Transfer function, Laplace Transform

AI Thread Summary
The discussion revolves around finding the transfer function V2(s)/V1(s) in the Laplace transform domain for a given circuit. The initial attempt at the solution involved applying Kirchhoff's Current Law (KCL) and resulted in an incorrect expression. After further analysis, it was clarified that the voltage divider formula applies, leading to the correct formulation involving the impedance of the resistor-capacitor pair. A minor oversight regarding a sign in the calculations was identified, confirming the correctness of the final answer. The conversation highlights the importance of careful algebraic manipulation in circuit analysis.
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Homework Statement



[PLAIN]http://img340.imageshack.us/img340/8508/circuit.png

Find V2(s)/V1(s) (Laplace transform domain)

Homework Equations


KCL, capacitor equation.

The Attempt at a Solution


\frac {-V_2}{R} + \frac {V_1-V_2}{R} + C \frac {d(V_1-V_2)}{dt}=0
But in Laplace domain it follows that
\frac {V_2 (s)}{V_1 (s)} = \frac {sRC+1}{sRC}
and that is apparently incorrect.
Any thoughts on what I did wrong, and what I should do?

Thanks in advance
 
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It's a voltage divider. Let z be the impedance of the resistor-capacitor parallel pair. Then

v2/v1 = R/(R + z)

But z = (R * 1/sC)/(R + 1/sC) = R/(1 + sRC)

Therefore,

v2/v1 = (1 + sRC)/(2 + sRC)
 
Sorry, I was actually correct. Forgot about a minus sign in one place. Anyway, thanks for the answer. At least I know that now I have the correct answer.
Cheers.
 

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