It depends what you mean by coexist. If there is a nonlinearity that, say, doesn't change with level, or time, or frequency, it's just a very constant type of nonlinearity, as time passes as small change in voltage will be associated with a small change in current, but the ratio between them will not be a constant, rather it will depend on the curve of the nonlinearity graph.
If we start at one point in time and let's say we have a knob we can turn to adjust the voltage, and whatever current will flow goes ahead and flows, we can turn the knob a little, stop, start, do whatever. Whatever happens, happens. The nonlinearity always stays the way it is, it's characteristics don't change.
Then, if we somehow happen to have turned the knob for awhile in a sine wave pattern in terms of the voltage, then the current will look like a sin wave and some harmonics, but it will only look that way if we decide to do a Fourier analysis to see what results it spits out, or do some other experiment that does something of a similar nature.
If we happen to turn the knob in a way that looks like two frequencies at once, which we could do, then the current that flows would have a more complicated looking wave shape.
If we did a Fourier analysis on the current that flowed it would spit out what looks like four frequencies. If we don't do the analysis it just looks like a more wiggly current waveform.
So what is it really, what would it be to some space aliens who don't think like us and who have their own math to work with their kind of brains? Well, they would probably still have a concept like time, as it seems to be pretty deeply connected with matter and energy. As far as a concept like frequency, that may be more a product of how our brains think and the math and science we have developed to work with how our brains can work. Maybe something like how colors, or sounds, or smells, don't exist in the same way outside our human perceptions. It could be that frequencies don't exactly exist outside of our conceptions either. They can seem hard to grok initially, but once familiar it's hard to understand things without those as concepts, so once understood we can no longer think of them as only conceptual, they become real to us.
In other words, philosophically, if we have a nonlinearity of a fixed nature, whether or not we have one frequency or two, or a million, it doesn't matter. We won't even know what we have until each moment comes into existence and we turn the knob some one way or the other or not at all. Whatever happens happens. In that kind of viewpoint, THD and IMD are just human mental constructs. The nonlinearity just produces an instantaneous result from instant to instant, so its no different if we come back later and do a Fourier analysis and become amazed by whatever numbers that happen to pop out of the math. If it pops out something that we take to mean multiple frequencies then it's seems as real to us as the color red seems real, or tuna smells like fish.
But, as we turn the knob we only have instantaneous voltage and current over time passed and up to the present. Whatever happens happens, numbers of frequencies don't change anything if we just keep focused on what happens with time, the knob, and current that flows according to what the nonlinearity allows. We move knob a little and the current changes a little, that's all there really is at some very basic level. THD and IMD are just concepts for more complicated ways of thinking about and analyzing what happened.
Of course, they can turn out to be extremely useful concepts, but that's a later part of the story.
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Peak levels are what matters since peak displacement is what pushes the driver into
distortion or Xmech limits. Average levels matter more from a thermal perspective.
Easier might be to just use a music signal (broadband) or noise. Pass it through the system and make a histogram out of the individual signal data points (digital of course). Do this for both the input and the output. Comparing the two will yield the transfer characteristic of the system. Once you have that you could simulate the distorted output for any input signal.
Not having actually tried this I am not sure how stable it would be for the higher orders, which are the most important ones. Multi-path, like reflections, and noise will also limit resolution so the technique would not be nearly as robust as the THD test.
"Does this make things any clearer:" Probably not Earl, you have to explain why that is the case.
I'll try to explain this in simple terms. Consider what causes distortion in the time domain,
you have a time domain waveform, a sine wave for HD tests or a pair for IMD tests. Many
would say that ideally we want Vout(t) = 10Vin(t) using a gain of 10 for example. If you
plotted this you'd get a straight line with a slope of 10. Any deviation from the perfect
straight line is non-linear distortion. An example might be that as Vin gets larger the gain
compresses to 9 then 8 etc. just using this as an example - not the case for a high feedback amp.
So, what Earl is saying is that if you give him the test signal and the harmonic structure with
amplitude and phase, he will "back out" the Vout(t)/Vin(t) non-linearity and then use that to
compute the distortion with any IMD stimulus.
This assumes of course that the non-linearity has no frequency dependency, etc.
There is an old EE book that has a diagram showing how to put the Vin(t) waveform on the
transfer function graph and plot the distorted Vout(t) waveform. I'll try to find it, and/or
explain this better when I have more time.
What is very interesting is that you will likely come to very different conclusions about distortion
when looking at it from the time domain vs. frequency domain.
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Yes, go ahead and walk through your understanding. I didn't take you at trolling as much as (immensely) frustrated.
Apologies the link didn't show up! Failure to paste it in.
Amplitude Modulation | Academo.org - Free, interactive, education.
