# Damping factor explained - or not?

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#### jan.didden

Paid Member
I know - the proverbial horse beaten to death. And thought I knew it all.
Yet, when trying to explain it in simple terms I found I didn't know enough detail to do that

Most explanations come up with an example of a kick-drum pulse that all of a sudden stops, and the speaker which continues to move, unless 'braked' by the low internal impedance of the driving amp. In moving, the speaker generates EMF that has to be absorbed by the amp. The lower the output impedance of the amp, the better it is at braking the speaker (plus a few other issues but this is the gist of it). So far so good.

But then I thought: the speaker generates EMF because the coil moves in a magnetic field. So I would expect the speaker to generate EMF continuously and not just when the kick-drum stops!

That leads to a realization (I think) that when you fix the speaker moving part and stop it from moving, the amp sees a different impedance then in normal operation. So the amp damping and speaker EMF generation is a continuous process and not just with impulsive signals.

Am I correct?

Jan

#### Mooly

Paid Member
Most explanations come up with an example of a kick-drum pulse that all of a sudden stops, and the speaker which continues to move, unless 'braked' by the low internal impedance of the driving amp. In moving, the speaker generates EMF that has to be absorbed by the amp. The lower the output impedance of the amp, the better it is at braking the speaker (plus a few other issues but this is the gist of it). So far so good.

The standard model

But then I thought: the speaker generates EMF because the coil moves in a magnetic field. So I would expect the speaker to generate EMF continuously and not just when the kick-drum stops!

Of course it does. It is also a microphone with a pretty impressive current delivery capability. Stereo set up... you have in effect two 'microphones' feeding back uncorrelated energy into the amp output nodes.

That leads to a realization (I think) that when you fix the speaker moving part and stop it from moving, the amp sees a different impedance then in normal operation. So the amp damping and speaker EMF generation is a continuous process and not just with impulsive signals.

Am I correct?

Jan

I think you are correct

Now ask the question about how we test amplifiers into 8 ohm resistive loads and leading on from the results of that, why amplifiers all seem to sound 'different' in subtle (and sometimes not so subtle) ways.

#### billshurv

Paid Member
I find it easier to view DF as an impedance in series with the speaker. But that doesn't help explain to the layman...

#### jan.didden

Paid Member
OK, I get all that. Then how about this: the amp sends a current trough the voicecoil and that gets the speaker moving. As a result of that, the moving voice coil generates current as it moves through the mag field. This current is opposite to the driving current, or not?

If it is opposite, the amp 'sees' a higher impedance (lower net current drawn) than with a nominal resistance. If the generated current has the same direction, the amp sees a lower impedance (more current) than in the case of a resistive load.

Or is it the other way around?

Jan

#### billshurv

Paid Member
But if you apply an impulse, the impulse pushes the cone out, but as it returns to zero does it pull the cone back, or is the restoring force supplied by the spider? It's a complex electro-mechanical system that behaves differently over frequency so I fear too hard to explain simply!

#### jan.didden

Paid Member
But if you apply an impulse, the impulse pushes the cone out, but as it returns to zero does it pull the cone back, or is the restoring force supplied by the spider? It's a complex electro-mechanical system that behaves differently over frequency so I fear too hard to explain simply!

I think it is partly spider, and partly the amp 'pulling' it back.
What I would like to get clear is the basics without worrying about the spider and such, without worrying about frequency dependence etc.

Assume a very slow varying DC ;-)

Jan

#### billshurv

Paid Member
hmm Well stepping back to F=BIL, with no spider and surround other than to stop the voice coil firing across the room application of F will move the cone, but removal of F will not pull it back. You need F in the other direction. Either mechanical, or from negative current.

#### wintermute

Paid Member
I would assume that the back EMF is also fed back through the feed back loop, does this create a correction for an error that wasn't actually there in the first place?

Tony.

#### planet IX

Paid Member
I would assume that the back EMF is also fed back through the feed back loop, does this create a correction for an error that wasn't actually there in the first place?

