Help me calculate the gain of close loop in OPA

[david753]

If there is a OPA, Input is connected to V- via R1, and R2 is connected from Vo to V-, and V+ is connected to Ground.
Av_c(The Gain of Close loop)=-(R2/R1)*1/((R2/(R1*Av_o))+(R2/Zin*Av_o)+(1/Av_o)+1), Av_o is the Gain of open loop of OPA.
Do you know how it derive from?

 

[alexan_e]

Re: simple OPA question?

I think this will help you, read the "THE REAL STORY OF GAIN" part


In a few words, the open loop gain is not needed to calculate the closed loop gain, it is set by the resistors (if the gain is less than the open loop gain which is almost always the case).

Alex

 

[LvW]

Re: simple OPA question?

The expression for Av_c is derived by applying the basic rules and sentences of linear circuit theory: Kirchhoff, Ohm, superposition.

Regarding the reply from alex:
In contrast to his answer, the opamp open loop gain Av_o is needed if you want to see and to understand why - in most but not in all cases - this parameter can be neglected.
I think, for an engineer it is absolutely necessary to see why and when (that means: under which conditions) some simplifications are allowed.