Music is more complex for audio amplifiers than sine and square waves - DEBUNKED

[@argcargv]

Part 3: While linearity is an important feature of an amplifier, it is not the only one. It is also important that signals at different frequencies have similar phase shifts (at least within a certain bandwidth). A completely linear amplifier may fail in this regard. The square wave is very good at evaluating this aspect of an amplifier. So assuming that we know an amplifier is linear because it has a low THD over a wide frequency spectrum, the square wave is the next go-to signal to understand how good the amplifier is at transforming the input signal into an unadulterated louder signal. The reason for this can be understood again from the Fourier transform which says any periodic wave form can be represented as a sum of sine waves. In the case of a square wave, the Fourier transform contains an infinite frequency content, so a square wave is a good way to measure how an amplifier performs on complex wave forms. Now that effect of the phase delay on each sine wave can be seen. If these delays are inconsistent then it will reveal itself in the edges of the square wave as oscillatory behavior at the edges. In addition, if higher frequencies aren't amplified with the same magnitude, this will be revealed as a smoothing of the square wave edges. Therefore, if we know the amplifier is linear, the square wave can tell us a great deal about the amplifiers frequency response which is the second feature of an amplifier that is needed for it to be as close to ideal as possible. That is why square waves are included in the evaluation of amplifiers.

[@argcargv]

Part 2: One of the desirable properties of an ideal amplifier is that it is linear. Most of the time, non-linearity in the amplifier adds unpleasant distortion to the sound (for example, clipping). Testing the amplifier with a sine wave signal over a wide frequency range and evaluating the THD for each of those is a good way to evaluate the linearity of the amplifier. The reason is, if the amplifier is linear, putting a pure sine wave into the amplifier should result in a pure sine wave out. The only way you get other frequencies must be due to amplifier non-linearity. Therefore an amplifier that has uniformly better total harmonic distortion (THD) on all frequency signals from 10-20khz is fundamentally a more linear amplifier. However, not all nonlinearity is as unpleasant, so THD doesn't tell you the whole story. Two amplifiers with the same THD may be very different with regards to musicality (subjective). However, if we can make the THD low enough then the nonlinearity of the amplifier will be imperceptible to the human ear. In addition, there could be intermodulation distortion (IMD) where two different signals can interfere with each other. IMD requires nonlinearity as well but could cause more significant differences than the THD would reveal. Therefore an amplifier that has a low THD may look less good on a more complex signal due to a multiplicative effect between signals if a bitonal signal was used. However, if the THD is made low enough, this will necessarily lower IMD, so a good general goal is to lower THD as much as possible.

[@cbcdesign001]

That moving card demo you did over the front of your scope was brilliant John. A really good way to explain what the amp deals with and how.

[@argcargv]

Another comment after looking at some of the conversations here. Some people seem to be focused on the input signal, being periodic or not, etc and comparing this signal to a signal that is actual music. And so there seems to be confusion why some people are discussing the amplifier characteristics (linearity etc.) when discussing the input signal. However, in this context the purpose of the input signal is to evaluate the amplifier and its ability to desirable in its function, presumably to make the signal louder without adding unpleasant or undesirable changes to that sound in the process. So the question is: is music better at that process than a sine or square wave or not. As was pointed out in this video, when you zoom in on the music, 9 times out of 10 the signal looks less challenging than the tests that we put the amplifier through with sine or square wave tests, and that is a very valid point. As was pointed out at the end of the video one could evaluate an amplifier by simply taking a difference between the input and output and how much that difference could be nulled out could be thought of as an evaluation of the amplifier on any input signal. The shortcoming of that evaluation is that there are many ways that test could show an amplifier as being one of poor quality when the human ear would not be able to distinguish the sounds. For example, lets assume the amplifier delayed the signal by 1 millisecond, then the signal would sound identical to the human ear, but it would appear to be miserable based on this simple test. However, if you put a sine wave into the amplifier and you get a square wave out, we can reasonably expect that you would be able to hear that this is a bad amplifier, whereas a 1 millisecond delay would pass the test. So in some sense the performance of an amplifier on sine waves can be a very good first order indicator of musicality of the amplifier.

[@ergindemir7366]

Square wave is the most challenging signal for the audio amplifier.

[@johnyang799]

@Douglas Blake Square wave has twice power. And sine wave no matter it's 20hz or 20khz the power output is the same.

[@ergindemir7366]

I want to test the fidelity, not the stress.

[@johnyang799]

@Douglas Blake Also on top of that z square wave has in theory infinitely high frequency content, so it's certainly most challenging signal.

