Feedback in amplifier is ultimately the driver of sound quality ?

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#161
Also, one of the most interesting things shown in the permanent NFB thread was that even simple emitter degeneration has the effect of initially increasing some of the higher order harmonics until the amount of NFB goes beyond 10 dB or so.
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I remember there's some post where the preferable sound comes from using no emitor degeneration resistors at all (its hard to control quiscent current or parrarel devices, though). Johan Potgieter wrote it with graph attachment, but I couldn't find it.
 
#162
andy_c said:
Oh, I think I see what you're getting at.
[snip]The idea was to isolate and simplify as Baxandall did. Since those sims were intimately connected to Baxandall's approach and results, it becomes confusing to discuss them outside that context. So the response to questions such as "Why was it done in such-and-such a way" becomes, "Because that's how Baxandall did it. The purpose and scope of the problem were to first duplicate his results, then extend them a bit". If you're not familiar with what Baxandall did, the article is a very worthwhile read. It would also make the discussion easier by putting the work of the Cordell feedback thread into context.
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Andy,

Are you guys aware of the similar work done by Boyk and Sussman :

"We examine how intermodulation distortion of small two-tone signals is affected by adding degenerative feedback to three types of elementary amplifer circuits (single-ended, push-pull pair, and differential pair), each implemented with three types of active device (FET, BJT and vacuum triode)."

Jan Didden
 
#163
rdf wrote:
I was thinking more the general case. For example, is the circuit below equivalent to MikeB's (ignoring for the moment the exact transfer function at the feedback return node might not be the same as the positive input)? The two transfer boxes and summing nodes represent of course components of a single device. If not, which is more representative of the general case?
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Don't forget that if N(x) is a non-linear function of x, then N(a - b) does not equal N(a) - N(b).
 
#164
MikeB wrote: But... exp() is special... feedback transforms exp(x) to some exp(-x). Maybe feedback'd transfer function is always some exp(), giving rich harmonic content? (exp(-x) = 1/exp(x)) My mathematical skills end here...
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If the forward gain function is exp(x) then to eliminate distortion at the output of exp(x) the input must be pre-distorted by a ln(x) function, ie: x= exp(ln(x)). So the FB system, in attempting to minimize the output error, is approximating a natural logarithm function. Obviously, it is impossible to generate a logarithmic function using only linear components and this is why such a network operates, like an ordinary control system, by hunting for a minimum error equilibrium.
Brian
 
#166
Hi Brian,

John was right. You'll see later in the thread that I fixed the sim. The error was caused by the resistor network in the base that I duplicated from Baxandall. It makes me wonder if Baxandall may have needed to scale that impedance down to duplicate the theoretical results. The fixed sim is here. The corrected graph shows a 30 dB dip in the third harmonic at 3 dB feedback. The math showing the dip should be the same as Baxandall's.
 
#169
Hi Andy,
Yes, I read through several pages of the FB thread. Lots of research effort has gone on. I sort of felt sorry for John Curl, though, who keeps having to defend his real experience against the tyranny of the theoreticians. 🙂

It's now clear that we are both talking about different things. I think you are talking about the circumstances where the ratio of harmonics to fundamental are non-monotonic with respect to FB factor. And this is what Baxandall investigates. My thesis is that the application of a linear FB loop around any non-linear gain element creates new spectral content.

I have read the Baxandall articles parts 5 & 6. I have also read the Boyk & Sussman paper that Jan posted.

Baxandall wrote this in 1978 and no doubt he didn't have a Spice simulator at hand or Mathmatica or even a mathmatician to help him out. So he explored what it was practical to analyse given these constraints: a single, fixed amplitude sinewave applied to some models of simple stages, with uniform FB factor and without any consideration of phase shift, with only the first few series expansions being used to approximate the results. Pretty good considering.

As I read the articles I was hoping he would address the 4 questions he lists at the beginning of section 5. I'm not sure he answered any of them completely but he had a stab at uncovering some non-intuitive characteristics of FB when applied to non-linear stages that inform those questions.

Brian
 
#170
Has anyone ever succeeded (or even tried) in making a circuit that is inherently linear without any feedback? One method that springs to mind is combining 2 circuits that balance out, i.e one has a concave transfer curve and the other a convex one, overall combining to give a straight line transfer over a wide range. It can't be impossible, surely?
 
#171
traderbam said:
It's now clear that we are both talking about different things. I think you are talking about the circumstances where the ratio of harmonics to fundamental are non-monotonic with respect to FB factor. And this is what Baxandall investigates.
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There were multiple conversations going on. Baxandall's distortion vs. feedback factor stuff was germane to the discussion Mike and I were having earlier. But also, Baxandall does investigate the generation of new spectral content as well. In the treatment of the ideal JFET, the open-loop amplifier generates only second harmonic, while with feedback, the input-output nonlinear relationship is an infinite series and thus consists of all harmonics of the input when a single sine wave stimulus is used. So new spectral content is being created.

My thesis is that the application of a linear FB loop around any non-linear gain element creates new spectral content.
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Let's consider memoryless nonlinearity. If the input-output relationship of the open-loop amplifier can already be expressed as a Taylor series with all its terms non-zero, then the feedback is not adding new spectral content at all. This was the example of the class AB output stage. The closed-loop nonlinear input-ouput relationship is just another Taylor series with different coefficients. Sure, the harmonics will be different, but there will be none in the closed-loop system that aren't in the open-loop one.
 
#172
Looking at the taylor series for y = 1 / (1 - x) Wiki You see that this functions is simply a sum of all polynomials.
This should mean, that a closed loop transfer is always rich of harmonics, if x is not constant. If x is constant, the result is also constant = distortion free.

I think, that if open loop distortion is reasonably low and feedback not too low, this effect is negligible.

Mike
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Mike, I've simulated your system model and have found new spectra but they are very small and hard to spot. Other new spectra share the same frequencies as the OL version and so are lost except in the relative sizes. It is much easier to see the effect when a two-tone signal is used with a less linear transfer function. Attached is a result when using an idealised, complementary exponential gain block: Vout = exp(Vin) - exp(-V(in)).

Red is OL and Brown is CL. Spot the differences.

I agree that this effect will be negligible in the circumstances you describe...but we can only say this within the limits of our theoretical model assumptions. The models are nothing like as complicated as a real circuit.
 

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#173
Let's consider memoryless nonlinearity. If the input-output relationship of the open-loop amplifier can already be expressed as a Taylor series with all its terms non-zero, then the feedback is not adding new spectral content at all. This was the example of the class AB output stage. The closed-loop nonlinear input-ouput relationship is just another Taylor series with different coefficients. Sure, the harmonics will be different, but there will be none in the closed-loop system that aren't in the open-loop one.
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Indeed, I am talking about the rarefied, idealistic, theoretical model of a non-linear gain element that has no phase shift or delays or hysterisis. Good to note that.

Regarding the Taylor series, with the assumptions you state, you may be right in the case of a single tone input of constant amplitude.
 
#174
Feedback in amplifier is ultimately the driver of sound quality ?
No. Some low distortion amplifier with many feedback sounds bad. And many single ended classA sounds pretty nice without feedback.

Feedback is the only way to achieve low distortion?
Not true:
Most precision DAC has no feedback from its output, it is still precise, 32bit version is used in VGA cards. 32bit has 2^32 resolution, what a linearity.
I ever built 8bit version 100W@4ohm precision power DAC in time domain conversion, the result is it has linearity as 8 bit DAC (1/2 bit error).
 
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