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First cycle distortion - Graham, what is that? - Click HERE for Original Thread

peranders

First cycle distortion - Graham, what is that?

I have never heard it before.

quote:

In another thread I mentioned distortion of the leading edges of first cycles, and called it 'FCD' = first cycle distortion.

http://www.diyaudio.com/forums/show...3559#post373559

Can you explain? Has music really signals that can be regarded as startup transients? Maybe for slow amp?

Can you give me any reference material?

sreten

From the accounts I've read so far it appears to be a rather
disingenuous way of referring to what is already known.

It is not as far as I can tell any sort of "new" distortion
mechanism, it appears to be the effect of closed loop
bandwidth and stability on a sine wave that abruptly
starts at t=0.

As far as I can tell reproduction of any discontinuity
emphasises wide bandwidth design over high feedback
levels in the audioband with the necessarily restricted
bandwidth required for stability.

And by definition such an approach would imply that
the JLH class A type circuit favoured by GM would
come out well under such analysis.

:) sreten.

peranders

quote:

Originally posted by sreten
on a sine wave that abruptly
starts at t=0.

But what has this to do with music?

sreten

quote:

Originally posted by peranders

But what has this to do with music?

I'm afraid I can't help you here, but IMO the
same as any waveform with discontinuities.

:) sreten.

peranders

Isn't this the same thing as step response?

boholm

It has do with music is this way (in my world ;-)):

Music is comprised of transients. There is almost - exept when a tone is prolonged on purpose - no steady-state in music. Hit a string on a guitar and it will start swinging as soon as the plectrum or your finger lets go of the string. But the amplitude of the swinging wil not be constant, it will decrease untill it stops. Concluding; No steady state. As you may or may not see/know, the first swing from start point to start point is the one with the biggest amplitude, as it will fade gradually as already sayd.

Here comes the question: What can cause for a signal to be dampened in it first swing - or cycle (as Graham appropiately calls it)?

Here comes another question: How important is this first swing? Would you be able to hear it, if it wasn't there or if it was unintentionally dampened? And since music is - almost - pure pulses (first swings) will you be able to hear this somehow?

If you have looked at the graphics Graham presented you could see that the first period was dampened before reaching a steady state, and I do not know what could cause this - I haven't seen it before. But what intriques me, is that the very sudden start of this first period. There is no "gentle" start of it. But maybe these two factors are not connected?

"Must figure this out . . . " he said leaving the house to visit some other friends . . .

sreten

quote:

Originally posted by peranders
Isn't this the same thing as step response?

Step, pulse, square, triangular doesn't make a lot of difference.

A discontinuity is a discontinuity, requiring theoretically infinite bandwidth.

And reproduction depends on closed loop bandwidth and stability.

:) sreten.

Nelson Pass

I was rather under the impression (and I could be wrong) that
Graham was making reference to distortion created by the
active character of the loudspeaker, not intrinsic distortion of
an amplifier using feedback.

Feedback in power amplifiers is far too fast to create first
cycle distortion due to feedback delay, at least in the context
of audio frequencies. The notion that it takes a cycle or two
for the amp to "get it" is erroneous.

The loudspeaker on the other hand may not exhibit the same
impedance on the first cycle as subsequently due to the back
emf generated by a moving voice coil, and so can draw more
current on the first cycle. It seemed to me that this or
something similar was the basis of Graham's argument.

Steve Eddy

quote:

Originally posted by Nelson Pass
The loudspeaker on the other hand may not exhibit the same
impedance on the first cycle as subsequently due to the back
emf generated by a moving voice coil, and so can draw more
current on the first cycle. It seemed to me that this or
something similar was the basis of Graham's argument.

But I'm left wondering the same thing I was left wondering in the previous thread; what's the fundamental difference between the back EMF of the loudspeaker and the back EMF of any other RLC resonant circiut?

se

andy_c

quote:

Actually, I believe Graham was talking about the amplifier itself, possibly including loading effects. He simulated the transient response to a sine wave in SPICE, then did an FFT on the first cycle to determine the harmonic distortion of just the first cycle.

I believe jcx summed it up best in this post http://www.diyaudio.com/forums/show...9915#post369915 when he pointed out that a single pole low pass filter has considerable "first cycle distortion" unless the bandwidth is quite large. It's clear from that post that "first cycle distortion" has little to do with non-linearity per se and is mostly due to the transient response of the circuit.

sreten

quote:

Originally posted by Nelson Pass
I was rather under the impression (and I could be wrong) that
Graham was making reference to distortion created by the
active character of the loudspeaker, not intrinsic distortion of
an amplifier using feedback.

Feedback in power amplifiers is far too fast to create first
cycle distortion due to feedback delay, at least in the context
of audio frequencies. The notion that it takes a cycle or two
for the amp to "get it" is erroneous.

The loudspeaker on the other hand may not exhibit the same
impedance on the first cycle as subsequently due to the back
emf generated by a moving voice coil, and so can draw more
current on the first cycle. It seemed to me that this or
something similar was the basis of Graham's argument.

quote:

GM :

In another thread I mentioned distortion of the leading edges of first cycles, and called it 'FCD' = first cycle distortion.

I would not build this amplifier because R1+C1, C3, R10+Q8/C9 and R11+Q9 are a series of first cycle distortion generators. Values and turnovers not known, the delays might be low, but I cannot assume that they are. Stable - yes; accurate - no.

Well you tell me, it all seems smoke and mirrors to me.

A cohesive account of the phenomena is lacking.

The dynamic impedance effects of loudspeakers has been
covered by D.Self using waveforms with discontinuities.

The question is : is FCD a genuine phenomena, or an
alternative viewpoint of known existing phemomena.

:) sreten.

PMA

Per,

have a look here: http://w3.mit.edu/cheever/www/cheever_thesis.pdf

Pavel

subwo1

quote:

When the moving mass of the cone is coupled to the voice coil, the result is an AC generator. How much this active power input to the amplifier's output terminal differs from the nominal inductive phase shift of the voice coil depends on the speaker.

peranders

Hm, all the experts are :scratch: their heads. Has Graham discovered something new? :confused:

quote:

Originally posted by PMA
Per,
have a look here: http://w3.mit.edu/cheever/www/cheever_thesis.pdf

Heavy report :att'n: I'm afraid I haven't got the time to read right now.

sam9

A-----------------
"Actually, I believe Graham was talking about the amplifier itself, possibly including loading effects. He simulated the transient response to a sine wave in SPICE, then did an FFT on the first cycle to determine the harmonic distortion of just the first cycle."