[@johna2327]

Actually @Douglas Blake is correct. Do the math on a square wave and a sine wave. The sine wave must be adjusted to not clip the tops. The power is calculated using RMS, which is 70.7% of the peak where as the square wave is calculated by the peak, not RMS. Square waves use more than twice the power as a sine wave. However the power supply and dummy load will hate it the most. The amplifier will hate it when you are at half the volume as it puts the most power loss across the output transistors. Wow, I am sure this will open a can of worms.

[@johnyang799]

@Douglas Blake And rms of sqarewave again? 50%? Can you just stop?

[@christopherkise]

i think one of the challenges the amplifier will meet in the real world is non linear speaker loads. I belive this is making the amplifier having a hard time at some frequencies and a better time on other. And of such, some amplifiers might not be up to deliver the current needed to keep the show running when the impedance of a speaker is falling. This might not be a good designed speaker, but sometimes one just have to accept some disadvantages.

[@micomrkaic]

John, this was brilliant, many thanks for the video. Also, looking forward to the 1W amp.

[@xraytonyb]

Just a couple of thoughts: First, it's difficult to really see all of the waveform on many of the digital scopes out there because of the limitations of the sample rate. Notice when you had the time base slowed down, the 20kHz sine wave looked all distorted (even though it wasn't), rather than a smooth sine wave. This was due to the limited sample rate of the scope. Second, I mostly agree with what you are saying, but I have found that intermodulation distortion (IMD) is a real thing. As you said, each component in each stage can only be at one voltage level at any given time,. However, when multiple components are working together in multiple stages, slew rate and time delay become very relevant. This can cause different stages of the circuit to be slightly out of phase due to differences in amplitude or timing between different components. This is why some service manuals have you adjust certain parts of the circuit for minimum IMD based on two tones at 4:1 amplitude ratio. Because of the limitations of the scope, you really can't see it unless you have a spectrum analyzer or IMD analyzer. Additionally, everybody has their own sensitivity to it. I can't personally hear it unless it gets pretty bad. Other people I know can hear it at much lower levels. Finally, most, if not all manufacturers design amplifiers to avoid all of these problems, which is why it's usually not an issue. It's also why so many amplifiers are similar in design, regardless of the manufacturer. It still amazes me how engineers figured all of this out so long ago! Just my two cents worth. Thanks for the great videos and best wishes!!

[@MM-ln9ey]

xraytonyb As you know quite well, this scope can go to 50 MHz ( or is it 100?). In other words, hundreds of times FASTER than needed for audio signals.

[@JohnAudioTech]

You are correct about IMD. I should have mentioned it. I consider it part of the simple periodic signals we use to test, just two tones played together. Music, OTOH, well you know... I think what you see on the scope is due to the low res screen. It has plenty of sample points for the frequencies used and memory depth for zooming in.

[@PeterMilanovski]

Wow! Two of my favorite content providers in the one place... It doesn't get any better than this! Collaboration is a very good thing indeed.

[@TheMovieCreator]

It's common knowledge for audio engineers that too much phase-shift (say from a heavily/badly adjusted equalizer) will absolutely obliverate any sharp/tight transients. However, the phase-shift of a decent amp should be nowhere near that level. What a lot of people forget is that the part of a HI-FI system that affects the sound the most, is the speakers themself and in particular the room theyre playing in. You can have an as good amp as possible, but if the room is unfit for close listening it won't help a bit.

[@ferrumignis]

Totally agree, audiofools fret over the last 0.01% distortion from a source or amplifier ignoring the fact that the speakers are by far the most non-linear component in the chain.

[@johnyang799]

@@ferrumignis That's not audio fools. Audio fools are people who owns one of the worst measuring equipments and claim they are transparent, resolving, engaging, musical and use expensice tweaks the have no effect. People who buys expensive products that have -120db distortion are rich people who just want to get best products. That's fine. And the best would be pay as little as possible to have near sota performance.

[@1pcfred]

KiCAD is a good capture program once you figure out the workflow.

[@argcargv]

Part 4: Subjectivity. A more complex problem is that for some users they actually like the distortion that is added by the amplifier. For example, electric guitar players may want the harmonics that the amplifier adds to their guitar and may prefer amps that would actually test very poorly in terms of THD. I think the same can be said about some tube amps. People like the distortion that these amplifiers provide. In that case it is a much harder task to evaluate an amplifier. If you like the sound of an amplifier subjectively, how can you change it so you like the sound even more? Some people have various opinions about the aspect of the amplifier that gives it the mystique that they desire. As this is much more subjective, it becomes almost impossible to address this by measurement. In fact, one could argue that there is no objective measure. The guitarist may like a particular distortion simply because it sounds most like the distortion that came from the crappy amplifier of their favorite guitarist from the past. In the future musical tastes may and probably will change. So once you enter this space there is no objective way to evaluate amplifiers, whatever suits your tastes is great for you but may not be great for someone else and good luck reproducing it in a different design.

