[jules]

Dan,

thanks for the offer and from what you say I take the goal of your paper to be slightly different to the impression created by the first few lines.

I stand ny what I said about the maths/physics in the early part of the paper and it seems the meat of your ideas is to be found in the graphs.

For this reason could I ask you:

  * you added "a 10AWG, 0.47 mH inductor". By this do you mean that you added an inductor in the circuit outside the driver OR you added 0.47mH of inductance (via extra windings) to the driver's voice coil?

Adding inductance to the voice coil (via extra windings) would of course add to the BL factor for the driver (and significantly to the voice coil mass). Inductance added outside the driver will cause increases to transient delay without the bonus of increased BL.

If your aim was to compare the results of adding, on the one hand mass and on the other inductance, they should each have been added to the same driver alternately.

Maybe I'm mis-reading your paper here but you use the word "inductor".

jules

[Mudjock]

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

Dan,

Thanks for chiming in - I have a little better idea now of what you were trying to say.  The quote above from your white paper on Woofer Speed is an example of the type of statement that causes me to get lost and wonder what level of understanding is really contained here.  Starting from the equation F=ma=BLi, the acceleration can be expressed as

a = (BL/m)i

and the change in acceleration with respect to time is

da/dt = (BL/m)(di/dt)

So, if you make the current change infinitely fast (di/dt approaches infinity), a (the cone acceleration) clearly does not approach infinity, but rather (da/dt) approaches infinity.  An infinite da/dt would look like a step change in acceleration, either from stopped to very rapid acceleration or from stopped to very slow acceleration, or from one value of acceleration to another.  To get infinite acceleration, you really need infinite current, which you correctly expressed in your post here, but seems less clear in your white paper.  The real underlying issue, though, is that there is just no way to drop mass or BL out of any of these equations.  A heavier woofer (all other things equal) accelerates less, and it changes acceleration more slowly.  You can integrate or take derivatives until the cows come home and BL/m term is still there, affecting the cone position, velocity, acceleration, change in acceleration, etc...  

That is not to say there isn't merit in improving di/dt, which I agree can be accomplished by reducing the voice coil inductance.  As Jules correctly points out, you can't change the voice coil inductance without also changing BL (unless you also change something else in the motor to compensate).  At this point the situation becomes more complicated and deviates from the test case you present in which an external inductor is added in series with the driver.

I also think that the manner in which terms like "speed", "excursion", "position", and "acceleration" are used in a confusing and inconsistent manner both in your response and in your white paper.  Specifically, in the quote above you equate the change in acceleration of the driver to how fast it can change position.  Maybe what you were trying to say was something different, but what you wound up saying is completely incorrect.  The change in acceleration is the derivative of the acceleration, whereas "how fast the driver can change position" is the velocity, which is the integral of the acceleration.  The presence of cone velocity does not even produce sound, only wind.  Sound comes from compression of the air, which requires cone acceleration (change in velocity).  I'm not insinuating that you don't understand these concepts, but rather that the words chosen do not properly communicate the concepts.

I want to make sure it is clear that I do appreciate your efforts in driver design and think you are an asset to the audio community.  I have a pair of Extremis drivers, have heard some of your larger subs, and will probably audition some of Danny's new drivers based on your technology.  The Extremis is an interesting and unique driver that, while not perfect (nothing is), has got a lot of people thinking in new ways about how to tackle the tradeoffs of driver design.

Cheers!

Scott

[jneutron]

I was just proposing possibly neglected terms. I've never studied in any depth the physics behind loudspeaker design. ...

They were good proposals.

The paper dealt with transient response - is it a mass issue (as many audiophiles believe), or is it an inductance issue (I as contend). The paper is pretty clear in its derivation - mass affects efficiency, but does NOT affect transient response. The proof is in the frequency response measurement (frequency response and transient response being related via the Fourier transform).

HI Dan

Mass affects both.  The fact that you did not see drastic changes as a result of mass addition simply shows that your amp was capable of providing the current necessary to satisfy the positional requirements of the amp output voltage...this being the generation of emf by the vc in the gap to try to follow the amp voltage.  The addition of an inductor subtracts from the drive voltage by the term L di/dt, so allows the vc to deviate from the desired position.

