Closed loop gain of this fully-differential amplifier

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tenso

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I am trying to figure out how Razavi in his book got the following expression for Closed loop gain of a fully diff. amplifier. The circuit schematic and the equation are below.






I have come across this explanation of the calculation of the feedback factor of an inverting amplifier. This is the first time I am seeing the factor "k" being mentioned in the closed loop voltage gain.

https://electronics.stackexchange.c...inbeta-derivation-for-the-inverting-amplifier

is there any book which talks about this?

- - - Updated - - -

NVM, after looking at this link https://electronics.stackexchange.com/questions/330638/beta-of-inverting-opamp-amplifier

I figured out how he got the expression.

Am I right about the taylor series approximation though? It is taken when x <<< 1?
 

I don't know how he got to the second line. He may have used the Taylor series or perhaps long division.
However, note that the result is approximately - R2/R1 Vin if the open loop gain is very high.

I have attached an analysis of a diff in, singled out amp that I did years ago. I used this method to analyse your amp.

Hope this helps
 

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tenso said:
Am I right about the taylor series approximation though? It is taken when x <<< 1?
Click to expand...

Yes.. If A0 is large (and is typically the case) then the 'x' term will be such that x<<1..
 

Of course, we do not need any Taylor series approximation or something like this.
We need only the classical feedback formula (for finite gain) introduced by H. Black - supplemented by a forward damping factor.
 
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