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Second Order Op Amp circuit: Find Vo for t > 0

  1. Apr 3, 2007 #1
    1. The problem statement, all variables and given/known data

    In the circuit below, determine [itex]v_o(t)[/itex] for t > 0. Let [itex]V_{IN}\,=\,u(t)\,V[/itex], [itex]R_!\,=\,R_2\,=\,10\,k\Omega[/itex], [itex]C_1\,=\,C_2\,=\,100\,\muF[/itex].

    [​IMG]



    2. Relevant equations

    [tex]i_c\,=\,C\,\frac{dv_c}{dt}[/tex]



    3. The attempt at a solution


    Add some node voltages:

    [​IMG]

    KCL @ [itex]V_1[/itex]:

    [tex]\frac{V_{IN}\,-\,V_1}{R_1}\,=\,C_2\,\frac{dv_2}{dt}\,+\,C_1\,\frac{dv_1}{dt}[/tex]

    KCL @ [itex]V_2[/itex]:

    [tex]C_2\,\frac{dv_2}{dt}\,=\,\frac{V_2\,-\,V_o}{R_2}[/tex]

    Substituting for [itex]\frac{dv_2}{dt}[/itex] in the KCL @ [itex]V_1[/itex] equation:

    [tex]V_o\,=\,-R_2C_2\left(\frac{V_{IN}\,-\,V_1}{R_1C_2}\,-\,\frac{C_1}{C_2}\,\frac{dv_1}{dt}\right)[/tex]

    Now what do I do to solve?
     
  2. jcsd
  3. Apr 4, 2007 #2

    berkeman

    User Avatar

    Staff: Mentor

    Set V2 and dV2/dt = 0. Does that help?
     
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