Efficiency is not directly related to Xmax, mathematically speaking efficiency = output (db) / input (power)
Greater Xmax means more output (assuming everything else equal)
More Xmax requires more power (assuming everything else equal), and will result in more output.
Lower notes required high Xmax drivers to reproduce them at a useable levels due to the inefficiency of our hearing down low. More power is also needed, that's true. To reproduce the same output down low, every octave down needs 4x excursion, hence the importance of a high Xmax for HT application.
The more SPL and the lower the freq's that you need to produce the more air you need the driver to be able to move (xmax). Each time you go an octave lower in frequency you need to quadruple the displacement to maintain the same SPL level. At 40hz you may be fine, but what about 20hz, or 10hz? In a normal system there will be some points where it is limited by the physical displacement of the driver( Xmech, really low notes, driver bottoms out) and at other points it will be limited by the ability of the driver to handle more power (heat, thermal power compression, the vc's burn). Ideally you would design your system to not exceed either limit.
There isn't really a guide for this but today's really long excursion drivers are generally thermally limited above the 30hz range and displacement limited somewhere below this. These are huge generalizations and depend a lot on the cabinet alignment being used, but basically true. If your intended range is 30hz-120hz you don't need a driver with 30mm xmax, you will never use it all. The driver's vc will melt first and would be better served with something like a pro audio driver with 10 or 15mm xmax but really high sensitivity and power handling. If your intended range is 8-80hz, that 30mm xmax is much more useful in the 8-25hz area. As you decrease in frequency the driver takes less power to move the cone and at something like 10hz in free air a very few watts can really get the cone moving. The more xmax that a driver is capable of the more power you will need to be able to apply to use it though.
The reason that you don't see very high xmax drivers with very high efficiency is because, long xmax necessitates a lot of power handling, and heavier cone and suspension components to deal with the increased stresses of such a long cone travel, also the peak BL of the motor is sometimes sacrificed to get a broader more even BL. You end up with a heavy cone assembly and a heavy massive vc combined with a reduction of peak BL. This all robs your efficiency greatly. It is not impossible to combine high xmax with high efficiency but it is difficult and the drivers that have done it are expensive because you need a really well engineered and powerful motor. (TC Sounds PA5100, ZR18, Worx 18, Aura 1808, JBL 2269H) none of them have class leading displacement either.
For what it's worth, the reason high xmax drivers tend to be low efficiency is because they are also intended to be placed into small enclosures...it's hoffman's iron law. If you designed the driver for the same bandwidth and output, but with a much larger enclosure, the efficiency would be much higher.
Another thing to note is that hoffman's iron law is mostly just addressing electrical efficiency. When you have a motor that stays linear with increased power, then the electrical efficiency isn't as important. The surface area of the driver determines the "acoustical efficiency", which is the ability to create acoustical power for a given excursion. In other words, drivers of the same surface area must undergo the same amounts of excursion for the same SPL. Most of the distortion from speakers comes from the motor nonlinearities that results from excursion (like in the voice coil gap or the suspension or cone stiffness, etc...). Really awesome drivers will maintain as linear as possible excursion performance, but you will always decrease distortion with increased surface area (ie, more drivers).
So really, the only difference between a large enclosure and small enclosure for the same surface area and bandwidth is the amount of thermal nonlinearity. In other words, if thermal nonlinearity is kept in check, then two same sized drivers are going to sound very similar (in fact, the smaller cabinet will probably sound better since the resonances are pushed further away from the passband). And since people want small enclosures, it just follows that the efficiency goes down and the motor complexity increases. It's also convenient that more watts from amplifiers is really cheap (and keeps getting cheaper).
All that to say, the absolute ideal doesn't support the latest trend in subwoofer design, but the greatest bang for buck within the constraints of aesthetics and practicality very much supports the latest trends.
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