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Homework Help: Wien Bridge Frequency Proof

  1. Apr 1, 2008 #1
    [SOLVED] Wien Bridge Frequency Proof

    1. The problem statement, all variables and given/known data

    The ac bridge circuit shown is called a Wien bridge (also Wein bridge).
    Wien Bridge.png

    Show that when the bridge is balanced, frequency is found by the Eqn attached. Eqn.png

    2. Relevant equations


    Using the number from each branch as a guide, the general solution to AC bridges is Z4 = (Z3/Z1)*Z2

    3. The attempt at a solution

    I keep trying to solve for impedences to plug into the second equation provided, but my j values do not cancel and the equation left is rather messy (R2R4C2C4*w^2 +jw(RzR4C2 -R2C2 -R4C4) +1 = 0.

    For my impedence values I have been using
    Z1 = R1
    Z2 = R2 -j/wC2
    Z3 = R3
    Z4 = (R4/jwC4)/(R4 +jwC4)

    Any help with this would be greatly appreciated.
  2. jcsd
  3. Apr 1, 2008 #2
    I think [tex] Z_4 = \frac {-jR_4} {\omega C_4 (R_4 - \frac{j}{\omega C_4})} [/tex]

    Both the real and the imaginary parts of Z4 = (Z3/Z1)*Z2 must be 0
  4. Apr 2, 2008 #3
    Actually, I think our Z4 values are the same, since -j = 1/j. But thank you! I managed to figure it out after you got me thinking about real and imaginary parts.

    It's fairly simple, actually: I just had to equate the real parts from my equation so that R2R4C2C4*w^2 + 1 = 0 (and then I took absolute value).
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