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Node Analysis problem

  1. Mar 18, 2006 #1
    Hi, I was searching google for answers about my problem and stumbled upon this forum. So I'll post my problem here and hope that some friendly soul can help me :)

    I need to do a node-analysis of the circuit that I've attached here. The opamp is ideal so Ri=inf and R0=0 and A=inf. I end up with 3 equations for the nodes v1,v2:
    eq1: (1/(1/jwC1)+1/R1)v1 = Uin/(1/jwC1)
    eq2: (1/R3 + 1/(1/jwC2))v2 = Av1/R3
    eq3: Uout=Av2

    I am pretty sure I've done wrong in the node analysis, but I am unable to find out what I've done wrong (or right ;)). The equations I get later by solving the equationsystems doesn't add up. Any input or help on this problem is greatly appreciated!
     

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    Last edited: Mar 18, 2006
  2. jcsd
  3. Mar 18, 2006 #2

    SGT

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    You did it wrong. Equation 1 should be:
    [tex]U_{in}\dot(j\omega C_1 + \frac{1}{R_1}) = V_1\dot\frac{1}{R_1})[/tex]
    or, in simpler form:
    [tex]V_1 = U_in\dot\frac{R_1}{R_1+\frac{1}{j\omegaC_1}[/tex]
    Since the amplifier is ideal, there is a virtual short circuit between the + and - terminals and the output voltage is [tex]V_1[/tex]
    Then equation 2 will be:
    [tex]V_2 = V_1\dot\frac{\frac{1}{j\omegaC_2}}{R_2+\frac{1}{j\omegaC_2}[/tex]
    and
    [tex]U_{out} = V_2[/tex]
     
  4. Mar 18, 2006 #3

    SGT

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    You did it wrong. Equation 1 should be:
    [tex]U_{in}\dot(j\omega C_1 + \frac{1}{R_1}) = V_1\dot\frac{1}{R_1}[/tex]
    or, in simpler form:
    [tex]V_1 = U_in\dot\frac{R_1}{R_1+\frac{1}{j\omegaC_1}}[/tex]
    Since the amplifier is ideal, there is a virtual short circuit between the + and - terminals and the output voltage is [tex]V_1[/tex]
    Then equation 2 will be:
    [tex]V_2 = V_1\dot\frac{\frac{1}{j\omegaC_2}}{R_2+\frac{1}{j\omegaC_2}}[/tex]
    and
    [tex]U_{out} = V_2[/tex]

    Reposted because I was not able to edit
     
  5. Mar 18, 2006 #4

    SGT

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    Still unable to write correctly the equations in LaTex I will write it in normal text.
    Eq.1: V1 = Uin [R1/(R1+1/jwC1)]
    Eq.2: V2 = V1 [(1/jwC2)/(R2+1/jwC2)]
     
  6. Mar 18, 2006 #5
    Shouldnt it be R3 instead of R2 in your equations?
     
    Last edited: Mar 18, 2006
  7. Mar 18, 2006 #6

    SGT

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    Yes, my mistake.
     
  8. Mar 18, 2006 #7
    oky, then it makes more sense :P

    thanks for the help, I'll sit down with the new equations and see if I can get a result out of it :)
     
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