[@strugglingparodox5709]

I accidentally discovered this before having seen this video. Playing with an amp I was running on a 5 volt USB battery, with a volt, amperage monitor running. I was goofing around with a tone generator, running at around 14Khz. I turned up the volume, and was very surprised to see the amperage shot up. Was all new to me. I thought that running higher frequencies wouldn't do anything, comparing to lower frequencies. (My ears were ringing for a while after that)

[@HammyTechnoid]

debunking audiophile mumbo-jumbo!!! *Count Me In!!!*

[@ferrumignis]

@HalfSpeedMastering If you cant hear or measure a distortion in an audio amplifier, then why worry about its existence?

[@johncoops6897]

@Douglas Blake - he's not overestimating anything. These kinds of bullshit claims are the fundamental basis of the audiofool industry

[@davidgriffin79]

@HalfSpeedMastering Dark matter is a mathematical hypothetical convenience; it may yet prove to be irrelevant if the mathematical models are changed.

[@davidgriffin79]

@HalfSpeedMastering Photo vs. gif. vs. mp4? The first is an analogue image, the second an 8 bit dithered image the third a movie. As a mathematician, I see JON's explanation making perfect sense. His description of how an amplifier increases a signal in the analogue domain is obvious; as is his description of the slew rate which is clearly the first derivative of the waveform. You seem to be trying to confuse the issue with technobabble.

[@ferrumignis]

@HalfSpeedMastering Because dark matter may be key to understanding the nature of our universe. Worrying about hifi audio artifacts that audiofools believe they can hear is just a waste of time.

[@Peltio]

The mystery of the non-appearing and disappearing comments intrigued me so much that I ended up writing this little rant. This is not a rant against this channel and especially not against @JohnAudioTech. It's just that I think that maybe not everyone noticed what is going on with the comments section of KZbin. So, John, I hope you will forgive my last comment here. KZbin's comments are gaslighting you. There is something curious going on with KZbin's comments. They are gaslighting you. When you post a comment and you see it published in the comments section of a video, it does not mean it has been published for the rest of the world to see (finally acknowledging your vast intellectual superiority, and possibly pave the way for that Nobel Prize that too many times has been undeservedly awarded to lesser people than you). It may have been classified as spam by KZbin's imperscrutable algorithms. This means that KZbin creators, who usually have a full time job and use up the little free time they've got to make new videos, are required to sift through their channel's spam folder in order to search for wrongly tagged comments. Chances are they simply won't (would you?), and your comment will never see the public light of day. The really evil part, though, is that YOU will see it published. At least on the computer you have used to post it. If you log off or use another device that is not logged into your Google/KZbin account, you will find out that your precious contribution to humanity has never reached its intended destination. A telltale sign of this evil behavior is the mismatch between the number reported in "View N replies" and the actual number of comments published. (Also note that if your comment can disappear even if it had been published and even received thumbs up - if you edited it, even to correct a typo). Why is that evil? Well, there are two reasons. The first is that you will never get that Nobel prize nomination you deserve - also, human progress will be irremediably stifled and it will no longer be possible to stop the end of the World. Your precious contribution has not enlightened the vast majority of lesser mortals who share the luck of living through your lifetime. This is terrible news for the whole of humanity. The other reason is terrible news for you. Because the fact that you can see a comments that was never published can lead to a confirmation bias, something KZbin seems to be pursuing actively in the last years. If you are using the comment section to have a constructive discussion with other viewers, you might end up thinking that, since nobody called you a dimwitted amoeba-brained idiot, you are right in what you said even if you actually are a dimwitted amoeba-brained idiot. You'll end up investing all your money into a rocket company that will finally prove the Earth is flat, as you brilliantly demonstrated in your supposedly published comment that received zero confutations. In the end, it seems that KZbin is doing all it can to make life harder for small content creators (forcing them to waste their time to remedy the shortcomings - or should I say features - of their not-so-transparent algorithms) and to limit the scope of the comments section to just showcasing sheeple that use monosyllables to express inconditional appreciation for the videos, so that advertisers are lured into pouring money into the platform. Maybe this is linked to the goals inferred here (in a post related to the obstacles laid on the road to monetization): www.reddit.com/r/youtube/comments/9huube/youtubes_endless_gaslighting/ "KZbin wants to shift to more paid content and transition to be mostly a platform for corporate-produced content." And everybody knows that nothing pleases corporations more than sheeple. Stable one, signing off.

[@Wolfgang3418]

Thanks for opening my eyes! I was wondering in some cases why my comments were deleted. I didn't use the word bastard. Well, this one will be caught by the filters too ...

[@amitanaudiophile]

Thanks lot to select this topic. What are the best measures by oscilloscope of real hi fi reproduction capabilities of stereo amp?

[@amitanaudiophile]

@Douglas Blake thanks a lot sir for the valuable reply and time you shared. Wish you all the best.

