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Barkhausen criterion and oscillation

Discussion in 'Electronic Basics' started by Manu Varkey, May 20, 2007.

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  1. Manu Varkey

    Manu Varkey Guest

    The usual explanation of a feedback oscillator goes like this. ""We have an
    Amplifier 'A(w)', a feedback circuit 'B(w)'. An initial input v=Ke(jwt)
    produses an output A(w)*B(w)*Ke(jwt) which in turn produces an output
    (AB)^2 * Ke(jwt) ...... => If the signal is to be sustained |AB|=1 and
    arg(A)+arg(B)=2*pi then each delayed echo or cycle of fluctuation
    will ‘tack itself onto the tail’ of the previous fluctuation with the same
    sinusoidal phase leading to oscillation."" I really don't get it . An
    Amplifier produces the output based on instantaneous value of input signal
    and there is no mechanism which stores an AC signal. Then how is the
    oscillation sustained if the initial disturbance is removed ? Please
    correct me if I am wrong.
     
  2. John Larkin

    John Larkin Guest

    Any real amplifier has time lags of various forms, the simplest being
    the limits of the speed of light through the amplifier and whatever
    path closes the feedback loop. Very high-frequency oscillators are
    dominated by this lag. Slower amplifiers have internal capacitive and
    inductive elements that slow them down, add phase shift, and
    effectively store information within the amp.

    The A(w) transfer function would be dimensionless (like '3' or some
    such) for an ideal, zero-delay, infinite bandwidth amp, but it never
    really is, except maybe in Spice.

    You can still build an oscillator from an ideal zero-delay amp, so
    long as the B(w) transfer function keeps things happy. If you connect
    the input of a very fast amplifier to its own output through a long
    hank of coaxial cable (the cable providing a nice time delay), that
    will oscillate too. The information storage is then inside the length
    of the cable.

    John
     
  3. Capacitence and inductanace store charge and delay the signal. Amplifiers
    are not perfect... there are also transient behaviors that you are not
    taking into account.

    Try this,

    http://www.st-andrews.ac.uk/~jcgl/Scots_Guide/RadCom/part4/page1.html
     
  4. Don Foreman

    Don Foreman Guest

    It is impossible to remove the initial disturbance. All electronic
    components, including resistors, exhibit some noise. At frequencies
    where Barkhausen's criteria are met, any signal at those frequencies
    will grow until limited. Limiting occurs when amplitude reaches a
    point where gain is reduced, often due to saturation of some
    component.
     
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