# Question about a specific OpAmp circuit

#### techie

Joined Jan 2, 2008
4
Hello there , first time poster .
I'm trying to find the Voutput of this circuit ( attachment ) but i think i am missing something .
Using the superposition principle i begin by grounding V2 to find the effect V1 has at Vo and then i ll do the same for V2 and add them to find the total output but im left with 4 equations and 5 variables system that i just cant solve .
Anyway these are the equations with V2 grounded :
Using KCL at the 4 nodes ( a , b , c , d ) :

a -> (v1-Va)/R1 = - (Vc - Va)/R2
b-> Vb/R1= (Vd - Vb)/R2
c-> (Vo-Vc)/R2 = (Vc- Va)/R2 + (Vc- Vd)/Rg
d-> (Vc-Vd)/Rg =Vd/R2 + (Vd - Vb)/R2

then we know that Va=Vb :

a -> (v1-Va)/R1 = - (Vc - Va)/R2
b-> Va/R1= (Vd - Va)/R2
c-> (Vo-Vc)/R2 = (Vc- Va)/R2 + (Vc- Vd)/Rg
d-> (Vc-Vd)/Rg =Vd/R2 + (Vd - Va)/R2

Thats the 4 equations/5 variables system and i just cant find an expression of Vo only dependant on V1
Some stuff i ve found : Vo = 2 ( Vc + Vd - Va )

(Vc-Vd)/Rg = - R2*V1/R1*Rg
So , is there something im missing ? (a current or voltage equation ? or some other method i could follow ?)

When i first saw the circuit i thought thats an opamp with both positive and negative feedback with Rg setting the amount of possitive feedback . Is this right in any way ?

Thanks for any tips/help/pointers beforehand and sorry for any grammatical errors i may have .

#### Distort10n

Joined Dec 25, 2006
429
Using Superposition would be the first step. Then I would use Thevenin to find the equivalent resistance of the 'T' type network.

#### The Electrician

Joined Oct 9, 2007
2,936
It's true that you have a 4 equations/5 variables system, but of the 5 variables only 4 are unknown; v1 is a given.

I was able to solve the system and I get Vo = - V1*(2*R2*(R2+Rg))/(R1*Rg)