Actually, I would suspect not. (re the dynamics statement.)
Because Self was using a special signal to force into a passive crossover multiple driver system, he was showing the result of parallel drivers. Single sine analysis assumes an almost static condition w/r to impedance.
It is easy for all of us to get trapped by the nomenclature and interpretation.
Jn
Ps. As an example.. Consider a driver with shorting rings to level out the vc inductance. As the vc drives into the slot, the ring lowers inductance by eddy loss and flux exclusion whereas towards the front inductance lowers due to reluctance increase. If the driver is receiving a mid frequency signal at the same time as it gets a high excursion low frequency, it will be dragging that mid frequency magnetic field through the shorting ring half the time? When a charged inductor changes it's inductance, where does the energy go? E =LdI/dt + IdL/dt.
I have never seen any speaker designer or audio guy ever consider this in any analysis whatsoever, not even hinting at it. This falls into the "dynamic system" category, and AFAIK, is beyond the current SOTA understandings (or at least practice as per the write ups I've seen to date).
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Agreed.
Impedance is a frequency domain concept and has no direct analogy in the time domain. On can always find the time domain response to any signal from the impedance and that will give you a time domain representation of the signal from which one could look at the instantaneous ratio of voltage and current and obtain a number, but that is not an impedance - it's a wholly new concept that has no definition to my knowledge.
As to jneutron's example, it is nonlinear and as such any linear concepts of impedance (there are no nonlinear impedance concepts,) etc. go out the window. (Although what he say's is correct - in the time domain.)
And anyways this discussion of EDPR has to do with the amplifier NOT the loudspeaker system as the OP's question dictates. Large peaks and dips in the loudspeakers impedance can be difficult for an amp to handle, but that's the amp designers problem. I did always design the crossover to minimize these problematic impedance areas, however.
Nonlinearity in any decent driver is very small. Otherwise they would be unlistenable. The ear is very sensitive to nonlinearity, but its actual effect on the load would be insignificant.
The modulus of an impedance Z is its absolute magnitude,
or sqrt(ReZ^2 + ImZ^2).
For example, if Z = (3 + j4) then the modulus of Z is sqrt(3^2 + 4^2) = 5 ohms
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Multiple frequencies in the same coil, one causing eddy dragging in a position dependent inductance environment, with the resultant time and position dependencies both on vc position and amplifier loading..
I have never seen anyone do the correct test required to verify what a driver truly does. Even the high end speaker driver designers miss things, advancement is quite slow from what I witness. Far too many of them do not really understand inductance, energy, and magnetic fields.
I do see many gloss it over, as the test hardware to verify is beyond most. To that end, many designers have to make assumptions, some do that better than others despite the limitations of understanding.
And the EDPR test? That is not designed as a small signal test. At 100 milli watts load, who cares how well the heat sinks do? By design, this discussion is all about pushing it.
If ya can't turn it up to 11, might as well go home.😀
But seriously, so much is there to learn.
Jn
Sheesh, that sounded like Yoda...
Oops, sorry, I stated that incorrectly. What I meant to say was it was the magnitude plot. Rayma stated it correctly.
Serves me right typing away on an IPad while on the exercise bike. For my next trick, I'll chew gum and walk.
Jn
I do.
And these things can be analyzed and quantified, but its importance, these days, is over emphasized because drivers have gotten so much more linear than in the past. While these effects can be seen in drivers, they are not at levels that make them audibly important (my views on this subject are well known.
To the extent that back EMF from the nonlinear components effect the amp adversely I have nothing solid, but I tend to believe that it would not be an issue.
The "advancement is quite slow" in driver evolution because it is a commodity and differentiation is hard to come by.
We are in violent agreement on all points.
I do know that the EDPR thingy is a good start however.
You stated you make sure the overall system maintains nice impedance, but do you ever concern yourself with how the three drivers load a music signal as opposed to a simple swept measure?
Jn
If you mean in the electrical domain, I could do that analysis (convolution of the music signal with the drivers current impulse response), but I don't work on electronics. In the acoustical domain then yes, I could also do this analysis (more difficult Green's function but still a convolution), but the answer would always also show in acoustic measurements and be taken care of there. Acoustic interactions between drivers cannot be hidden in polar plots and I have dealt with these for decades.
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Oh, MAGNITUDE [as of a polar coordinate value] ... poking around online, there's a possible use of the word modulus for something like that in physics, but geez.
"These are dynamic drivers, so their impedance must also be dynamic ..."
I've heard people say "I was electrocuted." Not only were they alive, I had no clue they had been convicted of a capital crime.
The hell of it is that such usage has become so common that dictionaries now include "to injure by electric shock" in the word's definitions.
Then there was the master of words, Humpty Dumpty.
No, as I said earlier, I always look at the impedance curve and would correct any serious problems. With my design I don't ever see any.
It's been a while since I was edumacated so, like all those who seek the light, I looked up Wiki for an explanation of what you and Jn are debating over! There follows a summary of what I found, which may be of interest to other followers of this thread:
I am proud to be in the company of guys who understand this stuff, but it's time for me to go sit in a darkened room, which is something I do with increasing frequency!
It's been a while since I was edumacated so, like all those who seek the light, I looked up Wiki for an explanation of what you and Jn are debating over! There follows a summary of what I found, which may be of interest to other followers of this thread:
I am proud to be in the company of guys who understand this stuff, but it's time for me to go sit in a darkened room, which is something I do with increasing frequency!
Where do you find this stuff? Please find a text with a better understanding, differentiating sine waves from music this way is just plain nonsense. This reeks of you can't use Fourier theory to explain what's going on with complex musical waveforms.