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Determine Posititive Feedback Gain in an Oscillator

  1. Apr 4, 2010 #1
    NOTE- Images are thumbnails, click to enlarge
    1. The problem statement, all variables and given/known data
    Show that the positive feedback gain expression for the circuit below is
    v2/v0 = 1/[3 + j(wL/R - R/WL)]

    (anything in red I added to the original problem)
    th_circuit.jpg

    2. Relevant equations
    (above)


    3. The attempt at a solution
    Along with the below calculations, I also attempted to combine the components but that didn't work either. I combined R and L2 in series, those in parallel with the other R and then in series with L1 (let's call all of that Zt). I then said (V2-V0)/Zt = 0 and proceeded to solve for V2/V0 but did not get the right answer. I thought that that should work since this is an ideal op-amp and no current is flowing between L2 and R, but alas I did not get the correct answer. Any guidance?

    th_calcs.jpg
     
  2. jcsd
  3. Apr 5, 2010 #2

    The Electrician

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    Gold Member

    One of your equations is (Vo-Vx)/jwL=0. This would mean that Vo=Vx which can't be true if you are applying a signal to Vo and then calculating the voltage resulting at V2. You have to imagine applying a test current signal (of unit value, say) at Vo, and then calculating the result at V2, and therefore Vx can't be equal to Vo. You would need to set (Vo-Vx)/jwL=1; from this you can calculate the voltage at V2 (and subsequently at Vo) from knowledge of the input impedance at V2.

    Another way to do it would be to calculate the gain from Vo to V2 as a cascade of two voltage dividers.
     
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