why the gain is wrong in this close loop?

[shanmei]

From the two inputs, we know the difference voltage is Vin-Vout, after amplifying A, Vout=(Vin-Vout)*A, Vout(1+A)= Vin, so Vout/Vin=1/(1+A). When A is infinite, Vout/Vin=0? it is wrong , why? Thanks.

 

[Dominik Przyborowski]

You lost one multiplication by A. The Vo/Vi=1/(1+1/A)

 

[shanmei]

Thanks. Dominik Przyborowski.

 

[Audioguru]

It is obvious that the gain is 1 like a piece of wire.