(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://img252.imageshack.us/img252/410/prelab4problem1tz5.jpg [Broken]

Find transfer function of the circuit above (i.e. - [itex]\frac{V_o(s)}{V_i(s)}[/itex])

[tex]\frac{V_o(s)}{V_i(s)}\,=\,\frac{a_1}{s^2\,+\,a_2\,s\,+\,a_3}[/tex]

1) Find a1, a2, a3 in terms of R, C1 and C2

2) Given that [itex]C_1\,=\,100\,\mu\,F[/itex] and [itex]R\,=\,10\,K\Omega[/itex], find [itex]C_2[/itex] such that the system has a pair of complex conjugate poles located at [itex]-1\,\pm\,j\,\sqrt{399}[/itex].

2. Relevant equations

KCL, OP Amp rules, complex numbers.

3. The attempt at a solution

Ok, I went through a nodal analysis, I'm not going to post the steps here, but here are the results...

[tex]\frac{V_o}{V_i}\,=\,\frac{1}{C_1\,C_2\,R\,s^2\,+\,2\,C_2\,R\,s\,-\,1}[/tex]

[tex]\frac{V_o}{V_i}\,=\,\frac{\frac{1}{C_1\,C_2\,R}}{s^2\,+\,\frac{2}{C_1}\,s\,-\,\frac{1}{C_1\,C_2\,R}}[/tex]

So that means that...

[tex]a_1\,=\,\frac{1}{C_1\,C_2\,R}[/tex]

[tex]a_2\,=\,\frac{2}{C_1}[/tex]

[tex]a_3\,=\,\frac{1}{C_1\,C_2\,R}[/tex]

That's for part one, does that seem right?

For part two, we want to MAKE the roots of the following equation (denominator):

[tex]s^2\,+\,2000\,s\,+\,\frac{1}{C_2}\,=\,0[/tex]

EQUAL TO...

[tex]-1\,\pm\,j\,\sqrt{399}[/tex]

How do I make that happen?

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# Homework Help: Circuit Problem:Find transfer function and value of C2 for poles at specific location

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