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Le(x) plots

Le(x) is a driver test result that shows how inductance changes based on the position of the voice coil in the magnetic gap. Generally, better performing drivers with complex motors do not have substantial changes in inductance throughout their operating excursion, while inexpensive low end drivers with simple motors have much higher inductance with coil inwards and lower inductance with the coil outwards. Le(x) related distortion is a major product of intermodulation distortion and amplitude modulation distortion. This is a form of distortion that is based purely on excursion, and is more of an issue with louder output and higher signal complexity.

There are two ways of displaying Le(x) results. One way is a curve with Le on the Y axis and MM excursion on the X axis, with 0mm in the center showing the at-rest inductance. This is how the Klippel testing system displays the results. The other way is an impedance vs frequency plot with impedance on the Y axis and frequency on the X axis. These are created with the driver cone clamped or held in place, and several plots are needed at various excursion positions. This form is much easier to do with cheaper testing software, and it is what we are showing below.

Each of these Le(x) plots is comprised of 3 impedance curves. One is at rest, one is at the full inward Xmax position and the other is at the full outward Xmax position. Of course, the mm of cone offset depends on the driver's available Xmax. In executing this test, to avoid inaccurate results, the operator has to be very careful of not exceeding the inward or outward excursion.

In these 3 curves, the one with the driver at rest is not clamped or held, and therefore has the full free-air resonance peak shown. The 2 curves with the driver held in position typically mangle the resonance however. As such, the curves are only accurate above roughly 300 or 400 Hz and grayed out below that. For drivers 7" and under, the typical change in Le impedance curves happen above 300 Hz anyway, so this is normally not a limitation.

Note that the vertical scale of these plots is relatively compressed, so minor curve offsets are relatively major in audibility at high output levels. Also keep in mind the expected bandwidth of the driver in question. Smaller drivers are expected to operate higher in frequency and top end Le(x) performance becomes more important in these cases. Along with harmonic distortion sweeps and response curve usability, Le(x) plots can also help you decide on an optimum crossover frequency.

Ideal performance in these test results would be all three curves falling on top of each other at least an octave past the driver's usable frequency range. (or up to 8-10kHz in the case of a wide/full range driver) Poor results would be three greatly offset curves way down into the lower midrange.

Small Drivers

5.5" Drivers

6.5" to 7" Drivers

8" Drivers

Commentary

Many budding DIY designers may wonder how Le(x) affects sound quality. Simply put, it is one of the indicators of how well a driver will handle complex musical passages and higher levels. To put it subjectively, a driver with poor Le(x) performance could still perform nicely at lower levels but seem to "fall apart" at higher levels with layers of grunge and edginess.

Other issues such as suspension linearity, flux modulation, and the BL curve affect non-linear performance. BL(x) is obviously excursion based, however in most drivers the middle part of the BL curve is plateau shaped and the spec is more used as a way to show behaviour as the excursion limits close in. While BL is a small part of harmonic distortion sweeps, suspension linearity and flux modulation play larger parts in that type of measurement. Thus Le(x) is an important test to compliment the other driver tests on Zaph Audio.

Simple motors with the mild enhancement of a few mm extended pole piece do well enough with lower excursion voice coils. On the other hand, a long excursion coil thrown into a simple motor becomes a distortion generator at high levels. Several other motor geometries greatly affect the Le(x) performance of high excursion drivers. A pole piece undercut does a lot, as does an extension of a copper sleeve over the pole piece. A copper ring under the top plate on the inside of the magnet helps. Underhung motors inherently have perfect Le(x) performance, and this is their primary benefit.

There is also the issue of balance in motor design. Placing a lot of copper or aluminum in a motor in a non optimized location may somewhat improve a driver's flux modulation performance, but completely destroy a driver's Le(x) performance. For example, an aluminum phase plug mounted to a basic motor in the vicinity of the top half of the coil. In this condition, as the coil moves out, Le goes way down while inward movement makes Le go way up due to the ferrous pole piece. This phase plug issue is just one example, and there are many ways to promote balance in a motor design.

Page done by John "Zaph" Krutke © 2008
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