Woofer Speed

[Electrodynamic 2]

From time to time I like to divulge information that helps people understand subwoofer performance. For this particular post I'm going to copy an article from Adire Audio on subwoofer speed.

"There's a common misconception out there that heavy woofers must be "slow", and light woofers must be "fast". If a woofer A's moving mass is higher than woofer B's, then woofer A is probably going to be sloppy, or slow and inaccurate. Can't keep up with the bass line. Woofer A simply can't respond as fast as woofer B.

There's also this concept that the "acceleration factor" (BL/Mms) is an indicator of woofer speed/transient response. High BL, combined with a low Mms, should give great transient response, right?

Well, on surface these might sound like logical assumptions. However, they are in fact incorrect! More to the point, moving mass has precious little to do with woofer speed or signal response! And we'll prove it...

Go back to good old Newtonian physics... We're going to start with the famous law:

F=ma (eq 1)

Or force equals mass times acceleration. Anyone who's been through introductory physics (or watched a bit of PBS) should be familiar with the equation above. It's pretty much the bedrock equation of Newtonian physics - it's number 2 of the Big 3 Newtonian equations (the first being about interia, and the third being about complementary/opposed actions).

Now, let's look at a loudspeaker... What do we have? We have a coil of wire which creates an alternating magnetic field which interacts with the static magnetic field in the gap (see our page on DVC subs for a bit more information on this). How does the alternating magnetic field of the coil come into being? Well, the magnetic field is created by passing a current through the voice coil. As the current through the voice coil changes, the magnetic field created by the coil changes. This field interacts with the static magnetic field of the permanent magnet, and you get a force - the cone moves in and out. Just like two permanent magnets will attract/repel each other depending upon how they are oriented. And a bigger current means more force. Just like bigger/stronger permanent magnets mean stronger attraction/repulsion.

Additionally, what if we make the field of the permanent magnet stronger? Well, that's call the B field in the gap. Increase B, we increase the force as well. Or, what if we could somehow make the magnetic field from the voice coil stronger? We can - increase the number of turns of the voice coil (increase the Length of the wire in the gap). Guess what - in both cases, we increased the BL of the speaker (yes, this is the BL of the T/S parameters - now you know where it comes from!).

Now, let's go back to equation 1... Let's define each of the terms in that equation so we know what we're talking about:

F= Force

m = mass (moving mass)

a = acceleration

So, what is the Force (NO Star Wars jokes, please!). From above, we see that the force on the cone is the motor force factor (BL) times the current. So, let's rewrite equation 1 in these terms that are applicable to the loudspeaker:

BLi = ma (eq 2)

So, the Motor Force Factor BL times the current i equals the moving mass of the driver m times the acceleration of the driver a. Note that we have italicized i and a. There's a reason for it!

Now, back to the original question - transient response of a driver. What is transient response? Simply a measure of how fast the driver can respond to the input signal. That means that - inherently - there is a time dependency on the driver. How much TIME elapses before the driver responds. So, let's look at equation 2, and cancel out all terms that are not based on time. After all, if a quantity is time-invariant, then it won't affect time-variant effects like transient response (think of this as a simple offset).

Or, to put it in an analogy, does the 1/4 mile time of a vehicle depend upon where you start? No, the distance over which you measure is still 1/4 mile. So whether you start in front of your house and go straight 1/4 mile, or motor on down to the dragstrip and go 1/4 mile doesn't really affect the car's 1/4 mile time. The 1/4 mile time is strictly dependent on how fast the car can accelerate from a dead stop over a 1/4 mile length.

So, looking at equation 2 we see that:

BL is time invariant, assuming small excursions (assume an ideal motor with a flat BL curve; I know, most drivers don't have that, but assume that it does, like our XBL2 enabled motors). So BL is essentially a constant.

i is the current into the driver (we used italics to indicate a parameter that is time-variant). This is the music, or test tone sweep, or whatever signal is coming from the amp. It's an AC waveform so by definition it changes with time.

m is mass. Well, if the moving mass of the driver is changing as you operate, you've got big problems! The weight of the cone, dustcap, former, voice coil, surround, and spider are pretty much fixed. The don't change either. So m is essentially a constant.

a is the acceleration. This is what we're after. After all, the rate of change of acceleration IS the transient response - it's what dictates how fast the driver can change speed, which also means it dictates how fast the driver can move from position to position. And note that it's in italics, too. After all, acceleration in the time-variant parameter we care about here!

So, let's rewrite equation 2, and replace the time-invariant parameters with a simple "C" to indicate a constant (a parameter that does not change with time):

Ci = Ca (eq 3) or i :: a (eq 4)

(note: the "::" symbol is the mathematical symbol for proportionality; that is, i is proportional to a).

