A primer into XBL², LMT, and Split Coil Subwoofer design

ssabripo

ssabripo

Audioholic
Ratings
2
#1
Thought some of you may find this interesting, as discussed with Dan Wiggins (from Adire Audio):
=================================================

XBL²
A speaker is essentially two magnets, pushing and pulling on each other. There's a static magnet and an electromagnet. The static magnet is the big stack you're used to seeing - the permanent magnets in the motor. The electromagnet is the voice coil. When you put a current through a coil, it sets up a magnetic field; the direction and strength of that magnetic field depends upon the direction and magnitude of the current. And the more windings that the current flows through, the stronger that magnetic field is.

The actual force - BL - is the integral of the flux over the voice coil. Basically add up all the flux that is passing through the voice coil and you get the BL. It's not a "flux in the gap times the length of wire" type approach, because flux is everywhere - in the gap AND outside the gap. It is weaker (and falls to essentially zero) outside the gap, but is still quite potent. And in fact, you can have up to 50-60% of the total flux in the system reside not in the gap, but outside the gap, or what is called the fringe field.

So we see that the actual motor works by the dynamic magnetic field set up by the voice coil interacting with the static magnetic field set up by the permanent magnet, and that the total field is the field in the gap and the fringe field. And the fringe field can be a significant contributor of the total flux in the system, so much so that you cannot ignore this field; the way the fringe field is integrated by the voice coil is critical, especially when looking to make this total integral constant over multiple locations (flat BL curve).

XBL² works by splitting the static field into two parts. Then you have a voice coil designed so that equal amounts of the voice coil sit - at rest - in each of the fields. Like this drawing:

As the voice coil moves up, some of it leaves the lower field, but an equal amount enters the upper field, meaning that you have a net zero loss/gain in flux over the voice coil, so the total flux integrated by the voice coil is constant. We also optimize the length of the voice coil and/or the depth of the rebates so that the fringe field between the gaps (inside the rebates) is roughly equal to that outside the gaps. This makes the total integration of the voice coil constant.

And in fact, it will be constant until the voice coil starts to leave both gaps. In the image shown, imagine the voice coil moving up. Some leaves the lower gap, and an equal amount enters the upper gap. Keep moving up, and the voice coil ends above the top plate and in the rebate, and completely covers the upper gap. Once the lower end of the voice coil starts to enter the upper gap do we start to lose BL - the integration is no longer constant. This is how you get such long stroke - you have to completely leave one gap, and start leaving the next before you start to lose motor force.

The advantages of XBL² are pretty self-evident:

1. Short voice coil, meaning low moving mass. This is not always required, but it's always easier to add mass to a driver than to remove it! Having a lower starting point in terms of moving mass is a huge benefit, because mass is your biggest enemy in terms of efficiency.

2. The short voice coil also means fewer turns, which means lower inductance. Inductance is the prime limiter in terms of extension on the top end of a speaker. You may not need extension to 10 kHz, but it's a lot easier to get there if you have low inductance!

3. Low inductance also means low flux modulation. Remember about the strength of the magnetic field relying on the number of turns? Well, the number of turns dictates the inductance as well. The lower the inductance, the fewer the turns. And for a given BL, if you can lower the number of turns, that means you're using more of the static B to generate the force. Which means the total force changes less with power applied (since the total force is a combination of the static field AND the voice coil's dynamic field).

4. Tolerance to production errors. The crucial dimensions in an XBL² motor are the sizes and position of the gap. Since these are either cut or forged in to the steel, it's pretty simple to get them accurate and repeatable. Errors in the critical dimensions are naturally pushed to the operations that are the easiest to control to tight tolerance - machining and forging.

5. Lower production cost. It should be obvious that the voice coil is cheaper - it's short. Less copper means lower price. But also with short voice coils come easier times with gap widths. You don't need as wide a gap to accomodate the voice coil. Why? Rocking. For a given angular deflection (rock),there's less radial (in and out to the side) deflection of the end of the voice coil.

6. Overall motor size. We see that since the voice coil is ENTIRELY within the height of the top plate, we can use a short stack of magnets. No need for huge stack heights, unless you want them from a cosmetic standpoint. And because we're always integrating more than 50% of the total motor flux (one full gap plus fringe around it; usually we integrate 70% of the total flux in the system),we don't need a huge diameter magnet, either.

The disadvantages are:

1. Short voice coils mean lower power handling. If you're looking to handle multiple kilowatts of power, this may not be the best approach. Sure, it works, but is not optimal.

