Understanding Excursion
It's been a while since I've put anything meaningful together, so it's time for another fun technical article!
Excursion is a large contributor to high output in any driver on the market. Typically, larger excursion (seen visually as how far the cone moves in and out) means more sonic output. However, with excursion come challenges.
As the driver moves outward, the voice coil begins to move out of the gap. This causes a drop in the magnetic force (or BL) and results in a few negative effects, including a large theile/small parameter shift, lower efficiency (magnetic flux decreases), less control over the voice coil (transient response increases, making the driver sound sloppy), and introduces distortion into the output.
Knowing these effects, there was a need to design a parameter to describe the limit of excursion while still remaining “linear”. The idea here was to define a point at which all other parameters remain the same and also consider the limits at which disortion becomes audible. This parameter is referred to as Xmax and, although extremely valuable, is highly controversial. The issue comes back to the actual definition.
Overhang
Traditionally, Xmax has been defined by the overhang method. Overhang is the length of coil in mm that extends past either side of the top plate and is determined by the formula:
Xmax = gap height – [voice coil length/2]
The theory here is that this measurement considers the maximum amount of travel the driver is capable of with the same number of windings (of the voice coil’s wire) in the gap. Once the number of windings decreases, the effects listed above will begin to occur. This is still one of the most commonly used definitions and does work fairly well, but it does not consider several factors, including the behaviour of the magnetic fringe field, any suspension compliance non-linearities, any inductance non-linearities, or InterModulation Distortion. From this lack of refinement, several other definitions have come about.
8mm In the Gap
Digital Designs Audio, famous for their high SPL drivers, use an "8mm in the gap" method. In their opinion, the percentage of coil still in the gap is what matters, rather than the overhang. For DD Audio, this is an important method to consider. They typically use tall top plates and, as such, have very long magnetic gaps that cannot be considered by the traditional overhang method of measurement. Using the overhang method has consistently given DD Audio very low numbers, although most newer and more accurate methods do as well. The issue here is that once the coil begins to move out of the gap, there is a drop in BL, whether there are 8mm of coil in the gap or not. Using DD’s measurement method, this drop in BL would not be accounted for. Due to the large gap that DD uses, this drop is not as drastic as others, but it is a drop in BL regardless. This measurement method also does not cover any of the other issues mentioned with the overhang method.
DUMAX and Klippel
There are two revolutionary measurement systems now available: the DUMAX from Dave Clark and DLC Designs, as well as the Klippel, developed by Dr. Wolfgang Klippel. These measurement systems compare BL with respect to x(mm of excursion). They also consider suspension compliance (Cms) as this will create many of the same issues that a shift in BL will. This is done as 1/Cms (which=Kms) with respect to x(mm of excursion). Both of these demonstrate through a graph the measurement of BL and Cms through both the positive and negative strokes. An example of each graph can be found below:
BL from Klippel
Kms (1/Cms) from Klippel
BL and Kms from DUMAX (scroll down to the graph section)
DLC defines Xmax as the smaller of 1: half of the peak to peak excursion over which BL retains 70.7% of it’s rest position value or 2: half of the peak to peak excursion over which Cms retains 25% of it’s rest position value. These values represent approximately 10% distortion, which is often considered the point of audibility. By using this method, we consider the full flux field as well as the suspension’s limits. Xmag is considered half of the peak to peak excursion of the 70.7% limit for BL, Xsus is considered half of the peak to peak excursion of the 25% limit for Cms, and Xmech is considered half of the peak to peak excursion of the absolute limit of the chassis. The smallest of these 3 values is considered Xmax.
Considering these points is imperative, as BL and Cms distortion accounts for roughly 80-85% of all distortion present in any given driver.
When is linear truly linear?
Dr. Klippel has made a push to consider other factors as well, primarily measuring inductance with respect to x(mm of excursion). This has more to do with how far the driver can be pushed before compromising some level of sound quality, rather than how far the driver can be pushed before compromising excursion. This opens up a possibility to consider cone break up, lead slap, any mechanical noise, air rushing around the basket or pole vent.
