[Davey]

Well, I guess we're getting into semantics here.......with "damping factor" being related to amplifier source impedance.....or transducer impedance.....or the combination of the two when coupled together....or other configurations.

I remember reading (many years ago) an article on various definitions of "damping factor."

I can't find that actual article, but I did find this from George Augspurger from JBL:

http://documents.jordan-usa.com/Famous-Articles/The-Damping-Factor-Debate-by-George-Augspurger.pdf

George breaks the Rvc out of the driver lumped elements and analyzes in that context to compute (what he calls) "Actual Over-All DF."  (See chart on second page.)
This would seem to be aligned with Steve's understanding/definition.

Anyways, the more contemporary definition seems to be Zload/Zsource where both amplifier/source and speaker/load are considered and Rvc is included in the "load" vice the older (alternate) definition where Rvc is removed from the "load" resistance.

Good fun.

Cheers,

Dave.

[Steve]

Well, I guess we're getting into semantics here.......with "damping factor" being related to amplifier source impedance.....or transducer impedance.....or the combination of the two when coupled together....or other configurations.

I remember reading (many years ago) an article on various definitions of "damping factor."

I can't find that actual article, but I did find this from George Augspurger from JBL:

http://documents.jordan-usa.com/Famous-Articles/The-Damping-Factor-Debate-by-George-Augspurger.pdf

George breaks the Rvc out of the driver lumped elements and analyzes in that context to compute (what he calls) "Actual Over-All DF."  (See chart on second page.)
This would seem to be aligned with Steve's understanding/definition.

Anyways, the more contemporary definition seems to be Zload/Zsource where both amplifier/source and speaker/load are considered and Rvc is included in the "load" vice the older (alternate) definition where Rvc is removed from the "load" resistance.

Good fun.

Cheers,

Dave.

So someone is claiming a change Dave? If you read of other electrical speaker/driver "damping factor" calculations, then either misunderstanding or marketing is involved. And we all know money has a way of changing science to marketing science.

What I presented is the scientific definition, thevenin equivalent circuit of electrical damping factor that electronics programs are using. The only difference in electrical thevenin equivalent circuit (TEC) is whether a resistor or speaker driver was/is used.

It appears someone editing on Wiki has confused using a speaker driver load VS using a resistor load.

The thevenin electrical equivalent circuit I presented is the scientific definition.  Unfortunately, the simplistic "load" presented is a misleading model as its thevenin model is incorrect. If the model is not correct, the conclusion is not correct.
 
As mentioned earlier, the only consideration pertaining to the correct thevenin electrical equivalent circuit is whether we use a resistor or a speaker driver.

Cheers.

[Speedskater]

But both Davey and Steve are correct!

If we look at it from the point of view of the speaker box terminals. Looking one direction we see the impedance of the loudspeaker (8 Ohms).  If we look the other direction, we see the series impedance of the amplifier's output and the cable (lets say 0.1 plus 0.1 Ohms = 0.2 Ohms).
So we have a "damping factor" of about 40.

If we look at it from the point of view of the loudspeaker's cone.  Looking one direction we see the impedance of the work the driver is doing (8 Ohms).
If we look the other direction, we see the series impedance of the amplifier's output, the cable and the voice coil's DC resistance (lets say 0.1 plus 0.1 plus 5.0 Ohms= 5.2 Ohms).
So we have a "damping factor" of about 1.54.

This second viewpoint is very legitimate and explains why a high "damping factor" doesn't change anything by it's self.

What does change is the series circuit voltage divider network, of the amplifier's output and the cable on one side and the loudspeaker on the other.

[Steve]

But both Davey and Steve are correct!

If we look at it from the point of view of the speaker box terminals. Looking one direction we see the impedance of the loudspeaker (8 Ohms).  If we look the other direction, we see the series impedance of the amplifier's output and the cable (lets say 0.1 plus 0.1 Ohms = 0.2 Ohms).
So we have a "damping factor" of about 40.

If we look at it from the point of view of the loudspeaker's cone.  Looking one direction we see the impedance of the work the driver is doing (8 Ohms).
If we look the other direction, we see the series impedance of the amplifier's output, the cable and the voice coil's DC resistance (lets say 0.1 plus 0.1 plus 5.0 Ohms= 5.2 Ohms).
So we have a "damping factor" of about 1.54.

This second viewpoint is very legitimate and explains why a high "damping factor" doesn't change anything by it's self.

