• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • Thread starter VinnyCee
  • Start date
  • #1
489
0

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 [Broken]



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 [Broken]

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?
 
Last edited by a moderator:

Answers and Replies

  • #2
berkeman
Mentor
56,811
6,776
Set V2 and dV2/dt = 0. Does that help?
 

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

  • Last Post
Replies
2
Views
933
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
6
Views
535
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
7
Views
534
  • Last Post
Replies
6
Views
3K
Replies
2
Views
2K
Top