The definition of Xmax as defined by the Audio Engineering Society as:
“The voice-coil peak displacement at which the “linearity” of the motor deviates by 10%. Linearity may be measured by percent distortion of the input current or by percent deviation of displacement versus input current.”
On the other hand, Dr. Klippel defines Xmax as such:
“The voice-coil peak displacement Xmax at which either the total harmonic distortion dt or the nth-order modulation distortion (where n=2 or 3) exceeds 10% in the sound pressure radiated by the driver in free air excited by the linear superposition of a first tone at the resonance frequency f1=fs and a second tone f2=8.5 fs with an amplitude ratio of 4:1.
The total harmonic distortion dt assesses the harmonics of f1 and the modulation distortion are measured by the modulation components f2± nf1 according to IEC 60268.”
Summary
With all that said, I personally agree with Dr. Klippel’s definition of Xmax. It considers Total Harmonic Distortion and, as such, seems to closely represent the sonic qualities over excursion. The issue here is that it does not consider Inter-Modulation Distortion and does not necessarily match hearing perception across the board.
To summarize, looking at Xmax can describe potential output while remaining linear, but it is important to understand the application of Xmax and how it is measured. If you see a graph from the DUMAX or Klippel measurement systems, I would be much more inclined to believe the parameters posted. Remember to look deeply into all information provided and that with any audio driver, the whole is greater than the sum of it's parts.
Cheers,
Neil
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..and i thought i knew alot about audio..Is there a way to use the back EMF of the system as a shock absorber of sorts to help save the speaker?
Last what of the magnetic pole was 10" long and the voice coil was 2" that way it could travel 8" without ever leaving the magnetic field?
Also What if the surround was removed and a Teflon style piston ring was used and polished cylinder wall. as well as a uniform spring return.
Ok little of topic but If you have a 12" driver with 12" of excursion capabilities would this be better or worse for you SPL? I would think worse for the time it would take to traverse this distance,.
With a long gap, short coil (LGSC or in this case, underhung) design, there are a few inherent issues. First problem is that production would be very very expensive. With a short coil, BL will drop very quickly as it moves towards the outer limits of the gap. The flux density and saturation would fall well short of our goals as well; these designs are typically very inefficient (in terms of actual flux used) and, as such, not as highly sought after, particularly considering the production costs. Yes, LGSC is capable of lower distortion in some regards (inductance is wonderfully low and there is less flux modulation until you reach the outer limits of the gap) but the cost of producing a driver like we are suggesting here is extremely expensive. Machining aside, the cost of raw materials would be quite high.
Surround changes are interesting to note. A surround is an important part of the suspension, but the spider is very very critical. The Arachnid from Adire Audio is actually a very ingenious step in this direction. HERE is a good thread on distortion generated from suspension non-linearities which also touches on underhung vs Adire's XBL^2 gap technology (US Patent 7,039,213)
In terms of raw SPL (from an engineering standpoint), massive excursion in a sealed enclosure is the way to go. There are a few basic issues with this so far, the first being availability. Right now, there are absolutely no stock parts to create anything near this level of excursion; it would have to be extremely custom and extremely expensive (Adire's Parthenon as well as Richard Clark and David Navonne's giant sub are two of very very few subs that are capable of doing well and are also extraordinarily expensive). Secondly, subwoofer drivers are highly inefficient (typically converting ~3% of input electrical power into acoustic output) and, thus, we would have extremely large power demands.
High spl is currently attributed to subs with large BL (and BL^2/Re) that are used in a bass reflex enclosure, as the use of the out of phase port causes it to be much more efficient than a sealed enclosure while still not requiring the large amount of room required by any 4th or higher order bandpass enclosure.
Hope that addressed some of your questions; I know you always have lots
Neil
to you,and you did answer all my questions and thanks for the link!
Neil
