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Q of a super-inductor

Discussion in 'Electronic Design' started by Joel Kolstad, Jun 13, 2006.

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  1. Joel Kolstad

    Joel Kolstad Guest

    Hey, if you guys were plotting Q of a simulated inductor (e.g,. from a
    gyrator), would you plot Q as just staying at infinity once the resistance
    goes negative? Or would you just plot it as negative Q?

    It's interesting to me that the resistance from gyrator inductors start
    heading south (drop below 0 ohms with a vengeance) generally well before the
    imaginary part starts to degrade similarly; anyone for an intuitive
    explanation as to why this is?

    ---Joel
     
  2. Jim Thompson

    Jim Thompson Guest

    If you'll thumb back through the old threads about gyrators I think
    you'll find that I attributed it to excess phase in the OpAmps.

    ...Jim Thompson
     
  3. Joel:

    So called "Q-enhancement" is common in active RC networks, is a well known
    phenomena and was studied and written about ad infinitum back in the 70's.

    As Jim [Thomson] points out Q-enhancement is usually caused by excess phase
    shift in the OpAmps.

    The search for better active RC circuits [gyrators, gic's, etc...] always
    led to inventions of novel circuitry that somehow reduces that excess phase
    shift.

    There are passive compensation methods that "tune out" the Q-enhancement,
    but...

    The "best" circuits use active compensation of the OpAmps wherein the excess
    phase of one [of usually two] OpAmp in a circuit approximately cancels that
    of it's paired [matched] OpAmp.

    The Akerberg-Mossberg circuit was the first such 'active compensation"
    circuit that appeared in the literature.

    There is a lot of information on excess phase compensation, and a catalogue
    of the "best" circuits, including the celebrated Antoniou gyrator invented
    by Andreas Antoniou, now at University of Victoria, in Victoria, BC Canada,
    laid out, analysed and described in the book:

    Adel S. Sedra and Peter O. Brackett, "Filter Theory and Design: Active and
    Passive", Matrix Publishers, Champaign, IL 1978.

    In fact the "best" gyrator circuit, the one invented by Andreas, is depicted
    in the cover artwork on that book.

    FWIW...
     
  4. Peter O. Brackett wrote:
    (snip)
    Another book that concentrates on active excess phase compensation is
    "Theory and Design of Linear Active Networks" by Natarajan. The
    performance of almost every opamp circuit described is compared to a
    similar one that has the excess phase shift compensated, to show how
    much more ideally it functions.
     
  5. Tim Wescott

    Tim Wescott Guest

    I would plot the Q as going negative, or I would plot 1/Q as a nice
    straight line. Plotting the Q as staying at infinity would indicate a
    lossless, mild-mannered circuit rather than the threat to system
    stability that you'd really be dealing with.

    --

    Tim Wescott
    Wescott Design Services
    http://www.wescottdesign.com

    Posting from Google? See http://cfaj.freeshell.org/google/

    "Applied Control Theory for Embedded Systems" came out in April.
    See details at http://www.wescottdesign.com/actfes/actfes.html
     
  6. So perfect, they seem a bit like Schroedinger's cat, always existing in a
    state of of crypto-stability. I've seen unplottable drifting Q's of maybe
    1000-5000 one minute and then to infinity and beyond when the temperature
    changes.
    Despite excess phase, pos or neg inductor "loss" resistance, appears from
    normal practical circuit layout.
    Predictable enough to allow fixing Q at say a much less perilous 100X. Or
    conversely, guarantee (in oscillator format) a gentle startup.
    john
     
  7. Joel Kolstad

    Joel Kolstad Guest

    An oscillator in a filter's clothing, eh? :)

    Thanks, I think I will just plot it as going negative... maybe on a log
    scale (something like sgn(Q)*log(abs(Q)))...
     
  8. Joel Kolstad

    Joel Kolstad Guest

    Thanks for the advice Peter, I do have your book sitting on the bookshelf
    and will take another look at it shortly (it was actually the first book I
    read that went through the whole approach of using 1/s as an op-amps gain if
    you're doing hand calculations and are looking to come up with the pole-zero
    locations of a given op-amp circuit... funny how somehow this never made it
    into my coursework in college...)

    ---Joel
     
  9. Joel Kolstad

    Joel Kolstad Guest

    OK... I'll have to drop your configurable op-amp into a simulation soon
    (since it of course includes that excess phasE) and see how it compares
    (using data sheet values) to simulations done with, e.g., Linear Tech. SPICE
    models.

    ---Joel
     
  10. Tim Wescott

    Tim Wescott Guest

  11. Joel Kolstad

    Joel Kolstad Guest

    Probably. :)

    That reminds me of a co-worker who is hesitant to use IIR filters since
    their stability is not guaranteed (as FIR filters are) nor completely
    trivial to predict once everything is quantizied (i.e., the Z-transform of
    the unquantized system don't tell you the whole story)... I tell him that he
    might as well protest any use of active continuous-time circuits containing
    feedback, since it's not completely trivial to predict oscillation given
    imperface real-world components either...!
     
  12. Tom Bruhns

    Tom Bruhns Guest

    Why are you using Q anyway? Just use the resistive (potentially
    negative resistance) and reactive components you know you have, if
    you're using a simple linear model, or better, put in a full model of
    the gyrator with decent models for the op amps, and you won't have to
    worry about "negative Q". As Tim was pointing out, remember that there
    are things we call "negative resistance oscillators." A "Q multiplier"
    (used in the old days to add selectivity to a receiver's IF section)
    could, of course, be made to oscillate by advancing the gain too much.
    Q is often an over-worked term (especially when people try to apply it
    to multiple-resonator filters, but that's a topic for another thread).

    Cheers,
    Tom
     
  13. Tim Wescott

    Tim Wescott Guest

    Don't forget anything with noise.

    I discuss predicting the effects of quantization in IIR filters in my
    book, by the way, including finding bounds on limit cycles (although I
    bet I don't say it quite so clearly -- hmm).

    Of course, you can't completely characterize your FIR filter performance
    with the z transform, either -- you can just come a lot closer because
    the quantization effects are less severe.

    --

    Tim Wescott
    Wescott Design Services
    http://www.wescottdesign.com

    Posting from Google? See http://cfaj.freeshell.org/google/

    "Applied Control Theory for Embedded Systems" came out in April.
    See details at http://www.wescottdesign.com/actfes/actfes.html
     
  14. Joel Kolstad

    Joel Kolstad Guest

    Because sometimes plotting Q is more useful than plotting re(Z), im(Z) or
    whatever... My original question was prompted just by building a bunch of
    "probe" components for SPICE that you could drop down on a schematic to plot
    various "useful" things; I was using a gyrated inductor as the test case for
    them.

    ---Joel
     
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