to be one standard, everyone agrees on that, but yet................

Best Regards,
TerryO

[johninCR]

Terry,

I understand and agree. Just give us the VC and gap dimensions. That should be the standard. Still I'm talking about fractions of a MM, for what we commonly consider Xmax. I think Martin is on to something even though I don't fully understand what he's saying.

[Pit Hinder]

John,
xMax as calculated by pole piece / voice coil dimensions is a worst case scenario, assuming that magnetic energy is "chopped off" as soon as the vc starts to leave the air gap. Fact is, however, the magnetic field reaches further out and the vc still gets some shove - the decline is gradual, not sudden.

Pit

[pjanda1]

Originally posted by johninCR
Paul,

I'm not really even thinking about bass. I see the little drivers exceeding Xmax with bass content in music. I'm talking about 200-300hz or more where the alignment isn't helping, and we're left with the driver only output. If my little 108's are Xmax limited to 84db at 300hz at 1m, how can I possibly play any semblence of good music from only a pair of them at 95db+ at my listening position? Yet I'm able to do so. We're looking at 1/4 the surface area and 1/7 the Xmax of your 8's.

I just guess, Martin actually knows stuff.

Let's say I play whatever pitch has a fundamental of 300hz on my trombone (about an F?), and the SPL meter registered 95db. When I play that note, then second harmonic (600hz) is nearly as strong as the fundamental, and the third is a little less strong that the second. They'll trail off, but you could still measure the eight or ninth. All of them would sum to 95db. If you could isolate the 300hz fundamental, it would be well below 95db (if I'm right.) 300hz is awfully low for a trumpet, but at 600hz, there is a good chance the 3rd harmonic would be louder than the fundamental!

Now, to match the acoustic power of my trombone playing, you'd have to have some serious kit. The 108's wouldn't come close. But many speakers can sound something like hearing me from an orchestra hall balcony. I've got some little old fullrangers in an open back cabinet. They don't sound like an orchestra, but they get closer than I thought they would. My big speakers come pretty close in my not-too-large room.

My point is that music is not a sine wave, nor made of anything that looks like them.

Again, I might be absolutely full of it. I'm an M.M., not an E.E.

Paul

[Audio_idiot]

Hi,

I had build a BLH for my Coral Flat 6B. The Flat 6B's have small Xmax too. Yet, they actually produce bass.

From visual observasion, you hardly see any cone movement even the window is rattling...

Is this the result of the cone being "loaded" and "pressure on both sides of the cone being "equilised?

Cheers

A_I

[freddi]

even large drivers in direct radiator can have more excursion than I like and when reach say 4mm peak to peak can "gargle" with say sustained bass and flute passage. do some FR not gargle?

the reflex here is "equivalent" to the K15 sans front section and Z input looks similar other than K's 3rd z peak.