I would want some assurance that what is being seen isn't just a
computational artifact from SPICE. I have doneof SPICE transient analyses and specified that recording of data does not start until after 1ms and found that the FFT looks better sometimes. I've assumed it had a lot to do with the math and next to nothing to do with circuit performance under normal conditions. Of course, I may be wrong which is nothing new.

B---------------------
"Music is comprised of transients. There is almost - exept when a tone is prolonged on purpose - no steady-state in music. Hit a string on a guitar and it will start swinging as soon as the plectrum or your finger lets go of the string. But the amplitude of the swinging wil not be constant, it will decrease untill it stops. Concluding; No steady state. As you may or may not see/know, the first swing from start point to start point is the one with the biggest amplitude, as it will fade gradually as already sayd.

Here comes the question: What can cause for a signal to be dampened in it first swing - or cycle (as Graham appropiately calls it)?"

This seems to imply that aqmplifier performance during the current cycle is dependant on it's state during the immediately preceeding cycle. "First cycle distortion" would just be a special case of this proposition. If you assume, for the sake of argument' that the slew rate is adequate for the peak voltages implied by the rails, then it seems to me you are arguing for some form of semi-conductor memory. I'm not familiar enough with the relavent literature to know whether this has been investigated or not, but it seems to me this is what the proposition comes down to if you eliminate inadequate slew rate as a mechanism.

jneutron

You cannot get accurate spectral analysis results with an FFT of one cycle....That is a horrible window.

Best you can do is record it, and duplicate it in time, making it a pseudo sine wave.

Or, record it, and apply nulling techniques with sine waveforms.

John

quote:

I'm afraid I haven't got the time to read right now.

Don't bother, it was a terrible piece of work. Amazing he got that thesis passed.

PMA

quote:

Originally posted by subwo1

When the moving mass of the cone is coupled to the voice coil, the result is an AC generator. How much this active power input to the amplifier's output terminal differs from the nominal inductive phase shift of the voice coil depends on the speaker.

The explanation hereabove is often used in the DIY community. In fact the electrodynamic speaker can be described by the attached schematics. R2 a L2 are the resistance and the inductance of the voice coil in the "braked" state (not moving). R1, L1 and C1 are the components calculated from mechanical side of the speaker to the electrical one. They describe the resonance effect of the speaker. The component values will differ according to the real speaker.

andy_c

quote:

Originally posted by sam9
I would want some assurance that what is being seen isn't just a
computational artifact from SPICE. I have doneof SPICE transient analyses and specified that recording of data does not start until after 1ms and found that the FFT looks better sometimes. I've assumed it had a lot to do with the math and next to nothing to do with circuit performance under normal conditions.(...)

Actually it's intimately related to the transient response of the circuit. What you're seeing is the need to wait until the transient response settles out until the signal you're doing the FFT of becomes truly periodic. You can show analytically (using Laplace transforms) that for a first order low-pass filter, the response to a pulsed sine wave is an undistorted pulsed sine wave with shifted phase, plus a decaying exponential. Since the FFT of a single cycle is just the spectrum of the periodic extension of that single cycle (provided the sample interval is chosen right), the spectrum is that of the periodic extension of the sum of two signals:

1) The undistorted pulsed, phase shifted sine
2) The periodic extension of the decaying exponential (from the transient response)

This is for a single pole low-pass filter only. The presence of (2) above causes the distortion to appear, since the periodic extension of a decaying exponential looks like a high-pass filtered square wave with every other half-cycle negated. It can be shown analytically that the amplitude of the component (2) above goes to zero when the phase shift of the sine goes to zero. Thus the "first cycle distortion" of the output goes to zero as the bandwidth goes to infinity.

PMA

So how about the transient response of the digital filter of the CD player, for example? It has rise time (10% - 90%) no shorter than 17us and limited initial dv/dt, far below slew rate of the contemporary amplifiers. And how about analysis of the transients of the musical instruments itself? ;)

andy_c

quote:

Originally posted by PMA
So how about the transient response of the digital filter of the CD player, for example?(...)

Exactly.

Steve Eddy

quote:

Originally posted by PMA
The explanation hereabove is often used in the DIY community. In fact the electrodynamic speaker can be described by the attached schematics. R2 a L2 are the resistance and the inductance of the voice coil in the "braked" state (not moving). R1, L1 and C1 are the components calculated from mechanical side of the speaker to the electrical one. They describe the resonance effect of the speaker. The component values will differ according to the real speaker.

Exactly.

And you don't hear people referring to capacitors or inductors as "AC generators."

The cone's mass and its compliance are energy storage mechanisms just as inductors and capacitors are. And in fact the cone's mass and compliance have their electrical analogues in inductance and capacitance respectively, which is why dynamic loudspeaker drivers are modeled electrically using R, L and C elements.

se

quote:

Originally posted by PMA
So how about the transient response of the digital filter of the CD player, for example? It has rise time (10% - 90%) no shorter than 17us and limited initial dv/dt, far below slew rate of the contemporary amplifiers. And how about analysis of the transients of the musical instruments itself? ;)

To square the circle, other sources (tape, phono) give pretty low slews also. This looks like yet one more solution in search of a problem.

Steve Eddy

quote:

Originally posted by SY
To square the circle, other sources (tape, phono) give pretty low slews also. This looks like yet one more solution in search of a problem.

Or a great business opportunity for someone looking to get into the problem creation industry. :)

se

traderbam

On the subject of speaker electrical models.
The speaker has the additional complexity of being coupled to air and of drive units being physically coupled to one another through the speaker box and the air within the speaker box. Speakers are also microphones, so there will be cone movements which are temporally delayed from the original signal and these will create impedance changes as seen by the amplifier.
Also, the speaker cables form transmission lines which can have very big effects on impedance seen by the amp at HF (as Nelson knows well).
Just for completeness.

subwo1

quote:

And you don't hear people referring to capacitors or inductors as "AC generators."

That is because they aren't, but a speaker nonetheless is. The model which approximates the real thing is interesting, though.

millwood

quote:

Originally posted by subwo1

That is because they aren't, but a speaker nonetheless is. The model which approximates the real thing is interesting, though.

that's the TS model that I referred to in the original thread. Nobody including Graham picked it up, tho, :)

yeah, if you write out the differential equiations describing the electro-mechanical movements of a real speaker, you get the same differential equations describing that RLC network presented by TS.

so as far as the amp is concerned, the rlc network and its equivalent speaker are one and the same.

