Nait XS-2 damping factor

Simon,

Correct, it is impedance, but the impedance from the voice coil, not the impedance from the speaker terminals, which makes it slightly more difficult to calculate (you need to use Thiele-Small parameters and take into account the reverse insertion impedance of the crossover).  As pointed out it also related to the difference between the amp output potential difference and the potential difference of the back EMF.  This makes analysis of transient conditions even more complicated.

However this is never less than the voice coil resistance, so that's a good place to start!

Simon, I've realised that, further to the above, a little more is warranted to help you get a more complete picture.

For a full analysis of the resistance / impedance question, you need to look at energy storage and release from inductive, capacitative electrical components and storage and loss moduli of the mechanical components in the system, and how, in transient conditions, these interact with the energy 'loss' (by conversion to heat) in the resistive elements.

The only true energy loss (and thus the only true damping) in the electric circuit is through the resistive elements; however, the energy stored in inductive, capacitative and mechanical components is usually released at specific time constants / frequencies, and so can time shift energy away from specific elements in the signal and push it into a general clutter of distortion components at other frequencies.  This has a similar psycho-acoustic effect to damping as these distortions don't have simple harmonic relationships to the excitation signal and hence are partially ignored by the brain.

And some people think speaker design is easy!

Huge posted:

IB,

Principles:

1  Whenever the amp is powered, it's ALWAYS controlling the speaker cone.  When there's a signal, the amp is trying to accelerate the cone according to the signal; when there's no signal the amp is trying to keep the cone at it's neutral point.

2  Any time the speaker cone is moving, the effect of the magnetic field and the movement of the cone generates a back EMF.  Anytime that EMF doesn't match the output voltage of the amp a current is flowing through the output of the amp (& influenced by the output impedance), through the speaker cables and their connectors (& influenced by the their resistance), and through the voice coil (& influenced by it resistance).

3  The damping of the cone is dependant on sinking this current (i.e. shorting it through a resistance) to absorb the kinetic energy of the moving mass of the cone and voice coil. 

 

OK, analysis using simple 325 year old mathematics...

Take a single turn in the centre of the voice coil, it generates a back EMF.  That EMF drives a current that flows from it through almost 1/2 the voice coil's resistance in each direction.

In case you haven't spotted it, then consider an infinitely small section of the voice coil (anywhere in the voice coil, it doesn't make any difference).  In this case, from the view of that section of the coil and looking both ways, ALL the resistance of the voice coil is in series with the amp, and this is the same no matter where the section is.

Ergo the DF MUST take the resistance of the voice coil into account as that's in series with the amplifier's output.
To take the speakers resistance out of the calculation is complete nonsense; any calculation on that basis is just meaningless.

Hi Huge,

I am not fundamentally disagreeing with your DF arguments, but I do disagree with the calculations you cited, namely

"Taking an amp with a high output impedance of 0.4Ω, adding 4x4mm connectors = 20mΩ total, 2 speaker wires (12AWG, 5M) = 0.05Ω and adding 6.9Ω, gives an electrical damping factor of 8 / (0.4 + 0.02 + 0.05 + 6.9) = 1.085."

In this you quote the nominal impedance divided by the sum of actual impedances ((or resistances). How is that damping factor? DF is speaker impedance divided by amp impedance, but you include the actual speaker impedance (or resistance) in the denominator..

I believe my calculation to be correct, not yours, in this scenario a DF of 17.4 not 1.085.

IB,

It's the speaker cone (via the voice coil) that's being damped, so why do you think it's correct to ignore it's resistance?  I have designed audio amps and I do know how they works and what is correct.

When an amplifier is connected to a speaker, the calculation I gave is correct - it gives the true damping factor of the system - i.e. the amplifier output and the speaker.

When an amplifier is not connected to a speaker (the only time you can ignore the speaker's resistance), there isn't a damping factor as there's nothing to damp - there's nothing mechanical moving and no resonance (at least for a properly designed amp!).

The formula you used assumes either
1  that the speaker being damped has zero resistance (not possible)
or
2  that the speaker being damped exists in one part of the calculation (the nominal impedance) and then doesn't exist in another part of the calculation (the sum of the resistances that oppose the back EMF).
This never makes any sense and makes the formula you used inappropriate and irrelevant.

An alternative approach to make the ratio you calculate valid is to multiply it by i (usually represented by j in electronic circles to avoid confusion with i which is used to represent current - in either case it's used to represent the square root of -1) - in either case it becomes purely imaginary!  

dayjay posted:

Simon-in-Suffolk posted:

TOBYJUG posted:

 Maybe " damping factor" as a descriptive term is misunderstood by so many that it might have a collective rightness in its wrongness.

Sounds a bit like a Rumsfeldism -  "There are things we know we know. We also know there are known unknowns......"

I don't know that one

well get to know it!

this is my favorite Rumsfeld-ism. it's very well said, universally applicable when you're trying to assess the risks of a given situation, and just cosmically absurd, in that he didn't quite account for the "known known" that occupations of other countries tend to go rather poorly.

i also find myself using "you go to war with the army you have, not the army you want to have" in my daily life.