Distortion microscope?

[wimms]

While trying to get a better idea what kind of distortions occur in a simulated amp I found an interesting way to present the signals.
Basically, you take the output of the amp, reduce its amplitude by gain to match that of input signal, subtract. Now feed the the result to the Y-axis of "scope" and the input signal to the X-axis of scope.

Ideal linear amp with zero latency must show a straight line. Real amp has propagation delay, that is ideally constant wrt input signal, and this must with sinusoidal input manifest as a perfect ellipse on the scope (wrapped sinewave). By stepping through few input amplitudes, and superimposing outputs of such graphs after normalizing, we expose the deviations from the ideal *shape* of the signal. It is visually very easy to see, and imo even gives very useful hints as to what is going on in the amp.

See the graphs below. In this case, graph is made for outputs of 50uW (THD 0.000006%), 55W (THD 0.0014%) and 178W (THD 0.0012%). THD of first 9 harmonics. Notice that THD calculation shows slightly lower THD for 178W output wrt to 55W output.

Look at the graphs. Blue is reference, 50uW output with lowest THD. Green is 55W output and red is 178W output. All graphs are zoomed suitably to approximate circle shape. Absolute values of graphs are meaningless, its only shape that matters here. It is immediately evident that 55W and 178W output graphs deviate very seriously from ideal circle, despite that total THD was 0.001% for both.

How to read the graphs. X-axis shows input voltage instead of time axis. Timing is hidden. As input sinewave develops in time, output signals circulate on this graph, rotating counterclockwise. There are 9 full circles of sinewaves, and they are there behind each other.

When input signal goes from zero to positive slope, watch output response in south-east sector. When input signal wraps from its positive peak and goes down towards zero, watch north-east sector, etc. Because output lags input, difference is initially negative (we start saving after 1st period), later when input goes down, difference becomes positive. Time is shown as signal on graph, just to help visualize how input signal is changing wrt time. Its not any kind of timing reference there.

Nothing quantitative can be drawn from such graphs, but only relative *shapes* of the signals can be compared. We know for sure that for sinusoidal input, ideal shape would be exactly circle or ellipse. Any deviation from that is distortion.

In this particular NFB amp simulation, it can be easily seen that positive going half of the 55W waveform oscillates around reference "ideal" (NFB in action?), and that the amp is asymmetric - negative slope is pretty nasty.
178W output shows more severe overcompensation, probably due to NFB lag and arising late compensation. In both high power cases negative slope on first glance seems to lead input, but I suspect it is late "catching up" due to NFB action (exact timing is lost on this graph).

Also note, that THD calculation gave 178W output lower THD than for 55W output. Its not because the distortion was lower, but only because nature of it was slightly different (less higher order harmonics due to evident slew rate limiting).

Because we are graphing *difference* between input and output, our sensitivity is pretty large, canceling out absolute output levels.

In conclusion, it seems to me that this kind of graph is exposing some details very hard to notice by any other means. I'd like to think that this helps to understand the nature of distortion, and perhaps even shed some light on how non-NFB amps differ from NFB amps.

Comments? Anyone used such graphing before and how its actually called?

[Graham Maynard]

Hi Wimms.

Your graphical representation clearly shows that the amplifier under test is not internally balanced, but are these measurements taken using a resistor load that ideally matches zero current crossover activity with the negligible power demand of zero voltage crossover ?

If yes you are not invoking the loudspeaker back-emf induced distortions that alter the sonic character of reproduction, and which will generate different diagonally opposite phase shifted wiggles.

Also can I suggest you study at 10kHz, because any half decent amplifier is okay at 1kHz.

Would it not be possible to zero null your input reference to match output before subtraction so that you end up with more of a straight line with +/- deviations ?

Unfortunately this would apply only for that given amplitude and frequency, for the phase shift changes with frequency, and the propagation delay with amplitude, the latter being impossible to observe by monitoring resistor/sine thd figures in output isolation with continuous sine wave drive !!!!!

This is why I have simulated use of my suggested X-Y monitor circuit, where when you use two amplifiers, both have the same nominal propagation delay to whatever input is applied..
Then any ovality will represent time and voltage shifted error arising at the loudspeaker terminals wrt that arising across a perfect resistor; ie; the display will show unwanted zero phase amplitude based as well as back-emf induced non-linearities.
Ovality = amplifier impedance. Shows back-emf induced time fuzzing of loudspeaker voltage !
Straight line = perfectly resistive.
Voltage errors = amplitude non-linearity, crossover distortion, slew rate limit induced error, voltage/current clipping etc.
This display could be observed in real time with sine or music input, just watch that scope is isolated.

