How to calculate gain of this circuit?

[dsk635]

Hi,

I have the following opamp circuit (attached). I would like to calculate the expression for the gain Vout/Vin. An offset voltage is present in the opamp.

The reference that I have sites the Vout as:

Vout = Vin - Vos(1 + R2/R1)

But I am unable to understand how to arrive at this result. Or is the result wrongly quoted?

Thanks,
-D.

 

[Davood Amerion]

equivalent circuit will be:
K is op-amp open loop gain

Vin = (R1+R2)*I1+ KV1
I1= V1/R1
thus
Vin = ((R1+R2)/R1) V1 + KV1
from figure
Vout = KV1
Vin = ((R1+R2)/R1) V1 + Vout
Vout = Vin - ((R1+R2)/R1) V1
or Vout = Vin - (1+R2/R1) V1
[V1 = Vos]

regards,
Davood.

 

[Miguel Gaspar]

You can apply supperposition.
1) VIO = 0, so calculate for Vin. The result is Vo1
2) Vin = 0, now calculate for VIO, put VIO betwen the invertin input and the node betwet both resistors. The result is Vo2
3) finally Vo = Vo1 + Vo2

I think this is the easyest solution.