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Barkhausen must be wrong.

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

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  1. The Phantom

    The Phantom Guest

    At this site:

    there is a schematic titled "A Practical Twin-T Oscillator".

    In the text under the schematic we find:

    "Now hold on a minute: an emitter follower has no voltage gain and surely
    you've been taught that an R-C oscillator must have voltage gain? Well this
    one works and has no voltage gain (of course it does have current gain)."

    The schematic does show two emitter followers closing the loop. One would
    think this couldn't work, but the poster says it does.

    Is Barkhausen wrong?
  2. MooseFET

    MooseFET Guest

    Look again at the schematic.
  3. The Phantom

    The Phantom Guest

    I've looked at it several times. What do you see there that's relevant?
  4. The signal input to the right transistor is not from an
    emitter follower.
  5. John Larkin

    John Larkin Guest

    You can make an oscillator with just an emitter follower and some
    r-c's... I did it accidentally ca 1975, and was surprised. The
    impedances are such that you usually need a darlington to pull it off.

    There are a couple of simple 2-terminal-plus-ground RC networks that
    can have an AC voltage gain above 1.

  6. The Phantom

    The Phantom Guest

    I'm not sure what you mean. Are you sure you're looking at the right
    schematic, the 5th one down? The one titled "A Practical Twin-T
  7. The Phantom

    The Phantom Guest

    But he says this one has no voltage gain. So how does this work?
  8. John Larkin

    John Larkin Guest

    I think he meant that the transistors have no voltage gain, and maybe
    he's assuming that an RC network can't have gain. Dunno.

  9. Jim Thompson

    Jim Thompson Guest

    POWER gain IS the requirement.

    ...Jim Thompson
  10. Sorry, I was looking at the second schematic.

    The unusual part of this twin T is that the component values
    are not the usual C and 2*C, 2*R and R. A ratio of about 5
    is used, instead. And the way it is connected, instead of
    the usual notch response, it has a broad bandpass filter
    response with a peak gain of about 1.089 at about 130 Hz,
    with the loading effect of the 1n cap but not counting the

    So it is possible to get a little voltage gain from an RC
  11. Simulating just the twin T, unloaded, the highest possible
    gain seems to occur close to an R and C ratio of about 4.75,
    and that voltage gain is about 1.094.
  12. The Phantom

    The Phantom Guest

    You get an A+. My mathematical assistant says the max gain of 1.08893
    occurs with a ratio of 4.83152 at a frequency of 129.128034 Hz
    See: "Synthesis of Passive RC Networks with Gains Greater than Unity",
    Herman Epstein, Proceedings of the IRE, July, 1951, p. 833.
  13. The Phantom

    The Phantom Guest

    My assistant says that under these circumstances the maximum gain of
    1.09384 occurs at a frequency of 132.629114 Hz with a ratio of 4.82843.
  14. I don't have access to this paper.
  15. Joel Kolstad

    Joel Kolstad Guest

    In Vorperian's book, "Fast Analytical Techniques for Electrical and Electronic
    Circuits" there's a 7-page discussion of it as well (under the heading, "RC
    Filters With Gain" in the chapter, "Passive Filters: Where Inductors and
    Transformers Still Get Respect," which I rather like :) ). That's probably
    short enough to fall under "fair use" if you'd like me to scan and post it.

  16. Rich Grise

    Rich Grise Guest

    I looked at it as, the Twin-T, because of the component values, is
    an impedance transformer. It has "voltage gain" in that the output
    volts are greater than the input volts; but it has a "current loss"
    which is why you need the darlington - for the light loading on the
    output end.

    The thing is, I don't know if an impedance transformer counts as
    "gain" - does an ordinary step-up transformer have "gain"?

  17. The Phantom

    The Phantom Guest

    You will very shortly.
  18. The Phantom

    The Phantom Guest

    Post away!
  19. The Phantom

    The Phantom Guest

    If one's definition of "voltage gain" is "ABS(Vo/Vi) > 1", then, yes.
    This is the sense in which Epstein used the word "gain". See my responses
    to John Popelish.

    And, of course, one could get even more particular and speak of "loaded
    gain" and "unloaded gain".

    I imagine that an oscillator could be built which used a small transformer
    on the output of a network giving phase shift, followed by an emitter (or
    source) follower for the necessary "current gain". The phase shifting
    network could even be an all-pass network.
  20. Tim Williams

    Tim Williams Guest

    Take a (triode, pentode, transistor, FET) and put the common
    (cathode/emitter/source) to the CT on a tapped tank coil. Ground one end
    of the coil. Cap couple the other end to the input (grid/gate/base),
    biasing as appropriate. Connect supply voltage to other terminal

    Voila. ;)

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