Now I want to write the transfer function in form of fig2.
So ,the forward transfer function and feedback loop transfer function can be writed as below Gforward=-A (A is the voltage gain of OP) β=R1/(R1+Rf)
But the result is wrong~~Who could kindly tell me why? Thanks~~
No, it´s not necessary as the neg. input resistance is considered to be infinite (in reality Rin>>R1 parallel to Rf).
In words, based on the superposition theorem:
Hfor=part of Vi appearing at the opamp input (if Vo=0)
Hback=part of Vo appearing at the opamp input (if Vi=0)
Yes, thus you can calculate both voltages appearing at point A (add them together according to the superposition theorem),resulting in Vin.
As a 3rd equation you use Vo=-A•Vin and you arrive at the final expression.