It is not the input signal that produces the harmonics. It's the amp.
Send a sine wave through a circuit that has a quadratic transfer function. What do you get at the output?
Say your amp has a transfer function (gain): Vo = (30 x Vi) + (0.1 x (Vi^2).
Now send in a 1V 1kHz signal: Vi = sin((1k/2*pi)*t). What is the output?
There is also an intuitive way to understand. Say your amp distorts, literally, your input sine wave. Maybe on the output the pos. part is a bit less in amplitude than the negative part (blue dotted wave). What is the shape difference between the input (black trace) and this distorted output? Fourier tells us the output is made up of the original summed with another wave that decreases the pos. part and increases the neg. part. Lo and behold, the 2nd harmonic (dotted red trace) fulfills that role!
Jan
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Regarding noise floor modulation, please see specifications section on page 2 of the datasheet at:
Overview | CSRA6620 | Qualcomm
Or, how about Texas Instruments, page 6: https://www.ti.com/lit/an/slaa114/s...74146&ref_url=https%3A%2F%2Fwww.google.com%2F
Comments:
I will admit it is specialist terminology. Bruno Putzeys described more or less the same measurement symptom caused by idle tones sweeping through the audio band caused by the audio signal, which is seen a modulation of the noise floor correlated with the audio. (My note: the measurement appears that way exactly because the because the underlying cause is not stationary relative the the FFT measurement time frame.)
Its also seen in the widely cited patent at:
GB2539517A - Systems and methods for reducing artifacts and improving performance of a multi-path analog-to-digital converter
- Google Patents
Also, described in an EE class (page 59):
http://cloudportal.sathyabama.ac.in/coursematerial_staging/uploads/SEC1319.pdf
In the AES document, "Why 1-Bit Sigma-Delta Conversion is Unsuitable for High-Quality Applications."
Lipshitz and Vanderkooy state (page 4): "...display gross modulation of the noise floor in the audio band"
https://timbreluces.com/assets/sacd.pdf
Overview | CSRA6620 | Qualcomm
Or, how about Texas Instruments, page 6: https://www.ti.com/lit/an/slaa114/s...74146&ref_url=https%3A%2F%2Fwww.google.com%2F
Comments:
I will admit it is specialist terminology. Bruno Putzeys described more or less the same measurement symptom caused by idle tones sweeping through the audio band caused by the audio signal, which is seen a modulation of the noise floor correlated with the audio. (My note: the measurement appears that way exactly because the because the underlying cause is not stationary relative the the FFT measurement time frame.)
Its also seen in the widely cited patent at:
GB2539517A - Systems and methods for reducing artifacts and improving performance of a multi-path analog-to-digital converter
- Google Patents
Also, described in an EE class (page 59):
http://cloudportal.sathyabama.ac.in/coursematerial_staging/uploads/SEC1319.pdf
In the AES document, "Why 1-Bit Sigma-Delta Conversion is Unsuitable for High-Quality Applications."
Lipshitz and Vanderkooy state (page 4): "...display gross modulation of the noise floor in the audio band"
https://timbreluces.com/assets/sacd.pdf
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(Wow you guys are amazing... 
And maybe a little bit (too) eager to judge...
But I guess it's such a good feeling to push somebody down so I forgive and simply ignore it.
BTW I didn't ask this because I don't know how harmonics are generated.)
Thanks Jan for your example and image! But let's just move on.
So my next question what other sources can you say what also can produce
harmonics except the "stateless" non linear gain of a device?
And maybe a little bit (too) eager to judge...
But I guess it's such a good feeling to push somebody down so I forgive and simply ignore it.
BTW I didn't ask this because I don't know how harmonics are generated.)
Thanks Jan for your example and image! But let's just move on.
So my next question what other sources can you say what also can produce
harmonics except the "stateless" non linear gain of a device?
(Wow you guys are amazing...
And maybe a little bit (too) eager to judge...
Not really. Have you understood yet how distortion in a first cycle, even if it was caused, is utterly meaningless?
If you want to see how the amplifier comes out of overload, then why do you need to come up with something exquisite, if there is a regular test with a rectangular signal? Why give a step in the composition of the burst in a veiled way, if you can do it openly and get a more convenient result for visual evaluation? I sincerely do not understand why I have to come up with methods to scratch my nose with my heel, if it is more convenient with my hand.
You have little idea of the processes that occur in an amplifier with NFB, so you are easily confused by the results of Petrov's simulations. With the proper level of knowledge in the head should already have a filter that protects against delusional ideas. I have shown enough in my posts throughout the topic to separate the wheat from the chaff. And other participants in the discussion showed even more and more versatile. When the sine is applied, there is no sharp start (there is no hidden modulating step) and the amplifier manages to work out the input signal rise without increasing the differential voltage at its inputs. As soon as we apply a step - there is a lag of the output signal from the input and the differential voltage between the inputs of the comparison node increases.
