This makes no sense at all. You will likely measure nearly the same non-linear current and (acoustic) THD with the amp welded to the speaker terminals.
I recall from a couple of other threads that you like a debate and dig in, so, except to say you have it wrong because the significnat harmonic numbers are determined by the wave period, I'm not going to take this one up here. I think my previous post sets it out quite clearly. You are free to post any actual algebra.
Another noted author, Ian Hickman if I recall correctly, covered this in Electronics World about 20 years ago - I'll find the precise reference for you and post again.
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This paper shows by analysis that neg fedback a) introduces distortion terms not present without it, and b) makes the spectrum look "messier" (their term) with more energy in higher orders. This is exactly what I've been saying and is something that has been known and written about more than 70 years ago. They've gone over old ground, except that they covered devices (eg FETs) not available 70 years ago.
They speculate that the higher orders sound messier, but offer no proof, neither mathematical analysis nor any sort of survey of listeners.
Sorry, I thought you wanted to see the algebraic derivation of DF96's statement, "In almost all practical cases the higher order terms created by re-entrant distortion are similar in size or smaller than the high order stuff already present without feedback.", which is shown here.
It is ugly and unfinished but if you want it send me a PM.
> You will likely measure nearly the same non-linear
> current and (acoustic) THD with the amp welded to the speaker terminals.
Point was that since the speaker draws a nonlinear current, you can measure a higher THD at the speaker terminals if the cable has high resistance, or if the amp has high output impedance. This may have an audible effect or not (it could be swamped by the loudspeaker's distortion). I tried measuring the distortion using a microphone and inserting resistance in series with the speaker, but the microphones I have suck, so I got no usable results. It could be an interesting experiment to do if you have a very good quality mike.
scopeboy:
since doug updates his amp book somewhat "frequently" (at least for an audio design book), send him a note and ask him to address it.
hmmm, maybe he'll see his name here and ask about it anyways ...
btw, those were really nice looking boards of yours in the the discussion on grounding!
mlloyd1
since doug updates his amp book somewhat "frequently" (at least for an audio design book), send him a note and ask him to address it.
hmmm, maybe he'll see his name here and ask about it anyways ...
btw, those were really nice looking boards of yours in the the discussion on grounding!
mlloyd1
I wanted to see his algebra that supports his statement:-
which is plain wrong, as for example the added waveform in cross-over distortion is a rounded trapezoid having a period equal to the input sinewave. Therefore, the most significant harmonic (apart from a bit of fundamental partially cancelling the desired input) is the 3rd.
Also his statement:-
implies he's actually done some relavent algebra.
When ever someone claims math will prove something that's not right, but doesn't actually present the math, I generally ask him to show the math. That has two benefits with people who genuinely believe they are right:-
a) it stops the erroneous claim;
b) they go and do the math, and discover for themselves why they are wrong.
Sometimes, not very often, they put up their math, and the math is wrong. That's ok, I or someone can point out the mistake in it.
The misconception that cross-over distortion necessarily involves high order products is a very common one. It can come as something of a shock to find that's not so. It is human nature to dig in and oppose in such situations. So the best approach is to get folk to work thru the logic themselves.
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It's actually proportional to the derivative of the tanh() function (for bipolars of course) you could do the Taylor series yourself or look it up it has many odd harmonics past the third. Why is it "plain wrong" even your trapeziods have 5ths, 7ths, 9ths, etc.?
Maybe we're talking about two different things. If your saying crossover distortion involves no orders above 3, then you are wrong and the one laboring under a misconception.
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Ans (1) The rising and falling slopes of the added trapezoid rapidly increase the rate at which the harmonics decrease with harmonic number, beyond a certain fairly low number, cf a square wave, which has a 1, 1/3, 1/5, 1/7, ... progression. In the limit, it would be a triangle wave with a 1, 1/9, 1/35. 1/49, ... progression. The curved 'corners' on the slopes make them drop way faster still and imposes an upper limit on the harmonic number containing significant energy.
Ans (2) No I did not say that. I said that most of the cross over distortion energy is in the 3rd. And that the energy drops away very rapidly with harmonic number. Before asserting I'm wrong, please go back and read what I actually said.
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Short cut thinking.
Just look at the transfer function. The deviation from a straight line indicates the distortion, the sharpness of the curvature indicates the order of the distortion products, sharper curve indicates higher order distortions.
Cross Over distortion is a step in the transfer function, that is about as sharp a curve as you can get, so high order distortions for sure.
If your maths doesn't show that then go back and find out what you did wrong in the maths.
Cheers,
Ian
Just look at the transfer function. The deviation from a straight line indicates the distortion, the sharpness of the curvature indicates the order of the distortion products, sharper curve indicates higher order distortions.
