maxdimario wrote on Thu, 30 November 2006 20:35 |
Feedback related.
I take a circuit built with a variable feedback control..
I have built my own from scratch using both tubes and transistors..
(...etc)
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I recognise this story, I've done similar batteries of tests. The result of this was that I've been "against feedback" for quite some time too. In fact, I've long preached precisely the same gospel as you do (uhh including that I could guess the sound quality by looking at a circuit).
What I've learned since is that "a little feedback is a dangerous thing".
Part 1: Free HarmonicsImagine you've got a circuit with only a 2nd order non-linearity i.e. a second order transfer like f(x)=x+0.1*x^2. Next, you put an ideal 20dB gain stage before it and close the loop (P control only for the time being). The result will be a transfer which is neither linear nor quadratic:
Before feedback: y=f(x)=x+0.1*x^2
After feedback: y=f(10*(x-y))
(write out f()) y=10*(x-y)+0.1*(10*(x-y))^2
(expand) y=10*x-10*y+100*x^2-100*x*y+100*y^2
(collect for y) 0=100*y^2-(11-100*x)*y+(10*x+100*x^2)
Right. That's a quadratic equation. I don't need to solve it for you to see that there are going to be square roots in this thing. The series expansion of a square root contains an infinite number of second order terms. You start with a circuit with only a second harmonic and you end up with a full set of harmonics after applying feedback. What this means is that a moderate amount of feedback will have created higher harmonics which are more audible than the second you started with. When we apply more and more feedback, the new harmonics will eventually come down again as well. In the end we'll need to apply quite a bit more feedback before the net improvement in second harmonic outweighs the presence of a (now small quantity) of higher harmonics.
Part 2: Making matters worseClean P controllers don't exist. Neither the controller, nor the system being controlled has infinite bandwidth. A normal control loop is asymptotically integrating. A circuit that has 60dB of loop gain at 1kHz will have 50dB at 3kHz, 40dB at 10kHz and 34dB at 20kHz. The 3rd harmonic of a 1kHz test tone will be reduced by 50dB. The 10th by 40dB. As a result, integrating loop control will skew the "harmonic balance" towards higher harmonics. This in addition to the fact that the problem outlined previously will also become greater as loop gain declines.
The curious result of this is that an amplifier with moderate loop gain will sound more "natural" if the loop gain is knocked flat below 20kHz (ie. if the dominant pole is real and at 20kHz).
Conclusion: Don't Be A WhimpWe now have two good reasons why low amounts of feedback may not sound all that good. When using feedback, use tons of it. In op amp terms that means: use wideband op amps. Make higher-order loops if your math skills allow you to (ever seen an inductor in a degenerated input pair). If you can't get really high loop gains at 20kHz, set the dominant pole at 20kHz. In this case, however, do not expect total freedom from colouration. The best you can get is a nonintrusive sound, but which at least leaves the music intact (and which is sometimes euphonic).