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Simple transfer function - algebra giving me problems

  1. Aug 4, 2007 #1
    1. The problem statement, all variables and given/known data

    Find a transfer function: [tex]\frac{V_o(s)}{V_i(s)} = \frac{Z_2 (s)}{-Z_1(s)}[/tex]

    2. Relevant equations

    [tex]Z_1(s) = R_1 + \frac{1}{C_1s}[/tex]
    [tex]Z_2(s) = \frac {\frac{R_2}{C_2s}}{R_2 + \frac{1}{C_2s}}[/tex]

    final solution should be:
    [tex]G(s) = \frac{V_o(s)}{V_i(s)} = \frac{C_1C_2R_1R_2s^2 + (C_2R_2 + C_1R_2 + C_1R_1)s + 1}{C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1}[/tex]

    3. The attempt at a solution

    - Give me a second i'm still typing up the latex commands

    [tex]G(s) = \frac{V_o(s)}{V_i(s)}= \frac{-\frac {\frac{R_2}{C_2s}}{R_2 + \frac{1}{C_2s}}}{R_1 + \frac{1}{C_1s}}[/tex]

    [tex] = -\frac {\frac{R_2}{C_2s}}{(R_2 + \frac{1}{C_2s})(R_1 + \frac{1}{C_1s}) }[/tex]

    [tex] = \frac{-R_2}{(C_2s)(R_2 + \frac{1}{C_2s})(R_1 + \frac{1}{C_1s})} [/tex]

    [tex]= \frac{-R_2(C_1C_2s)}{(C_2s)(C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1)}[/tex]

    [tex]=\frac{-R_2(C_1)}{(C_1C_2R_1R_2s^2 + (C_1R_1 + C_2R_2)s + 1)}[/tex]
    which is no where near the solution.
    Last edited: Aug 4, 2007
  2. jcsd
  3. Aug 4, 2007 #2
    I misread the problem - apologies - the transfer function for a Non inverting amplifer is in the form

    [tex]\frac{Z_1(s) + Z_2(s)}{Z_1(s)}[/tex] - now i get the right answer
  4. Aug 4, 2007 #3
    hehe good. Cause I quickly did it, and definitely did not get the "answer".

    I feel bad for you typing all of that up in Latex. Probably took a few ;)
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