# OP AMP Transfer function

clope023

## 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

$$\frac{vi-v'}{r1}$$ = $$\frac{v'}{r2}$$ + sC2v' + $$\frac{v'-vo}{(1/sC1)+r3}$$

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' = $$\frac{R2vi}{R1+R2}$$

or v' as a function of vo -

v' = $$\frac{R2vo}{(1/sC2)+R3 + R2}$$

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.

#### Attachments

• opamp.jpg
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