I will also attach approximate virtual equivalent of the well known 'Ariel' loudspeaker that is nicely awkward to drive at 10kHz but sounds excellent with a good amplifier; usually tube types. Sine display gives time expansion at centre of horizontal axis. The first four half cycle sinewave currents with this loudspeaker are quite different at 10kHz !!!!!

And finish off with four two 10kHz cycle X-Y / Ariel simulations with +/- 10V peak at the output terminal. (Which will always be more idealistic than real life)
A = D Self 'Blameless' like circuit showing effect of resistor damped series output inductance. (Loss of image accuracy)
B = same amplifier without choke. (C.dom causing amplifier impedance + degrading crossover suppression )
C = ditto but without 'C.dom' as well. (Phase shifted/back emf induced class-AB crossover still not gone with approx 80dB nfb)
D = my 25W class-A. (Not perfect, but excellent to listen to)


Cheers ............. Graham.

[Graham Maynard]

Useful virtual loudspeaker load.

[Graham Maynard]

Virtual scope traces.

[wimms]

hi Graham,
thanks for your interesting reply.

Originally posted by Graham Maynard
Your graphical representation clearly shows that the amplifier under test is not internally balanced, but are these measurements taken using a resistor load that ideally matches zero current crossover activity with the negligible power demand of zero voltage crossover?

If yes you are not invoking the loudspeaker back-emf induced distortions that alter the sonic character of reproduction, and which will generate different diagonally opposite phase shifted wiggles.

Also can I suggest you study at 10kHz, because any half decent amplifier is okay at 1kHz.

Yes, that was resistive load. My surprise was actually that the method so well exposes intrinsical nonlinearity of the amp into resistive load and at 1khz where it should be easy job for the amp. Remember, highest harmonics was 100db(!) down the 177W test signal. I didn't really expect to be able to see the nature of the distortion so clearly. THD plot is pretty useless in comparison. And even normal timebased subtracted error voltage is less striking.

Would it not be possible to zero null your input reference to match output before subtraction so that you end up with more of a straight line with +/- deviations ?

You mean to imitate ideal amp with matched prop delay of the DUT? It is possible, though difficult. But the result is much harder to interpret. See attach. Note that reference blue is basically straight line, its just so much zoomed into (1nV/div) that it appears as oval. There, nonlinearity errors of higher power signals exceed in magnitude of normal prop delay induced voltage, and it becomes hard to correlate with the signal. Imo slight suitable phase shift before subtraction actually helps to understand the result. Its about balance, too much, and you'll see nice ovals only.

Unfortunately this would apply only for that given amplitude and frequency, for the phase shift changes with frequency, and the propagation delay with amplitude, the latter being impossible to observe by monitoring resistor/sine thd figures in output isolation with continuous sine wave drive !!!!!

Agree on the first part, but I'm not sure I follow you on the second part.
In my view it is rather impossible to perform a null test with reactive load. Perfectly normal phase shifts stick out too much, and it is rather difficult to account for what is normal and what is not.
The same delay dependence on amplitude with reactive load is in my view pretty normal thing to happen.

This is why I have simulated use of my suggested X-Y monitor circuit, where when you use two amplifiers, both have the same nominal propagation delay to whatever input is applied..

No doubt this is very interesting approach, and perhaps even easier to conduct in real life. But I think this is cancelling out several amp nonlinearities (if they are perfect match), and exposes only effects that becomes visible thanks to reactance of speaker.
I understand that you are much more interested in amp-speaker interaction, thats what your method seems to try to expose. but wouldn't it be more correct to compare ideal amp into speakerload with DUT into speakerload? At least in simulations. Ideal amp would have to have roughly similar phase response as DUT though.

Then any ovality will represent time and voltage shifted error arising at the loudspeaker terminals wrt that arising across a perfect resistor; ie; the display will show unwanted zero phase amplitude based as well as back-emf induced non-linearities.
Ovality = amplifier impedance. Shows back-emf induced time fuzzing of loudspeaker voltage !
Straight line = perfectly resistive.
Voltage errors = amplitude non-linearity, crossover distortion, slew rate limit induced error, voltage/current clipping etc.

