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Thevenin Equivalent of AC RLC Circuit w/ Dependent Voltage

  1. Jun 15, 2016 #1
    1. The problem statement, all variables and given/known data
    Diagram.png
    Find Vth and Zth.
    frequency = 2kHz

    2. Relevant equations
    w = 2 * (pi) * f
    ZL = j w L
    ZC = -j / (w * C)
    V = I*Z
    ZR = R

    3. The attempt at a solution
    At first I tried using nodal analysis which I receive the value V = 0 v. I believe this is because this circuit only has dependent voltage sources. Therefore, the Vth is just 0 v.

    10mH ---> j125.7
    1uF ---> -j79.6
    100 ohms ---> 100
    w = 2*(pi)*2000 = 12566.37

    Essentially, I am stuck. I have some theories as to what I can do though. I remember from DC circuit analysis that we can either add a 1v or a 1A (the number is arbitrary) source between terminals a and b, but I'm not sure what to do beyond that. Could I add a 1A (i.e. 1*cos(wt)) between the terminals, and then do nodal analysis? Then after that, would I take that voltage and divide it by the 1A (1cos(wt)) AC source to get the Zth? And as I mentioned above, wouldn't the thevenin equivalent of this circuit not even have a Vth since there's no independent sources?
     
  2. jcsd
  3. Jun 15, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    A zero value for the Thevenin voltage is reasonable; zero is a perfectly good real number.

    For the impedance, your suggested approach has merit: add a generic 2 kHz current source ##I## at the load terminals. Use nodal analysis again leaving that current source as a variable and solve for ##v_{ab}##. Note that the desired impedance is ##v_{ab} / I##.
     
  4. Jun 15, 2016 #3
    I tried it out and it worked! Thanks for your help! All this circuit stuff is starting to really make sense now!
     
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