These statements are confusing to me. THD is Total Harmonic Distortion - in that it creates harmonics. If the fundamental has any distortion at all, then harmonics will be created.
I created one product where part of the design was to create 32 unique frequencies at whole number divisions of the sample rate. It should be mathematically obvious that some multiples would be harmonics of others. In my first design, I picked an op-amp with good rail-to-rail output, and general bandwidth, but I failed to notice that distortion increased with amplitude, so that rail-to-rail performance was a bit misleading. In any event, I could not tell the difference with my test equipment between the harmonics created by the distortion of the op-amp and the separate signals that happened to be harmonics of others. That's a long story just to show that it might be a bit meaningless to talk about distortion varying by frequency.
For the most part, it seems that distortion tends to be characterized as 1st harmonic, 2nd harmonic, 3rd harmonic, and on up, including combinations of different amounts of distortion at each of these harmonics. In general, it doesn't matter what frequency goes into the amp: You're going to see an, e.g., 3rd harmonic added on the output if the amp has 3rd-harmonic distortion. Low frequency input means low frequency distortion; high frequency input means high frequency distortion. The frequency of the distortion depends upon the frequencies of the signal on the input, not so much on the amplifier itself.
There's a ton of psychoacoustic research concerning Critical Bands; how harmonics fall into those bands; and how humans perceive loudness. So, yes, distortion can effect the tone of an instrument, but it's not like an EQ.
Yes, reading your posting I can see that you are a bit confused, to me it seems you’re following a wrong track.
Hans
Hans
Bootstrapped "blameless" = mostly 2nd harmonic
regular "blameless" = equal 2/3rd
"Leach" type symmetrical LTP amps = almost no 2nd , 3rd/5th dominant.
Most symmetrical designs cancel rail ripple (high PSRR) , as well.
Close to peak output , these tendencies are exaggerated. The exceptions are if they have either
non-typical VAS's or output stages. Near clip will do a lot of nasty stuff ... like saturation ("sticking").
Driven hard , you will hear whether a design has "grace under pressure".
An example of this were the JVC "super A" consumer amps. they would still not sound awful even as they were
overloaded. "Super A" chip would limit VAS/OPS saturation , no hard 5/7/9th to blow many a tweeter. JVC's also had a hybrid
symmetrical VAS that would not "stick" in saturation.
So , not totally THD ... but , quality of PS and design - and to a degree , the topology will set the character of a heavily driven amp
"under pressure".
SMPS vs. linear is also quite noticeable at clip. Linear will be louder with certain source material (peaks/disco/rap). SMPS will do better
at test tones. THD would be the same with either , dependent on amp PSRR.\
With speakers and crossovers being a wild mix of LLC tank peaks and dips plus having many percent THD , the amp's damping factor
will be a major factor. With audio , we are not recycling back EMF to get more efficiency ... like a SMPS. EMF is the enemy.
OS
regular "blameless" = equal 2/3rd
"Leach" type symmetrical LTP amps = almost no 2nd , 3rd/5th dominant.
Most symmetrical designs cancel rail ripple (high PSRR) , as well.
Close to peak output , these tendencies are exaggerated. The exceptions are if they have either
non-typical VAS's or output stages. Near clip will do a lot of nasty stuff ... like saturation ("sticking").
Driven hard , you will hear whether a design has "grace under pressure".
An example of this were the JVC "super A" consumer amps. they would still not sound awful even as they were
overloaded. "Super A" chip would limit VAS/OPS saturation , no hard 5/7/9th to blow many a tweeter. JVC's also had a hybrid
symmetrical VAS that would not "stick" in saturation.
So , not totally THD ... but , quality of PS and design - and to a degree , the topology will set the character of a heavily driven amp
"under pressure".
SMPS vs. linear is also quite noticeable at clip. Linear will be louder with certain source material (peaks/disco/rap). SMPS will do better
at test tones. THD would be the same with either , dependent on amp PSRR.\
With speakers and crossovers being a wild mix of LLC tank peaks and dips plus having many percent THD , the amp's damping factor
will be a major factor. With audio , we are not recycling back EMF to get more efficiency ... like a SMPS. EMF is the enemy.
OS
If you use "ideal" current/voltage sources in your simulation - yes. You can run a simulation in "pessimistic" mode.
Add trace capacitances , ripple to the rails ... serial resistance and inductance.
The way you are describing harmonic distortion is a bit unusual. Harmonic distortion is really just conceptual way of measuring distortion using a single test tone. If multiple tones are used then the applicable term would be intermodulation distortion.
