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Homework Statement
Find Vo(s)/Vi(s) for the OPAMP circuit in the attachements
Homework Equations
V = iR, Kirchoff current law.
1/sC = Laplace transform of capacitor impedance.
The Attempt at a Solution
Make the voltage at the node = v'.
ir1 = (vi  v')/r1
ir2 = v'/r2
iz = (v'vo)/z
z = (1/sC1)+r3
ic2 = (v'v)/(1/sC2)
Op amp inverting pin does not draw current and due to the virtual ground v=0V
Therefore,
ir1 = ir2 + ic2 + iz
[tex]\frac{viv'}{r1}[/tex] = [tex]\frac{v'}{r2}[/tex] + sC2v' + [tex]\frac{v'vo}{(1/sC1)+r3}[/tex]
Ideally I would do the algebra and solve for the transfer fuction by setting vo/vi to whatever what came out on the other side, what I am having trouble with is canceling out v', which I attempted to write as a multiple of either vi or vo via a voltage divider.
My attempts were as follows:
v' as a function of vi 
v' = [tex]\frac{R2vi}{R1+R2}[/tex]
or v' as a function of vo 
v' = [tex]\frac{R2vo}{(1/sC2)+R3 + R2}[/tex]
I'm just wondering which way of thinking in terms of v' is the right way to go, I keep on getting all of these horribly long equations that just don't seem right so I decided to ask on here, any help is greatly appreciated.
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