What is the Transfer Function H(s) for the Given Circuit?

[sinned4789]

Homework Statement

find the transfer function H(s)
[PLAIN]http://img192.imageshack.us/img192/4204/asdwoe.jpg

Homework Equations

H(s) = Vout/Vin
done in the frequency domain so: C1 and C2 turns into 1/sC
where C1 = C2 = .1F
and R1 = R2 = 20

The Attempt at a Solution

to find the transfer function, i have to apply an impulse source. therefore, Vin is just 1V.
my attempt at this by using node voltage method:
(Vx is the node that connects R1, R2, and C2)

(Vx -1)/20 + Vx/(10/s) + (Vx - Vout)/20 = 0

i am stuck with two unknowns and 1 equation. :[

 

[sinned4789]

bump, anyone?

 

[The Electrician]

Homework Statement

find the transfer function H(s)
[PLAIN]http://img192.imageshack.us/img192/4204/asdwoe.jpg

Homework Equations

H(s) = Vout/Vin
done in the frequency domain so: C1 and C2 turns into 1/sC
where C1 = C2 = .1F
and R1 = R2 = 20

The Attempt at a Solution

to find the transfer function, i have to apply an impulse source. therefore, Vin is just 1V.
my attempt at this by using node voltage method:
(Vx is the node that connects R1, R2, and C2)

(Vx -1)/20 + Vx/(10/s) + (Vx - Vout)/20 = 0

i am stuck with two unknowns and 1 equation. :[

Write another equation, then you'll have 2 equations and 2 unknowns. I would write one at the output node.

 

[CEL]

The difference between the voltages of the output and input nodes is the voltage across C1 and also the sum of the voltages across R1 and R2.

 

[DeeNos]

The transfer function can be found by taking the Laplace transform of the circuit equations. In this case, we have:

Vout/R2 + Vout/sC2 = Vin/R1 + Vx/R1 - Vx/R2

We also know that Vx = Vout, so we can substitute that in:

Vout/R2 + Vout/sC2 = Vin/R1 + Vout/R1 - Vout/R2

Now we can solve for Vout/Vin, which is the transfer function H(s):

H(s) = Vout/Vin = (Vin/R1 + Vout/R1 - Vout/R2)/(Vout/R2 + Vout/sC2)

Simplifying this expression, we get:

H(s) = Vout/Vin = (1/R1 + 1/sC2)/(1/R1 + 1/R2 + 1/sC2)

Substituting the given values for R1, R2, and C2, we get:

H(s) = Vout/Vin = (1/20 + 1/s0.1)/(1/20 + 1/20 + 1/s0.1)

Simplifying further, we get the transfer function:

H(s) = Vout/Vin = (10 + 0.1s)/(11 + 0.1s)