Steve Eddy

quote:

Originally posted by subwo1
That is because they aren't, but a speaker nonetheless is.

How is it exactly that a speaker is an AC generator but an inductor isn't?

Nelson Pass

quote:

Originally posted by PMA
http://w3.mit.edu/cheever/www/cheever_thesis.pdf

"Don't bother, it was a terrible piece of work. Amazing he got that thesis passed."

Well I thought the part where he quoted a paragraph of mine
was just great. :cool:

Also, I think there is some merit to the weighting of harmonics
in evaluating harmonic distortion. I know I'd rather listen to
1% 2nd or 3rd than 1% 4th and 5th.

"You cannot get accurate spectral analysis results with an FFT of one cycle....That is a horrible window."

You're right. I'd have to see some evidence of how you can
accurately get Spice to model THD on a waveform start that
has to be full of harmonics by itself, much less steady state.

andy_c

quote:

Originally posted by Nelson Pass
(...quoting jneutron...)"You cannot get accurate spectral analysis results with an FFT of one cycle....That is a horrible window."

You're right. I'd have to see some evidence of how you can
accurately get Spice to model THD on a waveform start that
has to be full of harmonics by itself, much less steady state.

I believe the problem that jneutron is referring to is the so-called "DFT leakage". Let's assume we have a single cycle of a truly periodic waveform. Ignore for the moment that the first cycle of GM's tone burst, when extended to be periodic, will contain discontinuities. That's because of the transient, which makes the initial value of the "cycle" different from the final value. Anyway, the DFT frequency bins are given by:

f_bin= m*f_s/N

where m=0, 1, 2, ...N-1 and
N is the number of DFT samples and
f_s is the sampling frequency.
The f_bin are the frequency "bins", that is, where the DFT is telling us the frequency components of the signal are, as opposed to where they really may be.

Suppose we choose the sampling frequency f_s to be exactly N times the fundamental frequency of the periodic signal we're sampling. That is, choose:

f_fund=f_s/N

Reffering to "Understanding Digital Signal Processing" by Lyons, page 72, he says this:

"The DFT produces correct results only when the input data sequence contains energy precisely at the analysis frequencies given in Eq. 3-24, at integral multiples of our fundamental frequency f_s/N"

Andy's note: his equation 3-24 is the same as what I've written above for the f_bin.

So if we choose our sampling frequency as exactly N times the fundamental frequency of the signal we're sampling (where N is again the number of DFT points), the bins will line up exactly with the frequency components of the signal we're sampling (assuming that signal is truly periodic). If we don't establish this relationship, the signal will appear spread out in all the DFT bins in general.

How do we make this work with SPICE? SPICE wants to pick its own, often non-uniform time steps based on the time rate of change of the signal. But we can specify a minimum time step, and if that minimum time step is way smaller than what SPICE would compute on its own, we'll get uniform time steps. We can choose these time steps, together with the number of points in the FFT to make the sampling frequency f_s an exact integer multiple of the fundamental frequency of the sine wave we're applying.

But the typical approach is to do the analysis on the last cycles of the sinusoid, so that any transient will have died out. Note that this is the opposite of what GM suggests. But GM's measurement really indicates the closeness of the first cycle to that of an ideal sinusoid. This isn't really distortion in the nonlinear sense. Note that I don't necessarily agree with this approach. I'm just trying to explain what I think he's doing.

subwo1

quote:

How is it exactly that a speaker is an AC generator but an inductor isn't?

An inductor is passive and is only able to store energy in a magnetic field (normally temporary). A speaker is a mechanical system which can actively convert the mechanical energy of a moving voice coil into electricity as the coil cuts through the lines of magnetic force (from a permanent magnet) during this physical motion. When the speaker is producing a sound, it is a motor, when it is moving in response to sound or simply pushed with fingers, say, it is a generator. The modeling with passive components is good in the standard use of the speaker, when driven by an amplifier, and that is what we care about here. ;)

Steve Eddy

quote:

Originally posted by subwo1
An inductor is passive and is only able to store energy in a magnetic field (normally temporary).

Last I looked, loudspeaker drivers were passive as well. And they also store energy.

quote:

A speaker is a mechanical system which can actively convert the mechanical energy of a moving voice coil into electricity as the coil cuts through the lines of magnetic force (from a permanent magnet) during this physical motion.

Actively convert? What's the active element in a loudspeaker driver?

quote:

When the speaker is producing a sound, it is a motor...

How does calling it a motor change its fundamental electrical behavior?

quote:

...when it is moving in response to sound or simply pushed with fingers, say, it is a generator.

But we're not talking about it moving in response to sound or being pushed with fingers. We're talking about it being driven by an amplifier.

But if you want to look at it in that context, then would you also call an inductor which is being impinged upon by a time varying magnetic field a "generator" as well?

quote:

The modeling with passive components is good in the standard use of the speaker, when driven by an amplifier, and that is what we care about here. ;)

Sure. So if we're talking about it being driven by an amplifier, then where does the "AC generator" come into it?

se

PMA

OK. Here is the more complex model, acoustical side included. But nothing is changed from the point of view of the amplifier.

peranders

Nice explanations (but I don't understand a thing....) but how can you measure this new distortion and how does is relate to music reproduction? It seems that noone knows really what Graham is talking about.

andy_c

Oh, you actually want to measure it? Well, there's always a troublemaker in every crowd :).

I'm thinking that you might be able to find a function generator capable of tone bursts with controlled start phase (set to zero) and very low "first cycle distortion", with an external trigger pulse to start the tone burst. Then a computer controlled digitizing scope or waveform digitizer, whose sampling was started by the same pulse that triggered the tone burst, might be used. The digitized data might be sent to a computer over the GPIB bus. The computer program that controls all this could also compute the FFT of the incoming samples and display them on a graph.

I don't really know if a suitable tone burst generator exists, nor have I tried to figure out how many bits of resolution you'd need for the sampling. I'm just dreaming here. But I did work for about 10 years in computer controlled RF/microwave test equipment, so it's not total BS, only partial.:)

PMA

quote:

Originally posted by subwo1

An inductor is passive and is only able to store energy in a magnetic field (normally temporary). A speaker is a mechanical system which can actively convert the mechanical energy of a moving voice coil into electricity as the coil cuts through the lines of magnetic force (from a permanent magnet) during this physical motion. When the speaker is producing a sound, it is a motor, when it is moving in response to sound or simply pushed with fingers, say, it is a generator. The modeling with passive components is good in the standard use of the speaker, when driven by an amplifier, and that is what we care about here. ;)

Oh no. The resonant circuit in the speaker electric diagram is really the what you are speaking about (exchange of the energy).

traderbam

quote:

What's the active element in a loudspeaker driver?

