Dan Wiggens has done a good job selling his story about higher sensitivity and lower inductance, but looking at the math we can see that XBLL does linearize the BL, but at the same scarifies that LMS has (and split coil for that matter). It will not beat a straight overhung coil at the same xmax.
Hi Kyle,
There are multiple advantages in terms of a rebate in the gap, especially when you consider placement of shorting rings and counter coils; this isn't just from XBL, but you can see the research of Doug Button, Marcelo Vercelli, Ejvind Skaaning and others with placement of shorting rings and coils. Suffice to say, putting a ring below the gap does not function nearly as well as one IN the gap; likewise, rings above and below still do not function as well since the bulk conductivity of the rings is most likely not balanced.
For example, consider the following measured impedance of midwoofer I designed a few years ago, which uses a 66mm diameter voice coil and a motor design with 18mm one way linear (as measured by a Klippel):
As you can see, there essentially IS no inductance; the bulk inductance is around 15 uH, about in line with the best tweeters out there. And this is for a 66mm diameter voice coil with 18mm one way linear stroke, and one that handles a 700W RMS amplifier all day, every day, in thousands of recording studios around the world. This is a direct result of putting the inductance reduction system IN the gap, rather than outside (which simply does not work as well).
This also is a great benefit from a cooling standpoint as the average position of the voice coil can contain a highly thermally conductive material like aluminum or copper; or, if desired, cross-drilled holes into the center of the gap forcing air over the voice coil itself.
With respect to motor design and its benefits, you're ignoring one of the major ones (and why you can find XBL in many products in different CE segments, including those you can buy in your local Best Buy): motor height. For a given stroke, an XBL motor can be significantly shorter. In general, an XBL motor can be roughly 60% of the height of an overhung and still have the same mechanical clearance. This means magnet stacks can be significantly shorter, and weight greatly reduced as desired. And one can push more of that magnet out in the radial dimension so as to better use the flux available in the magnet, if desired (as you know, for a given amount of magnet, you want to maximize the surface area touching the steel, so as to maximize flux density in the gap - spread your magnet out as much as possible rather than stack it up where you get precious little return in B in the gap).
So when you actually adjust for the same DCR of voice coil, same mechanical clearance, and keep the amount of magnet weight and steel the same (meaning going with a fatter but shorter stack) one will often see significant increases in B field strength - the shift of some magnet from height (for mechanical clearances) to width allows for big gains in B field. A lot of your analysis overlooks this basic benefit to underhung or XBL motors - you assume static magnet shape but that is NOT a static assumption that needs to be made, and in fact is a hindrance to the design of underhung and XBL drivers.
This shorter design for the same mechanical stroke was the primary reason XBL is used in so many conferencing phones from Polycom and others; a taller speaker leads to a taller physical package of the phone which has a measurable degradtion of the PESQ (objective measurement of sound quality) score for the phone, since multipath reflection is increased for the multiple mics. The greatly reduced distortion - relative to equivalently-sized overhung speakers - was a key in selection because THD from nonlinearities is extremely detrimental to echo cancellation techniques. So a low distortion, very shallow driver is essential to proper conference phone design. This is one example that simply cannot be equaled with any overhung (and indeed, both Microsoft and Polycom, independently at different times, spent months looking for a solution before stumbling across XBL and quickly licensing and using it - measurably lower THD in the shallowest package available).
Additionally, gap dimensions do not have to be kept the same; gaps on XBL (and underhung as well) drivers can be tightened because of the shorter voice coil. For a given level of mechanical stroke, and a given precession of the former, the shorter voice coil results in less radial displacement; basically, rocking of the cone will result in less sideways displacement of the voice coil before it touches the top plate or pole, meaning they do not have to be as wide apart as they do with an overhung. And as magnetic flux falls off with the cube of distance, even a small reduction (say 10%) in gap width can result in large gains in B field (28%, for the 10% gap reduction).
Likewise with total coil assembly mass. Because of the shorter voice coil length, the former is shorter and that mass is reduced. I know of no engineer who complains about a lower starting mass! As you know, it's always easy to add moving mass, but often difficult to remove. Having a lower mass means you can gain in total driver sensitivity, or - if you wish to "spend" that mass savings - go to a larger diameter voice coil and slightly larger diameter wire (so as to keep the DCR the same), and that larger diameter voice coil will increase the BL and thermal power handling. This is a tradeoff and option that's available because of the short voice coil of XBL (likewise with underhungs); it's not available with overhung designs. It's not necessary that one uses it, but it's an option at least with this approach.
Additionally, consider the impact of flux modulation under power and with transient bursts into the voice coil. The BL curve is skewed because of saturation effects in the steel from the voice coil. In a typical overhung, you'll find the B field becomes a continuous slope from one side to the other, and the BL curve will mimic that result. However, with an XBL motor the rebate assists in breaking up that saturation, and each gap has it's "own" slope associated, rather than a bulk overall slope for the entire single gap. As the voice coil integrates opposite sections of the two gaps, a symmetric slope in each gap is essentially negated, and the BL curve is considerably more stable in shape and magnitude. Meaning under power and heavy operation. The corners of the curve - where the voice coil starts to leave one gap, and mainly integrate the internal/external fringe fields and a single gap - are softened and sloped as one would expect, but for the center part of operation the effects of flux compression and B field distortion from power in the voice coil is substantially negated.
All this said, if one designs a full-out overhung or a full-out XBL motor with the goal being high sensitivity and stroke and bandwidth, you'll find that you typically get the same results but in a more compact, lighter (and therefore lower cost - you know you basically "pay by the pound" for motor parts), and linear design with the XBL. Only when you ignore some of the benefits you achieve from the shorter voice coil and the multiple gaps does an XBL design fall in line with most other motors. And when you add in scalability of design (there are 10mm microdrivers, headphone drivers, tweeters, and tiny to huge midranges and woofers with it) these benefits become realizable to all speakers. In many applications, longer overhungs simply are not an option for mechanical mounting purposes, such as in laptops, phones, and plasma TV speakers.
With regards to promises of clarity and bandwidth and sensitivity, I'll say no more than look at the recording monitor of the decade, the Event Opal. This is the monitor of choice by Alan Parsons, John Merchant, James Lovelle, Focus and dozens more of the top engineers and producers in all genres of music. Event Opals use the XBL motor with great results. Much of the reduced flux modulation (and hence, less dynamic compression) and greater bandwidth that comes from highly reduced inductance, and greatly increased linear stroke (and hence more dynamics) is what has led to this monitor's virtual takeover of the top end of the recording studio chain.
Perhaps you'll be at ALMA or CES and we can discuss this further? If so, drop me a line. If you do come to ALMA, look up my new FEA company - DYNE Analytics. We're releasing an FEA tool for motor design for loudspeaker engineers, one we wrote and rolled ourselves and have extensively tested and confirmed against other packages (notably Maxwell) and measured data (Klippel and others, for hundreds of built drivers of all sizes). Yes, I know a few things about FEA as well, at least enough to write and create FEA packages for magnetics modeling - you learn a lot about parasitic inductance, flux stability under power, and the like when creating the actual modeling tools loudspeaker engineers will use to design the next generation of products.
Dan Wiggins
CTO, ADI