Re: Stability in Feedback Amplifiers, Part Deux-A



Chris Hornbeck wrote:

Let's discuss a generalized case of a generic amplifier
at small signal. This will specifically exclude such
large-signal effects in the real world as variations in
inductance with signal voltage and non-linear capacitor
charging and discharging, and device non-linearity.

Discussion must initially be of a simplest case, and this
is it. We'll add onto it later.

Our amplifier is a three terminal device, two input terminals
and one output, with the two input terminals giving opposite
polarity effect on the output.

Feedback is a scaled (TBD) replica of the output terminal's
signal and is applied to the inverting input terminal.
Stability can be defined as assuring that that replica
(and, specifically, *not* the amplifier's output) is always
sufficiently inverting.

Note that the definition includes the complete path forward
through the amplifier and back through the "scaling". Signal
is applied to an input terminal, and feedback is applied,
scaled, to an input terminal (sometimes the same one; doesn't
matter). The signals add (algebraically); here's where things
get interesting.

Stability requires that the signal, passing through the amplifier
and back around through the feedback scaling, not add positively
to itself back at the amplifier's inputs at any frequency where
the amplifier still has unity gain (around the forward plus
scaled feedback path).

Period. That's it. This is pathetically general, and just
to be sure we're all on the same wavelength. And for comments.

Let us choose the terms used by the Radiotron Designer's Handbbook, 4th
Ed, 1955,
or otherwise there will be an insult match because nobody understands
or agrees upon the most very basic engineering terminology conventions.

So µ = tube amplification factor,
RLa = anode load,
Ra = anode resistance,
Rk = cathode resistance load,
A = open loop voltage gain without any NFB,
A' = closed loop voltage gain with NFB applied,
ß = fraction of output voltage fed back to be in series
or in shunt with the applied input signal to
either non-inverting input, NIN, or
inverting inpu, IN, respectively for the two types of NFB.
Phase shift is denoted with theta, but I don't know what
equivalent Alt + numbers to press to give all the members of the greek
alphabet.

So could someone list the full array of greek letters possible from a
keyboard?


So far what you have said is all ok except for your nitty gritty
guts of the matter statement, quote,

"Stability requires that the signal, passing through the amplifier
and back around through the feedback scaling, not add positively
to itself back at the amplifier's inputs at any frequency where
the amplifier still has unity gain (around the forward plus
scaled feedback path).

The matter of phase shift has not been mentioned, except all too vaguely
by talking about it under "not add positively to itself"

But you could have an amp with maximal positive NFB, ie the
fed back signal is a fraction of the output signal with 180 degrees of
"adding" ability, ie, there is positive feedback that causes a need to
reduce the input voltage
to keep the output signal at the same level as without any feedback of
any kind.
If ß is equal to 1/A, and the NFB is positive due to phases, then the
amp
will be on the brink of instability, but not if ß is less than 1/A.
At this point no input is needed, because the FB creates a signal equal
to the input
required for the output.
With ß greater than 1/A with adding phase, then the amp will definately
be unstable and oscilate.

So your simple statement which does not allow for phase shift or any
positive FB anywhere
is plain misleading and too simple, and talking about
amplifiers with lots and lots of phase shift LCR mechanisms in the open
loop gain character
talking about stability by trying condense book fulls of
information to one paragraph could make us look like blithering idiots.

A few people develop a vague idea about phase shift around their
favourite
old Williamson that took them 10 years to build, and they just keep
adding
R&C components until the bloomin thing damn well stops oscillating when
a cap load is used,
or when no load at all is connected, so they learn by trial and error,
talking to mates who know more, email me for a fix, and or
with very few book inspired ideas about PFB or NFB.

Such a ramshackle way of going about amp building harms nobody,
but it isn't how rockets are persuaded to idle slowly past a moon of
Jupiter
while taking snapshots.

What's in the books takes the kind of mind that can handle at least 3
concepts and interactive
behaviours going on simultaneously, so books present a real challenge,
like VRC manuals, and repair manuals.



