When designing a closed loop amplifier for audio the poles of the open-loop transfer function are usually only vaguely known.
\$\frac{1}{(s-p_1)(s-p_2)…}\$
These poles can be modeled as \$RC\$ low-passes which attenuate the signal from their break frequency and, more importantly, add phase shift to the signal.
To avoid to much phase shift before gain reaches the 0-dB limit usually a pole is deliberately added at a very low frequency so the open loop gain falls below 0 dB before the other poles kick in.
So far so good. But how can the second, third etc pole be estimated to get a clue where the first pole has to be?
What does the notion of "so much dB feedback is ok to be applied without threatening the stability" mean? How is the applicable amount of dB feedback defined?
An example: I want an amplifier to amplify a signal 30 times and have an open loop gain of say 10000. What does it mean when I say "I apply …dB of feedback"? Usually I would make a voltage divider of 29/1 and therefore get a gain of 30 (factor, not dB). I don't know how to put this any simpler, but doesn't the applicable amount of feedback depend on how my closed loop gain of the amplifier should be? It's often said that the more feedback the better but when I make a unity gain buffer It is useless since I want to amplify my music, right?
Long story short:
What is meant by the applicable amount of feedback?
How do I estimate the other poles?
Best Answer
I think the keyword is "loop gain" - and the most important point (as far as stability is concerned) is the frequency where the loop gain Alo is unity (0 dB).
Because the loop gain is the product of the amplifier´s open-loop gain Alo and the feedback factor Hr (Alo=Hr*Aol) you can find the BODE diagram for the loop gain response very easily:
Draw Aol=f(w) and 1/Hr(w) as a BODE plot and the difference between both curves gives you the loop gain Alo (in dB). The stability criterion requires that at the frequency where both curves meet (Alo=0 dB) the phase shift of the loop gain must not equal to (or even more than) 180 deg.
That means: The "rate of closure" (slope) of the loop gain at this crossing frequency must not be -40dB/dec. (Rule of thumb: If the second pole is identical to the frequency with Alo=0 dB we have app. 45 deg phase margin).
Based on this requirement you can derive the necessary/desired location of the second pole.
Remark ("It's often said that the more feedback the better"): You strictly must distinguish between DC and dynamic stability. Heavy feedback improves the stability of the operating point but - at the same time - degrades the dynamic stability (against oscillations).
EDIT: Sorry for the large picture. I don´t know if/how the size could be reduced.