What does change is the series circuit voltage divider network, of the amplifier's output and the cable on one side and the loudspeaker on the other.

Unfortunately, Speed, we cannot have it both ways. Electronics is a burger isn't it.
Neither thevenin equivalent circuit nor Kirchoffs laws can vary depending upon which "direction" one looks at it. We can not violate either.

The damping factor remains small, varying with frequency and resonance. Damping factors one sees from amplifier specs is from using resistors as the load. That is a different thevenin equivalent circuit and allows for high damping factors. However, it is just a marker to compare to the competition since speakers/driver vary to much in design/parameters.

Now back to the topic. The question starting this thread is if the speaker wire will cause changes. Yes, but very minimal.

Cheers

[Davey]

But both Davey and Steve are correct!

Nope. 

We'd have to agree on a definition for "damping factor" first.  Then we might get somewhere.

Anyways, I broke out some of my old (audio) textbooks and looked up "damping factor."  There's actually a consensus from three different authors......which is:

"Damping Factor" is defined as Zload/Zout.
"True Damping Factor" is defined as Zload/(Zout + Rvc).

Zload being the nominal impedance of the loudspeaker.
Zout being the internal impedance of the amplifier.
Rvc being the DC resistance of the loudspeaker voice coil.

Obviously, speaker wire resistance adds to the denominator of either calculation.

So, I completely understand where Steve is coming from, and his analysis is not incorrect.

Sorry for the "nonsense" comment earlier.

Cheers,

Dave.

[Steve]

Thanks Dave. Over the decades, between classes and later my professor
buddies, we have already dealt with this issue.
 
Pertaining to, "Damping Factor" is defined as Zload/Zout, Zload is a
resistor, what manufacturers use to test and post the large
damping factor specs.

Cheers.

[G Georgopoulos]

Amplifiers with high output transistor beta and high nfb, will have very low output stage impendance,now if youre concerned about series wire resistance,you could parallel wire to make it thicker and thus reduce the
resistance.

[Ethan Winer]

Your assertion is that transducer Rvc is part of the source and not the load?

Steve is absolutely correct. The "load" is the sum of all series resistances that occur outside the amplifier:

AMP > wire > voice coil > wire > AMP

--Ethan

[Speedskater]

For the serious technical readers:

Damping Factor: Effects On System Response
Dick Pierce - Professional Audio Development

http://www.cartchunk.org/audiotopics/DampingFactor.pdf

[Speedskater]

This is a discussion on the subject from way back in the news-group days.

Damping Factor

******************************
Gerral Hubbard    

Could someone please explain exactly what Damping Factors are?
I know that it is effected by somethings like speaker cable resistance, etc.
******************************
MKellom
   
Damping factor is a measure of the output impedance of an amplifier. It's
calculated by dividing the load impedance you're driving (4 ohms, 2 ohms,
etc.) by the output impedance of an amp.

The reason it's an important number is that speakers, and especially
woofers, don't stop moving as soon as the amp stops sending signal. The
inertia of the driver cone keeps the cone moving, and now all of a sudden
the speaker turns into something of a "microphone" in the sense that the
motion of the cone will induce some current flow in the voice coil of the
speaker. This current is going to get back to the amp, and an amp with a
lower output impedance is going to do a much better job of "resisting"
this current (and therefore resisting the continued motion of the cone)
than a model with higher output impedance. The net result is better
control of LF drivers, i.e. "tighter" bass.

The speaker wire gets involved in the picture because it has some
resistance of its' own. Any resistance the wire possesses will be added in
series to the output impedance of the amp. So if an amp has an output
impedance of .01 ohms (at 2 ohms, 2/.01=damping factor of 200), and you
add 1 ohm of resistance due to speaker wire, your damping factor is now
about 2/1.01=2.
*********************************
Shankar Ramakrishnan

The above definiton of damping factor (i.e., the ratio of speaker impedance
to amp. output resistance) is not very significant as the true damping factor
of the overall system (which, by the way, is of the order of unity for most
systems). The first definiton only gives a qualitative estimate as to how
much the non-zero impedance of the amp and the speaker cable would affect
the actual damping factor of the overall system. For sealed woofer systems,
a value of 20 would suufice; for vented systems (which are typically more
sensitive to overall Qts of the driver), a value of about 50 or more
is adequate.
*********************
Al Borr

This sounds like gibberish to me .  Perhaps I'm missing something fundamental
here.  All the amps I own are solid state and have typically have
source impedances of a tiny fraction of an ohm.  My speakers represent
a load that is tens or even hundreds of times as large over the whole audio
range.  Where do you get your notion that damping factors of the order of unity
are typical?
***********************
David I. Baldwin