[@davekazoroski6548]

Music and voice are the easiest signals to reproduce without audible distortion. A sine wave, in it's purest form contains only the fundamental frequency. With a sine wave anything the amplifier adds is clearly audible. A square wave shows how well an amplifier's output can follow it's input. Sine and square waves are the only true test of an amplifier's performance. But, I must admit that some amplifiers that don't test well do sound pretty sweet with music or voice passing through them (until driven into hard clipping).

[@danielsaturnino5715]

We want snickers opinion.

[@collinsmwaura1833]

Love the video, hahaha, I believe this video was from my comment on your previous video. One aspect on music signals that you didn't touch on is their influence on the power supply voltages (say a 100W power amp driving a 4 ohm load). PSRR reduces at higher frequencies for any given amp, also amount of feedback available available reduces with increasing frequency. So i was wondering how this slight variations in power supply voltages (especially at mid to high frequencies) affect the output. Don't you think that damping out these variations by using stiffer supplies would be better even for stereo separation for a shared power supply? By stiffer supplies i mean using capacitor values that exhibit very low impedance in the audio frequency band. (most power supply decoupling caps only cater for impedance at 100KHz + range and assuming the amp has excellent PSRR in the entire audio band). Lets say one test uses only small decoupling caps, vs another with beefy low-esr caps, any differences in performance with music signals? Tell me your thoughts on the subject, I would really appreciate.

[@JohnAudioTech]

Yes, your comment is what triggered my desire to make the video. I've heard this so much in the past, I thought it would be a good subject. Having high loop gain at high frequencies will help keep power supply noise out of the amp as well as distortion low. I would agree that stiffening the supply for high frequencies would be advantageous. For example, if one channel on the same PSU is playing a high frequency and some of the signal ends up on the rails due to high supply impedance at high frequencies, it can affect the other channel. I question how audible this really is with most music. The best thing to do is give each channel its own supply. The bottom line is how much money and effort do you wish to put in to get diminishing returns.

[@collinsmwaura1833]

@@JohnAudioTech ooohh yeesss, now we are on the same page... By the way, greetings from Nairobi Kenya.. Hahaha

[@JohnAudioTech]

Cool! Nice to have viewers from Africa.

[@auburnrelaxation9691]

I think SMPS are a great idea for amplifiers. I had a Rotel with class d icepower modules that used a switching ps. It was very light and was silent. I think consumers expect a light amplifier to be weak at low frequencies, lol. Like those 5,000 watt car audio amplifiers that knock shit off your shelves are starved for current.

[@johnyang799]

There are inter modulation distortions. So two tone or multitone can be useful. But signals are still sine waves nonetheless.

[@johnyang799]

@Douglas Blake Oh come on. Are you ..... I kinda know you from different videos. Seriously, there are imd that's not as simple as driven by a voltage.

[@KissAnalog]

Douglas Blake Hi Douglas, of course you are correct, but I think John Yang was pointing out - it is that next point on the line that is important. If the direction changes too suddenly and the amp missed the trail, then there are IMD issues. So yes, an amplifier can only be in one place in space - but is it the right space? ;)

[@argcargv]

@Douglas Blake except that the amp has many nodes so there are many voltages at any moment of time.

[@argcargv]

@Douglas Blake I didn't say it had more than one path, I said it had more than one voltage. These voltages may be coupled but they also have delays due to capacitances and inductances (parasitic or component-wise). As a result there is some time history to the signals in the amp. If not, amplifiers would not need compensation.

[@argcargv]

@Douglas Blake Ok, then tell me something: Do the power supply rails sag under load? This sag, does it happen instantaneously with the signal path or is there a phase lag? Are the power supply rails a node in the circuit that have a voltage independent of the signal path? Do you think there is no coupling between the power supply rails and the signal path? There are many signals in an amplifier and while they may all be coupled to the signal path they are not and it is physically impossible for them to be coupled without any phase delay. There is not only one voltage at any moment of time in the amplifier, that is silly. Every node of the circuit (including the power supply rails) have an independent voltage and they have a different (although dependent) response to the input voltage.

[@Helectronics]

Informative video, thanks!

[@stanyoung4974]

yes, plz make your amp available for purchase.

[@Krmpfpks]

Everything is quantifiable, I agree, but there is a ton of effects that you do not mention. You are not debunking if you leave too many holes in your proof. Things you are missing: - the ability of an amp to hold a voltage at a certain level, that's something you sometimes see in the scope with square waves, but you won't see it with sines. output capacitance can create these issues. - the linearity of the amplification, if your amp turns 0.1V to 1V (10x gain) and 1V to 8V (8x gain) you will hear that as compression, but you don't necessarily see that in the scope with squares and sines. - the dependency on the load, if your amp behaves very different when presented with different loads, you will hear that. Speakers are terrible loads with impedance curves like roller coasters - the ability to reproduce a quiet sound in one frequency at the same time of a loud sound of another frequency.