If you had measured the current and power delivered to the system, you would have seen that the addition of mass, or the addition of inductance, are very different when it comes to the power delivery and subsequent spl numbers, the difference being sufficient that overlaying the three graphs is misleading in the context of the paper.

While your intent with the paper is noteworthy, you based your conclusions on partial information.

A higher mass cone certainly will tax the amp and speaker wires more.

Also, one must consider the affect the higher mass or inductance will have in the ITD localization parameter should the cone be required to run in the 500 hz or so region, the delays will affect imaging.

Your intent to incorporate changed to your white paper in response to constructive criticism is very very commendable.  It is rare that a manufacturer will listen to others.  I like you..

it might be construed that you attribute this quote to me where it is actually an extract from the paper.

""In fact, if you could make the current change infinitely fast then the driver would accelerate infinitely fast.""  

That was not my intent, sorry if it came across that way.  My point was a rapid change of current is not a rapid acceleration, it is a rapid change in acceleration..

Cheers, John

[jules]

Ok, this is my final word on this one as I'm going to start going round in circles if things continue:

Dan,

thank you for interacting here. These days it seems to be popular for CEO's to set up a firewall between themselves and the public so your approach is great. Your paper is engagingly written and makes an attempt to keep things clear rather than to impress with pompousness.

My feeling is, that as a designer your experience tells you that a certain weight/strenth of cone is a necessary given [constant for a particular driver] and thereafter the problem the irks you is the resultant inductance generated in the voice coil required to drive the cone however ...

I believe your paper should be withdrawn.  This assertion, quote Dan:

"The paper dealt with transient response - is it a mass issue (as many audiophiles believe), or is it an inductance issue (I as contend)."

is simply not supported in anyway, either by the physics/maths or by the experiment.

John, your comment that:

'While your intent with the paper is noteworthy, you based your conclusions on partial information."

is polite but in terms of it's expressed goals this paper is only noteworthy in that it does absolutely nothing to prove them.

In explaining the aim of his experiment Dan says that he wants to compare CHANGES IN VOICE COIL INDUCTANCE with CHANGES IN CONE MASS making the assertion that the former has more influence. HE DID NOT DO THIS!!!

Certainly Dan added some mass to the cone of his driver but to prove his point in terms of inductance being of more significance than mass he should have added the appropriate BL required to keep "a" the same TO THE VOICE COIL. [I point out again that this inductance appears to have been added in series with and external to, the speaker.] I think this would be considerably less than 0.47 mH which is a large inductance in the circumstances and would be a very large addtion of mass and excessive addition of BL to the voice coil.

In conclusion, the physics and the maths presented in this paper do nothing to support Dan's view and the test data, even using a large external inductor, doesn't back up the claim.

Sorry fellas, but this is way, way off and while some of my earlier comments might have been overly colourful in extrapolating bizarre conclusions based on the logic of the paper that was the logical outcome. The reason I raised this issue was that Dan's paper was quoted to support a view on the time honoured cone mass/responsiveness issue but it does not do that and in fact muddies the water for novices like myself unless they take the time to go into some detailed analysis.

jules

[DanWiggins]

Mudjock,

For your differential equation, my claims hold true; if current changes infinitely, then the change in acceleration is infinite.  Note that I specifically state the change of acceleration, implying the differential of acceleration.  Not the value of the acceleration itself!

JNeutron/Jules,

Here's one example that should completely put this all to bed.  The WR125S and the FR125S drivers I designed for Creative Sound.  They use the exact same cones, and even the same voice coils.  The FR125S has the addition of a Faraday ring, with a corresponding reduction in inductance.  The FR125S has nearly an octave wider bandwidth.

This was ZERO change in moving mass - just the inductance.  And bandwidth increased.

Mass simply scales your output; it does not affect frequency response.  Hence it does not affect transient response.  It can affect amplitude, but not time.

Adding an inductor in series is a perfectly suitable approach; a loudspeaker is a fairly simplistic model of linear components, and with linear filter theory we can place extra inductance in series with the voice coil inductance and it will give us the same response as if the voice coil had the higher inductance.  Like the FR/WR comparison.

I hope the FR/WR comparison really cements this - it's about the closest thing you'll see to two identical drivers save for the inductance, and you see a very dramatic change in bandwidth.  And the measurements of the driver I took with and without extra mass certainly confirms that the bandwidth was NOT affected by the extra mass!

