Originally Posted by SteveCallas
jakeman, that is all fine and good, but you are still missing the point. A high excursion driver, for a given level of output, all else being equal, will have the same or less IM distortion as a low excursion driver. You are only getting more benefits with more excursion - you are not losing anything.
According to Klippel, there are three dominant contributors to modulation distortion. Doppler distortion (resulting from cone motion relative to a fixed point) is only one of them. The other two are BL and Le non-linearities. To focus on only Doppler distortion and ignore the other two contributors is an incomplete analysis.
We all know that Doppler distortion is reduced at Fb in a reflex alignment. But that reduction only occurs over a very narrow bandwidth. At all other frequencies in the pass band (i.e., the majority of them), the woofer is solely responsible for generating sound pressure. And except in the Fb bandwidth, sound pressure is direct function of excursion.
Except at Fb, two woofers of the same diameter generating the same sound pressure at the same frequency must - by definition - have the same cone excursion. And if they have the same cone excursion, they generate the same amount of Doppler distortion.
That leaves us with BL and Le non-linearities. These types of non-linearities are minimized when the woofer is operating within Xmax. And when the woofer exceeds Xmax its behavior is - by definition - non-linear and subsequently all forms of distortion (including modulation distortion per Klippel) increase drastically.
Compare two 10" woofers, one with a 10mm Xmax, and the other with a 20mm Xmax. Up to 10mm of stroke both woofers will generate the SAME Doppler distortion. For the sake of discussion BL non-linearities are assumed to be equally low in both woofers at this excursion point (although in reality the 20mm unit will already be showing an edge).
At 15mm of stroke, both woofers will STILL be generating the same amount of Doppler distortion. But the 10mm Xmax woofer will also be generating significant BL non-linearities - and by definition more modulation distortion - since it has already exceeded Xmax by a significant margin. In comparison the 20mm Xmax woofer is still operating within its linear limits and its BL non-linearities are still low and hence so is this form of modulation distortion.
So at 15 mm of stroke, the 20mm Xmax woofer will be generating lower overall modulation distortion that the 10mm Xmax woofer, despite the fact they are both generating identical levels of Doppler distortion.