how to get the voltage gain of this circuit?

[amwygah]

Thanks for all your discussions at first.
1).Just as what godfrey has said，I did mean that Vid = differential input voltage and Vic = common mode input voltage.
2).my question comes from the pdf at the end of this message.
3).I did know this circuits can be used to test CMRR after the op amp was manufactured.
But i am confused about the result of the gain, because the result in the pdf is 2 times bigger than mine.
4).Thanks godfreyl and FvM very much, i did make a mistake on the sign of Vid.
it should be Vid = -Vout*R1/(R1+R2), and then the result should be given by FvM

Originally Posted by FvM
Vout/Vin = + 1000 * Acm / Adm

5). And at last, thanks anybody takes part in my thread very much, include FvM,LvW,dselec,godfreyl,varunkant2k,and so on...
6).Similar to godfreyl

Originally Posted by FvM
Re: how to get the voltage gain of this circuit?

OK, I tried working it out differently, in terms of the voltages at the inverting and non-inverting input pins (Vinvert and Vnoninv respectively), but got the same answer:

Vout/Vin = 1000 * Acm / (1001 - Acm * 0.5 - Adm)

If we assume that Adm >> Acm
and we assume that Adm >> 1000,
then we can simplify it to:

Vout/Vin = -1000 * Acm / Adm

And my result is Vout/Vin = 1000 * Acm / (1001 - Acm * 0.5 + Adm)
and then it can be approximately Vout/Vin = 1000 * Acm / Adm.

 

[dselec]

Common-mode rejection ratio
From Wikipedia, the free encyclopedia



all good still i cant understand how the amp can be calculated
cmmr is given by the manufacturer i have some knowledge about that when desugn my amps and use the acm adm cmmr Numbers given by manu... not calculate them.

 

[godfreyl]

For normal design work, we use the CMRR figure given by the manufacturer, but what if you have to find the CMRR by measurement? That is the problem. In other words, if you were given an unmarked, unidentified opamp, how would you find it's CMRR?

It has already been explained that the voltage gain of the circuit in post 1 is given by:
Gain = Vout/Vin = 1000*Acm/Adm
Therefore:
Adm/Acm = 1000/Gain
so:
CMRR (in dB) = 20 * log(1000/gain)

So if we build the given circuit and measure it's gain, we can calculate the CMRR of the opamp.