Tony.

I think thats why some prefer to use low global feedback.

How I see it:
the current from the amp moves the coil
the moving coil generates a back-emf voltage (with opposite direction), corresponding to the speed with which the coil moves through the magnetic field
soundwaves (reflections, other speaker,...) generate a voltage in the coil, as it acts like a microphone
the mechanical system (spring-damper) adds is contributions to all this
the output-resistance of the amp (in series with the the crossover parts) dampens the current generated in the speaker coil

#### Hiten

Can we simulate and exaggerate this back EMF artificially, so we can measure and audition its effect.
Regards.

#### cwtim01

I found this very old document, from more than 60 years ago, very enlightening about damping factor (well, at least for me).

#### Attachments

• Critical Damping for Speakers.pdf
130.6 KB · Views: 190

#### DF96

jan.didden said:
Am I correct?
Yes. This is partly why the impedance of a speaker varies with frequency.

This current is opposite to the driving current, or not?
Generally, yes. Resonance and stored energy can do strange things, though. However, the net result is that this complex electromechanical system can be represented by an equivalent circuit of electronic components - so all the effect of 'back EMF' is summed up in the speaker impedance.

Even the speaker acting as a microphone does so via adding voltage sources to the equivalent circuit so the impedance is unchanged, unless the incident field is closely related to the driving signal. This will be the case in stereo, but fortunately the coupling between two speakers via the room will be relatively weak so not a problem.

wintermute said:
I would assume that the back EMF is also fed back through the feed back loop, does this create a correction for an error that wasn't actually there in the first place?
No. The effect of a voltage applied to the amp output is fully described by the amp's output impedance.

planet IX said:
I think thats why some prefer to use low global feedback.
Yes, those who don't understand circuits with feedback may prefer to avoid that which they don't understand.

Hiten said:
Can we simulate and exaggerate this back EMF artificially, so we can measure and audition its effect.
You measure its effect every time you measure the output impedance of an amp, or the input impedance of a speaker. You audition its effect every time you listen to music.

Can we please stop this becoming yet another 'back EMF' thread, which rambles on for 100s of posts as everyone pitches in and shares their misunderstandings and confusion about impedance, feedback etc.

#### Hiten

Thanks DF96.

Read the pdf file posted by cwtim01. A little offshoot question. With reference to back emf criteria amongst others; wouldn't this be a good proposal of having an active crossover two amplifier (if two way speakers) system? We can control low frequency driver more effeciently where back emf is considered more.
Regards

#### ilimzn

jan, you are correct in principle, just try to view the speaker as a motor - which it really is. This means that EMF continuously changes as the speaker membrane accelerates and decelerates. In other words, you are dealing with INERTIA of 'something' coupled to the 'motor'. If there was no inertia, speakers would have something much more approaching resistance in the audio band, rather than impedance.
Now, let me assure you, in the above the amount of stuff I have idealized and disregarded is staggering which is why speaker driver design is very much art as well as science. Some of the parameters are quite intractable.

So on this level of abstraction we have a 'motor' which is not ideal (it's coils have resistance and inductance - and ideal motor would behave much like an ideal transformer, no coil resistance, and infinite inductance free running), so the 'electric' part of the motor has an 'electric' inertia, you cannot make it start or stop immediately, because the maximum current is at any point limited by a combination of inductance and coil resistance. This means that for slow lower acceleration and deceleration, the motor is more controllable as lower rates of change of the driving voltage are needed. This is why in speakers the damping factor produced by a driving amplifier is important mostly at 'low' frequencies and at 'high' frequency the damping is mostly mechanical as the influence of the coil inductance rises. Of course, you should use 'low' and 'high' relatively, in particular to speaker size. Also, there are ways to lower coil inductance.
This also points to your conclusion that measuring the impedance of a speaker with a 'stuck' membrane that is unable to move will give you a rather un-glorious plot you would see with any series RL circuit. There are some extra effects due to the 'core' of the L actually being rather bad quality in most cases