However HD and IMD are caused by the same thing, which based on the idea of a transfer function. If the transfer function of an amplifier is not a perfectly straight line, then the amplifier is nonlinear. If we measure that nonlinearity with a single tone then we will see results we call HD. On the other hand if we measure with multiple test tones the results we see are called IMD. In other words, they are two different ways of trying to measure the exact same thing, which is the curvature of the nonlinear transfer function.
That's the basic idea. Of course, reality can be more complicated than basic theory. For one thing the transfer function nonlinearity may vary under different operating conditions, such as occurs with thermal distortion when we use a low frequency test tone.
Anyway, the whole idea of using HD/IMD and or THD as a way of measuring the effects of a nonlinear transfer function has been criticized for a long time. Some published research on distortion, along with some criticism of how its measured, can be found at: http://www.gedlee.com/Papers/papers.aspx
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Had until yesterday two or three weeks a small single stage complementary transistors half wave symmetric push-pull follower to run. Now again a single stage single ended. The push-pull sounded like doll box, toys: small, doll colors, rumpy, angular, broken contours, a Spanish wall across in spatial imaging;-)
Had the complementary pp converted to a Sziklai for a few hours in between: duller, grayer, hazier, colorless, less smooth...-)
I think many would think the SE sounded "better" because its distortion spectrum was more "ear-friendly"-) I mean, the ear perceives differences first: And push-pull amplifies the half-waves with different components, the halfwaves sound different, which the ear perceives - as noise;-)
Had the complementary pp converted to a Sziklai for a few hours in between: duller, grayer, hazier, colorless, less smooth...-)
I think many would think the SE sounded "better" because its distortion spectrum was more "ear-friendly"-) I mean, the ear perceives differences first: And push-pull amplifies the half-waves with different components, the halfwaves sound different, which the ear perceives - as noise;-)
Sorry, but harmonic distortion and intermodulation distortion are not the same thing. Harmonic distortion only creates frequencies that are a multiple of the input frequency, and it can happen on inputs with one or more frequencies due to superposition. Intermodulation distortion requires more than input frequency, and results in the output containing sums and differences of the input frequencies, which are often not harmonics. When there is only one input frequency, intermodulation distortion is 0% by definition.
A static transfer function can only create harmonic distortion. Intermodulation distortion requires a dynamically changing transfer function.
Of course, amplifiers aren't generally designed to create distortion on purpose, and distortion measurements cannot assume that only one kind of distortion is occurring, nor can they assume that the types of distortion are known in advance, so the measurement techniques assume one or the other and try to estimate the amount.
Not really. You can test for THD and IMD using appropriate tests. Estimation is not necessary.
Both are caused by non-linearity as has been mentioned by others.
I didn't say they were the same thing.
Not exactly. Passing a sine wave through a nonlinearity produces harmonic distortion, and the harmonic distortion consists of harmonics of the sine wave. This is an important distinction from what you said.
No, superposition applies to linear systems only. We are talking about nonlinearity when we talk about HD and or IMD. Therefore, superposition does not hold.
True by definition.
Not exactly. The production of HD or IMD is purely a mathematical result of passing a signal through a nonlinearity. The only difference is the type of test signal used. There is no requirement that the nonlinearity be changing over time (non-time invariant).
Not so. Don't know where you got that idea. The math is very clear. So is practical experience. For example, simple small-signal diode frequency mixers produce intermodulation products without having a non-time invariant diode transfer function.
rsdio,
Don't know if anyone's efforts to explain are helping or not. Of course if you are not interested in having a better understanding of distortion, nobody is going to force you.
OTOH if you want to know more than you know now there are some EEs here with a lot of experience that would be willing to help.
Mark
Thanks for the careful response, Mark.
One assumption I'm making is that the typical THD test involves an input at a single frequency, e.g., 1 kHz, followed by a notch filter to remove 1 kHz and then a very simple measurement of the amount of output there is at any frequency other than the input frequency (with the inherent inaccuracies that would occur in the transition bands of the notch filter). Such a THD measurement will not be able to distinguish IMD from THD (well, except for the fact that if you're certain you only input one frequency, then you can't have IMD by definition, but there are always ways for noise to creep in).
I assume that IMD tests are similarly oversimplified, and potentially lose details that could distinguish between types of distortion.
I'm also assuming that if IMD involves amplitude modulation of the output, then there must be some form of dynamic gain. Isn't IMD a multiplication of two signals? i.e. where one controls the gain of the other, so to speak?
I should scan Bob Cordell's book to see if there is any discussion of distortion and measurement. It's been a while since I read "Designing Audio Power Amplifiers"
I'm leaning heavily on Fourier in thinking of any periodic waveform as a sum of sine waves. Harmonic distortion can change the weight of the harmonics from 0 (not present) to non-zero (present) - which is what I mean when I say that HD "creates" harmonics.
p.s. I should have used the term additivity instead of superposition.