From standard wire tables, ten feet of 16 gauge speaker cable (20 ft. of
wire total) has .08 ohms of resistance, and ten feet of 12 gauge has .032
ohms of resistance.  On simple terms, if your amp has .01 ohms output
'resistance', the wire dominates the damping.  Connectors also add
resistance.  With 8 ohm speaker load and 0 ohm wire, the damping factor
would be 800; with the 16 gauge wire the damping drops to 88.  With 4 ohm
load, the damping would be 44.  This is a simplified calculation, a
number of things are left out that reduce the effective damping even more.
********************
Dick Pierce

Wrong, if you amp as 0.1 ohms output resistance, your cables have .08
ohms resistance, and your speaker's voice coil has 6.5 ohms resistance,
the voice coil dominates the damping. If fact, this is true of pretty
much every situation, save some very rare pathological cases.

>Connectors also add
>resistance.  With 8 ohm speaker load and 0 ohm wire, the damping factor
>would be 800; with the 16 gauge wire the damping drops to 88.  With 4 ohm
>load, the damping would be 44.  This is a simplified calculation, a
>number of things are left out that reduce the effective damping even more.

Yeah, like the DC resistance of the voice coil, which has been shown time
and time again to be the dominant resistance in the entire chain (see
Small, et al).
**********************
David I. Baldwin
   
I'm sure Dick Pierce is right, but I think he's answered a different
question.  The 'common' definition of damping factor that I know is viewed
from the speaker terminals with the speaker load on one side and the
amplifier and cables on the other.  'Amplifier' damping factor is
something people can play with and make changes to whereas the 'system'
damping factor as I think Dick is refering to is beyond most of us to do
anything about.
*****************
Dick Pierce

Well, given that adding a few milliohms here, and a centiohm or two
there, and STILL you are faced with a single parasitic series resistance
that is a couple of orders of magnitude larger, what possible differences
does it make.

And what is "amplifier damping factor?" What difference is there between
that and the system damping factor, which, in and of itself, is a pretty
meaningless term invented SOLELY for specsmanship. As such, it is
officially defined as the ration of the nominal load impedance (say, 8
ohms) to the amplifier source resistance). It's a meaningless
specification, in that, again, ignores the fact that a factor of 100
change in the amplifier source resistance (say, from 0.001 ohms to 0.1
ohms), equivalent to a difference of damping factors of 8000 vs 80, is
not going to make one damned bit of difference how the system performs.

Here's an excerpt from a post I made a while ago on an analysis of the
utter myth of damping factor:

> There are a lot of things that decrease the damping factor of the whole
> system:
>
> 1) speaker cable
> 2) coil in the speaker
> 3) plugs etc.

I've done this analysis SO many times, I can do it in my sleep, but here
goes again.

The damping factor proponents start throwing things like cables and plugs
and even the inductors (what I presume you mean by "coils") into the
equation. Unfortunately, they ALL ignore the largest single resistance in
the whole chain: the one the utterly swamps ALL other resistances
combined: the DC resistance of the voice coil.

Assume (which is reasonable) an amplifier with a rated 8 ohm damping
factor of, say, 1000.  Add .25 ohms for speaker cables, .25 ohms for
inductors, .25 ohms for plugs (pretty awful, but what the hey), for a
grand total series resistance of 0.008 (amp) + 0.25 (cables) + 0.25 (coil)
= 0.758. Now, it's argued, the damping factor has been spoiled to a
whopping figure of 10.6.

That's awful, right?

Well, it's a factor of 100 poorer than the spec of 1000, for sure, but
neither the damping factor NUMBER of 1000 nor of 10 HAS ANY SIGNIFICANCE IN
DETERMINING THE BEHAVIOUR OF THE LOUDSPEAKER ITSELF.

The amount of ACTUAL damping of the driver is determined by a DRIVER
figure called the total system Q, or Qtc. This is the ratio of the amount
of energy stroed in the resonance to the amount of energy dissipated, and
is a DIRECT determination of how well the speaker is damped. It is made
up of two major parts, the system Q due to mechanical losses Qmc and the
system Q due to all electrical losses Qec'. The total Q is related to
these by the following relation:

            Qmc * Qec'
     Qtc = -----------
            Qmc + Qec'

Now, the part the "damping factor" or ALL series resistance play is in
changing the electrical Q, Qec'. There is a figure, Qec, for the
electrical Q with 0 source resistance. The two are related:

                 Re + Rg
     Qec' = Qec ---------
                    Rg

where Re is the voice coil DC resistance and Rg is the TOTAL source
impedance.