The permanent magnet.

quote:

would you also call an inductor which is being impinged upon by a time varying magnetic field a "generator" as well?

Yes. That's how a generator works.

peranders

quote:

Originally posted by andy_c
Oh, you actually want to measure it? Well, there's always a troublemaker in every crowd :).

I still say that this distortion isn't a separate phenomenia (hard to spell).

It's just step response :att'n:

phase_accurate

The problem with this kind of distortion has nothing to do with either:

Feedback
driver Back EMF
FFT behaviour

It is simply generated by expecting the wrong outcome of the simulation. A simple lowpass would generate the same kind of distortion with the same type of signal.
The signal in question is NOT a SINUSOID but the multiplication of a Sinusoid by a step function. Every lowpass will definitely distort such a signal, like every filter would distort a dirac pulse !
The signal in question and the Dirac pulse have something else in common: The do NOT EXIST IN THE REAL WORLD !

Regards

Charles

/wearing his flame-resistant suit !;)

janneman

Yeah! Nothing beats knowing what you are talking about....

Jan Didden

subwo1

quote:

Last I looked, loudspeaker drivers were passive as well. And they also store energy.

You are correct here.

quote:

Actively convert? What's the active element in a loudspeaker driver?

It is the cone assembly including the voice coil which are coupled to the permanent magnetic field, which traderbam mentioned.

quote:

How does calling it a motor change its fundamental electrical behavior?

It doesn't, really.

quote:

But we're not talking about it moving in response to sound or being pushed with fingers. We're talking about it being driven by an amplifier.

But it is also pushed by the sound reflecting around inside the enclosure.

quote:

But if you want to look at it in that context, then would you also call an inductor which is being impinged upon by a time varying magnetic field a "generator" as well?

Yes.

quote:

Sure. So if we're talking about it being driven by an amplifier, then where does the "AC generator" come into it?

It comes in when the physical movement in the system is converted back to electrical energy.

subwo1

quote:

Oh no. The resonant circuit in the speaker electric diagram is really the what you are speaking about (exchange of the energy).

The resonant circuits you show are good for our purposes to approximate the behavior of a speaker driven by an amp. In fact, the circuit values of some of the elements should be changed if any element of the physical set-up is changed, like cabinet volume or damping material, for example. I am not trying to imply that the models do not work or anything like that.

runebivrin

On the topic of knowing what you're talking about, and in loose connection with the topic at hand:

Are step response and transient response different things?

My thinking is that a transient in the musical sense very rarely means the signal goes from zero to full amplitude in a microsecond. It's rather a question of an instrument (or several) suddenly striking a very loud note. That note would still consist of several sinusoidal ccomponents, wouldn't it?

If this is true, why would a transient be noticably harder to reproduce than the same spectrum played continously?

If the power bandwidth of the amplifier is sufficient (whatever that means...), the only thing I can think of is the power supply somehow not being instantly able to deliver the required power. As if more power requires a phone call to the power company, telling them to crank the generators.

Rune

sreten

quote:

Originally posted by peranders
Nice explanations (but I don't understand a thing....) but how can you measure this new distortion and how does is relate to music reproduction? It seems that noone knows really what Graham is talking about.

No.

IM0 your last sentence needs rearranging.

I'm tempted to quote Barnum at this point, IMO your
assumption that FCD is a new distortion is misguided.

:) sreten.

peranders

quote:

Originally posted by sreten
The implication for your last sentence is the other way round.

Yeah, becuase that I think this is a product of simulation which is not the real world.

Has anyone heard it before?

What is the defenition of FCD?

Anyone who knows how FCD is measured?

millwood

quote:

Originally posted by runebivrin
My thinking is that a transient in the musical sense very rarely means the signal goes from zero to full amplitude in a microsecond. It's rather a question of an instrument (or several) suddenly striking a very loud note. That note would still consist of several sinusoidal ccomponents, wouldn't it?

Rune

yes it would. And it stands to argue that physical instruments are less likely to produce a Dirac-like spike (you need infinite amount of force to move a mass suddenly, however small the mass is). so to produce an electronic step function, you need infinite bandwidth. But to produce anything less, you don't need infinite bandwidth.

The "first cycle distortion" is nothing but a gimic for marketing purposes, a problem created by those marketing types.

traderbam

quote:

My thinking is that a transient in the musical sense very rarely means the signal goes from zero to full amplitude in a microsecond. It's rather a question of an instrument (or several) suddenly striking a very loud note. That note would still consist of several sinusoidal ccomponents, wouldn't it?

As an aside, try not to think of a step waveform as the same thing as a collection of harmonic sinusoids. It most certainly isn't. It is a step waveform.

Representing things as a sine series is just a mathematical convenience which works under special circumstances. Don't lose sight of reality. :earth:

runebivrin

Oh, I'm not sure it's just a marketing thing. As a software developer, I do recognize a general pattern. Once the audio designers of this world arrived at designs that were essentially distortion free (in the traditional sense), and with flat frequency response, it's rather unlikely there would be consensus, and all designers would stop improving their designs.

It's certainly turned in to a game of finding problems, such that they may then be solved.

I think this is what Graham is trying do do. Whether it will prove to be real is another issue, and if it's relevant to reproduction of audio is yet another - completely different - issue, and much harder to determine.

It would make sense that Graham can hear a difference, since he wants to hear it. I don't see the point in flogging him for that, but I also don't see the point in not realizing the dangers that lie in judging the results of your own efforts.

Rune

phase_accurate

quote:

It's certainly turned in to a game of finding problems, such that they may then be solved.

Could indeed be, but not necessarily. If a system is getting more transparent in one domain it might reveal problems in other ones that otherwise have been masked.

It is also clear that for a 100% accurate reproduction the WHOLE chain has to be able to reproduce from DC to infinity in terms of frequency response. And this is only one requirement out of many ! While the upper cutoff frequency of the amp should be quite high in order to not generate too much transient distortion one has to be aware that the real culprits in this respect are the speakers, microphones and storage media.

