# Nyquist Stability Test

Discussion in 'Electronic Design' started by Active8, Aug 16, 2003.

1. ### Active8Guest

hi:

just a note on an old thread where Kevin Aylward discussed stability of
systems with gain greater than 1 and positive feedback.

i checked out a paper on the Nyquist stability test, which shows he's
right about the possibility of a stable system with positive feedback
and gain greater than 1. not that it's demonstrated or even mentioned in
so many words, but it does at least agree with Kevin's statements
regarding the net encirclements of the (0, -1) point.

well, the same guy also wrote a paper on feedback (for the same class
he's teaching) in which he says that you can't have a stable system if
af >> 1 (af being loop gain) because "all real systems eventually
exhibit increasing negative phase shift with frequency."

at first this seemed like a contradiction, but it may be that "much
greater than 1" is the qualifier, not to mention the fact that the
system may be band limited.

gain and phase margin are a subset of the Nyquist test.

http://www.stanford.edu/class/ee214/Handouts/nyquist.pdf
http://www.stanford.edu/class/ee214/Handouts/HO17.pdf

http://www.stanford.edu/class/ee214/Handouts/

the last link is the index of the rest of the papers and that's how i
found HO17.pdf on feedback. note the simple trick used to get it.

enjoy...

br,
mike

2. ### Kevin AylwardGuest

Its not uncommon for phd's in control theory to have missed this basic
point about what encircling the minus one point really means.
Yep, you can. It has been used in practise quite extensively. A typical
example is the nested feedback compensation. You essentially have a
deliberate steep N*20db/dec roll off starting at say 20Khz, then
compensate them all out, bar one somewhere before the unity gain point.
The phase will drop way down to hundreds of negative degrees, but then
get pulled up again. All that matters is what the phase does at around
the final unity gain point.

The basic rule of thumb here is, so long as the final xing of the unity
gain point is at a single order, 20db/dec, response, the system will be
stable. (for 99.99%)

The advantage of this approach is that the final gain can be clobbered
to unity at say 1Mhz, so you don't have to worry about all those other
extraneous h.f. poles, yet still have very large gain for distortion
reduction at 20 khz. For example, a single order roll off at 20khz,
would only allow 40 db of loop gain for a 2Mhz unity point. A 4th order
would allow some 80db.
But this dose not matter. So long as the gain has finally dropped below
unity before this occurs.

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

3. ### Roy McCammonGuest

Such systems are sometimes called "conditionally
stable" and can exhibit bad behavior when the
gain of the amplifier is less than it should
be such as during power up or if the output is
driven to the rail. Although the fully powered
small signal model is stable, you can still
wind up with the output banging rail to rail
in an uncontrolled fashion.

--
Achilles: I wish my wish would not be granted.
< an undescribable event occurs >
Achilles: What happened? Where's my Genie?
Tortoise: Our context got restored incorrectly.
Achilles: What does that cryptic comment mean?
Tortoise: The system crashed.

To email me send to :

rb <my last name> AT ieee DOT org

4. ### Fred BloggsGuest

Right- this is what's going on with those damned LDO's and their picky
requirement for output capacitor with ESR> 1 ohm....

5. ### Active8Guest

right, same as the article on pole-zero compensation in Win's book
says/implies(memory failure) , except it says 6dB/octave instead of
20dB/dec. same thing.