Let's look at the change in Qec' and thus Qtc win the difference between
a damping factor of 1000 and 10, due to a change in source impedance of
.75 ohms. Let's assume a PERFECT 2nd order maximally flat butterworth
sealed box system, with a Qtc of 0.7071. Assume (which is reasonable) the
mechanical losses in the system (including absorbtion andfrictional
losses) result in a Qmc of 4.0. We can derive the electrical losses as

           Qmc * Qtc
    Qec = -----------
           Qmc - Qtc

which means a Qec of 0.859. Now, the typical resistance of a voice coil
on an 8 ohm driver is around 7 ohms (go measure it). Now, we can
recaculate the new Qec' with the added 0.75 ohms of series resistance:

                   7 + 0.75
     Qec' = 0.859 ----------
                     0.75

or a new Qec' of 0.951. Put that back into the total Q:

            4.0 * 0.951
     Qtc = --------------
            4.0 + 0.951

With a new system Q of 0.768. That's an increase of about 9% in the
system Q. It's VERY important to note at this point that this is less
variation then you find in manufacturing tolerance of high quality
woofers, or variation in performance due to atmospheric changes, so from
this viewpoint alone, the change is swamped by other effects.

Now, how much is the response of the speaker changed at resonance due to
this. In otherwords, how has the new series resistance, which lowered the
damping by a factor of 100 (oh gosh) decreased control of the speaker at
resonance? How much is the speaker underdamped?

Well, the original system is maximally flat, it's response show no rise
to cutoff and then rolls of smoothly. A higher Qtc results in a bump in
the response at resonance. The magnitude of that bump is both measurable
and calculatable:

                        4
                     Qtc
   Gmax = sqrt [-------------]
                    2
                 Qtc  - 0.25

Thus, this new series resistance generates a peak of 0.1 dB, FAR less
than perturbations caused in manufacturing tolerances, environmental
tolerances, room response and so on.

Now, this is not to deny that there may be an audible difference between
amolifers with different damping factors, but until you rigorously
eliminate all other possible causes, then you cannot point at damping
factor as a cause of such differences because damping factor, over the
ranges we have explored has an influence that is FAR lower than any one
of a vast number of other influences.
In cleaning up the original post, I added a typo. The correct equation for
the corrected Qe SHOULD be:

                  Re + Rg
     Qec' = Qec ---------
                    Re

Sorry for the confusion this might have caused.
****************************
Shankar Ramakrishnan    

You forget that the overall damping factor of the amp is largely determined
by the sum of the Dc resistance of the woofer's voice coil, crossover
inductor(s), the speaker cable, and the amplifier's output impedance.
generally, the latter is an insignificant part of the overall contribution.
If the damping factor of the amp is low, this leads to a higher resistance
which, paradoxically enough, increases the damping factor fo the overall
system.
Oops. The last statement was a mistake. Increasing total resistance increase
Qts leading to a lower damping factor.
Shankar
***************************


             

[*Scotty*]

I will repeat my earlier question. In as much as most amplifiers incorporate negative feedback, how does one then account for the virtual negative source impedance that its use engenders when attempting to calculate an amplifiers damping factor?
Scotty

[Speedskater]

If you want, you can build a real amplifier with a negative output impedance!  Audio Amateur magazine had one paragraph on the subject decades ago. It would act like a negative resistor.  In a normal resistor, the more current flow the more voltage drop. In a negative resistor, the more current flow the more current gain.

[*Scotty*]

This is what I was getting at. An amplifier with negative feedback can behave as though it has a negative impedance under dynamic conditions. In addition, in solid state Class A and Class AB amplifiers, the output devices act like a valve and are constantly varying their conductive state which also causes their output impedance to vary because the output devices are not always all the way on.
A Class D amplifier uses the output devices as a switch and alternates between fully on and completely off several thousand times a second.
Negative feedback and the constant very low RDS(on) of the MOSFETs may account for the frequently reported bass control that Class D seem to exhibit when compared to conventional SS amplifiers.
Scotty

[Speedskater]

For more on amplifier negative output impedance see:

Conceptual Negative Impedance Amplifier  (about half way down the page)

Variable Amplifier Impedance
Rod Elliott (ESP)

http://sound.westhost.com/project56.htm

[Davey]

Jim,

Did you get a sufficient answer for your initial query?

