# Confusion closed-loop gain equation inverting amplifier

#### hoyyoth

Joined Mar 21, 2020
312
Dear Team,

I was going through this article. In the inverting amplifier section you can see the below thing.

May I know how that _R2/R1 term came there.

Regards

#### crutschow

Joined Mar 14, 2008
34,706
As you can see, the only difference between the inverting and non-inverting configurations is the location of the source voltage, so the gain equations are similar.
The difference is the non-inverting amp adds the source voltage to the output, so the ideal gain for the inverting amp is R2/R1 and the non-inverting amp is 1+R2/R1.

#### LvW

Joined Jun 13, 2013
1,766
For an inverting amplifier you must consider the fact that the input signal to be amplified does NOT directly arrive at the opamp inputs.
Therefore, in your block diagram there must be an additional input block Hf (forward damping) in front of the summing junction having the transfer function Hf=-R2/(R1+R2). The corresponding feedback function in the return pass Hr (you call it beta) is Hr=R1/(R1+R2).
(These expressions result from superposition of both, input and feedback signal, at the inverting input.)
As the result - the closed-loop transfer function is

Acl=Hf * Ao / (1+Hr * Ao)

As you can see, for Ao approaching infinity this expression simplifies to

Acl=Hf/Hr=-R2/R1