# OP Amp-Difference amplifier

I have a question about an exercise considering op amps. 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.

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?

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

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

• 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. – Harry Svensson Jul 12 '17 at 20:37