All feedback amplifiers, including various nested feedback
path schemes, are included. Each nested loop would first
be parsed for closed-loop response; then that loop is
plugged into its place in the complete circuit.

Unfortunately, there are no generic solutions, and all solutions
accurately discussed must be around specific actual amplifiers about
which everyone knows all about.

Nested FB needs to be defined when it is encountered,
such as the slight NCFB from an unbypassed Rk, or the screen FB in UL,
although when UL becomes 100%, its triode, and we don't
talk about pentodes with 100% NVFB.

Notice how I use NVFB, NCFB, because one is neg voltage FB and the other
is neg current FB
and either could be series or shunt, and could be positive or negative
feedback.
And then you have the variations between positive FB and NFB depending
on the phase shift away from where it is 0 degrees in the
middle of the bandwidth somewhere.


Hoping someone more fluent in the English language would
continue with Part 2B, Bode Plots and How They Make Life
Simpler. Then I'd like to make some comments with a Part 2C, The
Strange Case of the Valve Amplifier in the Night (Low Frequency
Effects) and large-signal effects, Part 3.

Without images being allowed to be posted at r.a.t,
How the hell do you explain a Bode plot without drawing one?
It'd be like teaching medical students about the Heart,
but without cutting open a cadaver to show students what it is.

I wish you good luck in teaching the 0.0001% of r.a.t members who find
Bode
plots rivetingly interesting. Nobody I know here has any idea.
I don't have any interest myself, and Bode plots don't appear
at my website. Nor at anyone else's website, and very few ppl here have
a website.

One would need to know all the LCR parameters of an OPT
for an accurate Bode plot to be drawn to enable an engineer to
design an optimally flat blameless unconditionally stable tube amp
that could not be improved upon by the trial and error brigade.
Lemme tell ya, OPTs cannot be fully qualified in equivalent LCR terms
to give a model which can be accurately simulated for a Bode plot.
Engineers today never actually work all this *** out.
None of the DIYers I have ever witnessed at work do either.
They or the firms they work for have purchased software, and it does the
design, right, but the design is BS if we feed in BS data.
So the trial and error brigade methods are beginning to look more
successful, less time wasting, cheaper, and effective compared to the
pure theorist who needs perfect data input for a perfect outcome.
Engineers became ever more clever when we got rid of awkward horrible
things like transformers from electronics.
However, diyers or engineers have some idea about the concept of phase
shift
and tailoring the shift and the acompanying circuit gain so the
amount of NFB being applied at any F will never become positive FB
and cause oscillations.

The apprenticeship which must be served for stability is to
work on 3 amplifiers designed by accountants allergic to OPTs with low
capacitance
and low leakage inductance and low primary inductance
and allergic to using two low µ triodes and in favour of a single EF86.
The Leak range of amps is a classic example.

If the apprentice manages to produce unconditional stability, AND a
closed loop
BW of 20Hz to 30kHz into an R load, without peaking of more than 1 dB
within the band
with an equivalent ESL load network and 15dB GNFB, and low Ro, lo
THD/IMD et all, he has succeded,
and it should not take 10 bloomin years, but no more than a week for all
3 amps.

Naturally, his efforts should sound well.


Chris Hornbeck
"If you're doing this as a volunteer, don't."
- Paul Stamler

I am indeed a volunteer here, and I will!
Give my regards to Mr Stamler.

Som ppl never get the hang of phase shift.

Then gradually, you can teach them about phase lag,
where the crests of the waves at the output of an amp lag behind
the crests at the input. Delay is as easy to digest, a train takes time
before it arrives.

Not so phase lead, where wave crests at the output appear ahead of those
at the input.
People feel they are being forced to believe the train arrived
at its destination before it left the station. Its time travel, not
possible.

But phase lead does happen.

And just how transient input signals behave with almost instant input
rise times with
the LCR phase and lead lead of the amp's networks is a whole study in
itself.


Patrick Turner.
.

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