Cross Over distortion is a step in the transfer function, that is about as sharp a curve as you can get, so high order distortions for sure.
If your maths doesn't show that then go back and find out what you did wrong in the maths.
Cheers,
Ian
Nice article but I'd get failed for submitting work like that. It should have referenced:
Hamm, R. O. (1973). Tubes Versus Transistors-is there an Audible Difference. Journal of the audio engineering society, 21(4), 267-273
Temm, S (1992) "Audio Distortion Measurements" AES 11th International Audio Test and Measurement Conference, Portland, Oregon, U.S.A., May 31,1992.
At the very least.
They can be excused for not knowing about
Geddes & Lee (2003) "On Distortion Perception"
which was presented the same year
AndrewT,
Which part rings of "can't be" for you? The rounded trapeziod having a period equal to the input sinewave? Or that it has it's most significant harmonic the 3rd?
Why can't it be? What is your reasoning?
It's just basic Fourier analysis that you most likely did at university. If you didn't, look at http://www.till.com/articles/QuadTrapVCO/trapezoid.html If you understand fourier series, you'll know it's actually hard to make a waveform that is symmetrical about zero and does not have as its most significant harmonic (apart from the fundamental) the 3rd harmonic.
Or, better, as it in a form that can be applied directly to cross-over distortion,
http://www.mosaic-industries.com/em...oller-projects/reducing-emi/slew-rate-limiter and shows that for a rounded trapezoid, the harmonics ultimately roll off at 60 dB/decade.
Which part rings of "can't be" for you? The rounded trapeziod having a period equal to the input sinewave? Or that it has it's most significant harmonic the 3rd?
Why can't it be? What is your reasoning?
It's just basic Fourier analysis that you most likely did at university. If you didn't, look at http://www.till.com/articles/QuadTrapVCO/trapezoid.html If you understand fourier series, you'll know it's actually hard to make a waveform that is symmetrical about zero and does not have as its most significant harmonic (apart from the fundamental) the 3rd harmonic.
Or, better, as it in a form that can be applied directly to cross-over distortion,
http://www.mosaic-industries.com/em...oller-projects/reducing-emi/slew-rate-limiter and shows that for a rounded trapezoid, the harmonics ultimately roll off at 60 dB/decade.
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The THD scope pic shows a spike/s coinciding with the crossover of the signal.
The repetition is half the sinewave period.
The duration of the spike/s is a tiny proportion of the whole half period of the sinewave.
That to me means the spikes consist of high harmonics that are not the 3rd.
The repetition is half the sinewave period.
The duration of the spike/s is a tiny proportion of the whole half period of the sinewave.
That to me means the spikes consist of high harmonics that are not the 3rd.
Not only is cross-over distortion NOT a sharp curve, and NOT a step, even if it was (ie a trapezoid distortion), fourier analysis shows that the stringest harmonic is the 3rd, at 1/9 the amplitude of the distortion fundamental, the 5th at 1/25, 7th at 1/49, after that it falls at 40 dB/octave.
What scope pic?
This thread is about vacuum tube amps. Cross-over distortion can and does occur in Class B vacuum tube amps, but there is NO mechanism to gnerate spikes.
In Class B bipolar transistor power stages, you can get spikes, but not with a competent designer. Cross-over distortion doesnot inherently produce spikes even if the gain transition is abrupt. Something that is almost a spike can occur the power stage is common emitter and the emitter resistors are wire-wound. So don't use wire-wound resistors unless they are the non-inductive type.
Something a bit more like a spike can occur with bipolar transistors if the choice of transistor and the driver stage design is such that the e-b stored charge cannot be pulled out when the signal reverses. Only a stupid design engineer would allow that to happen.
And, even if spikes do occur, as they can only be very narrow, there cannot be much energy in the harmonics they generate. Energy corresponds to area-under-the-curve.
Forgot this is a valve/tube discussion.
Energy content of a narrow spike is not the dominant issue.
It's the relative signal strength compared to the fundamental that we hear as objectionable.
Energy content of a narrow spike is not the dominant issue.
It's the relative signal strength compared to the fundamental that we hear as objectionable.
Energy content is EXACTLY the issue. That's what signal strength is - the energy in the signal.
Just to clarify, I (and many others) are not claiming that crossover distortion only involves high order distortion, as it obviously includes lower orders too. However, it you analyse (or synthesise) a waveform with a sharp kink in it you will find that significant amounts of high order terms are needed to reproduce it. A smoother bend needs less high order stuff. The two most common causes of this in real systems are crossover distortion (near the zero crossing) and peak clipping. In each case the biggest terms may be low order, but high order stuff tends to be much more audible so although not dominant in a mathematical sense they may dominate our hearing.
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