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When to transform the current source to voltage source?

  1. Apr 14, 2013 #1
    1. The problem statement, all variables and given/known data
    BBPYCZn.jpg


    2. Relevant equations



    3. The attempt at a solution

    First, I found all the impedance values.
    (starting from the left)
    Z1 = 1 / (j * 16E5 * 15E-9) = -j41.67
    Z2 = 80
    Z3 = 30
    Z4 = j * 16E5 * 60E-6 = j96

    I then combined Z1 and Z2.
    Z1 || Z2 = (-j41.67 * 80) / (80 - j41.67) = 17.07 - j32.78

    Now this is where I'm stuck. I'm wondering if I should have transformed the current source, Ig, before combining Z1 and Z2 or if I should transform it after combining Z1 and Z2. I'm not really sure when to do a source transformation.

    If you could explain your reasoning I would greatly appreciate it.
     
  2. jcsd
  3. Apr 14, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    There are several possible approaches. Finding the individual component impedances, as you've done, is a good start. To find the output voltage you could apply nodal analysis and solve for the voltage at the Vo node (two node equations). Or you could transform the current source along with the 80Ω resistor, 15nF capacitor, and 30Ω resistor into a Thevenin equivalent, then form a voltage divider with the 60μH inductor to solve for Vo. Another method would be to use mesh analysis (three meshes) to find the current through the inductor, hence the voltage across it.

    If you want to go the source-transformation route as you've started, then use your Z1||Z2 along with the given current source to find the equivalent voltage source and series impedance. Then proceed to work your way to the Vo terminals, absorbing the components into the model, until you're left with a single voltage source and series impedance.
     
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