Preposition: Tubophiles listen for distortion.
Fact: Large amounts of distortion, particularly high order distortion, are unpleasant.
Conclusion: There is an optimal amount of distortion which appeals to tubophiles.
Suppose: The ideal distortion did not vary with signal intensity. What if it were constant for all signal levels?
We need a transfer function which has a resulting distortion:
THD = Pdist / Ptotal = constant (independent of input amplitude)
Further suppose Pdist is entirely second harmonic, just to make this simpler. We'll start with a sinusoidal signal, on the assumption that this still works for complex signals, understanding that IMD is inevitable, and hoping that THD doesn't increase much.
Then,
THD = V2^2 / (V1^2 + V2^2)
where Vn = amplitude of nth harmonic (1 = fundamental, 2 = distortion).
For this to be constant, we need
V2 = V1 * sqrt(THD / (1 - THD))
So if we have an input,
Vi = A*sin(w*t)
we need a transfer function f(x) such that:
f(A*sin(w*t)) = V1*[sin(w*t) + sqrt(THD / (1 - THD)) * sin(2*w*t)]
Is this function linear? Well, obviously not, because it's making distortion. But then, if A = B + C, we should get V1 = (B + C) / A, which means the amplitudes are linear, but the products are not. This suggests one possible way to construct a circuit: perhaps we "100% distort" the signal (like with a squaring function biased around zero, so it contains no original signal -- it's 100% distortion), adjust it for proportional amplitude, and mix it in. The amplitude control stuff necessarily has some delay, so it's not a time-invariant system, which means solving for f(x) analytically will be a pain, if possible at all.
Will it actually SOUND better? Who knows. Some features of tube amps are their "terrible" recovery behavior, arising from distortion shifting bias voltages, which takes time to return to zero. The amplitude control in the proposed system will take time, too. Maybe it will have a more pleasing effect?
Some experimental features are appealing. The type and quantity of distortion can be varied by song and user. By using other functions, 3rd harmonic could be explored, for instance.
The system could be implemented in tubes, SS or DSP. Tubes are uniquely suited, as a variable gain amp (VGA) can be made with a dual control tube (6HZ6, 6HS8) or heptode, while an envelope detector can be made with a 6AL5, resulting in no minimum signal offset that would result from silicon diodes (which would otherwise require op-amps to make a precision rectifier circuit!).
Tim
Fact: Large amounts of distortion, particularly high order distortion, are unpleasant.
Conclusion: There is an optimal amount of distortion which appeals to tubophiles.
Suppose: The ideal distortion did not vary with signal intensity. What if it were constant for all signal levels?
We need a transfer function which has a resulting distortion:
THD = Pdist / Ptotal = constant (independent of input amplitude)
Further suppose Pdist is entirely second harmonic, just to make this simpler. We'll start with a sinusoidal signal, on the assumption that this still works for complex signals, understanding that IMD is inevitable, and hoping that THD doesn't increase much.
Then,
THD = V2^2 / (V1^2 + V2^2)
where Vn = amplitude of nth harmonic (1 = fundamental, 2 = distortion).
For this to be constant, we need
V2 = V1 * sqrt(THD / (1 - THD))
So if we have an input,
Vi = A*sin(w*t)
we need a transfer function f(x) such that:
f(A*sin(w*t)) = V1*[sin(w*t) + sqrt(THD / (1 - THD)) * sin(2*w*t)]
Is this function linear? Well, obviously not, because it's making distortion. But then, if A = B + C, we should get V1 = (B + C) / A, which means the amplitudes are linear, but the products are not. This suggests one possible way to construct a circuit: perhaps we "100% distort" the signal (like with a squaring function biased around zero, so it contains no original signal -- it's 100% distortion), adjust it for proportional amplitude, and mix it in. The amplitude control stuff necessarily has some delay, so it's not a time-invariant system, which means solving for f(x) analytically will be a pain, if possible at all.
Will it actually SOUND better? Who knows. Some features of tube amps are their "terrible" recovery behavior, arising from distortion shifting bias voltages, which takes time to return to zero. The amplitude control in the proposed system will take time, too. Maybe it will have a more pleasing effect?
