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RLC Circuit Transfer Function (Vout NOT referencing ground; want to check solution)

  1. Nov 19, 2011 #1
    Hi all,

    New to the forums here, but I've got a question for you guys:

    I've ran into this rather peculiar circuit. In all the circuits I've seen (as far as transfer functions go), Vout has always referenced ground (e.g. one node of Vout is ground); in this one, however Vout is across an inductor. I've attached the circuit diagram. (excuse the crudeness of the circuit diagram...quickly whipped it up on Paint :rolleyes:).


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

    Find the transfer function Vout(s)/Vi(s) of the circuit.

    R=1Ω, L1=2H, L2=3H, C=0.1F

    2. Relevant equations

    Zr = R; Zl=Ls; Zc=1/Cs; KVL; KCL, etc.

    3. The attempt at a solution

    Since Vout wasn't referencing ground, I figured that I needed to use the mesh-current method to get equations for Vi and Vout for each loop. After some rather nasty symbolic matrix algebra, I got expressions for I1 and I2 (loop currents), plugged each of those back into the mesh-current equations, and obtained:

    [itex]H(s)=\frac{V_{out}}{V_{i}}=\frac{3s^2}{6s^3+5s^2+20s+10}[/itex]

    Is this correct? Also another question: is there a simpler way to do this? Forgive my idiocy but I might be missing something terribly obvious...

    It's been a while since this textbook stuff! I tinker around quite a bit with circuits, but I'm no EE...I guess that's what I get for being mechanical :biggrin:

    Thanks everyone!

    -Leo.
     

    Attached Files:

    Last edited: Nov 19, 2011
  2. jcsd
  3. Nov 19, 2011 #2

    gneill

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    Staff: Mentor

    Re: RLC Circuit Transfer Function (Vout NOT referencing ground; want to check solutio

    Your solution looks good. Your method is fine too.
     
  4. Nov 20, 2011 #3

    The Electrician

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    Gold Member

    Re: RLC Circuit Transfer Function (Vout NOT referencing ground; want to check solutio

    Nodal analysis also works well for these transfer function problems. See the image.
     

    Attached Files:

  5. Nov 21, 2011 #4
    Re: RLC Circuit Transfer Function (Vout NOT referencing ground; want to check solutio

    Sounds good! Thanks a lot guys.

    -Leo.
     
  6. Nov 21, 2011 #5

    rude man

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    Re: RLC Circuit Transfer Function (Vout NOT referencing ground; want to check solutio

    I too can corroborate your answer as being correct. Happy days!
     
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