Interesting. I may be wrong, but I interpret differently. Ovality that appears when you compare resistive load with reactive load is in my view reactance of the speaker, time shift between current and voltage. I don't see this as impedance of amp, although nonzero impedance of amp allows us to see that. Back-emf is not necessarily real there. Time fuzzying shouldn't happen for sinusoidal signals. This hints that you used discontinuous test signal, like positive half of sine starting right from zero. This is like impulse that causes some oscillation, and that is what manifests as time fuzzying. It occurs in sim too. To make "clean" test, you'd want to use AM modulated sinewave that rises smoothly (and cosinusoidally) from zero. Imo that kind of time fuzzying disappears then.

That straight line in your test. This is what my sim above zooms into. Its not so straight at all.

'Ariel' loudspeaker..
Sine display gives time expansion at centre of horizontal axis. The first four half cycle sinewave currents with this loudspeaker are quite different at 10kHz !!!!!

If you simulate with sinewaves starting from 0 volts, then this is wrong. Not only first 4 cycles are different, but theoretically all of them. Sim assumes all currents and voltages to be zero at time0. It is unrealistic increase of amplitude. You get impulse response of the bw-limited amp-speaker system superimposed with the test signal.

I've tried speakerloads with bandwidth limited squarewave (composed from 20 harmonic sinewave generators) with simulated amps before (though not with this method), and it very well shows how stored back-emf energy forces output stage to crossover currents upto several times after voltage crosses zero without voltage errors actually developing. Very interesting to observe - you realize that during these moments NFB is completely detached and amp output impedance is doing crazy dancing on its own.

In my case the speakerload is not wanted. It actually makes it harder to observe amp nonlinearities. The phase shift is unavoidable, especially if we use most convenient pure sinewave test signal. To use speakerload, I'd have to use the raised cosine windowed test signal, and it produces spirals instead of ovals. Becomes pretty cluttered there. I'll attach an example graph. It isn't really much different from what I learned with resistive load.

A = D Self 'Blameless' like circuit showing effect of resistor damped series output inductance. (Loss of image accuracy)
B = same amplifier without choke. (C.dom causing amplifier impedance + degrading crossover suppression )
C = ditto but without 'C.dom' as well. (Phase shifted/back emf induced class-AB crossover still not gone with approx 80dB nfb)
D = my 25W class-A. (Not perfect, but excellent to listen to)

Very interesting graphs. It is evident though that you indeed use sinewave starting with rectangular windowing. I'd distrust the fuzzying part and also compare only general shapes of these graphs. Of course, the crossover distortion spikes are pretty striking. Though, when you look at the scope divisions, then despite awful shape in graph C, it must be admitted that this amp is showing *least* of error voltage. This only underlines that phase shift is causing "static" error that hides the details and should be ideally canceled to a reasonable degree.

[wimms]

The raised cosine test signal into speakerload graph.

[Graham Maynard]

Hi Wimms.

Nice to be able to chat with you about this, even though in public.

You wrote agreed first - not second. Amplifiers quite literally slow down as output stage current demands increase, the nfb loop then causes their internal impedance, and the delay caused by that impedance, as seen by the load, to become momentarily increased.

The X-Y method shows the error due to resistor load wrt loudspeaker, plus error due to loudspeaker load wrt resistor. As the amplifier's internal impedance reacts differently to each load I am not so sure that there is any 'cancellation' of non-linearities. My thoughts are that the amplifier will actually look worse, but then there is at least an opportunity to deal with all errors resulting from passive and dynamic loading.

Ovality is due to amplifier impedance allowing the reactive load to drive its output terminal wrt amplified input voltage; if you simulate with 'ideal' amplifiers the result is a straight line.

You appear to concerned that I am using a suddenly starting signal.
Don't forget that audio waves start suddenly to the bandwidth limit of the system itself.
It is pointless to filter say a 1kHz signal before applying it to an amplifier so that it cannot suddenly start with a change equivalent to real-world sources !
Strike a triangle and it does not slowly build up its first cycle, there is a singularly rich harmonic leading edge, some of which is both inaudible and not picked up by microphones !
Currently CDs are circa 20kHz, DVD-A/SACD 40kHz+, so these should set our filtering bases.