(P.S. if any of the mods are watching, and want to throw this link into my #1030 here, I'd be much obliged!)
Usually we don't and that's because in practice such a thing would be very rare. The non-linearity tends to be designed in and is an integral part of the design. Production variance can have a huge effect on non-linearity for example. Accidentally build the speakers with an off center voice coil and you will see the distortion skyrocket. This is why speakers are tested with THD at end-of-line because these kinds of defects can be easily detected with that system.
great stuff!
Dph many thanks again i'm making inroads on creating a mental link between sonic phenomenon i've heard over the years and the math component.
i still think that there is some stuff i've heard over the years that suggests that there is a non linear connection between amplitude and frequency in a loudspeaker.
Dph many thanks again i'm making inroads on creating a mental link between sonic phenomenon i've heard over the years and the math component.
i still think that there is some stuff i've heard over the years that suggests that there is a non linear connection between amplitude and frequency in a loudspeaker.
^ Just remember that, unless your nonlinear distortion is extremely high (we're talking >25%), the actual output/amplitude response is going to be dominated by the linear distortion. Not getting into the discussion about the magnitude of audibility in nonlinear distortion right now, just saying that, energy-wise, most everything is still held in the fundamental harmonic (and thus drive the amplitude).
And happy to help.
And happy to help.
Here's an example of the graphical understanding of distortion in the time domain,
think of the IC1 axis as Vout and then the red line is the Vin vs. Vout transfer function.
This is not a good example for speakers because they should not have crossover
distortion rather it just shows the method:
From (I've not read this so not endorsing it just found the image there):
Crossover Distortion in Class-B Power Amplifiers
think of the IC1 axis as Vout and then the red line is the Vin vs. Vout transfer function.
This is not a good example for speakers because they should not have crossover
distortion rather it just shows the method:
From (I've not read this so not endorsing it just found the image there):
Crossover Distortion in Class-B Power Amplifiers
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Learning new and difficult mathematics topics is always frustrating, but usually worth the effort in the end.
As to your second point, I completely agree, but that also gets quite complicated. It involves the fact that our ears become more sensitive to certain linear artifacts as the absolute SPL goes up. But these artifacts will NOT show up as THD, IMD or anything else because they are linear - independent of amplitude. It is our perception of them that is non-linear, not the artifact itself.
That's a good example, and we know that feedback is used to "correct" this. But here is a problem with that approach.
Working in Active Noise Control (ANC) for many years we discovered a strange phenomena. ANC is a feedback system attempting to cancel what we don't want, taking it to zero. We found that in practice we could drop the fundamental down by 20 dB and the perception was as if nothing changed. What we found was that while the fundamental is being dropped the harmonics were going up. This resulted in a net null experiment as the higher harmonics were more audible than the lowers one so lowering the lower one while raising the higher ones nulled out the effect.
It turns out in feedback theory that any errors in the feedback, i.e. the inability to do a perfect job, will be reflected as higher orders in the nonlinear transfer characteristic. So while the THD numbers may fall, it is perfectly possible that the audibility goes up. Nelson Pass has also talked about this.
Let me relay an example of what I mean about perception.
Last week Lidia and I went to see Saint Vincent in concert. Initially the sound was very loud and quite distorted. So I put in my trusty Musicians Ear Plugs and low and behold the sound was very clean.
Now reflect on that for a minute. If the speakers were distorting then lowering my own personal level would not have changed anything on the speaker side.
Just "hearing" distortion does not mean that it is generated in the manner that one usually assumes. It's way more complicated than that.
Last week Lidia and I went to see Saint Vincent in concert. Initially the sound was very loud and quite distorted. So I put in my trusty Musicians Ear Plugs and low and behold the sound was very clean.
Now reflect on that for a minute. If the speakers were distorting then lowering my own personal level would not have changed anything on the speaker side.
Just "hearing" distortion does not mean that it is generated in the manner that one usually assumes. It's way more complicated than that.
You mentioned something very similar a while back and I suggested your ears were distorting (seems likely) If I remember correctly, you said something like, yes, distortion is complicated
"we should instead get out and actually talk to each other.", unfortunately that's not possible here is it.
It could be my specific ears, it could be universal as well, there are simply too many complications to know for sure without some exhaustive research. But what I do know for certain is that after studying nonlinear distortion perception for decades nothing that I initially thought turned out to be true.
My thought now is that as we age we become more sensitive to the linear SPL related distortions than younger ears are. But I have no evidence of that beyond my own experience. Did the younger people in the audience (the other 99%) hear the same distortion that I heard? Did it just not bother them? Did the PA operator just blame it on "speaker distortion" and hence there was nothing that they could do about it?
It's not simple, that's for sure.
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