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AC Equivalent Circuits

  1. Oct 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Determine the T-network equivalent of the ∏ (Pi) network shown in the Figure?

    2. Relevant equations

    I started working on this question and dont know if I am heading in the right direction.

    The impedances of the T network (Z1, Z2, Z3) can be found from the impedances of the equivalent pi network with the following equations:

    Z1= ( Za x Zb ) / ( Za+ Zb + Zc )
    Z2= ( Zb x Zc ) / ( Za+ Zb +Zc )
    Z3 = ( Za x ZB ) / ( Za + Zb + Zc )

    And then we can use our details:
    C1 = Za
    L1 = Zc
    C2 = Zb

    Z1 = (-j20 x j10 ) / (-j20+j10-j20)= -200j^2 / -30j = j6.67
    Z2 = (-j20 x j10 ) / ( -j20+j10-j20) = -200j^2 / -30j = j6.67
    Z3 = ((-j20 ) x (-20j )) / (-20j+ 10j -20j) = 400j^2 / -j30 = -j13.333

    and now we come out with equivalent T -network. At least I hope!!!

    3. The attempt at a solution
     

    Attached Files:

    Last edited: Oct 7, 2013
  2. jcsd
  3. Oct 7, 2013 #2
    Yes i know, I had to edit my post and add my attempt!
     
    Last edited: Oct 7, 2013
  4. Oct 7, 2013 #3

    gneill

    User Avatar

    Staff: Mentor

    No worries. Next time perhaps, leave a message in the post indicating that it's "in progress". That'll help us to avoid jumping the gun.

    The approach you've shown looks fine. It's a basic Δ-Y transformation and appears to be correct.
     
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