• WANTED: Happy members who like to discuss audio and other topics related to our interest. Desire to learn and share knowledge of science required as is 20 years of participation in forums (not all true). Come here to have fun, be ready to be teased and not take online life too seriously. We now measure and review equipment for free! Click here for details.

Theoretical soures of amplifier distortion

Joined
Sep 11, 2019
Messages
38
Likes
17
#1
It seems when measuring distortion in audio circuits we look for four possible types of distortion:

  • Harmonic distortion - unwanted components are multiples of each tone in the signal
  • Intermodulation distortion - unwanted components are multiples of the difference between each pair of tones in the signal
  • Noise - unwanted components are spread out across a wide band of frequencies
  • Interference (e.g. power supply hum) - unwanted components are specific frequencies, independent of the signal
I was wondering, are there any other possibilities? When looking at the theoretical operation of amplifier circuits, are there any other possible relationships between the signal and the distortion? And if so, what sorts of test signals would look for those other distortion types?
 

sergeauckland

Major Contributor
Forum Donor
Joined
Mar 16, 2016
Messages
1,632
Likes
3,490
Location
Suffolk UK
#2
Harmonic distortion and intermodulation distortion are both due to the same mechanism, that of non-linearity of the transfer function, i.e. the relationship between input and output, which should be only one of amplitude.

Noise isn't normally classed as 'distortion' as it's there regardless of signal presence. Some processes, like tape recording, can modulate the noise floor depending on the signal, but that's not a process normally seen in amplifiers.

Interference, whether RF or mains hum again isn't something normally considered 'distortion' although definitely in the case of hum, can be signal dependent, as the amount of residual ripple on the power supply depends on the current being drawn and therefore on the output level. RF interference, just like distortion caused by non-linearity, can be due to multiple reasons, minimised by good design, but can't be completely eliminated.

S.
 
OP
T
Joined
Sep 11, 2019
Messages
38
Likes
17
Thread Starter #3
What is the transfer function of a transistor or tube amplifier? Is there a place I can find those equations without buying a $200 textbook?
 

kn0ppers

Active Member
Joined
Jul 4, 2019
Messages
172
Likes
208
Location
Germany
#4
Douglas Self wrote a lot about the different sources of distortion in his power amplifier book. I think the same texts are also in "Self on Audio".

To understand what a transfer function is, you'd probably have to learn the basics of control system theory. Not necessarily going to cost you money, but time. Essentially it describes the relationship between input and output regarding amplitude and phase shift for a given input frequency. And usually it would be given as a Laplace transform, because that's easiest to further work with. You can get a rough estimate for the transfer function of opamps by looking at their open loop gain and phase plots to identify the poles and zeros, but this method is not very accurate I would say.
 
OP
T
Joined
Sep 11, 2019
Messages
38
Likes
17
Thread Starter #5
Douglas Self wrote a lot about the different sources of distortion in his power amplifier book. I think the same texts are also in "Self on Audio".

To understand what a transfer function is, you'd probably have to learn the basics of control system theory. Not necessarily going to cost you money, but time. Essentially it describes the relationship between input and output regarding amplitude and phase shift for a given input frequency. And usually it would be given as a Laplace transform, because that's easiest to further work with. You can get a rough estimate for the transfer function of opamps by looking at their open loop gain and phase plots to identify the poles and zeros, but this method is not very accurate I would say.
I am an electrical engineer and I do know the theory you're talking about. I don't remember the specific equations for different circuits though, and I didn't keep my textbooks from school. Was wondering if there's a reference available online.
 

kn0ppers

Active Member
Joined
Jul 4, 2019
Messages
172
Likes
208
Location
Germany
#6
I don't know what specific equations for different circuits you mean? You would have to analyse the individual circuit, setup a system of differential equations and go from there. Sure for some standard building blocks you will probably have equations that you can easily fill in, but you won't get those for complete amplifiers I think? Maybe I'm wrong.
 
