[sdiy] Simple discrete Unity-Gain Follower ?

[Magnus Danielson]

From: Don Tillman <don at till.com>
Subject: Re: [sdiy] Simple discrete Unity-Gain Follower ?
Date: Fri, 2 May 2003 01:52:12 -0700

>    > Date: Thu, 01 May 2003 11:39:20 -0500
>    > From: Grant Richter <grichter at asapnet.net>
>    > 
>    > Most of the "audiophile" distaste for feedback loops refers to
>    > the failure of the feedback loop, not when it's working properly.
> 
> Grant, you didn't really mean to say that, did you?  
> 
> There are a number of serious problems with feedback loops, even when
> they're working properly.  The most blatent is that the output is the
> amplifier gain times the error.  That's just philosophically wrong at
> a deep fundamental level.

Don, you didn't really mean to say that, did you?

Again, it is about applying the technique adequately. If you look deeper into
the theory you find that the simple model of the op-amp as a pure gain-cell
forms only a 0-degree feedback system. You can improve things immensly by
including integrating terms prior to the output. There are many ways to apply
integrating terms to op-amps, so it's a real connection here.

If you look into phase-locked loops you find that you have 1-degree, 2-degree
and 3-degree loops mentioned. You can go higher, but mostly the bucks stops at
3-degree (which is considered "complex" there). What the hell does PLLs have
to do with op-amps? Well, they follow the same control theory rules in the
linear range, so the math, stabilisation analysis, error analysis etc. turns
out to be about the same with only local differances (like different types of
error sources, which is only natural).

You can integrate up the error by introducing integrating terms, and the
analysis of this can be done by tools at hand.

A 0-degree feedback system is still very usefull, just as 1-degree PLLs even if
both of them seems like very bad designs in comparision with higher degree
systems. For PLLs I lean towards 2:nd and 3:rd degree systems and good phase
detector designs to fit the problem at hand.

Also, the 2-degree PLL design world is very conservative and there is a
handfull of tricks that I invented that I've also put into production which
even further reduces certain flaws and this gives a much higher freedom in the
design.

The points that I have heard from the feedback discussions in the audio-world
relates to non-linearities and the behaviour that strong negative feedback
acheives. The point there is that strong feedback increases distorsion.
Here I use distorsion in a very generic sense, such that both harmonic
distorsion and intermodulation products get included. The analysis of
non-linear control systems have been difficult, but with the comming of the
sigma-delta A/D and D/A technology which uses strong non-linearities,
integration and multiple feedback loops and gross over-sampling I think that
there is much more material available on such systems then when the big debate
where running in the 70thies.

> And, of all the truly cherished pieces of audio equipment (hifi amps,
> guitar amps, signal processors, etc.) it's really hard to name any
> that use large amounts of feedback in the audio chain.  And of all the
> truly despised pieces of audio equipment, most use a lot of feedback.
> The correlation is pretty significant.

The problem here is that "truly cherished pieces of audio equipment" may be
apparent to you, but is surely not apparent to me and many others. The
objectivity in the truth of the statement remains to be prooved. But don't
fall for the normal audiophile ways of prooving it to me, I won't care.
I stopped listen to that in the 80thies. I am interested in figuring out things
and also figuring out why things are bad and why they are good. I have however
yeat to see very sober discussions on this.

A fellow Synth-DIY-man (and a respected tube-head no less) wrote a good article
in the IEEE Spectrum some time back. It was good for the forum it went to and I
much enjoyed it as such. Do read!

As for ways to design things, it is *really* hard to judge a design. You must
quantify aspects, and the human hearing and perception is as such not very
easy to grasp. There is many concepts you got to get really right, and I've
found that some of the concepts is not even well understood in the audio world
at large. What I've learned was that there where really few authorities that
really grasped all the peculiarities and could rationally explain them, and I
mean *REALLY FEW* (approx to 0).

Where am I going with all this? Slam the audiophiles? No, not really. My point
is that when you are on the border between science and human conception, you
have to be _very_ carefull to make sure that your physcoacoustic interpretation
of the sound and your ability (or lack of) to measure something matches.
Also, you might to really dig into a field (and not necessarilly the field you
initially thought off) to find the material which helps you along the right
path. This also accounts for the system analysis. With this in my mindsetting,
I don't take things for "real truth" but rather "our experience so far gives
this as the best" which moves things of from the field of logic to the field of
subjective judgement and accumulated experience, which is not to be spit upon,
but whose value can degrade by addition of new knowledge, and the field of
science shows exactly this (compare for instance Newton's physics etc.).

Disagreeably yours,
Magnus