Besides if you run the X-Y examinations for many cycles they do not change much beyond say the third cycle, so the fuzzying (time based amplifier-loudspeaker interface energy storage and release exchange) is not merely a leading edge problem. Also the back emfs from different composite loudspeaker elements all arise at different time periods after initial music energisation, which is why the early half cycles are so asymmetrical.

So many folks seem to think that I do not understand this suddenly starting aspect, but equally I think that those who express such comments are the very ones who wrongly test amplifiers with 'non-musical' waveforms.
By rigidly applying their theoretical pre-filtering they are denying themselves the opportunity to see and make their designs capable of coping with what really can happen as a result of sibilant and transient loudspeaker energisation.

Re your harmonic square wave test and cosine test illustrations - very interesting. So many designers once believed that nfb 'protected' their amplifiers, and that increased levels made for endless improvement - not so.

You say that the speaker load is not wanted because it makes it harder to observe amplifier linearities. But maybe it is actually the amplifier's nfb reaction to the phase shifted loudspeaker generated back emf that is the significant problem, and, not the Nth degree of nfb loop generated amplitude linearity. Tube amps can be as 'bad' as 1% in the thd stakes, yet still drive real world loudspeakers better than 0.001% solid staters - they do not react as badly.

Yes figure 'C' has the lowest amplitude error. The phase shifted loudspeaker current is causing the complementary output stage to reverse commutate through a portion of its fixed common bias before the nfb loop regains control, and thus the waveform appearing at the tweeter will have an entire new and non coherent waveform across its terminals. This cannot happen with class-A, but phase shift can still introduce transient induced offsets where the amplifier has insufficient bandwidth/speed.
'D' has much less damping, but the error shows little in the way of generating a separately identifiable product.


Cheers ............. Graham.

[Mark A. Gulbrandsen]

Guys,
While I have not had time to digest what you've written those traces look to have been made with a virtual "Etch-A-Sketch".....

Mark

[wimms]

hi Graham,

Originally posted by Graham Maynard
You wrote agreed first - not second. Amplifiers quite literally slow down as output stage current demands increase, the nfb loop then causes their internal impedance, and the delay caused by that impedance, as seen by the load, to become momentarily increased.

Shouldn't amp slow down happen equally with resistive load? I don't understand well how you relate variance of delay of amp with reactive loading; you said its impossible to observe with R load. How you measure that delay when current and voltage are shifted wrt time as normal part of reactance? When I tried, looking at zero crossing instants, then variance of prop delay was so unbelievable that I had to stop thinking that voltage on amp outputs is right thing to look at. In fact, I started to suspect that its even not right to use voltage as a feedback signal. I wonder even if perfect voltage source is the ideal amp to drive reactive speakers..
What are your thoughts on this?

The X-Y method shows the error due to resistor load wrt loudspeaker, plus error due to loudspeaker load wrt resistor. As the amplifier's internal impedance reacts differently to each load I am not so sure that there is any 'cancellation' of non-linearities. My thoughts are that the amplifier will actually look worse, but then there is at least an opportunity to deal with all errors resulting from passive and dynamic loading.

Y-axis shows difference between outputs. That imo cancels errors that are common with both loadings, cancellation not necessarily complete. Thats what I meant. Reactance would cause the errors to manifest shifted in time, and exposed, but imo they are then mixed with speaker late reaction to new signal and that makes it difficult to tell what is exactly what, or when. Very drastic things stick out, like the crossover spikes, but fine details stay hidden.

You appear to concerned that I am using a suddenly starting signal.
Don't forget that audio waves start suddenly to the bandwidth limit of the system itself.
It is pointless to filter say a 1kHz signal before applying it to an amplifier so that it cannot suddenly start with a change equivalent to real-world sources !
Strike a triangle and it does not slowly build up its first cycle, there is a singularly rich harmonic leading edge, some of which is both inaudible and not picked up by microphones !