I'm still not sure I understand where this recommendation came from that says speaker wire resistance must be less than amp output impedance.  I read your other thread, and I don't see how this rule-of-thumb was originated.

Clearly, I didn't understand all the details of "damping factors," but maybe there's another reference on (maximum) speaker wire resistance (as it relates to amp output impedance) that I'm not aware of?

Cheers,

Dave.

[G Georgopoulos]

MKellom
   
Damping factor is a measure of the output impedance of an amplifier. It's
calculated by dividing the load impedance you're driving (4 ohms, 2 ohms,
etc.) by the output impedance of an amp.

The reason it's an important number is that speakers, and especially
woofers, don't stop moving as soon as the amp stops sending signal. The
inertia of the driver cone keeps the cone moving, and now all of a sudden
the speaker turns into something of a "microphone" in the sense that the
motion of the cone will induce some current flow in the voice coil of the
speaker. This current is going to get back to the amp, and an amp with a
lower output impedance is going to do a much better job of "resisting"
this current (and therefore resisting the continued motion of the cone)
than a model with higher output impedance. The net result is better
control of LF drivers, i.e. "tighter" bass.

The speaker wire gets involved in the picture because it has some
resistance of its' own. Any resistance the wire possesses will be added in
series to the output impedance of the amp. So if an amp has an output
impedance of .01 ohms (at 2 ohms, 2/.01=damping factor of 200), and you
add 1 ohm of resistance due to speaker wire, your damping factor is now
about 2/1.01=2.
*********************************

I have devised an equation for calculating the damping factor with series resistance
from the numbers of the example above we have

(3 / .01) / 3 = 100

cheers

[Steve]

Jim,

Clearly, I didn't understand all the details of "damping factors,"

Cheers,

Dave.

Hi Dave,

I understand the confusion. My points are not necessarily in order of importance.

Maybe the article, their explanation etc is for clarity, simplicity along with what
the public is used to? It does simplify things as seen below.

I would suppose that comparing damping factors (DF) of 250 vs another of 175 looks better to the public than 1.454 vs 1.439. And using a resistor results in a relatively constant DF figure spec vs a speaker which gives variable DF results for a variety of reasons.

Basically they appear to be saying that since we are doing comparisons between amplifier specs, we can define the definition of damping factor by simply using a typical "speaker impedance" vs amplifier output Z. The public does not know the difference.

As mentioned above, a variable DF figure from a speaker would cause confusion as  several additional explanations such as what frequency (Z varies with frequency), what type of speaker is used. Conformity would be missing, confusion would reign.

Performing a basic thevenin equivalent circuit (TEC) clearly proves they are referencing with resistors/DC resistance, not speakers to obtain the large damping factor figures.

Cheers.

[JohnR]

"Damping Factor" is defined as Zload/Zout.
"True Damping Factor" is defined as Zload/(Zout + Rvc).

So the ideal "True Damping Factor" is 1? (amplifier with zero output impedance, speaker with no inductance e.g. planar-magnetic driver, zero speaker lead impedance)

And if the amp's output impedance was half of Rvc, then true Damping Factor is 0.5?

I'm just unclear on what the significance of this definition is then.

[*Scotty*]

John, I think this is called an academic discussion.
Scotty

[Davey]

John,

I don't think you can infer there's an "ideal" damping factor.

Since (in most cases) Zout << Rvc, "True Damping Factor" is essentially Zload/Rvc.  Some speakers (as you mentioned) are essentially resistive, so the TDF is equal to 1.0.  However, even for most of those systems, the crossover network probably creates a phase angle which skews the impedance relative to the Rvc in a part of the frequency range.

If you're an amplifier manufacturer and want to advertise the output impedance of your product, you don't have much choice.  You either have to express it as "damping factor" with a defined resistive load, or just quote the number directly.  Bigger numbers look better so 100, 200, 1000, etc, is preferable to 0.001, 0.0153, 0.02, etc, ohms.

I suppose the whole concept of Damping Factor as it relates to the amplifier/speaker interface is fairly meaningless.  The speaker transducers are real-world, electro-mechanical devices and there's only so much effective "control" that a source could have on their operation.

I'd still like to know where this (supposed) rule-of-thumb came from regarding wire resistance not exceeding amp output resistance.  I think maybe James lost interest in the thread. 

As Scotty says, it's an academic discussion.

Cheers,

Dave.