- #1
VinnyCee
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Homework Statement
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].
http://img249.imageshack.us/img249/3840/problem867cg5.jpg
Homework Equations
[tex]i_c\,=\,C\,\frac{dv_c}{dt}[/tex]
The Attempt at a Solution
Add some node voltages:
http://img413.imageshack.us/img413/2935/problem867part2vn2.jpg
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?
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