- #1

arhzz

- 268

- 52

- Homework Statement
- Find the output voltage

- Relevant Equations
- Circuit analysis

Hello! Consider this operational amplifier circuit,a subtractor to be more precise

I need to find the Ua (output voltage) using superposition; Now I dont have any values given for the resistors but that they are all the same (R1=R2=R3=R4=R5) so I just need to find the expressions.I've tried it like this. I let U1 be active and all of the other voltages get short circuited. When I simplify the circuit in that way I get a simple inverting operational amplifier that looks like this;

By no means a pretty picture but I think it will suffice. So I get that Ua is simply ## U_{A} = -\frac{R5}{R1}U_1## And according to the solutions this is correct. Now I did the same thing for U2 and I get the same circuit (simplified) but the first resistor is R2 and not R2 so the voltage is ##U_{A} = -\frac{R5}{R2}U_2 ## But according to the solutions it shouldnt be the resistor R2 but rather the resistor R1

It states "Same circuit as for U1" and gives the same equation but with voltage U2. I do not understand this; how can it be the same resistor? If we put it on ground and give voltage to R2 how can we get the same circuit if we do it vice versa? I'd assume I am simplifying the circuit wrong,that is why I posted the second picture,is the simplified circuit correct?

Thanks in advance!

I need to find the Ua (output voltage) using superposition; Now I dont have any values given for the resistors but that they are all the same (R1=R2=R3=R4=R5) so I just need to find the expressions.I've tried it like this. I let U1 be active and all of the other voltages get short circuited. When I simplify the circuit in that way I get a simple inverting operational amplifier that looks like this;

By no means a pretty picture but I think it will suffice. So I get that Ua is simply ## U_{A} = -\frac{R5}{R1}U_1## And according to the solutions this is correct. Now I did the same thing for U2 and I get the same circuit (simplified) but the first resistor is R2 and not R2 so the voltage is ##U_{A} = -\frac{R5}{R2}U_2 ## But according to the solutions it shouldnt be the resistor R2 but rather the resistor R1

It states "Same circuit as for U1" and gives the same equation but with voltage U2. I do not understand this; how can it be the same resistor? If we put it on ground and give voltage to R2 how can we get the same circuit if we do it vice versa? I'd assume I am simplifying the circuit wrong,that is why I posted the second picture,is the simplified circuit correct?

Thanks in advance!