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Nyquist Stability Test

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

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  1. Active8

    Active8 Guest


    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.

    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.


  2. 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
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
  3. Roy McCammon

    Roy McCammon Guest

    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 Bloggs

    Fred Bloggs Guest

    Right- this is what's going on with those damned LDO's and their picky
    requirement for output capacitor with ESR> 1 ohm....
  5. Active8

    Active8 Guest

    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.
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