Regards

Charles

runebivrin

quote:

Originally posted by phase_accurate

Could indeed be, but not necessarily. If a system is getting more transparent in one domain it might reveal problems in other ones that otherwise have been masked.

Certainly. That's pretty much what I meant to say, with that added caveat that can be quite hard to find the problem that causes the unmasked artifacts. Several candidates may exist. You find a problem, solve it (you think), and analyze the results. Either way, you go on to uncover the next problem...

And the beat goes on, so to speak.

Rune

PMA

quote:

Originally posted by runebivrin
On the topic of knowing what you're talking about, and in loose connection with the topic at hand:

Are step response and transient response different things?

My thinking is that a transient in the musical sense very rarely means the signal goes from zero to full amplitude in a microsecond. It's rather a question of an instrument (or several) suddenly striking a very loud note.
Rune

If this was true, then audio and music signals would have bandwith to 350kHz. I an sorry but there is exactly defined relation between rise time of the transient response and -3dB high frequency limit.

traderbam

quote:

the WHOLE chain has to be able to reproduce from DC to infinity in terms of frequency response

I respectfully disagree. Leaving aside those among us who have a few bat genes in their helix I think a perfect system need only reproduce 20Hz to 20kHz perfectly. A rather less ambitious goal.

phase_accurate

I added a simulation graph below, showing what happens when one passes a simulated sinusoid through an RC lowpass (green trace). I left away the original sinusoid for clarity. One can clearly see that there is something going on at beginning of the green trace. But that is simply due to the fact that the source signal is basically the same as the red trace shows: the product of a sinusoid and a step function. No one could reasonably assume that such a signal would be left untouched by a filter of ANY sort. But no one can assume such a signal to exist in reality either.
If one runs an FFT of the green trace from 0 to 1 ms then there is definitely a deviation from the spectrum of a pure sine to be seen (not in terms of harmonics but as a spectral envelope, due to the one-time character of the event). When transforming a subsequent full cycle, no distortion is present anymore (beware of the phase-shift).
So this definitely seems to be an artifact not present in the real world.

Regards

Charles

janneman

quote:

Originally posted by traderbam

As an aside, try not to think of a step waveform as the same thing as a collection of harmonic sinusoids. It most certainly isn't. It is a step waveform.

Representing things as a sine series is just a mathematical convenience which works under special circumstances. Don't lose sight of reality. :earth:

Well, any PERIODIC wave form can be constructed (in reality, with real signals) from a certain number of sinussoids in the correct amplitude and phase relation ship. There is nothing artificial about that, it is reality.

What is not clear to me is whether a step function can be thought of as a periodic waveform. Maybe with an infinite long period? Anybody can shine light on this?

Jan Didden

traderbam

quote:

No you have no evidence of this. Nobody has. You are highlighting my point...on paper you can model a real, periodic waveform perfectly as a summation of sinusoids but you can't in reality. Practicalities make it impossible - and practicalities is what this whole discussion is about.

millwood

quote:

Originally posted by traderbam
As an aside, try not to think of a step waveform as the same thing as a collection of harmonic sinusoids. It most certainly isn't. It is a step waveform.

Representing things as a sine series is just a mathematical convenience which works under special circumstances. Don't lose sight of reality. :earth:

but even in the real world, if you were to feed all those harmonic sinusoids into a summing resistor network (or perfect speaker), you get a step function.

The real question is that can we humans hear those step functions, either directly or indirectly through a set of decomposed harmonic sinusoids.

For example, let's see a (less-then-perfect) step function can be decomposed into a set of harmonic sinusoids from DC - 1Mhz. And we will also produce an almost identical set ofo harmonic sinusoids from DC - 20Khz (or 30Khz, take your number).

when I feed those harmonics into a speaker, can a human reliably detect the difference between the two sets of harmonics? If she cannot, what does that mean for amp designers?

millwood

quote:

Originally posted by traderbam
on paper you can model a real, periodic waveform perfectly as a summation of sinusoids but you can't in reality.

I have in reality and on computers.

when I was in school, my professor did demonstrate the validity of FFT by suming increasing number of harmonics to show how the sum started to ressemble a step function.

You can also do this very easily in Matlab. and I am sure pretty much any spice program that has a sine function.

PMA

quote:

Originally posted by phase_accurate
I added a simulation graph below, showing what happens when one passes a simulated sinusoid through an RC lowpass (green trace). I left away the original sinusoid for clarity.
Regards

Charles

But it is not a sinusoid at all. There is a sudden turn-on from the zero voltage (dv/dt = 0) to sinusoidal shape at the point of highest dv/dt (red line). Such a signal has wide frequency spectrum, just because of this turn-on. Nothing new that the beginning of the curve is smoothed by RC, depends only on this time constant. A question is whether a musical instrument can do something like this. The time shift between the two sinusoids is exactly equal to the time constant of the RC filter.

IanHarvey

Let's nail once and for all the idea that this truncated single cycle of sine wave has anything to do with musical signals. I think there is a major misunderstanding going on between mathematicians and non-mathematicians here - see if this helps:

1. Imagine a physical object - a guitar string, a microphone diaphragm, a loudspeaker cone, your eardrum - trying to trace the this waveform. Up to time t=0, it is stationary; after time t=0 it is tracing the sine wave.

2. As soon as it starts tracing the sine wave, it begins moving with a particular velocity (dependent on the amplitude and frequency of the sine wave). Visually, imagine drawing a straight line touching the sine wave at t=0 and measuring its slope - this is its initial velocity.

3. In an instant, this object has changed from being stationary to moving with a given velocity. What is its acceleration - i.e. how quickly did its velocity change? It changed from nothing to something in no time at all: its acceleration must be infinite.

4. For the object to move, it must have a force acting on it equal to its mass times the acceleration. To produce infinite acceleration requires, therefore, infinite force.

Obviously, in the real world, you cannot generate an infinite force. The force which sets a guitar string moving has to come from the (finite) tension in the string; the force which moves a drum head is derived from the (finite) momentum of the drumstick. In other words:

No real physical signal ever looks exactly like Graham's single-cycle sine wave

What's more, the sort of limitations imposed by a finite force acting on an object of finite mass are exactly the same kind of limitations imposed by an amplifier of finite bandwidth; there is no justification for thinking the ear treats them differently.