You have little idea of the processes that occur in an amplifier with NFB, so you are easily confused by the results of Petrov's simulations. With the proper level of knowledge in the head should already have a filter that protects against delusional ideas. I have shown enough in my posts throughout the topic to separate the wheat from the chaff. And other participants in the discussion showed even more and more versatile. When the sine is applied, there is no sharp start (there is no hidden modulating step) and the amplifier manages to work out the input signal rise without increasing the differential voltage at its inputs. As soon as we apply a step - there is a lag of the output signal from the input and the differential voltage between the inputs of the comparison node increases.
I showed you how the amplifier responds to a sine with a step here
https://www.diyaudio.com/forums/att...89d1608660303-cycle-distortion-graham-288-png
Let me explain - you see a "floating" sine at the output, which consists of the sine itself and the hump of the transition process caused by the step
If you look at Petrov's graphs and see sharp peaks of distortion as a result of the influence of the sine, you should have a natural question - what causes it and what is the mechanism. These are the right questions. A sharp peak can only give the same sharp impact on the input. If you don't see it, it's veiled by the signal it modulates. But it is there!
https://www.diyaudio.com/forums/att...n-graham-composit_vs_lpf_speed_distortion-png
Here you see Petrov laid out a graph with different sinuses, but there are gaps between them, which are step effects and it is at these moments that distortion peaks appear as if by magic. And since the simulator calculates everything step by step, there is always a transition if the source is glued together from pieces. Don't you believe it? Apply the sum of 19kHz and 20kHz and you will not see such peaks in the signal between the outputs, although the signal jumps up and down at almost the maximum speed for the audio range.
And in addition... It amuses me when a person like Petrov talks about the bad sound of amplifiers that he has not collected or heard in his life. This is at least false information, which has a desire to support its arguments with pseudo-facts. That is why I have long ceased to believe his words and ask for links to primary sources and mathematical calculations that you can check and read yourself.
You got that right. Since I and many others here are not, hopefully if you are interested enough to obtain measurement you will finally gain the proper understanding of the matter.
Sorry, frantically searching Google for a string also doesn't cut it. The Qualcomm product overview (which is anything but a technical description, and to add insult to injury is about Class D amplifiers) doesn't explain anything and qualifies as a marketing material. I can only wildly assume it is about overloading effects, which, as I mentioned in my original question, do create a noise floor "grass" due to the harmonic components resulting for intermodulation. The rest of quotes also don't explain a iota of your understanding of the "noise floor modulation" concept. If you would read my original question carefully, you would for sure realize that it is not the concept of "noise floor modulation" that was under question, but your use (and abuse) in the noted context. It is funny that the TI white paper you quoted above, and the EE class material you quoted next, illustrate exactly what I have mentioned:
These are well known effects and nobody debated them.
L & V AES paper has nothing to do with "noise floor modulation" but only sets the foundation for an ultra known fact, that an 1-bit modulator has limitations (and that's why the ESS DAC, for example, is using a 6-bit modulator, no idea about the AKM devices).
About your own comment, there is only one qualifier: doesn't compile whatever way or direction it is read. Name dropping (Bruno Putzey) is not helping.
If you want to have an educated discussion about DAC limitations, we can do so, in another thread. But the pre-requisite is to set aside any techno babble, use a language that belongs to the EE body of knowledge, and refrain from using subjective BS, abusing known facts, name dropping, and unsubstantiated claims.
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And then as the distortions begin to circulate in a circle in the NFB circuit... What are we going to do about it then?
I wasn't saying overload testing. And neither a response to a step signal.
But your (russian? labeld) figure shows that the response has a decaying settlement section at the beginning.
And if this settling response to a (not infineitely) fast signal shows different behaviour
between 2 amps then why we couldn't use this method to get some additional info..?
And as I said earlier (for me) 2 main interpretations can be made about FCD:
a) the step signal response -> here the input signal is a suddenly starting sine wave
I leave this FCD type on Petr as I'm more intrested on option "b)"
b) settlement response -> here the step test signal is not a must at all
and a "slowly" staring sine wave is perfect (but under slowly I mean a few periods not 100).
And then we check the response for the very first complete (100% normal amplitude) sine wave at the output.
And then we compare this result with the 10th, 30th, ..., 100th periods as well.
If the 1st (few) one has a much higher distortion then the later ones, the system has a decaying distortion profile.
And if an "A" amplifier differs in this aspect from amp "B" then we
could say that it's "faster" even if they have the same bandwidth.
And after that we could check the correlation with the final sound quality as well.
But maybe this b) option is just my false interpretation of FCD and I shouldn't hijack this topic with it at all...
Isnt that what were talking about. A square wave or any signal that has fast risetimes like pulsed sines as a test signal? This whole first cycle nonsense.
Just as explanation of what I meant: If I hit an LTP (with no LPF at input) with a fast 1v square the + side goes to 1V while the - side is still at zero. This drives the LTP (which only sees milivolts across +/- in normal operation) into saturation, non linear region. I am asuming a reasonable amount of feedback in the design.
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