different methods for stability analysis

[senmeis]

Hi,

in control theory stability can be analyzed with Routh-Hurwitz criterion, Nyquist criterion or Bode diagram. For HF-amplifiers stability analysis is carried out with S parameters.

Question: why are there different methods for stability analysis? Or are they in fact the same things?

 

[FvM]

They are basically the same or limited to specific conditions.
Routh-Hurwitz is the general mathematical form, Nyquist and Bode are graphical methods, whereby Bode is limited to a subclass of problems.

 

[dick_freebird]

I'll say that small signal stability is the beginning,
not the end, of stability analysis. There are many
circuits which exhibit small signal stability but
large signal instability under the right, wrong
conditions.

Like, pick the wrong shunt cap value for a bipolar
shunt voltage reference, and see the sawtooth
as it hits into and relaxes out of output device
saturation. Perfectly small-signal stable, until
something kicks it out of its "happy place".

 

[FvM]

All stability criteria mentioned in post #1 are applicable for LTI systems but insufficient to describe the behaviour of systems with relevant non-linearities.

During my study of analog circuit design, large-signal instability seemed to be treated as a "non-issue, it's not analyzed or at least mentioned in my text-books.
It can be however easily experienced, e.g. with an OP based active filter that turns into an oscillator when signal dV/dt exceeds the slew-rate limit.
Fortunately, large-signal stability was an advanced topic in control engineering, so you could know about it.