Cheers
IH

phase_accurate

quote:

But it is not a sinusoid at all. There is a sudden turn-on from the zero voltage (dv/dt = 0) to sinusoidal shape at the point of highest dv/dt (red line).

That's what I am desperately trying to explain all the time, but maybe I wasn't clear enough. It is the same sort of signal as the red trace shows, only difference being the point in time when it starts.

While musical instruments can generate spectral content that is reaching quite high in frequency, such a signal definitely doesn't exist in reality.

Regards

Charles

runebivrin

quote:

Originally posted by PMA

If this was true, then audio and music signals would have bandwith to 350kHz. I an sorry but there is exactly defined relation between rise time of the transient response and -3dB high frequency limit.

Not quite sure if you agree or disagree with what I meant. What I meant was that when transients are discussed, they are often equated with step responses. That's certainly one way of looking at it, but such signals are rarely a part of music. I don't know of a real instrument that could produce such signals. And even if it existed, after passing through a CD with its associated filtering, would it still be there?
A musical transient is just a sudden crescendo, and as such unlikely to be a special case for an amplifier.

Rune

PMA

quote:

Originally posted by runebivrin

Not quite sure if you agree or disagree with what I meant. What I meant was that when transients are discussed, they are often equated with step responses. That's certainly one way of looking at it, but such signals are rarely a part of music. I don't know of a real instrument that could produce such signals. And even if it existed, after passing through a CD with its associated filtering, would it still be there?
A musical transient is just a sudden crescendo, and as such unlikely to be a special case for an amplifier.

Rune

I am sorry that I have not read patiently. I was supposing that you were thinking that there are musical transients with rise time as short as 1us. This I assume to be completely impossible.

phase_accurate

Though a step is a theoretical signal it can be used to test transient accuracy. I by myself do not except any sound system to accurately reproduce a step. Far from that. But there are some reasonable limits whithin those the response should lie. An amp with an upper cutoff frequency of 150 to 200 kHz and no overshoots is fully satisfying my taste since other parts of the system are much more constrained.

Regards

Charles

PMA

Charles,

I completely agree.

Regards,
Pavel

gmarsh

quote:

Originally posted by traderbam

No you have no evidence of this. Nobody has. You are highlighting my point...on paper you can model a real, periodic waveform perfectly as a summation of sinusoids but you can't in reality. Practicalities make it impossible - and practicalities is what this whole discussion is about.

It sounds like you're keen on proving that the fourier transform is a farce... Just so you know, you're going against decades and decades of real world experience in hundreds of scientific, mathematic and engineering fields.

I'm sure that this has been stated, but here's how things work:

(1) Any steady state waveform can be modelled as a sum of sinusoids. Even a square wave can be created from sinusoids; the only condition is that an infinite number of sinusoids approaching infinite frequency is required to produce a "perfect" square wave.

And real world experience supports fourier theory; for example, if you trim off the higher frequencies of a square wave using a low pass filter (or an amplifier with a finite bandwidth, or so forth) then the square wave will look more and more like a sine wave as the cutoff frequency is lowered.

(2) Any non-steady-state waveform can be modelled as an amplitude modulated signal. In a simple case, a fading tone can consist of a downward ramp (modelled out of sinusoids) multiplied by a fading tone (a sinusoid) which causes heterodyning in the frequency domain. Or you can multiply together an audio signal and a high frequency sinusoid and amplify the output power to tens of kilowatts and create an AM radio transmitter.

(3) The statement in (2) allows you to model a transient using fourier series. Your "first cycle distortion" waveform consists of a step response multiplied by a sin() function - essentially, a modulated step response. The frequency components of such a signal are very easily calculated.

Since a step response has infinite frequency components, so will the "first cycle distortion" signal.

The only thing is, THESE SIGNALS DON'T EXIST IN THE REAL WORLD! To reproduce such a signal perfectly, the following conditions have to exist:

- Using a "guitar player" example, the guitar player will have to pluck a string with zero inertia. After the pick leaves the string, the tension introduced on the string by bending it with the pick combined with the natural tension on the string will cause the string to begin accelerating towards the "zero" position - It will *not* suddenly "snap" from zero to high velocity as depicted in the FCD waveform; this requires infinite acceleration. Since F=M*A, for such a condition to exist the string would either have to be hit with an infinite amount of force (which isn't true; only the string's tension is accelerating it) or the string will require zero mass... come to think of it, wouldn't a guitar string with zero mass oscillate at infinite frequency?

- A cymbal strike is probably a better example; a cymbal hit hard with a drum stick will accelerate much faster than a guitar string. The same thing applies though; the mass of the cymbal combined with the ductility of the drum stick's wood and cymbal's metal will limit the acceleration of the cymbal.

But assuming that a diamond cymbal was hit by a kryptonite drum stick and the cymbal had instantaneous velocity (eg, FCD waveform) then the air in the room would then have to instantly accelerate (which it can't, it has mass and compressibility), the recording microphone's element would have to move instantly (same thing), and finally the recording medium would have to carry such a signal. CD's have a nyquist limit, and LPs have a frequency limit imposed by the mass of the stylus.

Anyhow, I think I've typed more than enough :D

traderbam

quote:

Not at all. I am quite familiar with the technique. So familiar with mathmatics that I know when it is a good idea to use it and when it isn't. One must use those little grey cells when applying "modelling" methods to real systems.

gmarsh

quote:

Originally posted by traderbam

Not at all. I am quite familiar with the technique. So familiar with mathmatics that I know when it is a good idea to use it and when it isn't. One must use those little grey cells when applying "modelling" methods to real systems.

My job involves doing quite a lot of fourier stuff too (i'm an engineer at a radio broadcasting equipment company)

I've also got a physics background. The point of my post was to say that creating an "instant-on-sine-wave" is impossible for two reasons - (1) fourier theory says that such a signal has infinite frequency components, which you can't have in the real world, and (2) an "instant-on-sine-wave" signal cannot come from any sort of mechanical instrument, since some component inside would have to undergo infinite acceleration, which is not possible. And such a signal cannot be recorded for the same reasons.

traderbam

Oh. We must be agreeing then. :)

gmarsh

quote:

Originally posted by traderbam
Oh. We must be agreeing then. :)

cheers :)

sam9

Steve Eddy

quote:

Originally posted by traderbam
The permanent magnet.

Huh? Permanent magnets are decidedly passive elements. How do you conclude that they are active?

se

sam9

"yes it would. And it stands to argue that physical instruments are less likely to produce a Dirac-like spike (you need infinite amount of force to move a mass suddenly, however small the mass is). so to produce an electronic step function, you need infinite bandwidth. But to produce anything less, you don't need infinite bandwidth."