Please don't take this as arguing, but just as clarification of my view.
When I was exposed to fourier analysis, I realised that there exist no instantaneous changes in nature. BW limiting is not limiting only maximum bandwidth, but also maximum rate of change of the spectrum. Thats nature of filtering.
Perfect full amplitude 10khz sine signal appearing from silence is not realistic signal due to the first cycle. It would require huge bw. It never happens in reality either. When you strike a triangle, first there appears cosinusoidal increase of amplitudes of large number of harmonics, including the lowest one. Its like a preringing of digital filters. The signal develops for finite amount of time. Check it: http://www.pcabx.com/technical/reference/triangle.wav

I understand that you try to simulate 'attack' of a musical instrument, but I've found that suddenly starting sine is overloading the system's expected bw usage more than is realistic. It is not a problem normally in sims, as it is wrappable/extendable, but with reactive loads this isn't resolved right due to missing past history. It overloads the reactive load and produces ripples that aren't real. That imo only clutters the graphs and confuses.
I've found that I'm able to better analyze results when signal spectrum is better controlled. I've opted to use toneburst signals instead of more severe pulses or sudden sines. For eg. see this http://www.diyaudio.com/forums/showt...152#post528152 as example of most severe toneburst.

But afterall, it doesn't matter what signal you use if you know what you're doing and looking for.

Besides if you run the X-Y examinations for many cycles they do not change much beyond say the third cycle, so the fuzzying (time based amplifier-loudspeaker interface energy storage and release exchange) is not merely a leading edge problem. Also the back emfs from different composite loudspeaker elements all arise at different time periods after initial music energisation, which is why the early half cycles are so asymmetrical.

Can you be sure only first few cycles are affected? That depends on the load reactance, signal, source impedance. Check the attach. Thats speakerload I use, energized from perfect amp, just static 1mOhm impedance added. What can we say about that perfect amp? Wildly different shapes, fuzzy, and rings for long time. If I'd see that on amp output, I'd not know - to worry or not. But this one is perfectly normal behaviour, there is no first cycle distortion there, no changing output impedance, no NFB.
Have you checked the step response of Ariel load with your method? It does not settle in 100ms. IIR. That fuzzying is purely due to impulse energy from the first cycle imo. I can't extract any amp impact there.

So many folks seem to think that I do not understand this suddenly starting aspect, but equally I think that those who express such comments are the very ones who wrongly test amplifiers with 'non-musical' waveforms.

By rigidly applying their theoretical pre-filtering they are denying themselves the opportunity to see and make their designs capable of coping with what really can happen as a result of sibilant and transient loudspeaker energisation.

Yes, but isn't impulse or step response better method for testing such things? It seems easier to interpret. Or the harmonic synthesized squarewave, it has benefit of being spectrally clean and not overload the system.

You say that the speaker load is not wanted because it makes it harder to observe amplifier linearities. But maybe it is actually the amplifier's nfb reaction to the phase shifted loudspeaker generated back emf that is the significant problem, and, not the Nth degree of nfb loop generated amplitude linearity. Tube amps can be as 'bad' as 1% in the thd stakes, yet still drive real world loudspeakers better than 0.001% solid staters - they do not react as badly.

When I said not wanted, I meant my initial post approach. There, maximal zooming effect occurs when phase shift is minimal and controllable. It shows magnified nonlinearity of amp with closed loop. Of course you may be right and we should focus on amp-load interaction instead of amp linearity, but my first post focused on amp nonlinearity only.

Adding speakerload changes the game alot. Phase shift is huge, partly due to finite output impedance. That makes the X-Y ovals very large, hiding fine details. Size of the oval is depending most of all on the time shift. It could be impedance, delay, NFB induced error. When the oval is large, its resolution is low. The variations around the ideal line (oval) are exposed only when you can get the timeshift small.

For eg. in your virtual scope traces, it is not easy to compare them, because they are in different scales. Fig. A is so far apart from the rest, that it is impossible to say if it is actually better or worse than say C. Series inductor increases output impedance, but *tubes* have huge Z too, that can't be bad for the sound and imaging? I'd try to bring them to common scale, by adjusting reference amp's delay and impedance. If there are similar problems in all of them, they should appear in sorta fair comparison.

I thought you might want to compare DUT with ideal amp into the same load. If ideal amp's phase response is matched to that of DUT, then time shift induced errors are minimized, and Y-axis will show more detail about DUT issues.

Btw, have you tried connecting the load resistor instead of to ground to another signal generator? It is effectively controlled reactive load. You avoid that way resonances and oscillations of passive speakerload.

[AudioWizard]

A spectrum analysis (both magnitude & phase) seems more accurate and simpler to interpret.