2. Licensing. Yes, you do have to pay for it - but it's quite reasonable, typically being a percent or two of the retail price of a speaker. But you still have to deal with licensing.
 
ssabripo

ssabripo

Audioholic
Ratings
2
#2
LMT
Now the LMT design. This design is based on the standard overhung motor, but with a few extra layers of turns right in the middle and at the ends. The idea is that the extra turns increase the integration of the stray flux outside the gaps, so that you end up raising the "ends" of the BL curve. Like this:

It was hinted at several times in the 30s and 40s, and we described the basic approach in our patent as well, for the compare/contrast with existing technologies.

This approach works as advertised; LMT does flatten the BL curve. You also have massive power handling from the huge voice coil; it will take a ton of power to cook one!

However, it also carries with it several, IMHO fatal, drawbacks:

1. High moving mass. You start with an overhung, and add even more turns to it. And to get long stroke, you need a really long overhung voice coil to start with, which means the ends are so far out into the far fringe field you need a LOT of extra turns at the ends to add the proper amount of integration. And of course lots of turns means point 2 -

2. High inductance. Lots of turns = lots of inductance. This can be combated quite effectively with shorting rings; however, to lower the inductance linearly requires copper lining the gap, and that widens the gap. And you have to add a LOT of copper (in terms of thickness) to significantly affect inductance in the lower frequencies, meaning a really wide gap. Which brings us to point 3...

3. Low B field. Because you have extra layers in the voice coil, you need to widen the gap to account for the extra layers. This can double, or even triple the required width across the gap, meaning the flux in the gap will significantly decrease. Now, you get some total BL back from the extra turns, but it's usually better to get BL from B, not L. So you have to go to point 4,

4. Big motor size. To get lots of stroke in an overhung driver, you need a LOT of height. Imagine a 2" long voice coil with a 0.5" tall gap. Just at rest you must have 0.75" ((2-0.5)/2) of magnet stack, with ZERO motion. Now say you want 1" of backward stroke. That magnet stack is now 1.75" tall, minimum. Backplate thickness is added to it.

And it typically takes WIDE magnet stacks. Magnet force really goes as the area of the magnet, not the thickness. Since we're starting with really low B fields (see #3),we need a LOT of flux to make up to get anything decent in terms of B field in the gap. So we need to use bigger diameter magnets. Not only do we need a thick magnet stack, we need a wide magnet stack, which means a lot of extra weight, more volume occupied in your box, and limits how far down you can scale the design.

The most obvious example of this motor is the SoundSplinter RL-s design. A quick look at the T/S parameters will confirm that it has a VERY high moving mass (200+ grams for the voice coil alone, over 7 ounces!),and while it has a very long stroke (the voice coil is probably 3.5" long to reach the rated Xmax),it is VERY lossy; a BL of 13 N/A for a 3.5" long voice coil is extremely low (consider that the lowly Shiva Mark I, with a 1.5" long, 2" diameter voice coil - less than 30% of the copper - had a BL of 13 N/A).

This manifests itself most obviously via the extremely high Qes; it is over 1 for a 12" driver. Now, it does have a stiff suspension, no doubt; the Vas is a miniscule 27L, but not enough to account for all that Qes there (note that the Brahm

So the LMT does have high stroke, and because of the massive voice coil, it can handle a ton of power. BUT, it comes with some significant drawbacks that really restrict application of the motor to anything but big sealed boxes or IB installs (and lots of power as well).
 
ssabripo

ssabripo

Audioholic
Ratings
2
#3
Split Coil Design
The original concept to this approach was patented in the early 1970s, and used off-and-on in a few drivers here and there. As I hinted at earlier, we're actually licensing XBL² to the owner of this patent; they've used both topologies and decided that when all things are considered, XBL² simply works better. If that's not the biggest "plug" for the superiority of XBL² over the Split Coil, I don't know what is...

Anyway, Split Coil basically operates as XBL² but in reverse; rather than having dual gaps with a single coil, you have dual coils with a single gap. Here's the basic design:

You have two voice coils - each wound in the same direction - and seperate them. You space them such that there is ~50% of the gap height between the two windings. Then you make each winding about 50% of the height of the gap as well (so the winding:separation:winding:gap ratio is 1:1:1:2).

As the voice coils - on their common former - move up, an equal amount of the upper winding leaves the gap as enters the gap from the lower winding. And it continues to move that way until the lower winding starts to leave the gap. So you get some good stroke!

The advantages of this approach are:

1. Long stroke. You can get long stroke from a total voice coil height that's not too much longer than the gap height itself.

2. Flat BL. You do get flat BL, just like XBL² and LMT.

3. Royalty free. The patent on this approach expired in the early 90s.

There are several downsides, though:

1. Higher moving mass compared to XBL² from the dual sets of windings. This is actually the biggest reason that the split coil inventor is moving to XBL&#178. Much lower mass for a given stroke.

2. Higher inductance versus XBL² because of the multiple turns. And again, this brings with it lower bandwidth, greater flux modulation.