[@JohnAudioTech]

Everything you mentioned here can be tested without music. The proper test setup will quantify the problem with the amplifier. Amplifiers should be tested with complex loads (no argument there). I'm not clear on what you mean by holding a voltage at a certain level. Do you mean the sloping tops of square waves?

[@Krmpfpks]

​@@JohnAudioTech In conclusion I agree with you, no argument. My point is that looking at sine-sweeps and frequency response graphs does not measure everything that you can hear. You should also measure square waves at different levels/frequencies, impulse response and phase stability. All that at different loads (as speakers are terrible loads). Maybe also check some white noise to be on the safe side. To your question: I have seen amps that convert a square to a weird looking sawtooth wave. I think a voltage drop of the power supply under load might be a cause for this (caps too small?). Also sometimes the power supply is slowly changing its output voltage a small amount under load (e.g. it might slowly drift +- 10% over several seconds under load). You can hear that, especially if it's different for left and right channel, but it would be hard to measure with clean sine or square waves. Also I forgot to mention a common problem of poorly designed class-d amps: they change the phase depending on frequency. They measure ok with sine sweeps but you can hear sound stage breaking down as phase is an important factor for the brain to pinpoint a sounds origin.

[@martinst]

What you are saying at 9:30 is not correct. Music often contains short parts with a full scale high frequency content. For example when you listen to a crash cymbal with your speakers at 110dB with maximum volume setting, you will get the same voltage on your speakers as for a bass drum kick at 110dB. The music part with the big HF part is short for normal music so the drivers survive also because of the heat capacity of the voice coil. For most speakers because of the higher sensitivity of the HF-drivers not so much power is needed as on the LF part. The HF-impedance of the loudspeaker is often raised due to an attuation network and not so much current is drawn from the amp at high frequencies. But the slewrate must be so high that at maximum frequency the FULL voltage swing can be reached without distortion. Often good active speakers with HF drivers with sensitivity in the range of the LF drivers have an HF amplifier with the same voltage swing as the LF part. HF-RMS will be lower of course, and a limiter circuit protects HF driver and amplifier(!).

[@andymouse]

Love this explanation...cheers.

[@patrick_test123]

I mean just differenciating the step response like with any other systsm would be to easy, or something?

[@Peltio]

@JohnAudioTech Hi John, I have a curiosity about disappearing comments. This is the second time it happens in this channel so I would like to know if you as the channel owner have an opinion on this. I posted two replies to Mark Fischer comments below, starting with "It has been nearly 200 years since the French mathematician Joseph Fourier...", but the second reply does not show up on systems different from the one I have posted it. Here I see "View 7 replies" under Mark's comment but when I open it I count 8 replies, two of which are mine (my second reply is located between Mark Fisher's "Yes but I do." and Douglas Blake's "Ain't that the truth" replies). But on other systems, namely my smarphone where I have another gmail account, it only shows 7 replies. I wonder if you, as the channel owner can see my second reply in that thread and also if you were aware of the fact that KZbin can hide replies from your followers. (The other occurrence in this channel was on --Douglas Self-- Bob Cordell book's review - there I posted a reply to my own comment saying "No wonder Snickers is mounting guard to the book" and that too is not visible to other systems - back then I thought it was because I replied to myself but... it seems there is something strange going on). For the record, this is the reply missing in Mark Fischer's comment: (I will add it with an edit, after someone can confirm this post is visible) EDIT: no need to add it here, it's where it was supposed to be now. Also edited right name for the book's author: it's Cordell, not Self.

[@JohnAudioTech]

KZbin has been overly aggressive in putting comments in the spam folder. I found 18 comments that had no hint of spam. Your comment was in there as well. I have to approve them to make them visible again. This has gotten bad over the last month. It is just another malfunction with this site. I will (sometimes) delete comments from obvious trolls or people who are are disrespectful. I haven't done this in a while.

[@Peltio]

Thanks for clarifying this. I wonder what made the algorithm think my comment was spam. Probably because it contained some sentences that looked like a repetition of what was said earlier? I guess we mortals will never know.

[@Peltio]

Ok, it did it again. Twice. There's no point in posting comments on youtube.

[@kamikame9952]

amp. done. when will someone talk about dac?

[@gino3286]

hi thank you very much for trying to fight the voodoo with science To the people who sustain that music is a more complex signal tha a SW i would say if an amp is already bad with the simple SW just imagine how bad will be with a more complex signal like music There is a very trivial concept in fidelity the wire with gain If i send in a sw i would expect to get at the output another sw with an amplitude dependig on the gain If this does not happen there must be a problem with the design or parts or both

[@JohnJackson66]

A 1 watt amp could be very nice for headphones.