Dan Wiggins
Adire Audio®

[Mudjock]

Dan,

I still can't follow your reasoning that mass does not affect transient response, or frequency response.

The equation does not lie.  da/dt = (BL/m)(di/dt).  Since cone acceleration produces sound pressure, da/dt would logically represent "transient response".  I agree that reducing the voice coil inductance would increase di/dt in a situations where all else was equal - increasing da/dt as a result.  This is what you demonstrated with your WR/FR example, because as you state inductance was reduced but mass was not.  The real disconnect between my interpretation and yours is that, while your assertion that BL and the mass are a scaling factor for how much acceleration (SPL) you get for a given amount of current is borne out by the math, your assertion that mass does not influence the transient response simply is not borne out by the expression for the transient response (da/dt).  According to the math, the transient response is dependent on BL, m, and di/dt (which is inversely related to the voice coil inductance).  This results in 3 choices for improving transient response:

1.  Increase BL
2.  Decrease mass
3.  Decrease Inductance

Do you agree that da/dt = (BL/m)(di/dt)?
Do you agree that da/dt represents transient response?
Do you agree that inductance is inversely proportional to di/dt?

If you do agree with those, I just can't see how it is possible to conclude that transient response depends on inductance, but not mass.  If you don't agree with those statements, please clarify.

Scott

[DanWiggins]

Mudlock,

Transient response is the rate of change of acceleration - the Jerk force.  The BL and the mass are scalars, and will affect the magnitude independent of time; they will adjust the frequency response up and down, but not limit it.

Do the equation - replace BL/m with 2, or pi, or 42 (a good number! ).  What happens to the equation?  Does the quantities being differentiated change?  No, the relationship between them changes, but the number itself does NOT affect the time-variant parameters.

The rate of change of acceleration will not vary over time for a given Bl/m ratio.  Yes, BL/m will scale the rate of change of acceleration - no argument there!  But it will not affect the rate of change of acceleration over time.  It will not affect the derivative.

Do you agree that da/dt = (BL/m)(di/dt)?

Yes.

Do you agree that da/dt represents transient response?

Yes.

Do you agree that inductance is inversely proportional to di/dt?

Sure.  L di/dt...

Run your differential equation.  Now play with frequency - which is essentially time.  How does the BL/m depend upon frequency?  It is a constant to start with, meaning that if you differentiate it, it still stays constant.  It scales your time relationship between acceleration and current, but does not limit the ability to change the acceleration, or the current.

Mass and BL simply affect efficiency in a driver - they will change how much acceleration you get out for a given current in, but they will not limit your ability to change the current.  Only how much acceleration you get for a given current in.  And that amount of acceleration is SPL.

Dan Wiggins
Adire Audio®

[Mudjock]

Dan,

If a = (BL/m)i and da/dt = (BL/m)(di/dt), then it seems to follow that BL/m scales da/dt, which IS the transient response.  This means to me, based on the definitions we agree on, that for two otherwise identical drivers with one having a heavier cone and one having a lighter cone, the heavier cone cannot change SPL as quickly as a lighter one, when responding to the same signal.  

As I think about this with regard to an SPL vs. time plot, it seems that the shift for the heavier cone plot would be along the SPL axis rather than the time axis.  But this would also reduce the slope of SPL vs. time - which we have defined as transient response.  So, in some sense I agree with you that the timing of the musical events or ability to reproduce higher frequency is not directly influenced by mass, but in order to precisely track the SPL vs. time plot of the lighter cone driver, the heavier cone driver would have to be driven with an increased EMF and everything that goes along with that (voice coil heating, etc....).  

I guess I'm starting to see that the main issue here is semantics.  Is a woofer "slower" if it responds in the same time, but with less magnitude?  In the strictest sense of the definition of transient response, I still say it is - but I'm not sure in the context of a real world application.

Ultimately, the deeper question is:

Are the drawbacks of lower efficiency (vc heating, comlex, high power amps) preferrable to the drawbacks of taking mass out of an otherwise equivalent cone (increased flex and related distortion)?  If the answer was simple, we'd all be using the same driver....

Cheers,

Scott

[jules]

Dan and others,

there's a world of difference between the [practically] inviolate truth of F=ma and a the undefined vagueness of a generally held audio belief. For this reason it's going to be as hard to disprove a "myth" as it is to prove it.