Interesting! This says that the change in acceleration of a driver - how fast it can change position - is strictly a function of the current through the driver. In fact, if you could make the current change infinitely fast, then the driver would accelerate infinitely fast, and we'd have infinite transients - zero time to change between states. Infinite frequency response.

So, now that we know that current is the driving force (pun somewhat intended) behind driver acceleration changes, let's look at what limits how fast we can ramp current through the driver. Because if we are not restricted in how fast we can change the current, then we are not restricted in how fast the driver can accelerate - transient response is not limited at all.

So, back to that loudspeaker model... A loudspeaker is a coil of wire wound on a former that attaches to the cone. The current flows through the coil, creating an alternating magnetic field that interacts with the static magnetic field of the permanent magnet. So, what could limit current flow? Well, what does a voice coil look like?

How about an inductor? You know, those coils of wire (hey, isn't that what a voice coil is) that you use in crossovers? Guess what - a voice coil IS an inductor! In fact, an inductor stores its energy in the magnetic field (as opposed to a capacitor which stores its energy in the electric field). It is this magnetic field of the voice coil "inductor" that interacts with the permanent magnet field we talked about above. Hey, a loudspeaker is an inductor hung on the end of a cone in a static magnetic field!

So, what about an inductor will alter the way current flows? Well, inductors don't like to have the current flowing through them change. They like to hold the current constant. They will allow you to change the current flowing in them, but the bigger the inductor (or, the higher the measured inductance) the longer it will hold the current before it starts to change (I'll leave it to the reader to go research inductance on their own, to learn why this happens).

So, the voice coil is an inductor. And we see that inductors don't like to change current. But we also see from equation 4 above that we need to change the current if we want to change the acceleration. So, the voice coil doesn't want us to change the current. How good is it at holding the current? Depends upon the inductance! The higher the inductance of the driver, the longer it can hold the current flowing through it. Which means the more time elapses before it starts to respond to the amplifier's applied voltage. Which means we have slower transient response.

Guess what - we just answered the original question! It turns out that transient response of a woofer is not a function of the moving mass, as is commonly espoused (one of the most infamous audio myths). In actuality, it is based upon the inductance of the driver. And the greater the inductance, the slower the driver - the lower the transient response."

There is a graph and measurements that follow the above information. I need to host the image, however, in order to show it to you. The information / text won't really help without the graphs. The final paragraph of the article reads:

"Mass isn't the problem - inductance is. So if you want faster transient response, ignore that moving mass parameter that some manufacturers push - look at the inductance! And if they don't list the inductance, ask yourself why - is there something they don't want to show? Inductance is the key to driver transient response - ask for it when transient response comes up!"

[UndercoverPunk 0]

INDEED! So what's the inductance on the new mags?

[sundownz 197]

INDEED! So what's the inductance on the new mags?

It's low I'm sure Nick will post full specs soon.

[Electrodynamic 2]

It's 0.8 mH on the new Mag.

The previous Mag was 3.5 mH.

[Hayabusa 0]

What exactly in laments terms does mH do? My SDX15 has 1.8 mH what does that mean to a normal person that doesn't understand all of the technical jargon that you guys do?

[JimJ 11]

http://www.adireaudio.com/Files/WooferSpeed.pdf

[Adrian_D 520]

mH = measuring unit of inductance. mili Henries.

[Electrodynamic 2]

http://www.adireaudio.com/Files/WooferSpeed.pdf

I'm surprised it's still there. A lot of the files they used to host are gone now.

[NDMstang65 403]

Take an inductance of 0.8 and put 800 grams of mass on it with a motor with 6tm of bl and tell me it's still gonna have good transient response and higher frequency extension as one with ~3mH and ~230 grams of moving mass......mass does matter

You've just got to weigh out the point where bl/mass/vas and factor in the DAF, the lighter you build something the more prone it is going to be to breaking...cross the line and you've got failures, stay on the edge of the line and you have the best of both worlds, good transient response, solid response curves..and things don't break.

[Electrodynamic 2]

Take an inductance of 0.8 and put 800 grams of mass on it with a motor with 6tm of bl and tell me it's still gonna have good transient response and higher frequency extension as one with ~3mH and ~230 grams of moving mass......mass does matter

You've just got to weigh out the point where bl/mass/vas and factor in the DAF, the lighter you build something the more prone it is going to be to breaking...cross the line and you've got failures, stay on the edge of the line and you have the best of both worlds, good transient response, solid response curves..and things don't break.