At the next level of abstraction we now have to introduce the fact that the speaker is a spring loaded mass - we already introduced mass through inertia, but spring loading gives it a very important new element - a resonance frequency. This means we are talking of a system capable of oscillation (Albeit damped) which gets us into the frequency domain and impedances. This means that as the voice coil moves through a cycle, the current follows the voltage 'with inertia' - unless we are close to resonance.
Just like any resonant system the speaker has a Q factor. For analysis purposes it is normally split into two Q factors - one is a purely mechanical one, and is what you would see if you applied a pulse to the voice coil and then removed the source from the voice coil altogether (open circuit) - the speaker has it's own mechanical resonance, defined by the moving mass and spring constant of the spider and (in some cases) surround, and mechanical damping (spider impregnation which tunes how 'hard' the spring is, is also lossy, there is some plastic and not only elastic deformation - and in case you were wondering, yes, this implies some hysteresis and other unwanted stuff).
However, since the mechanical parts behave as a spring coupled mass and damping, you can transfer them to the electrical domain, i.e. as viewed 'from the voice coil'. And this is where you get the total Q, resonance frequency, impedance curve.

What this gets you is the fact that the 'damping factor' is not a constant, because the speaker impedance is not a constant, but rather depends on frequency - and that is all in the domain of small signals, or, if we take the mechanical view, small membrane excursions. The reason why it is specified is not directly for transient signals, but rather to predict how much of the speaker impedance change will appear as a factor in the speaker amplitude vs frequency response curve. This is important because the amplitude vs frequency response curve you get as a reference measurement for a driver is dune under certain conditions, namely, the voice coil is driven by a 'zero' impedance source. In real speakers pronounced differences in performances of the same set of drivers appear in cases when active vs passive crossovers are used (in the passive case the series impedances are higher, sometimes bu orders of magnitude) and, when high output impedance amplifiers are used (tube vs solid state, current vs voltage drive).

So where does the transient behavior come in?
This actually presents a big and rather unpredictable problem, which is generally easier to solve on the amplifier side, which is why it is mostly insisted that the amplifier output impedance is as close to zero as possible. It should also be noted that it is one of the contributing factors as the combined resistances of binding posts and cables often get to be within the same order of magnitude as the amp impedance, and sometimes, shamefully, even more.
So where is the problem on the speaker side? It is a list of issues almost to long to enumerate:
Speaker impedance is not a constant with amplitude. The geometry of the magnetic field around the coil shifts quite wildly at larger excursions to the point where some of the iron can even go into saturation, not to mention the effects of hysteresis, eddy current losses in the magnetic system, and even skin effect.
Nonlinear behavior of the suspension results in changes in the Q factor with everything, from temperature and amplitude to possibly the zodiac and to make things worse, the membrane has the same effects so sometimes it behaves as if it was the membrane, and sometimes as if it is the suspension, and sometimes, when there is partial deformation, it seems to vanish from the system altogether, only to release stored energy a bit later when the waveform changes. With this form of deformation we can get traveling waves in the membrane (Walsh type operation) which reflect off the surround and in fact anny place where two different materials are glued together.
And all of this is when it's not even mounted in an enclosure - where even the very air trapped does not behave linearly, not to mention standing waves in it or in the material of the enclosure etc. Obviously, impedance of the loudspeaker changes with it being applied in a box or other type of 'interface to the surrounding space' - more elements get coupled to the mechanical system of the driver and it's all seen through the voice coil.
And then the whole thing is put in another place called a room, and yes it couples too - just like the other speakers in the box do as well.
Now, if you were to measure very precisely the impedance curve of this speaker, many of these effects can be seen. It is not as evident in any driver, some effects are seen more in LF and others in HF drivers.