[@argcargv]

I am pretty much in agreement with your analysis but there are a few pedantic points I might make: 1) The compensation does provide the amplifier with some memory of past signals so it isn't quite true that there is no "algorithm". 2) As long as the amp is behaving in a linearly we can think of the input wave as a decomposition of frequencies (e.g. sum of pure sine waves), but any non-linearity will break this. Of course we design the amp to be linear as much as possible and to the extent it is, these arguments hold. 3) To the extent that the amp is non-linear, a square wave input will likely be one of the best tests to evaluate the quality of this non-linear response. 4) Short of anything else, there really isn't any quantitative way to use "music" to measure an amplifier and so even if we could, the approach would be meaningless in amplifier design.

[@Peltio]

Exactly. Also, all dynamic circuits have 'memory' in the sense that their response depends on the integral of some electric quantity up to that time. This of course does not mean that the amplifier is a sentient being but only that inertia and damping (both electrical and mechanical) have a role in determining its response to a given input. So, it's not only the instantaneous values that matter, but also its 'history' (integral) and 'future' (derivative), the more so the higher the order of the dynamical circuit.

[@argcargv]

@@Peltio Yep, and the challenge is to handle the non-linear elements in the circuits (usually the semiconductors) to try to minimize distortion. This is made more difficult because coupling between nonlinear components in the circuit is usually parasitic and outside of our direct control.

[@EJP286CRSKW]

If the system was linear there would be no decomposition of a sine wave input. Just one term, the same sine wave. The Fourier series is an analysis of the non-linearities. You are however correct about the memory. Any electronic system with capacitance or inductance, and that's all of them, stores energy and releases it later.

[@argcargv]

@@EJP286CRSKW if a system is linear then we can decompose a signal into any sum of signals and the superposition principle says the resulting signal is simply a sum of the decomposed signals. For a nonlinear system we loose superposition and we can no longer think of the sine waves that come from the Fourier transform as independent. This is a why intermodulation distortion comes from an amplifiers nonlinearity.

[@Peltio]

I answered to this very objection into another thread but it won't show up. I guess it's in John's spam folder again. I am curious to see if reposting it here will make it go through. [EDIT from the future: it didn't work, it still had to be retrieved from the spam folder - thanks John]. Anyway here it is, with some more grammar corrections: @EJP The input is a complex waveform that can be decomposed into its Fourier sine components. Each component goes through the system, being transformed by the system (the amplifier). If the system is *linear*, not only each component gets transformed into another single sine of the same frequency with different amplitude and phase, BUT you can also reconstruct the output by superposing the individual responses to each component. F[ a + b ] = F[a] + F[b] If the system is *not linear*, you can no longer do that. F[ a + b ] != F[a] + F[b] You can still decompose the output of the composite signal via Fourier (lhs of the above equality), but it won't be the same as the sum of the outputs of the individual components (rhs of the above equality). In fact, the nonlinearity would introduce spurious frequencies. (Note: a and b should be thought as phasors, thereby carrying both amplitude and phase information. Also note: the symbol F above stands for the transfer function of the amplifier, not the F of Fourier Transform, which by the way is defined on linear spaces such as L^2 - this should tell you something on the importance of linearity when dealing with Fourier) The way I see it, there are two kind of problems with the fidelity of the output of an amplifier: 1) If the system (the amplifier) is *linear*, the shape of the output waveform can differ from the shape of the composed input because each component gets amplified with a different magnitude and a different phase. Even if you managed to flatten the magnitude of your amplification, you would still have to cope with the different phase shift imparted to different frequencies. In physics terms, you will have dispersion. For example, imagine composing sin(wt) and sin(2wt), and in output you get 10sin(wt) + 10cos(2wt) or 10sin(wt)-10sin(2wt) [these are extreme examples in order to make evident where the problem is, in reality you might get some 30-40 degrees of phase shift between the extremes of your bandwidth, probably less but I seriously doubt that you can get rid completely of dispersion, even with a custom all pass filter on the output] 2) if the system (the amplifier) is *NOT* *linear*, the shape of the output waveform can differ from the shape of the input waveform even for a single pure component, because nonlinearities introduce new frequencies. Even worse, the shape of a composed output differs from the composition of the shapes of the individual input components because, for example, the sum of two components will allow the level to reach a part of the transfer curve that is more different from a linear transfer characteristic. Think for example of amplifying 1*sin(wt) and 15 + sin(wt); the latter will be closer to clipping. So in the first instance you will get more or less a bigger almost pure sinusoid, but in the second instance you won't get a bigger pure sinusoid with an offset, you would get a clipped signal. Finally, allow me to stress once again that I am not implying are right. I am just saying that things are not as simple as one might think at first: the amplifier is a dynamic-al- circuit and as such its output does depend on the (recent) past and future (basic physics tells us). The amplifier is in general nonlinear and its output is just not simply the composition of its amplified individual components (basic math tells us). The key aspect in both these scenarios is: how much does it matter? How much recent is this past (due to integrals) and future (due to derivatives)? Very recent, I'd say, especially considering how small are parasitic capacitances. How much different from a straight line is my transcharacteristic? Not much, I'd say, especially if you do not pursue insane levels of amplification. In the end, how much do dispersion and harmonic generation matter? Probably very little, since one can design amplifiers with an almost linear response, very flat magnitude in the frequency response and manageable phase shift across the whole bandwidth of the audio signal. But the output waveform of a composite signal won't be an exact magnified replica of the input waveform, and how much perceivable - if at all - this tiny difference happens to be for the human ear is a matter of physiology, not electronics. (As for me, not only I cannot tell the difference between a tuned and an untuned piano, I cannot even tell the difference between white and black keys!) EDIT: typos and formatting EDIT: some minor fixing to formatting and grammar. I also tried to use bold face text but I failed miserably.