3. EXTREME sensitivity to winding length and winding spacing. Get the spacing off by a turn of wire, and you get a pretty significant peak in the BL curve center. Likewise, make it a shade too long in spacing, and you get a big dip. Much more sensitive than XBL² to winding errors. Winding tolerance is much harder to control versus machining tolerance, as it takes a LOT more effort to get proper stacking for the correct lengths.

4. Low efficiency. Because you're purposefully avoiding a good chunk of the gap, you trade off high flux (in the gap) for low flux (fringe). You can get high overall BL, but it's not very efficient at flux utilization, being somewhere between 25% and 50% efficient in terms of flux usage.

5. Motor size. Because the overall voice coil effective length is much longer, you simply need to have a deeper/taller magnet stack. And that brings the issues with rocking, etc. with it.

6. Shorting-ring-versus-flux tradeoff. I should have brought this up with the other motors, too... If you want to use a shorting ring, the best place to use it is in the gap (where the steel is closest to both sides of the voice coil),and then plate the pole in its entirety. However, that means you widen the gap, so you lose flux. So do you want lower inductance, or lower efficiency? That's often the tradeoff.

Look at the LMT and Split Coil - both would need a wider gap to get a shorting ring in the gap. You have to shave back the steel to put copper in there. And of course, the lower in frequency you want to operate, the thicker the ring must be, meaning the wider the gap. Want to be effective below 300 Hz or so? Get ready to shave off 5-6mm of your gap, which REALLY widens things out and loses a LOT of flux...
 
J

jmprader

Audioholic Intern
#4
Aren't you supposed to be testing your new DIY sub instead of engaging in subliminal efforts to foment the next Burn Baby Burn session?

Actually, this would be a fun topic to see some smart guys discuss and explore the benefits and burdens without it turning into the usual back biting session replete with the usual brand names.

In fact, downright refreshing, no retail/e-tail box involved, just some education...go man, go.:)
 
J

JonnyOzero3

Audioholic Intern
#5
jmprader said:
Actually, this would be a fun topic to see some smart guys discuss and explore the benefits and burdens without it turning into the usual back biting session replete with the usual brand names.
I Hsu your SVS!!! But, not without a Mirage of Axiom. Didn't you realize that DIY is a Paradigm? I can't stand how you Cadence like Mark Seaton. And how dare you Bob Carver this Velodyne? It's people like you who ACI this place into a pile of Infinitly Baffled. You are such a Rocket.
 
J

jhan1000

Audioholic Intern
Ratings
2
#6
Thanks SS for your informative post. Great stuff to read. :)

BTW - I have been out of the loop for awhile... do you have a thread regarding your DIY project?
 
I

Ilkka

Audioholic
Ratings
6
#9
ssabripo,

I would be MORE impressed if you had written that text yourself, but it's ok. :p
 
ssabripo

ssabripo

Audioholic
Ratings
2
#10
Jmprader....yes, I am, but given that my wife is upset at me, I am left at typing this in my laptop in the guest room upstairs....measurement are on hold till the weekend :( :D

JonnyOzero3, literally I almost spit my coffee onto my laptop's screen when I read that...some really funny stuff man! :)

I just asked Dan a question about these technologies, and he was kind enough to share his thoughts with me. Deon Bearden, and Tom Nouissaine, also shared some thoughts on the subject a while back when I asked......anyways, thought it was really neat info, so I wanted to share with you guys. At least you guys will enjoy some good info without problems....................even if just for one week.
 
ssabripo

ssabripo

Audioholic
Ratings
2
#11
Here is a follow-up question that I and another poster asked Dan regarding point 5 on the Split Coil Design:
5. Motor size. Because the overall voice coil effective length is much longer, you simply need to have a deeper/taller magnet stack. And that brings the issues with rocking, etc. with it.
we asked:
What are the Pros and Cons with using multiple spiders in Split Coil designs to help reduce Rocking? Of course using them will alter some of the T/S parameters but it should definitely help with rocking issues and the designers could always use softer spiders to counteract the use if multiple units, right?

Interesting response from Dan Wiggins:
====================================

First off, linearity. For an ideal spring, your have a force F(x)=kx, where k is the spring stiffness, and x is displacement from rest. A very linear force function! Stretch the spring a certain amount, and we can directly calculate the force, and it's nice and linear. Here's a cool page that shows how consistent this really can be:

http://www.myphysicslab.com/spring1.html

Note that the spiral is nice and consistent, proportional as it "damps down". Spacing between the cycles are proportional, etc. It all looks good, and it should, because of the math involved - F=kx, it doesn't get much simpler than that! For the math, and those interested in it, read the rest of that page. Quite instructive!

