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"Stretching" an inductor

Discussion in 'Electronic Design' started by Joel Kolstad, Oct 3, 2006.

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  1. Joel Kolstad

    Joel Kolstad Guest

    Does anyone know of a simple network that has, say, more than twice the
    reactance at 2*f0 as it does at f0? Essentially I'm after a reactance of
    2*pi*f*(something super-linear).

    You can readily convince yourself that going the other way is no problem... if
    you put a small capacitor in series with an inductor, the slope of the
    reactance is lowered (since the capacitor's reactance is dropping with
    frequency), hence making the reactance at 2*f0 less than twice what the
    circuit has at f0.

    ---Joel
     
  2. Jim Thompson

    Jim Thompson Guest

    Huh? Won't a parallel tank do what you want? Although you're saying
    reactance, rather than "real".

    ...Jim Thompson
     
  3. There may be some version of a generalized impedance converter that
    produces a resistive impedance proportional to frequency squared. I
    have seen some that produce a negative resistance inversely
    proportional to frequency squared, i.e. -1/D*w^2, where D is a
    constant based on resistor and capacitor values in the circuit.
     
  4. Tom Bruhns

    Tom Bruhns Guest

    Huh?? If I put 100nH in series with 30pF, at 100MHz the net reactance
    is +j9.78 ohms; at 200MHz, it's +j99.14 ohms. Last time I checked, 99
    is more than twice 9.8, not less. In general, if you double any
    frequency above the resonance, you get a reactance more than twice as
    high, though the effect is the strongest for starting frequencies near
    the resonance.

    Cheers,
    Tom
     
  5. TuT

    TuT Guest

    That's an FDNR, (Frequency Dependant Negative Resistor), and can be realised
    with the basic four-op-amp gyrator circuit using two capacitors and three
    resistors. You can get a negative resistance that either increases or
    decreases as the square of the frequency, depending where you put the
    capacitors, but I've never found a way of doing anything useful with this
    circuit.

    You can make a frequency dependant voltage divider with an FNDR and a
    resistor, but the circuit goes through a phase inversion, the point of
    inflection being at the frequency where -R = R
     
  6. TuT

    TuT Guest

    [snip]

    Make that "two-op-amp gyrator circuit".
     
  7. Tom Bruhns

    Tom Bruhns Guest

    You wrote, ". . . but I've never found a way of doing anything useful
    with this circuit."

    If as you wrote in the paragraph after that, you put it in series with
    a resistor, you get a circuit that behaves much like a series resonant
    circuit. Not only does it go through a phase inversion, but it goes
    through zero resistance. Similarly if you put it in parallel with a
    resistor, you get something that behaves much like a parallel resonant
    circuit: where the gyrator negative resistance equals the parallel
    positive resistance, the net resistance goes to infinity. If you think
    of C-R-L circuits (or better, 1/sC, R, sL) as having components that
    contribute in quadrature, with 90 degrees going from C to R and R to L,
    you see that you can have the same effect with three components that
    behave as R, sL and s^2Gyrator; you've just multiplied everything by s.
    Or you can have a {1/s^2Gyrator, 1/sC, R} set. And you can expand
    your filtering horizons by having a set {1/s^2Gyrator, 1/sC, R, sL,
    s^2Gyrator} . . . that lets you implement higher order filters in
    simpler topologies (if only the gyrator were a simple passive two-lead
    part!)

    Gyrators don't seem to be used very often, but I have seen them used to
    (presumably) keep the op amp out of the direct signal path, in an
    attempt to have it contribute less distortion in the passband.

    Cheers,
    Tom
     
  8. Joel Kolstad

    Joel Kolstad Guest

    Thanks Tom, that'll certainly do it. When I said "small capactior," in my
    case I was thinking "below resonance" -- as you say, when you're above
    resonance the reverse is true. I should have thought it through some more
    before posting.

    ---Joel
     
  9. Joel Kolstad

    Joel Kolstad Guest

    Hmm... in fact... ignore that bit about above vs. below resonance too -- turns
    out I dropped a minus sign in my original calculations. :-(
     
  10. Don Bowey

    Don Bowey Guest

     
  11. Jim Thompson

    Jim Thompson Guest

     
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