So What’s the Deal with Xmax?

Posted In: Subwoofers 101

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    stryke on #230

    The first part of this is really Xmax History 101, so feel free to skip the first 4 paragraphs if you want. 🙂 Back in the mid 90’s when I first got into the DIY audio thing, Xmax wasn’t nearly what it is today. I was on this somewhat well known email list with something like 1800 other people called the “bass list.” At that time the champion of all Xmax was the NHT1259. It was the greatest driver ever and I believe it had 11mm Xmax. Shortly after that the ACI DV12 came out with 12mm Xmax and became the new champion. Then Dan Wiggins decided to go for even more and the Shiva came out with I believe 15mm Xmax at that time. But something changed. People stopped using just the physical overhang to rate Xmax. DUMAX came out with the .707x the rest BL value to rate Xmax. This is when I started playing around with drivers as well as Nick at Lambda Acoustics.

    We found that you could take a driver with the same physical overhang, say 14mm overhang, but vary the top plate thickness and get different results. For example a 10mm gap with a 38mm coil has 14mm overhang but acts totally differently from an 18mm gap plate with a 46mm coil. Both have 14mm overhang, but the BL curves are totally different and you have much more usable excursion on the driver with the thicker top plate. Likewise, taking a driver with the same 38mm coil and using the two different 18mm and 10mm mm gaps gives nearly the same results. Going by traditional standards of just coil length minus gap and divide by two, you’d think that one would have 14mm and the other 10mm, but in reality they are very similar with the edge actually going to the shorter overhang driver in terms of usable excursion. This is about the time people started throwing out the generally accepted ideas on Xmax and started investing more time and money in FEA analysis and real world testing.

    The Xmax race as I remember it was on. TC sounds came out with their 3HP motor after a lot of FEA work. It had a 1.4″ gap plate with a 2.3″ long coil. By traditional standards the overhang was only 12mm, but by DUMAX results based on the BL curve Xmax was in the range of 23-27mm. This extremely tall gap really changed the way people looked at Xmax. Our HE15 was based on this design with 27mm. We were for a short time the Xmax champions… but it only lasted a few months.

    Dan Wiggins came out with the XBL^2 motor topology that would again totally change the way people look at Xmax. There was no simple formula to give Xmax as the coil essentially traveled back and forth between multiple gaps while creating linear force on the coil over a longer range. They achieved Xmax in the 30mm+ range and no longer was the motor design the limiting factor. Now the physical clearances in the frame and suspension parts became the limits. Things were never the same again.

    So that all said, what does Xmax really mean? It’s a good way to tell how much range of the driver is really useful while keeping distortion inaudible. In speakers, the low end limit for being able to notice distortion is considered to be about 10%. In reality most people can’t hear distortion and notice the audibility up until way over 25% even. That seems high, but while at Michigan Tech, the regional AES vice president, Tom Nousaine, came and did a discussion on distortion. Nut just subwoofer distortion, but distortion full range. He played a track of Tom’s Diner by Suzanne Vega. This was a blind listening test where the track was played over and over again with progressive amounts of distortion added. The trick was to say when you could hear audible distortion, but we didn’t know the amounts until later. In a room of about 20 people, all audio geek AES members, we all sat and listened and would say “ok, the 4th time i could hear it”. It turned out that only a couple in the room claimed to hear distortion at the point where 10% was added. Most claimed at 25-50% distortion.

    This means that if distortion isn’t audible until 10% we can use the driver up until 10% distortion and it will sound clean. Therefore taking the point at which Bl drops to 70% of it’s rest value is usually considered the point where the motor will cause the driver to reach 10% distortion and the reason that point is chosen for Xmax ratings.

    However, the motor isn’t the only thing that causes distortion. Parts physically making noise during their motion, resonances in parts, power compression, etc can all cause distortion to rise over 10% well before the motor is the limit. Klippel had all kinds of other standards to simply measure 10% distortion points. In many cases this would correlate quite well to the 70% Bl mark, but some drivers would hit 10% distortion above and below that point. IMO this is the best way to truly rate a driver by looking at all the factors that contribute to distortion and seeing which brings it to an audible point first, then rating Xmax based on that point. Not everyone has money for a Klippel though 🙁

    That all said, how much Xmax is enough? It really depends on so many factors. The largest being the enclosure. You can take a driver with a given Xmax and have it reach that point with 100W or need 1000W depending on which enclosure you put it in. In a sealed enclosure, Xmax is more easy to compare. You also need to factor in the Sd of the driver though. Your maximum output is directly equal to how much air you can move before you reach 10% distortion. The more air you move, the louder you can play. How loud you play at any given point is determined by this formula:

    SPL = 20 * Log (Vd * F^2) + 48.4

    Vd in liters being calculated from Sd x Xmax

    This doesn’t tell you how much power you need to reach that level. It just tells you that if you can move the driver a certain range at 10% distortion, it will result in that SPL. The more Xmax the better, but at some point you become impractical as you need unrealistic amounts of power to reach that distance. That is when it becomes more practical to use multiple drivers, each only having to move shorter distances with less power.

    In vented enclosures it’s harder to compare. The driver has to move less as the port is creating the majority of output around tuning. The point then is that you need to further excite the resonance of the port, and the motor strength of the driver becomes more important at that point than the long travel. However, as you do now have other issues like group delay to contribute to “distortion” of the system, you want the driver operating in an even more linear range. You also still have the driver excursion peak above resonance to deal with, but as others said, with smaller enclosures you typically hit thermal limits before excursion limits. That is a whole different writeup to get to though….


    killjoy on #3099

    So, based on your explanation of xmax and large gap heights it would seem that guitar speakers with average overhang lengths of .8mm would display greater xmax than calculated based simply on the voicecoil length overhang. If this is correct then would the fact that the pole piece ends at the same height as the top plate affect the useable xmax? Would they require an extended pole piece as shown in the Lambda to have the same benefits in xmax as you discuss below? Basically would you explain if your explanation below would apply to guitar speakers–always wondered how a speaker with such a short overhang can have as wide a frequency response as it does.

    simon5 on #3100

    Guitar speakers are usually large (15″ or so), light cone, sensitive, efficient and wideband drivers, with very poor low frequency response, which is very good for a guitar, because a guitar doesn’t need low frequency response, but preferably need all the rest. 1 mm Xmax is plenty, but yes if you Klippel test it, it may show more measured Xmax. Only low frequency sounds need Xmax.

    With 1 mm of Xmax, you can reach about ~110 dB/1m at 100 Hz, plenty for most guitar players. That’s in a sealed box, in a ported box you can go higher in loudness or lower in frequency at the same loudness. At 20 Hz, it’s another story, that kind of driver will barely reach above ~80 dB. To reach the same 110 dB/1m at 20 Hz, you now need more than 26 mm of Xmax. That’s in a sealed box, in a ported box you can go higher in loudness or lower in frequency at the same loudness.

    FE3T on #3101

    So thats the reason why JBL states a 7,6mm Xmax on their 2226 despite their 5,45mm overhang
    I guess that also means that my custom reconed drivers with foam edged 2235 cones, 2235 spiders and 27mm voicecoils in reality will have higher real xmax than the 9,45mm overhang i calculated?

    I have had lots of fun with this adventure into reconing with other than stock parts, and have found this “child” of mine to be an excellent performer.

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