Now, let's look at the twin-spring situation - two springs controlling the mass. The best page with graphics to show this is:

http://dept.physics.upenn.edu/course..._TwoWalls.html

Stop the graph, and enter the following different values:

Initial pos. = 0 (we start at the rest point)
d = 0.1 (initial tension in the springs)
Initial vel. = 1 (we start off with a velocity of 1, to the right).

Look at the upper graph you get now - it's not nice and round, but figure-8 shaped. That graph is the velocity versus displacement, and we see that it is NOT nice and smooth. The lower graph shows this in another view - energy versus displacement is not continuous, meaning that the force is not continuous.

Scroll down that page a bit, and you'll see why - look at the equation of motion! It's nice and high-order. That's the reason for the nonlinear motion and forces.

Now, keep in mind that these examples assumed the springs are perfectly linear, and obey the F=kx equation. However, real spiders are NOT linear, and the stiffness function is typically of the form:

F(x) = kx + bx² + cx³

Add that into the above mix, and we see things get REALLY ugly. Using more than one spring in a system will create greater nonlinear behavior - it's a bad thing.

Now about rocking. Dual spiders again don't help. Why? Consider the following diagram:

So, we have a stiff rod (blue line) that rests on a fulcrum (the green checked triangle),connected to the ground via a spring (the red circles on the right),and pulled down by a weight (the black trapazoid on the left).

This is analogous to a driver. Let's assume that the cone/former (the blue rod) is infinitely stiff. And let's assume the spiders (the green checked fulcrum) won't give left or right - they will always keep things centered left and right.

The red spring represents the surround - the front of the cone.

The weight represents the mass of the voice coil, trying to pull the system to the side. It will scrape if it touches down on the rectangle below it. So we see that we want to keep the red springs (surround) strong enough that the mass won't touch down, right? The only way the voice coil can scrape is if the springs aren't stiff enough, the fulcrum collapses, or the rod bends. If none of those happen, the voice coil won't scrape.

Now, let's add a second spider into the mix...

We now have two of the fulcrums on which the rod rocks. So let's try to rock once again... We pull down with the weight, and if the fulcrum doesn't collapse, the rod doesn't bend, and the springs are strong enough, we don't touch down.

What did the second fulcrum do? NOTHING. In fact, it's widened the pivot point, but that's it. It has done nothing to stiffen the rod, or to strengthen the springs, or lighten the weight. All it has done is created a wider fulcrum on which your rod can rock.

Think about a lever - to lift your car, do you want a wider fulcrum under your lever, or more force down on your end of the lever? Simple choice, isn't it?

In fact, rocking is controlled by the spider-to-surround distance! That is what allows the spider to keep the voice coil from rocking - the lateral stiffness of the surround, and the distance over which the surround can work. Make the cone taller, and the surround stiffer laterally, and you end up with greater resistance to rocking.

Now, all this goes away if your spider isn't stiff enough to hold up laterally - if it squishes to one side or another. However, spiders tend to be quite stiff in a side-to-side motion, so that really isn't a real-world concern. If it can squish, then you need a stiffer spider in the first place (you tend to have a LOT more stiffness in the radial - side to side - dimension than the axial - in and out - dimension).
===========================================

I guess it is somewhat obvious then, that dual spiders do two things:

1. Reduce suspension linearity (make it worse)
2. Do not reduce rocking
 
K

---k---

Junior Audioholic
Ratings
1
#12
This Post ----> ------------





Me ------------> :eek:



(This looked a lot better in my old school ascii art, but they won't allow all the spaces need to make it look right.
 
J

JonnyOzero3

Audioholic Intern
#16
ssabripo said:
JonnyOzero3, literally I almost spit my coffee onto my laptop's screen when I read that...some really funny stuff man! :)

Thanks, I aim to please :)
 
J

JennAir

Audioholic Intern
#17
XBL^2 - it's not just for woofers anymore

Heady stuff but excellent thread.
One minor thing, the title suggests that the XBL^2 is just for subwoofer drivers, however, it's also being used in mid-woofers and full range drivers as well (trying to be all humble with my XBL^2 based speakers).
 
ssabripo

ssabripo

Audioholic
Ratings
2
#18
it's actually a fairly easy read....He put it in pretty simple terms. :)

I actually want to get more info regarding why exactly the LMT, although capable of higher outputs, didn't sound as good as an XBL^2 (TC sounds LMT15 vs Adire Tumult) back in late fall last year when I had them and tested them.

interestingly, here is a graph of the linearity of BL
 
ssabripo

ssabripo

Audioholic
Ratings
2
#20
very good point, and link JennAir..;)

although I was thinking more from a purely subjective standpoint, but yes, the woofer speed could definitely influence this...
 

newsletter
  • RBHsound.com
  • BlueJeansCable.com
  • SVS Sound Subwoofers
  • Experience the Martin Logan Montis