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

1. Apr 3, 2007

### VinnyCee

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 [Broken]

2. Relevant equations

$$i_c\,=\,C\,\frac{dv_c}{dt}$$

3. The attempt at a solution

http://img413.imageshack.us/img413/2935/problem867part2vn2.jpg [Broken]

KCL @ $V_1$:

$$\frac{V_{IN}\,-\,V_1}{R_1}\,=\,C_2\,\frac{dv_2}{dt}\,+\,C_1\,\frac{dv_1}{dt}$$

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?

Last edited by a moderator: May 2, 2017
2. Apr 4, 2007

### Staff: Mentor

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