Transfer functions?

Discussion in 'General Electronics Chat' started by Valce, Sep 27, 2008.

  1. Valce

    Thread Starter New Member

    Sep 27, 2008
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    0
    How do I find the transfer function of an STC circuit?

    For example, suppose I am given the circuit (attached), and want to find the transfer function of OUT relative to input V1.

    My answer would be to use a voltage divider of (R1||C1) in parallel with C2, this gets me: s/[s+1/[(C1+C2)R]]

    But this answer is off by a factor of C2/(C1+C2) - what am I doing wrong?

    Thanks a ton!

    -V
     
    Last edited: Sep 27, 2008
  2. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    Valce,

    Use the potientiometer method.

    R1||C1 ===> (R1/sC1)/(R1+1/sC1) = R1/(sR1C1+1)

    R1||C1/(R1||C1+C2) ===> sR1C2/(sR1C2+sR1C1+1)

    Ratch
     
  3. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    You have the denominator of your answer correct.

    Can you post your effort so that we can take a look to see if we can determine where you got off track?

    hgmjr
     
  4. Valce

    Thread Starter New Member

    Sep 27, 2008
    4
    0
    I get the right answer for R1||C1... but it seems I'm not getting the right total impedance for the circuit...?

    I'm doing...

    (R1||C1)+C2 --> R1/(sR1C1+1) + 1/sC2

    ... which doesn't seem to get me the right answer at all :(

    -V
     
  5. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    All you are computing using your technique is the impedance across the input voltage.

    You need to be calculating the attenuation.

    hgmjr
     
  6. Valce

    Thread Starter New Member

    Sep 27, 2008
    4
    0
    The attenuation is R1||C1/(Total impedance) right?

    With the value of total impedance that I get, I don't seem to get the right attenuation :(

    Sorry for my continued ignorance :(
     
  7. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    What I mean by attenuation is outlined below.

    \frac{Z_{o}(s)}{Z_{i}(s)}=\frac{Z_2}{Z_1+Z_2}

    Where:

    Z_{1}=X_{C2}=\frac{1}{sC_{2}}

    Z_{2}=R_{1}||X_{C1}


    hgmjr
     
  8. Valce

    Thread Starter New Member

    Sep 27, 2008
    4
    0
    Thank you!!

    My algebra is absolutely horrible... Thanks for putting up with it :)

    Much love,
    -V
     
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