[@prashanthb6521]

Thanks a lot for this explanation.

[@DAVIDGREGORYKERR]

Then base your audio power amp on a Video amp that also happens to have Class A characteristics.

[@Tbonyandsteak]

Do not know this would be a debunk, but who had ever heard high end audiophiles and made AB test? The change of current and voltage in filters and feed backs makes the difference. Besides power supplies can that follow the music output on any speakers? Cables abilities of the dielectric and magnetic does have a lot influence, do not believe that. Just make a AB test with a long cable. Best cables are the short cables. There is a huge effect on changing power, that is how filters work. Simple electric science, those things affect it one way or another and is not neutral. That is why audiophiles have terms like Transparency and detail, dynamic and expressions of the music, from cold to warm sounding. Cold and non transparent when to many filters is applied to warm sounding tube amps. In bad amps it is like several curtains are in front of the speakers that mask the music. I think that is very established proves.

[@johnyang799]

There are very poor measured high end equipments. So they can be too bad so that it's audible.

[@jaredgray7872]

Hi John, thanks for tipping me onto Bob Cordell's book, I picked up a copy as well. I ran across a 2016 burning amp video where he was talking about amplifiers misbehaving with real music kzbin.info/www/bejne/jGiQY2qcecykmdE and I'm curious your thoughts on that. Also, thanks so much for this series. Outside of books there is very little out there on designing and building audio amplifiers, I have really enjoyed your take on this subject.

[@markfischer3626]

It has been nearly 200 years since the French mathematician Joseph Fourier showed that any arbitrary waveform could be analyzed as the sum of an infinite number of sine waves of different amplitudes an infinitesimal increment in frequency apart. The powerful tool of the Fourier transform and inverse transform was created. It allowed us to shuttle back and forth between the frequency and time domain. Analyzing and solving problems in the frequency domain is often much easier than in the time domain. Every scientist, engineer, and mathematician believes it and relies upon it. The only ones who don't believe it are audiophiles. A look at the fully expanded Fletcher - Munson curves shows us that at 20 khz the curve for threshold of hearing, the softest sound you can hear, and the threshold of pain where vibrations are experienced as physical pain intersect. Therefore no music sound recording or reproduction system needs to exceed 20 khz in bandwidth. Signals above 20 khz add nothing of value and can create problems. If frequency response were measured at full power output instead of one watt the concept of transient intermodulation distortion or as its also called slew rate distortion would be refundant. Audio amplifiers run into problems with highly reactive loads and very low impedance loads. Highly reactive loads are usually caused by complex crossover networks to make speakers sound flat with no active equalization which is far superior to passive equalization provided by the crossover network.

[@prashanthb6521]

"Audio amplifiers run into problems with highly reactive loads and very low impedance loads" I was planning to attach 10 peizo tweeters in parallel. What kind of problems audio amplifiers will run into ? Please explain this noob atleast briefly.

[@Peltio]

Look, I'm not even thinking of defending audiophools, but there's a problem in your reasoning - I am pointing it out just for the sake of nitpicking :-) . Fourier works for _linear_ systems. As much as designers strive to make their amplis linear, they are not. So, there is - theoretically - room for arguing that the response at the sum of two frequencies is not the same as the sum of the response at those two frequencies alone. Is this difference relevant? I don't think so. But if I were selling equipment in a market full of gullible people, I would probably convince myself that yes, someone might - theoretically - feel the difference. The ones with more money.

