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Barkhausen must be wrong.

Discussion in 'Electronic Design' started by The Phantom, Oct 10, 2007.

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  1. That's what I always thought. One doesn't, per se, care about "gain"
    from the negative resistance viewpoint either.
  2. John Larkin

    John Larkin Guest

    Presumably one could cascade such circuits.

  3. The Phantom

    The Phantom Guest

    One could certainly cascade them (I'm assuming you mean without an
    intermediate buffer), but would you expect the cascade to have voltage
    gain? Care to guess what the result will be with the network we've been
    discussing? I'll run the analysis and report the result.
  4. The Phantom

    The Phantom Guest

    I think "power gain" is necessary, but not sufficient, to give oscillation.
    If the RC network in the example under discussion is replaced with one
    which doesn't have "voltage gain", then in spite of the substantial power
    gain in the cascaded emitter followers, there will be no oscillation.
  5. John Larkin

    John Larkin Guest

    Certainly the voltage gains would multiply, if the component values
    were right. But the impedances would get crazy fast.

  6. The Phantom

    The Phantom Guest

    When you said "such circuits", I assumed you meant the very circuit we've
    been discussing, the one in the oscillator on the referenced web page. I
    didn't realize you intended "such circuits" to mean something like "similar
    circuits, but with varying impedance levels". With that meaning, I suppose
    that cascading might give even more gain. But, Epstein showed in his paper
    that the maximum gain that a passive network can have is 2. So, if one
    cascaded networks with impedance levels going up by an order of magnitude
    or so ad infinitum, one would think that the voltage gain would be
    unlimited. What would cause the voltage gain to remain below 2?
  7. John Larkin

    John Larkin Guest

    Not having seen the paper, I can't say. Possibly a gain of 2 requires
    an infinite output impedance, or something like that, which prevents
    unlimited cascading.

    Can anybody post the paper?

  8. john jardine

    john jardine Guest

    Greater than 2 seems certainly doable. Did Epstein add some of those
    weasely "yes but's" or "assuming ... "?.
  9. John Larkin

    John Larkin Guest

    You'd think that if you can get a stage gain of, say, 1.1 with maybe a
    100:1 loading ratio, then 10 stages would get you above 2. Spice could
    do that, but the real world probably can't.

    100^10 is a bunch of ohms.

  10. The Phantom

    The Phantom Guest

    On Wed, 10 Oct 2007 17:24:16 -0700, John Larkin
    I'll post it over on ABSE
  11. Robert Baer

    Robert Baer Guest

    Could have fooled me; the two look exactly like a darlington emitter
  12. john jardine

    john jardine Guest

    I'm up at 1e11!.
    For fun I'll put a sim pic on A.B.S.E.
  13. Fred Bloggs

    Fred Bloggs Guest

    Get real. I don't recall that the basic criterion for feedback
    oscillation is called Barkhausen's Conjecture, it is called the
    Barkhausen rule or something dumb like that.
  14. John Fields

    John Fields Guest

  15. Phil Hobbs

    Phil Hobbs Guest

    This is very well known. It's not difficult to make high order PLLs (for
    example) that behave pretty well. Third order PLLs are especially
    useful for situations involving constant frequency drift rates, e.g.
    accelerating spacecraft, because third order loops have zero phase error
    due to a linear rate of change of frequency.

    You do have to make it act like a second-order loop during startup and
    big transients, or it's liable to exhibit nonlinear oscillations.


    Phil Hobbs
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