OP
T
Joined
Sep 11, 2019
Messages
38
Likes
17
Thread Starter #7
I mean, are there any examples where someone has done those calculations for common amplifier circuits. Maybe comparing a tube stage to a solid-state stage and examining the differences in the theoretical distortion terms. I know it won't match specific implementations.

What I'm looking for what probably be on some university classroom page if it exists.

In particular, I'm wondering if it's possible for a the output of any circuit to have a frequency that isn't a multiple of either some tone in the input, or the difference between two tones in the input.
 

Blumlein 88

Major Contributor
Forum Donor
Joined
Feb 23, 2016
Messages
9,649
Likes
12,894
#8
It all starts with these curves for the basic device. Then you have ways of connecting them and feedback etc. Do any of them have absolutely linear transfer functions which would create zero distortion? Not yet, and probably never, but who knows what might be discovered by clever people in the future. Below are bipolar transistors, FET, and triode curves.


1596423975427.png

1596424003894.png


1596424042909.png
 
Last edited:
OP
T
Joined
Sep 11, 2019
Messages
38
Likes
17
Thread Starter #9
Okay, I'm starting to remember now. We bias the components to get them into a region of those curves that looks reasonably linear, then apply feedback to further "flatten" the curve at the expense of gain.
 

waynel

Senior Member
Forum Donor
Joined
Nov 14, 2019
Messages
430
Likes
404
#10
It seems when measuring distortion in audio circuits we look for four possible types of distortion:

  • Harmonic distortion - unwanted components are multiples of each tone in the signal
  • Intermodulation distortion - unwanted components are multiples of the difference between each pair of tones in the signal
  • Noise - unwanted components are spread out across a wide band of frequencies
  • Interference (e.g. power supply hum) - unwanted components are specific frequencies, independent of the signal
I was wondering, are there any other possibilities? When looking at the theoretical operation of amplifier circuits, are there any other possible relationships between the signal and the distortion? And if so, what sorts of test signals would look for those other distortion types?
Ideally amplifiers are memoryless and time invariant but that’s not always the case, so you can add memory effects (sometimes thermal) to your list. That is the transfer function can change as a function of time, temperature, or previous state.
 

bobbooo

Addicted to Fun and Learning
Joined
Aug 30, 2019
Messages
872
Likes
1,021
#11
what sorts of test signals would look for those other distortion types?
On this specific question, I'm not aware of any real hard evidence that the signal degradation of a device when playing sine tones is representative of its degradation when playing the complex waveforms of actual music. There is in fact evidence this correlation is a poor one in DACs / DAPs, from null difference measurements done by Serge Smirnoff at SoundExpert, which show the difference signal between the original and recorded output from a device (a measure of its degradation of the signal) when playing sine tones is poorly correlated with the same measure when playing real music, or the industry standardized 30-second 'Program Simulation Noise' (BS EN 50332-1), which was devised to be representative of the spectral content of music and speech, and so could be the best of both worlds (a test signal that is closer to real music, yet standardized and repeatable by others).

Such difference signals would reveal all possible distortion/changes to the input signal, for any signal, including music, or a close spectral analogue thereof in the form of the Program Simulation Noise. See the original thread by Serge and the recent discussion of the idea here if you're interested.
 
Last edited:
OP
T
Joined
Sep 11, 2019
Messages
38
Likes
17
Thread Starter #12
Such difference signals would reveal all possible distortion/changes to the input signal, for any signal, including music, or a close spectral analogue thereof in the form of the Program Simulation Noise. See the original thread by Serge and the recent discussion of the idea here if you're interested.
This is basically what I'm asking. Linear systems follow the superposition principle, meaning the total output is the sum of the output for each of the input's frequency components. I.e. total music or individual tones doesn't matter.

We know that THD and IMD violate this, which is why we have specific tests to stress and maximize these distortions. If those are the only possible distortions, then the sine wave tests are still valid. But if there are other distortions, that are not multiples of the tones in the input or the differences between them, then these additional distortions could show up in music, even though the standard test suits might miss them.