And if we are talking about a recording of a live musical event the mass (strings, diaphrams etc, PLUS air) being moved is far from arbitrarily small. Pure computer generated electronic music may be another matter as you could concievably create a file where the data at word #1 has minumum value and at word #2 has the max. It's still not instantaneous but limited only by contraints of sampling requency and word length.

traderbam

Steve,
Please define what you mean by "active".

Steve Eddy

quote:

Originally posted by subwo1
It is the cone assembly including the voice coil which are coupled to the permanent magnetic field, which traderbam mentioned.

But all of those elements are passive. Not active. The only active elements involved here are the tubes and/or transistors in the amplifier. Everything else is either resistive or reactive.

quote:

But it is also pushed by the sound reflecting around inside the enclosure.

But that's ultimately just energy being returned to the system. Not from an external energy source.

quote:

It comes in when the physical movement in the system is converted back to electrical energy.

You mean like how the collapsing magnetic field around an inductor is being converted back to electrical energy?

Which takes me back to my previous question. How is it exactly that a speaker is an AC generator but an inductor isn't?

se

sam9

Whether the sinusoidals comprising an FFT "exist" in the real world or not is just part of a broader question of relating a "real" phemonon to it's model. The question exists with regard to anything physical that is described by a model or equation. As a famous example, recall that Einstein never really could accept the probabalistic aspects of quantum theory even though he was the developer of the theory. You can also expect that if string theory is successful, the next century or so will filled with tortuous debates about whether the universe in really constructed of multidimentional strings or if that is just a useful mathematical tool.

I'm inclined to think that the question in it's various forms is just a koan. Something to think about when there is nothing better to do.

Steve Eddy

quote:

Originally posted by traderbam
Please define what you mean by "active".

By "active" I mean an element which requires an external source of power in order to perform its basic fuction.

se

traderbam

By that definition a speaker isn't "active". But it does rely on a permanent magnet which is an "external" field source as opposed to an external voltage source as it were.

In any case I think your questions are about what the differences are between motors, ac generators and inductors. They aren't really different at all. They all rely on Faraday's Laws (with some Ampere thrown in) which connect magnetic fields, current flows and mechanical forces. These effects are bi-directional so a speaker is also a microphone and vise-versa. A speaker is both a motor and a generator and is so at the same time, regardless of whether an amplifier is driving it or not.

It is sort of splitting hairs to try to define how much cone movement is due to the intended amp signal and how much is due to airborn reflections or even someone tapping on the cone with their finger. Everything is bidirectional. But quite unlike a simple inductor a speaker presents complex resonances and real time delays due to the speed of sound in air.

sreten

quote:

Originally posted by runebivrin
Oh, I'm not sure it's just a marketing thing. As a software developer, I do recognize a general pattern. Once the audio designers of this world arrived at designs that were essentially distortion free (in the traditional sense), and with flat frequency response, it's rather unlikely there would be consensus, and all designers would stop improving their designs.

It's certainly turned in to a game of finding problems, such that they may then be solved.

I think this is what Graham is trying do do. Whether it will prove to be real is another issue, and if it's relevant to reproduction of audio is yet another - completely different - issue, and much harder to determine.

It would make sense that Graham can hear a difference, since he wants to hear it. I don't see the point in flogging him for that, but I also don't see the point in not realizing the dangers that lie in judging the results of your own efforts.

Rune

I couldn't agree less.

Amplifier design still has real problems that need quantifying and addressing.

GM aural observations I've no qualms with at all.

There are very good reasons why the amplifier designs he favours
sound the way they do, and I'm not questioning aural quality, they
are good sounding amplifiers.

What is dubious is GM attitude as to why they sound that way.

His technical approach cannot be called rigorous.

Despite all the debate here I maintain his FCD is just another
way of observing technical parameters already well understood.

:) sreten.

Ultima Thule

"...if there is FCD then there is also LCD!" :yes:

Cheers ;)

Dave S

I encountered this on my first MTB when I tried to go too fast down a rocky descent. The transient at the bottom felt pretty much like infinite energy!

subwo1

quote:

But all of those elements are passive. Not active. The only active elements involved here are the tubes and/or transistors in the amplifier. Everything else is either resistive or reactive.

Your definition of active is more specialized than mine.

quote:

But that's ultimately just energy being returned to the system. Not from an external energy source.

Your definition of the electronic component is broader since the voice coil is what I was considering.

quote:

You mean like how the collapsing magnetic field around an inductor is being converted back to electrical energy?

The magnetic field is electromagnetically part of the inductor which is an electronic component considered a normal part of the electrical circuit while the cone is not part of the circuit.

quote:

Which takes me back to my previous question. How is it exactly that a speaker is an AC generator but an inductor isn't?

An inductor can only convert a finite amount of stored energy back into electricity while a motor like a speaker used in reverse can do it indefinitely. A battery is not even considered a generator since its energy is only stored also.

I propose we retire this line of discussion. :emoticon:

Steve Eddy

quote:

Originally posted by traderbam
By that definition a speaker isn't "active". But it does rely on a permanent magnet which is an "external" field source as opposed to an external voltage source as it were.

But it isn't active. Which was my point.

quote:

In any case I think your questions are about what the differences are between motors, ac generators and inductors.

Actually my questions are about what I asked originally. Which was:

What's the fundamental difference between the back EMF of the loudspeaker and the back EMF of any other RLC resonant circiut?

The answer it appears, disregarding issues wholly irrelevant to the issue of the supposed "FCD" such as flicking the cone with your finger, is "none."

Electrically, the fundamental behavior of a loudspeaker is that of an RLC resonant circuit. The back EMF of the speaker is fundamentally no different than the back EMF of an RLC resonant circuit.

se

millwood

quote:

Originally posted by Steve Eddy
Electrically, the fundamental behavior of a loudspeaker is that of an RLC resonant circuit. The back EMF of the speaker is fundamentally no different than the back EMF of an RLC resonant circuit.

se

I think that's correct.

a 2ndary issue, one that some of us seemt o be arguing for, is that the RLC circuit does not represent the exact behavior of a real speaker in every circumstance. For example, the speaker emf may deviate fromt hat of the rlc circuit when it is overdriven.