[@markfischer3626]

@@Peltio Fourier analysis is strictly a mathematical tool for analyzing. waveforms. It doesn't care how the waveforms are created, analog, digital linear, non linear, scribbled on a piece of paper. In the example given the difference between the input and output waveforms can be compared to understand its distortion frequency distribution. In non linear systems when the conditions change such as overloading the input of an amplifier the Fourier transform of the distortion will change too. Describing the performance of an electronic system with a few numbers is entirely misleading. Its why two amplifiers may measure identically on standard bench tests but perform entirely differently in use. The tests aren't wrong, the problem is that they are far from complete. People want a few numbers to make comparisons. Life is not so simple

[@markfischer3626]

@@prashanthb6521 probably no problem at all. I've yet you create problems for an amplifier paralleling lots of tweeters.

[@markfischer3626]

@@ralfstocker7742 Yes but I do. I'm an electrical engineer. It takes a year of calculus before you are ready to tackle Fourier Transform theory. BTW frequency tesponse and square wave response are interchangeable. Its an exercise for students to be given either one and derive the other.

[@Mark-ej3oi]

Try to use a high-resolution oscilloscope, 12 bits or more, and you will discover a full new world that that 8 bits oscilloscope cannot show

[@mattportnoyTLV]

Personally I like to look at ITU-R (CCIF) or SMPTE intermodulation distortion as a test for how a circuit will handle complex signals. I’ve seen circuits that look decent with sine or square or THD tests, yet sound like absolute doo-doo. Put ‘em under the CCIF test and you’ll see why because they fall apart like wet paper.

[@johnyang799]

CCIF is two high frequency sine waves Smpte is one low one high. They are still sine waves. And normally CCIF is related to 20khz(high frequency) single tone thd.

[@steveswan5714]

Interesting vid cheers john

[@JohnJackson66]

Logic says any decent amplifier should sound the same as any other. But they don't.

[@ferrumignis]

Logic doesn't say that. Any non-ideal amplifier will colour the sound to some degree, and ideal amplifiers do not exist. The biggest change in sound you will get in a system is from changing or even just moving the speakers, the effects of a well designed amp pale into insignificance next to that.

[@JohnJackson66]

Optimising speaker location is important for sure, but is a different set of problems. I have never heard of anyone moving their speakers after changing amplification, to get the sound right again.

[@thedays365]

Problem is a practical amplifier have nonlinear phase delay and not constant amplitude gain with respect to a different frequency.

[@EJP286CRSKW]

Jeevan Shrestha Practically any amplifier designed in the last 75 years does indeed have 'constant gain with respect to a different frequency'. Leaving aside various freak topologies, they are all ruler-flat within their specified passband, and this is assured by the mathematics of the situation. Harold Black, 1927. 'Non-linear phase delay' is meaningless unless you specify the X axis.

[@thedays365]

@@EJP286CRSKW with respect to different frequency (common axis for both argument).

[@EJP286CRSKW]

Jeevan Shrestha I am unable to ascribe any further meaning to your remarks beyond what I have already addressed. If there is any, please express yourself more clearly.

[@dilbyjones]

Crossover kits!

[@rogersmith2129]

An observation on fighter plane speed (F111B) , radar terrain following and delay of information. Think hifi 1969 (dynamo, MAC tube) and analog signal coloring of music by very early Tube amps and transistors. The circuit response rate allows speakers to move slower on input creating a signal delay which gives music that warm sound. In 1970’s the F111B fighter is 50 feet above the earth at close to 800 miles per hour approaching a peak and the analog circuit is 6 sec’s behind the nose of the plane. Talk about fun. Does the autopilot allow you to hit the peak or rise over it. If you improve your circuit so the delay is only .25 sec,s you rise above the peak and are now having a less choppy ride and you remain unnoticed by enemy radar. Early analog is thus warm and fuzzy feeling and high speed circuits are not.

[@manFromPeterborough]

That looks like digital audio with those steps in the sinewave - one reason I hate digital audio

[@joshhyyym]

Most digital audio is recorded at 16bit ie 65536 steps, that's an 8bit oscilloscope which only shows 256 levels. On top of that, you are only looking at the aliased pixels. Digital audio really isn't an issue.

[@manFromPeterborough]

@@joshhyyym Then why does CD sound crap compared to vinyl? the 44K sampling, pre ring post ring and time smear

[@joshhyyym]

@@manFromPeterborough can you personally hear above 22khz? That is very unusual for someone over the age of 15. I assume most of the difference is in mastering. Lots of CDs are mastered very loud which causes clipping. Do you buy recently recorded music on vinyl?

[@manFromPeterborough]

@@joshhyyym I buy all kinds of vinyl, 78's to recent

[@joshhyyym]

@@manFromPeterborough Modern music pressed (or cut) for vinyl is almost always from a digital master. The recording and mixing is all digital, then CDs, and records are then produced. You really can't get away from 'digital audio'

[@davidgriffin79]

You have an attention seeking cat.