I would note that the result you posted above doesn't necessarily mean the sine wave tests are invalid. Even if THD and IMD are the only sources of distortion, we would expect a more complex input to have more harmonics and intermodulation tones, which would increase the total distortion. And this wouldn't necessarily be audible, because the more complex input would mask the increasing number of distortion tones. Two white noise signals could have nearly 100% difference, but they would sound identical to you.
 

Vini darko

Addicted to Fun and Learning
Joined
Jun 1, 2020
Messages
605
Likes
641
#14
Clipping, especially hard clipping are the nasty-est distortion I can think of.
 

scott wurcer

Major Contributor
Audio Luminary
Technical Expert
Joined
Apr 24, 2019
Messages
1,072
Likes
1,689
#18
What is the transfer function of a transistor or tube amplifier? Is there a place I can find those equations without buying a $200 textbook?
There is a problem involved when you apply feedback, the resulting non-linear differential equations often don't have closed form solutions. This is where you need an iterative technique such as a transient analysis. Sometimes you can get information from expanding the transfer function in a Taylor series. This paper remains very informative (Gerry Sussman is one of the greatest minds I have ever known). https://www.its.caltech.edu/~musiclab/feedback-paper-acrobat.pdf
 

DonH56

Major Contributor
Technical Expert
Forum Donor
Joined
Mar 15, 2016
Messages
4,460
Likes
6,962
Location
Monument, CO
#19
If you do the expansions you'll find BJTs' series is exponential and tubes' factorial so fundamentally for the same conditions tubes actually have lower distortion than BJTs. An ideal FETs' series ends at the second term (square-law device) but of course real-world FETs are not ideal and in fact submicron FETs start looking exponential as well. The physics gets... interesting.

I'd have to dig up my reference -- I remember the answers, and have the derivations in one of my "general" notebooks, but the original reference is from an old college text (i.e. ~40 years ago). Prof made us work through them all...
 

bobbooo

Addicted to Fun and Learning
Joined
Aug 30, 2019
Messages
872
Likes
1,021
#20
This is basically what I'm asking. Linear systems follow the superposition principle, meaning the total output is the sum of the output for each of the input's frequency components. I.e. total music or individual tones doesn't matter.

We know that THD and IMD violate this, which is why we have specific tests to stress and maximize these distortions. If those are the only possible distortions, then the sine wave tests are still valid. But if there are other distortions, that are not multiples of the tones in the input or the differences between them, then these additional distortions could show up in music, even though the standard test suits might miss them.

I would note that the result you posted above doesn't necessarily mean the sine wave tests are invalid. Even if THD and IMD are the only sources of distortion, we would expect a more complex input to have more harmonics and intermodulation tones, which would increase the total distortion. And this wouldn't necessarily be audible, because the more complex input would mask the increasing number of distortion tones. Two white noise signals could have nearly 100% difference, but they would sound identical to you.
Yes the total distortion from a complex input such as music will always be higher than that for sine tones, but what I was referring to with those difference signal results I linked to is that they do not show a monotonic correlation between the median difference signal level (Df value as Serge calls it) when playing sine tones and the difference signal when playing music. For example, from those results the FiiO M11 has a slightly lower Df value (less signal degradation) for a 1kHz sine wave than the Questyle QP1R, yet the former has a significantly higher Df value (more signal degradation) when playing real music or the Program Simulation Noise. This suggests sine tones tests are not adequate for measuring the true signal degradation and distortion of a device when actually playing music, and so music (real or simulated) would be the required test signal for a true measure of this.

As for audibility, Dr. Sean Olive and Steve Temme for example have shown in this AES paper that a non-coherent distortion metric using real music has a much better correlation to sound quality than standard multitone distortion metrics, which along with IMD are poor in this regard, as well as beating THD (results are at 31:24 in the video):


More details on the non-coherent distortion metric can be found in this paper.
 
Top Bottom