True. But you went to the extremes. 800 grams of mass is quite a bit with a motor that wasn't designed to accomodate the mass. When you build to meet your design goals with the appropriate materials the probaility of it breaking should be mimimized. Over-building with lots of mass just to avoid failure is just as counter productive as is under-building with as little mass as possible. If you have a driver with 46tm of bl and 400g of moving mass and try putting it in a small sealed enclosure the LFE is going to suffer quite a bit. All you've got is a tough, tin-can sounding subwoofer.

In the link that Jim provided to the actual document (which includes the graphs), you can see that they almost doubled the mass of the Extremis and when that "heavy" Extremis was compared to the Extremis with added inductance, the transient response of the added mass example was still better than the increased inductance example.

[JimJ 11]

Hopefully if you're designing things for the chasing-the-law-of-diminishing-returns crowd, the DAF is next to none, like the Fostex's

I don't see tons of people on DIYAudio complaining they roasted their Sigs...wonder why that is

[todd.brust 29]

very interesting article...read it a long time ago but my memory is at best sub par....nice refresher

[Electrodynamic 2]

very interesting article...read it a long time ago but my memory is at best sub par....nice refresher

Same here. I've had articles like these for a while now and a lot of the articles on Adire's web page had been taken down last time I looked, so I decided to post one up on here.

[todd.brust 29]

i think i actually have a bunch of those files/articles on my home computer....all the ones that were available when i DL's them

[bose301s 1]

http://www.adireaudio.com/Files/

Figured I'd just link to all of Adire's files.

[Electrodynamic 2]

http://www.adireaudio.com/Files/

Figured I'd just link to all of Adire's files.

Good post. I see this is where they have all the DUMAX files for various drivers too.

[Electrodynamic 2]

What exactly in laments terms does mH do? My SDX15 has 1.8 mH what does that mean to a normal person that doesn't understand all of the technical jargon that you guys do?

In addition to what Adrian said (which is correct, by the way), inductance is the rise in voice coil impedance. Inductance in the "super woofer" category usually ranges from 2.5 mH to 6 mH. The lower this number is, the higher the driver will play (which is where your blending comes into play) and, of course, the other benefits as described in the Adire article apply too.

But 1.8 mH is really low for a woofer of that calibre, which is a good thing.

[bumpncarstereo 0]

very good read, thanks for posting it up.

[king alpha 0]

http://www.adireaudio.com/Files/

Figured I'd just link to all of Adire's files.

Any idea where I can find the specs on a 12" Brahma MkIII? I've been looking all over for that.

Now that I think of it, if I get a new Mag, I'll be able to compare old Mag vs. new Mag, and an XBL^2 Mag vs. an XBL^2 Brahma.

[Acidburn 10]

Here's another discussion we've had on it

http://www.soundsolutionsaudio.com/forum/i...mp;#entry299154

[DevilDriver 28]

Yes, the problem with this discussion is perhaps a semantics question...what is woofer "speed"?

Does it describe the initial response to a signal (the rise time) only? Or does it also describe the decay time as well? If it is the former, then we can somewhat agree that "speed" is a strong function of the inductance and a weak function of other factors including BL and Mms. If it is the latter (which I believe it is), then inductance is now a small(er) variable that describes only the effective low-pass effects of the voice coil in the time and frequency domain. And especially for subwoofers, mass, BL, enclosure, and room are significantly more important. You see how critical they are in the frequency domain...thus, as described by Fourier, they must be critical in the time domain as well.

For those comparing inductance, it is best to compare as a measure of mH/ohm. To do otherwise is misleading.

[DevilDriver 28]

Also, as Tom mentioned in a post in the thread he just posted, it is fair to assume BL and Mms to be constant and demonstrate the proportionality of input current (i) and acceleration (a) if we are comparing a single driver. But when comparing two different drivers (ie. those of different masses), we can see fairly clearly the effects of mass on acceleration (if we assume this model is correct enough to use).

[dustin420 0]

so what is a good overall inductance rating? i think my atlas's are around .9 is that good? from what i read the higher the number the more sub will be based towards spl and the lower the more the sub is baised towards sq, is that a correct assumption?

[Electrodynamic 2]

so what is a good overall inductance rating? i think my atlas's are around .9 is that good? from what i read the higher the number the more sub will be based towards spl and the lower the more the sub is baised towards sq, is that a correct assumption?

The higher the inductance, the narrower the bandwidth and poorer the transient response will be with all factors remaining equal. However, like Neil and others have pointed out, the box that you put the sub in makes a difference as well.

[coobies5 43]

awesome article = ]