Getting back to the damping factor - some of the above should now point easily to where the problem might arise in the electrical domain of the amplifier. Mostly it has to do with the fact that the basic (no NFB applied) transfer function of the amplifier always to an extent depends on the actual impedance of the load. Classic NFB can only reduce the influence. A typical contrast here would be an amplifier which has a follower on the output, where the local NFB action already uses gm (or equivalent) to reduce the influence of the load impedance, versus an amplifier where the output works in common source/emitter/cathode and has an inherently high output impedance in parallel with the load impedance so the latter heavily influences the transfer characteristic (SIT amplifiers excluded the output impedance tends to be on the same order as load impedance or less), while we rely on not so local NFB to reduce the apparent output impedance of the amplifier in comparison with the very thing that largely defines it.
At first glance, one would say one problem reduces to the other - but here we forget that the analysis is most often done for small signals. In large signal situations, like clipping, the second case might have a lot more problems.
In the real world, most of this is substantially mitigated by real speakers using a passive crossover which has it's own series impedance often orders of magnitude larger than a typical (SS) amp, so most of the work of the damping factor happens around the speaker resonance(s) which is exactly where most work is needed as the whole point of implementing a loudspeaker (box, not driver) is to manage the driver resonance inside the audio band. But then try to drive the same drivers directly, and effects can happen in places you would not expect.

#### ilimzn

Can we please stop this becoming yet another 'back EMF' thread, which rambles on for 100s of posts as everyone pitches in and shares their misunderstandings and confusion about impedance...

Amen to that!
Back EMF is just a fancy name for saying something is an impedance rather than a bog standard resistance. And also 'back' is a misnomer as it can be negative or positive so if negative is it then 'forward'?

#### DF96

Hiten said:
With reference to back emf criteria amongst others; wouldn't this be a good proposal of having an active crossover two amplifier (if two way speakers) system? We can control low frequency driver more effeciently where back emf is considered more.
No. LF behaviour is controlled by a combination of mechanical damping in the speaker, and electrical damping provided by the amp plus crossover. If the speaker system is designed to be fed from a low impedance (approaching zero) then it doesn't know and doesn't care how that is provided.

If you want to remove the passive crossover and wire the woofer directly to the amp output (with a crossover before the amps) then you need a slightly different speaker design as the mechanical damping will need to be adjusted. A well-designed speaker will work best when used under the conditions it was designed for.

#### P.Lacombe

I think it is partly spider, and partly the amp 'pulling' it back.
What I would like to get clear is the basics without worrying about the spider and such, without worrying about frequency dependence etc.

Assume a very slow varying DC ;-)

Jan
Many years ago, G.A.Briggs wrote that it is essential that the spider recall the moving coil in the center of the magnetic plates, because of the poor efficiency of the amp to do this. But at the time, I must admit that valve amplifiers, even with big output transformers, exhibit low damping factor in the bass range*.

G.A.Briggs wrote also that good spider makes audible difference in sound of a piano. Mr Briggs seem not to like other percussions, I suppose.
___________
*(Yes, damping factor is not constant vs frequency, even in best amplifiers...)

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#### billshurv

Paid Member
*(Yes, damping factor is not constant vs frequency, even in best amplifiers...)

At danger of veering OT don't forget that if you monitor current and voltage at the drive unit you can calculate position and correct. Feedback, but using a hunk a DSP. This in theory gives you almost infinitely adjustable DF across the frequency band. It may be the future (and present for those lucky to have kii-3)

#### Eldam

newbie alert bis : A big amp with low BL driver should be really better ? with a single layer voice coil as well ? and a return gnd wire with less R ? ... to allow to minimize the EMF !

#### DF96

P.Lacombe said:
*(Yes, damping factor is not constant vs frequency, even in best amplifiers...)
Valve amplifiers may achieve reasonably flat DF. Most SS amps will have DF falling with frequency, but even at HF it is likely to be larger than valve DF. Fortunately, this doesn't matter, as DF merely has to be large enough and then its exact value is irrelevant (apart from marketing purposes).

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