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I have a question about an exercise considering op amps.

schematic

simulate this circuit – Schematic created using CircuitLab

The task is to give an expression for V_OUT as a function of V_IN, V0, R1 and R2.

Could anyone explain me how to solve such a task? Because I've always had struggles with op amps.

Thank you for your help!

EDIT:

I tried to solve this task using superposition. My result was:

\$V_{OUT}=V_0-V_{IN}*\frac{2*R_2+R_1}{2R_1+R_2}\$

Is this correct?

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    \$\begingroup\$ I'm voting to close this question as off-topic because homework with no attempt at a solution \$\endgroup\$ – Matt Young Jul 12 '17 at 2:24
  • \$\begingroup\$ Well I tried superposition now which gave me the result: V_OUT=V0-V_IN*((2*R2+R1)/(2R1+R2)). \$\endgroup\$ – Viviane Jul 12 '17 at 2:44
  • \$\begingroup\$ Could you tell me if that's right? \$\endgroup\$ – Viviane Jul 12 '17 at 2:45
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    \$\begingroup\$ Doesn't look correct to me, you have made a mistake gain of Vin to Vout \$\endgroup\$ – sstobbe Jul 12 '17 at 5:11
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I'll assume that it's an ideal OP-amp (voltage at (+)input = voltage at (-)input)

So, voltage dividing gives:

\$_{(+)}input=V_0\frac{R_1}{R_1+R_2}\$

And for (-)input: current from left = current from right

\$\frac{V_{IN}-_{(-)}input}{R_1}= \frac{_{(-)}input-V_{OUT}}{R_2}\$

\$\frac{R_2(V_{IN}-_{(-)}input)}{R_1}= _{(-)}input-V_{OUT}\$

\$_{(-)}input - \frac{R_2(V_{IN}-_{(-)}input)}{R_1} =V_{OUT}\$

(+)input into (-)input

remember: (+)input = V0*R1/(R1+R2)
remember: (-)input = (+)input

\$V_0\frac{R_1}{R_1+R_2} - \frac{R_2(V_{IN}-V_0\frac{R_1}{R_1+R_2})}{R_1} =V_{OUT}\$

Tidy up:

\$V_0-V_{IN}\frac{R_2}{R_1}=V_{OUT}\$

Verified here

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  • \$\begingroup\$ Instead of using voltage dividing at the +input I could've used kirchoffs current law (which I did use for the -input). But I used both to help as much as possible. Good Luck in your adventure of learning electronics :) And if you think my answer is correct, mark it as your answer. \$\endgroup\$ – Harry Svensson Jul 12 '17 at 20:37

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