That is true. But end of the day, the back emf from an rlc circuit is foundamentally the same as the back emf from a speaker. That seems to be the concensus here.

Steve Eddy

quote:

Originally posted by subwo1
The magnetic field is electromagnetically part of the inductor which is an electronic component considered a normal part of the electrical circuit while the cone is not part of the circuit.

Since the cone is fixed to the voice coil, that makes the cone decidedly part of the circuit.

quote:

An inductor can only convert a finite amount of stored energy back into electricity while a motor like a speaker used in reverse can do it indefinitely.

It can only do it indefinitely if you indefinitely keep putting energy into the system. Same holds true for an inductor.

se

fdegrove

Hi,

quote:

Since the cone is fixed to the voice coil, that makes the cone decidedly part of the circuit.

The circuit would be exactly the same without the cone.

Cheers,;)

fdegrove

Hi,

quote:

It can only do it indefinitely if you indefinitely keep putting energy into the system. Same holds true for an inductor.

And if you pull the plug all active circuitry becomes rather passive all of a sudden...I wonder why...

Cheers,;)

john curl

You folks are really confusing me. First, a loudspeaker is NOT just an inductor. In fact, that is a very small part of the speaker circuit. The moving loudspeaker is a resonant SYSTEM all of its own that CAN be represented by an 'equivalent' R, L, and C model. Also, loudspeakers are microphones and pretty good ones at that, so any sound in the room can be put back into the loudspeaker an emf generated across the speaker terminals. What about a resonant cabinet? What about a port?
Loudspeakers may be 'simply' modeled as an equivalent RLC circuit, but that is not their complete response in the back EMF.

Steve Eddy

quote:

Originally posted by john curl
You folks are really confusing me. First, a loudspeaker is NOT just an inductor.

No, they're not. Who said they were?

quote:

In fact, that is a very small part of the speaker circuit. The moving loudspeaker is a resonant SYSTEM all of its own that CAN be represented by an 'equivalent' R, L, and C model.

Yes. Because that's how it appears electrically to the amplifier.

quote:

Also, loudspeakers are microphones and pretty good ones at that, so any sound in the room can be put back into the loudspeaker an emf generated across the speaker terminals.

Sure. But what has that to do with the issue of FCD?

quote:

What about a resonant cabinet? What about a port?

Those also model as RLC equivalents.

quote:

Loudspeakers may be 'simply' modeled as an equivalent RLC circuit, but that is not their complete response in the back EMF.

Sure, the model doesn't account for microphonics, but then that hasn't anything to do with the FCD issue.

Remember, Graham's plot illustrating what he was referring to as FCD used an idealized loudspeaker model using nothing but ideal RLC components.

What prompted me to reply here was this notion that the "back EMF" of a loudspeaker is somehow fundamentally different than the "back EMF" of an RLC resonant circuit, looking at loudspeaker back EMF as a voltage source driving the amplifier's output (i.e. the "AC generator" notion) rather than the reactance of the energy storage mechanism that it is.

As an aside, it's interesting to note that with a typical dynamic loudspeaker driver, the "back EMF" is greatest at the driver's resonant frequency (F_s), and at that point, current and voltage are in phase and the loudspeaker presents a purely resistive load to the amplifier.

se

traderbam

quote:

Sure. But what has that to do with the issue of FCD?

I'm looking for a "smilie" named "red herring" but can't find it.
1st cycle distortion doesn't bother me...it's the distortion on all the subsequent cycles that I notice. :clown:

quote:

What prompted me to reply here was this notion that the "back EMF" of a loudspeaker is somehow fundamentally different than the "back EMF" of an RLC resonant circuit.

You seem to be mixing concepts up here. A speaker or motor or generator need not resonate at all. EMF is not a resonance effect. Resonant circuits do not have "back EMF" - this is to do with the opposition to force caused by a current flow within a magnetic field. Resonance is an entirely different thing.

Steve Eddy

quote:

Originally posted by traderbam
I'm looking for a "smilie" named "red herring" but can't find it.

Red herring? This thread is solely about FCD.

quote:

1st cycle distortion doesn't bother me...it's the distortion on all the subsequent cycles that I notice. :clown:

Hehehe. True. But the issue here is FCD.

quote:

You seem to be mixing concepts up here.

I don't believe I am.

quote:

A speaker or motor or generator need not resonate at all.

But dynamic loudspeaker drivers are a inherently resonant devices.

quote:

EMF is not a resonance effect. Resonant circuits do not have "back EMF"- this is to do with the opposition to force caused by a current flow within a magnetic field.

Back EMF is really nothing more than Lenz's Law in action and is a fundamental property of simple inductance. So a circuit which includes inductance, which includes RLC resonant circuits, do indeed have back EMF.

If you build the RLC loudpeaker model, the impedance peak at F_s is every bit as much due to back EMF as the impedance peak at F_s in a dynamic loudspeaker driver.

se

peranders

It seems that Graham is the only one that can answer this. Noone knows what Graham has invented.

My question was very short and can probably be answered with not too many words.

JensRasmussen

Hello,

I�m following this discussion with a lot of interest. I�m not sure what to think FCD, as I tend to think that it�s not a problem at audio frequencies.

However I�d like to give my point of view on the EMF debate related to the topic.

It�s quite easy to MODEL the speaker using an RCL circuit. This circuit is however a LINEAR circuit and therefore not capable of acting like the highly NONLINEAR system that a speaker is.

I�m not talking different speaker setups like ported or non ported systems, by a driver in general has pretty much no linear properties, but of cause it can be roughly described using the linear Thiele Small Parameters, small signal parameters.

The EMF generated by the normal linear model is based on a steady state scenario, and therefore it has IMO no meaning to talk about RCL circuits and it�s EMF in the discussion of FCD and speakers. If you want to take this stuff into account I believe it is necessary to use some form of NON LINEAR model � and just take my word for it � that will not make it easier to understand as it is quite heavy on the math side, and there are not many places that you can get the non linear model parameters needed for speakers.

Just my thoughts

If you want to know more about it try the www.klippel.de

\Jens

millwood

quote:

Originally posted by JensRasmussen
It�s quite easy to MODEL the speaker using an RCL circuit. This circuit is however a LINEAR circuit and therefore not capable of acting like the highly NONLINEAR system that a speaker is.

\Jens

what if you change the values of the rcl depending on some varianbles?

If you can, what does that say about the foundamental difference between a speaker and a RCL?

In my view, a system is linear or not isn't the point: any non-linear system