There's nothing vague or ill-defined about Dan's drivers. They are distinctive with a well defined character.

Thanks Dan, Mudjock, kneutron, kfr01 and others for making us think about the many issues involved and I hope everyone celebrates easter (if you do) to the full

jules

[DanWiggins]

As I think about this with regard to an SPL vs. time plot, it seems that the shift for the heavier cone plot would be along the SPL axis rather than the time axis. But this would also reduce the slope of SPL vs. time - which we have defined as transient response. So, in some sense I agree with you that the timing of the musical events or ability to reproduce higher frequency is not directly influenced by mass, but in order to precisely track the SPL vs. time plot of the lighter cone driver, the heavier cone driver would have to be driven with an increased EMF and everything that goes along with that (voice coil heating, etc....).

Right - amplitude is independent of timing.  Transient response is a timing thing; we're not skewing the timing of events at all by adding mass.  Meaning that a heavy woofer won't be any "slower" that a light woofer - if they have the same bandwidth, they will start and stop at the same time.

I guess I'm starting to see that the main issue here is semantics. Is a woofer "slower" if it responds in the same time, but with less magnitude? In the strictest sense of the definition of transient response, I still say it is - but I'm not sure in the context of a real world application.

That is my point.  Often people categorize big woofers as slow because they must be heavier than small woofers.  The reality is completely opposite.  A big, heavy cone may be less efficient, but it will not necessarily be slow!  I want to make sure that I do all I can to keep the terminology clean...

Ultimately, the deeper question is:

Are the drawbacks of lower efficiency (vc heating, comlex, high power amps) preferrable to the drawbacks of taking mass out of an otherwise equivalent cone (increased flex and related distortion)? If the answer was simple, we'd all be using the same driver....

You forgot one of the biggest "forcing issues" in driver design today - the insatiable drive towards smaller and smaller boxes that play deeper and deeper.  Hoffman's Iron Law wins every time - you want to play lower in a smaller box?  You give up efficiency.  Every time.

For 99%+ of the people out there, this is a worthwhile trade.  A quality 100WPC amp is dirt cheap now; heck, for under $1000 you can build a seriously good 2x200W at 8 Ohms amp using Hypex UcD400s.

Once that's factored in, things get even murkier!

Dan Wiggins
Adire Audio®

[jneutron]

Here's one example that should completely put this all to bed. The WR125S and the FR125S drivers I designed for Creative Sound. They use the exact same cones, and even the same voice coils. The FR125S has the addition of a Faraday ring, with a corresponding reduction in inductance. The FR125S has nearly an octave wider bandwidth.

This was ZERO change in moving mass - just the inductance. And bandwidth increased. ...

Your example is entirely consistent with my assertions, including the shorting ring working via Lenz's law.  Indeed, as you show, it is an extemely effective method for stiffening the gap flux while reducing coil inductance.  Too bad you can't use a shorting ring on all those car sub bandpass one note systems..It'd be the size of Toledo

Mass simply scales your output; it does not affect frequency response. Hence it does not affect transient response. It can affect amplitude, but not time.

Adding an inductor in series is a perfectly suitable approach; a loudspeaker is a fairly simplistic model of linear components, and with linear filter theory we can place extra inductance in series with the voice coil inductance and it will give us the same response as if the voice coil had the higher inductance. Like the FR/WR comparison.

I hope the FR/WR comparison really cements this - it's about the closest thing you'll see to two identical drivers save for the inductance, and you see a very dramatic change in bandwidth. And the measurements of the driver I took with and without extra mass certainly confirms that the bandwidth was NOT affected by the extra mass!
...

The overall system is the concern.  You do not mention the additional drive that results from the additional mass.  From your paper, it looks like adding mass is just a free ride, which is not the case, as you just pointed out the reduction of everything as a result of the added mass. (scales the output, in your words.)  But yet, your paper shows the bare and mass loaded drivers as overlapping.

So, your paper shows plain and mass loaded as identical via plots, while you stated here that efficiency will scale..your statement here and the plots in the white paper are not consistent with each other.  You did not indicate that the identical response of the higher mass driver was obtained via higher power drive requirements.  That is a valid tradeoff, one which you should mention within the paper.

My main concern is that the paper is not written sufficiently well to appease the more technical people...but then again, I am sure that was not your target audience.

Cheers, John