# Current to Voltage Converter Circuit

1. Sep 10, 2011

### p75213

1. The problem statement, all variables and given/known data
Refer Attachment.
I can derive a) easily enough but am stuck on b). Can somebody give a hint to put me on the right track?

2. Relevant equations

3. The attempt at a solution
R3*V0/(R3+R2)=-isR1
V0/is=-R1((R3+R2)/R3)
V0/is=-R1(1+R2/R3)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

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2. Sep 10, 2011

### fleem

Hint: You know that the voltage on the neg input is zero (because there's only real negative feedback and the positive input is grounded) and you know there's no current entering the negative input (because op amp inputs are high impedance). So there are two current loops.

3. Sep 10, 2011

### p75213

I think I need more hints. I tried solving with mesh analysis.
As a result I get
i2R2=-isR1
i2=-isR1/R2
substitute i2 into V0=-R3(is-i2)
V0/is=-R3(1+R1/R2)

I cant see the forest for the trees. Or is it the other way around?

4. Sep 10, 2011

### Staff: Mentor

There are two components to the current that flows through R2 to ground: that from the O/P of the amplifier via R3, plus is via R1.

5. Sep 11, 2011

### p75213

I got it - at last.

is+(V0--isR1)/R3=(-isR1)/R2
isR3R2+R2V0+isR1R2=-isR1R3
isR3R2+isR1R2+isR1R3=-R2V0
is(R3R2+R1R2+R1R3)=-R2V0
V0/is=(R3R2+R1R2+R1R3)/-R2
V0/is=-R3-R1-R1R3/R2
V0/is=-R1(1+R3/R1+R3/R2)

I couldn't see the trees for the forest.

Thanks guys.

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