From: Richard Hosking on Tues 31 May 2005 20:05

I have struggled with this in the past
It is a function of the behaviour of the servo loop at low freq and I
dont have the theory to analyse it properly.

The "theory" part should be evident to anyone who has made
a negative-feedback amplifier, single transistor to op-amp.
Getting to know op-amp responses both open-loop and closed-
loop (with negative feedback) can be helpful. Note that
op-amp designers actually build in open-loop phase shifts
at high frequencies to avoid oscillation with feedback.

The only difficult part is in MEASURING the PHASE at low
frequencies in the 0.1 to 10 Hz range...especially that of
the AGC control-line (feedback) circuitry. If not, some
dog-work on analyzing the magnitude and phase response of
that circuit will show that. [ability to handle complex
quantities is preferred there]

If the phase response is 0/360 degrees between AGC control-
line input and output (to the gain-controlled stages), AND
the closed-loop gain of the system is greater than unity,
there be troubles there! :-(

To get a view into AGC behavior with any general receiver,
disconnect the AGC control-line from the gain-controlled
stage and substitute a small variable DC source for the
AGC control-line input to that gain-controlled stage.
Using a reasonably-well-calibrated RF source, pick some
RF levels over the expected dynamic range of receiver input.
At each input level, adjust the DC control-line substitute
to be the same as the value of the disconnected AGC control-
line. Measure the DC value of both the input and output of
that AGC control-line circuitry.

The reason for doing that is to remove any phase effects
at low frequencies. That's a baseline value set that
SIMULATES the closed-loop control range of the AGC.

With enough RF input signal levels, the characteristic curve
of the closed-loop AGC action at DC can be seen...from no
AGC (maximum receiver gain) to high values of AGC control
(essentially minimum receiver gain). That will show the
delta of tiny AGC-control line variations which is the
equivalent of the "feedback percentage" of a negative-
feedback amplifier simple formula.

Alternately, one can do an open-loop gain measurement using
a series of AGC control-line value increments from minimum
to estimated maximum. Setting the simple DC supply (substitute
for the AGC control-line) to those increments will do it nicely.
Log the RF input level for those DC increments and measure the
input to the AGC control-line feedback circuitry (even though
it is disconnected from the controlled stages). That will
result in the same input signal characteristic curve.

Either way will result in "seeing" what the RF input signal
characteristics are, allow one to use the AGC line for things
like an S-Meter indicating circuit, squelch control, etc.
Note: The alternate method can also be done analytically on
paper if the controlled stages' gain v. control line is known.
A "gain budget" can be tabulated of the total receiver
sensitivity to various RF input levels that produce various
AGC control-line values.

That takes part of an afternoon's bench data logging, dreary
though that may be. It will establish THE characteristics of
that receiver, valuable reference for later work on it. That
curve will be no different than that of a single amplifier
stage with varying amounts of negative feedback.

Next is to either measure or calculate the low-frequency
magnitude and phase characteristics of the AGC control-line
circuitry (ALL of it, even to bypass caps at the controlled
stage input connection). Magnitude alone will yield the
feedback percentage of the equivalent negative-feedback
amplifier. The phase response at various low frequencies
has to be compared to the "attack" and "decay" times as
desired. THAT is not intuitive but must be examined to see
if the low-frequency AGC control characteristics will result
in a negative-feedback or positive-feedback (oscillatory,
motorboating) amplifier equivalent.

A stable receiver WITH AGC should ALWAYS have some error.

If actual low-frequency oscillation occurs, one cure is to
attenuate the AGC control-line range. A voltage divider if
the AGC control is through voltage does that. Such
attenuation works on the magnitude of the AGC control but
will also affect the phase.

I hope this simplified explanation is a help for all who
aren't familiar with Control System theory. Control Systems
aren't as intuitive as many instructors on the subject claim
so there isn't a lot of literature on it in popular
publications for hobbyists. Those usually present some
very simple analogue such as the ball governor valve on a
steam engine of old and let it go at that. :-(