VinnyCee
Apr3-07, 10:13 PM
1. The problem statement, all variables and given/known data
In the circuit below, determine v_o(t) for t > 0. Let V_{IN}\,=\,u(t)\,V, R_!\,=\,R_2\,=\,10\,k\Omega, C_1\,=\,C_2\,=\,100\,\muF.
http://img249.imageshack.us/img249/3840/problem867cg5.jpg
2. Relevant equations
i_c\,=\,C\,\frac{dv_c}{dt}
3. The attempt at a solution
Add some node voltages:
http://img413.imageshack.us/img413/2935/problem867part2vn2.jpg
KCL @ V_1:
\frac{V_{IN}\,-\,V_1}{R_1}\,=\,C_2\,\frac{dv_2}{dt}\,+\,C_1\,\fra c{dv_1}{dt}
KCL @ V_2:
C_2\,\frac{dv_2}{dt}\,=\,\frac{V_2\,-\,V_o}{R_2}
Substituting for \frac{dv_2}{dt} in the KCL @ V_1 equation:
V_o\,=\,-R_2C_2\left(\frac{V_{IN}\,-\,V_1}{R_1C_2}\,-\,\frac{C_1}{C_2}\,\frac{dv_1}{dt}\right)
Now what do I do to solve?
In the circuit below, determine v_o(t) for t > 0. Let V_{IN}\,=\,u(t)\,V, R_!\,=\,R_2\,=\,10\,k\Omega, C_1\,=\,C_2\,=\,100\,\muF.
http://img249.imageshack.us/img249/3840/problem867cg5.jpg
2. Relevant equations
i_c\,=\,C\,\frac{dv_c}{dt}
3. The attempt at a solution
Add some node voltages:
http://img413.imageshack.us/img413/2935/problem867part2vn2.jpg
KCL @ V_1:
\frac{V_{IN}\,-\,V_1}{R_1}\,=\,C_2\,\frac{dv_2}{dt}\,+\,C_1\,\fra c{dv_1}{dt}
KCL @ V_2:
C_2\,\frac{dv_2}{dt}\,=\,\frac{V_2\,-\,V_o}{R_2}
Substituting for \frac{dv_2}{dt} in the KCL @ V_1 equation:
V_o\,=\,-R_2C_2\left(\frac{V_{IN}\,-\,V_1}{R_1C_2}\,-\,\frac{C_1}{C_2}\,\frac{dv_1}{dt}\right)
Now what do I do to solve?