Some experimental features are appealing. The type and quantity of distortion can be varied by song and user. By using other functions, 3rd harmonic could be explored, for instance.
The system could be implemented in tubes, SS or DSP. Tubes are uniquely suited, as a variable gain amp (VGA) can be made with a dual control tube (6HZ6, 6HS8) or heptode, while an envelope detector can be made with a 6AL5, resulting in no minimum signal offset that would result from silicon diodes (which would otherwise require op-amps to make a precision rectifier circuit!).
Tim
One big snag: VGA tubes have inherently higher thd, probably far higher than the incoming signal.
I'm not sure your preposition: Tubophiles listen for distortion: you will find it at very low levels in my stuff so I'm not earing out for it. Since distortion is proportional to level in class A, one can calculate it quite predictably. A well designed tube amp with plenty of power headroom easily fulfills listening level requirements; in fact an overkill. When the volume is ramped up, other material in the room vibrates,also the back panels of loudspeaker cabinets resonating adding more colouration & thd than the listened passage. Run a few watts in to a LS from a low thd signal genny+amp going up the audio scale and take notice of all the buzzes.
The real problem is the quality of modern recordings......some have imbedded a worse signal/noise ratio than the early recordings which came off analogue mixdesks. The recording bandwidth may have widened over the years but quality seems to have gone downhill. In one instance I suspected the tweeters in my system had loose coils, but the blame was a lousy signal. So we have it.
If you want constant thd for all signal levels, then it's SS and use DSP to do the harmonic cancellation. SOme years ago this was "brainwaved" on the forums but idea stalled do to low processor speed. Now MHz speed is plentiful and cheap to enable the algorithm vs. bandwidth and Fourier bandwidth criteria. Remember to deal with 5th harmonic from 10Khz = 50Khz i.e bandwidth musn't drop by more than -3dB at that point and have extremely fast switching without introducing more distortion.. very fast zero point signal switching....The mathematics and powerful number crunching is there to do it....but no-one in the industry thinks about distortion in the source material. SOme is quite shocking: Human thd as coughs and colds in quiet classic passages; stage Mics >1% thd or more and the list goes on.
richy
Human hearing is highly non-linear. I cannot see an advantage in having constant THD. Let's simplify a lot and just consider what happens at physiological level. If I have 90dB speakers and the amp has got 3% 2nd harmonic only from 0 to 10W, I will clearly spot THD for SPL below 90bB, i.e. 1W, while I will not for higher SPL because the threshold will increase. Typically max sensibility to distortion happens in the range 65-80 dB's and it decreases quickly out this range. So the sound character will be different anyway. If I decide for 10% THD at all levels it will sound sloppy. Good for a guitar amp, I guess.....
45
45
Interesting thinking, Tim - but rather old news I'm afraid.
You should check out some stuff from about 90 years ago: Phys. Rev. 23, 266 (1924): Auditory Masking
There are follow-ups to this in the 1950s thru the 90s, at least. And plenty of "tube sound" plugins in the pro audio world.
IMO, you'd have to know the distortion spectrum of your system before you could get a get approximation of the "tube sound." And a MacIntosh doesn't sound like a Scott, which doesn't sound like a Dynaco, which doesn't sound like an SET. So you have to know what you have before you know what to add. At least for a good approximation, that is.
.
You should check out some stuff from about 90 years ago: Phys. Rev. 23, 266 (1924): Auditory Masking
There are follow-ups to this in the 1950s thru the 90s, at least. And plenty of "tube sound" plugins in the pro audio world.
IMO, you'd have to know the distortion spectrum of your system before you could get a get approximation of the "tube sound." And a MacIntosh doesn't sound like a Scott, which doesn't sound like a Dynaco, which doesn't sound like an SET. So you have to know what you have before you know what to add. At least for a good approximation, that is.
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... Or try to find an old APHEX "Aural Exciter" which works basically on the same principle: aurally pleasant harmonics addition a.k.a distorsion by techs and engineers. Nothing new...
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simple through use of negative feedback... http://www.diyaudio.com/forums/solid-state/168503-tgm-amp-goes-tubey.html
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