One assumption I'm making is that the typical THD test involves an input at a single frequency, e.g., 1 kHz, followed by a notch filter to remove 1 kHz and then a very simple measurement of the amount of output there is at any frequency other than the input frequency (with the inherent inaccuracies that would occur in the transition bands of the notch filter). Such a THD measurement will not be able to distinguish IMD from THD (well, except for the fact that if you're certain you only input one frequency, then you can't have IMD by definition, but there are always ways for noise to creep in).
I assume that IMD tests are similarly oversimplified, and potentially lose details that could distinguish between types of distortion.
I'm also assuming that if IMD involves amplitude modulation of the output, then there must be some form of dynamic gain. Isn't IMD a multiplication of two signals? i.e. where one controls the gain of the other, so to speak?
I should scan Bob Cordell's book to see if there is any discussion of distortion and measurement. It's been a while since I read "Designing Audio Power Amplifiers"
I'm leaning heavily on Fourier in thinking of any periodic waveform as a sum of sine waves. Harmonic distortion can change the weight of the harmonics from 0 (not present) to non-zero (present) - which is what I mean when I say that HD "creates" harmonics.
p.s. I should have used the term additivity instead of superposition.
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You are most welcome, of course!
It turns out there is very good software these day to generate test signals and to analyze distortion results. REW is a fabulous freeware for that. There is a long thread here in the forum on how to use REW for various things: https://www.diyaudio.com/community/threads/how-to-distortion-measurements-with-rew.338511/
Indeed, but that is usually treated as a separate subject from basic steady-state distortion measurement and analysis (aka 'PSS' measurements, where PSS = Periodic Steady State).
Not necessarily. Actually REW can be very helpful (and powerful) so its probably worth checking out to start with.
The subjects of noise, signal-correlated noise, EMI/RFI related distortions, etc., is usually discussed separately. For Cordell, 2nd Ed, IIRC Chapter 16 covers 'other sources of distortion.' We could also talk about such things in more detail here in the forum, but maybe better to not try to cover too much ground in one post. It can get rather involved, depending.
In the time domain, and in theory, both IMD and HD result from multiplying the input (or forcing function) by the transfer function (where both are written as mathematical functions). In that case the forcing and transfer functions are multiplying each other. That's essentially how HD/IMD results.
We could also contrive a situation where one signal multiplies another, but not the other way around. An example might be using a VCA control input for a modulator signal which controls VCA gain, to then modulate a signal which is passed through the VCA amplifier processing signal path.
Okay.
As a practical matter sometimes it can be useful to distinguish the continuous time Fourier Transform, as versus a sampled-time DFT/FFT. There can be some practical differences in how and where they can be usefully applied.
One factor to consider might be the theoretical requirement for an LTI system, or else a system that is no more than 'weakly' non-LTI (where what constitutes 'weakly' may depend on what sort of analysis is close enough for the purpose at hand). Then again there are pretty highly non-LTI systems where short-time DFTs may find practical use
Not sure sure exactly how you are defining additivity as versus superposition? Applying a nonlinearity to multiple frequencies then summing the results is a different process from summing frequencies then applying a nonlinearity to the sum.
If we add to two frequencies then we get envelopes that may sound as beat notes. Some examples: https://www.google.com/search?rlz=1...YX2BMAQ0pQJegQICxAB&biw=1494&bih=714&dpr=1.25
OTOH, if we multiply frequencies we get intermodulation products, which to a first approximation are sum and difference frequencies. Higher order intermodulation products (distortion of the distortion, so to speak) tend to be at a much lower, often negligible level. Some examples for that: https://www.google.com/search?rlz=1...ZCSDZ4Q0pQJegQIDRAB&biw=1494&bih=714&dpr=1.25
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I think I see what I missed: If two frequencies are summed, then fed through a non-linear transfer function - particularly a transfer function that is linear below an amplitude threshold and non-linear above that threshold - then one frequency could effectively "change the gain" on the other frequency by moving the summed amplitude above the threshold where things start becoming non-linear. i.e. One doesn't need a dynamically-changing transfer function (gain) to product IMD. In fact, both frequencies could affect the gain of the other, since it's their sum that pushes the response from the linear to non-linear range (or even through a point where the transfer function "gain" changes).
Anyway, I can see how HD and IMD could both result from the same, static transfer function.
Mark, do you have any comments on distortion that "varies by frequency" - that's one of the phrases from earlier in this thread that most confused me.
Anyway, I can see how HD and IMD could both result from the same, static transfer function.
Mark, do you have any comments on distortion that "varies by frequency" - that's one of the phrases from earlier in this thread that most confused me.
There is something called 'memory distortion' where distortion depends on the past state of a signal. A common example is thermal distortion that may occur in power amplifiers at low frequencies. Cordell's book should cover thermal distortion. Another type of memory effect might be hysteresis distortion (looks like the webpage needs some attention): https://purifi-audio.com/blog/tech-notes-1/this-thing-we-have-about-hysteresis-distortion-3
Another common frequency dependent effect is that the closed loop gain of an amplifier tends to drop off as frequency increases (i.e. the amplifier is an integrator). As a result feedback can be less effective at minimizing distortion at higher frequencies. Of course, this assumes we are thinking of the effect in terms of the frequency domain. If we were to think about it in the time domain, it would seem to have to do with how fast the slope of a signal is changing (which is only to say that, the slew rate and the frequency components of a time-domain signal are two different things -- hope I explained that correctly 🙂 ).
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Ah, yes, hysteresis distortion - something that magnetic tape has (but I'm sure there are many other kinds).
I won't ask you to explain the difference between slew rate limiting and a lowpass filter (but I'll accept a link to another discussion).
Thanks again.
I won't ask you to explain the difference between slew rate limiting and a lowpass filter (but I'll accept a link to another discussion).
Thanks again.
Harmonic distortion can be thought of as a special case of inter-modulation distortion where the output just so happens to be a harmonic multiple of the input.
Take an amplifier with negative feedback for example. Since the signals are circulating close to the speed of light, let's do a walk-through. On the first pass, like in open-loop mode, the output only produces the fundamental and some H2, just for instance.
On the 2nd pass, the input now has 2 frequencies passing through the non-linear gain stage, so, even if -H2 mostly gets subtracted, new harmonics like H3 and so on will be created via inter-modulation of H1 and H2, ad infinitum.
At least that's how I like to think about it. Maybe it's simplistic, but I'm running a simulation and not even trying to come up with an analytical model.
Take an amplifier with negative feedback for example. Since the signals are circulating close to the speed of light, let's do a walk-through. On the first pass, like in open-loop mode, the output only produces the fundamental and some H2, just for instance.
On the 2nd pass, the input now has 2 frequencies passing through the non-linear gain stage, so, even if -H2 mostly gets subtracted, new harmonics like H3 and so on will be created via inter-modulation of H1 and H2, ad infinitum.
At least that's how I like to think about it. Maybe it's simplistic, but I'm running a simulation and not even trying to come up with an analytical model.
The former is a nonlinear process, whereas the latter is linear.
It that enough to help?
Okay.
Maybe getting into controversial territory there. The idea that signals are 'circulating' is probably not a good way to think about what's happening, unless maybe the amplifier is approaching instability, or maybe if the input signal frequency is more or less getting to be on the same order as the feedback loop propagation delay. Something like that.
A book you might find useful for giving more and better insight into feedback amplifier errors, nonlinearities, etc., could be: "Operational amplifiers, Second Edition (EDN series for design engineers)" by Jiri Dostal. If you can find a copy around somewhere at a good price, IMHO its a good one to have on the bookshelf.
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Well in that case, my cup of coffee isn't circulating unless I can see the ripples. And even then, I've seen waves on rivers moving in the opposite direction to the water current.
You simultaneously saying this happens almost instantaneously (speed of light), yet is slow enough for an audio frequency and its harmonics to be involved... That's not consistent or meaningful I suggest.
And circuits don't really know about signal flow, that's our intuition about circuitry, the physical components just sit there enforcing their behavioural equations - a transistor can be used with collector as input and base as output if you really want - circuit simulation is also agnostic like this and doesn't have a notion of signal flow (except for ideal dependent sources).
Better to think of negative feedback as a circuit topology that constrains the error between the input and output to very small values. If the feedback is stable, the error is constrained mathematically to a fraction of the open loop error. The more surplus open loop gain, the smaller the fraction. (Assuming the feedback network itself is linear).
In a typical multistage amp with global negative feedback distortions tend to appear magically at the output of the differential input stage, then usually decrease with each subsequent stage, then magically almost disappear at the output. This is all about the mathematical constraints the feedback topology enforces - the error has to have distortions that are the inverse of the rest of the amp, so that they cancel by the time the signal reaches the output (which is where the feedback samples things).
Of course the issue of stability is not trivial, Nyquist's criterion is not an obvious thing I think you'll agree.
Closing the loop is extraordinarily powerful, yet brings the danger of instability.