To find worst case of CMRR

To calculate the worst case of CMRR, do we want common mode gain to be small or large?

For e.g.
if Acm = R2/R1 - R4/R3 , to find worst Acm what should we let it be ?
R2(1+ε)/R1(1-ε) - R4(1-ε)/R3(1+ε)
or
R2(1-ε)/R1(1+ε) - R4(1+ε)/R3(1-ε)

* (ε = resistor's tolerance)

and would the equation change if Ad = R1/R2 or Ad = R2/R1?

Manchested said:

To calculate the worst case of CMRR, do we want common mode gain to be small or large?

Click to expand...

Large. CMRR_w.c. = Acm/Dcm (e.g.: CMRR_typ = 10dB - 80dB = -70dB ; CMRR_w.c. = 20dB - 80dB = -60dB) .

Manchested said:

if Acm = R2/R1 - R4/R3 , to find worst Acm what should we let it be?

Click to expand...

R2(1+ε)/R1(1-ε) - R4(1-ε)/R3(1+ε)
-- largest term -- - -- smallest term --

Manchested said:

and would the equation change if Ad = R1/R2 or Ad = R2/R1?

Click to expand...

No, if you exchange the subscript numbers consequently.

I just found this circuit in my textbook.


This circuit has Acm = 1 - (R2*R4) / (R1*R3) & Ad = 1 + R1/R2
If for the worst case CMRR, Acm should be large, so the algebric term in Acm should be small.
then I thought it would be

Acm = 1 - (R2(1-ε) *R4(1-ε) ) / (R1(1+ε) *R3(1+ε))
Acm = 1 - (1-ε)² / (1+ε)²

however, in the book it says worst case Acm = 1 - (1+ε)² / (1-ε)²

so did I get it wrong? I am confused :-?

Normalized Common Mode Gain Acm

Manchested said:

Acm = 1 - (1-ε)² / (1+ε)²

however, in the book it says worst case Acm = 1 - (1+ε)² / (1-ε)²

Click to expand...

For a normalized Acm representation (values between 0 and 1) only your representation can be correct, s. the PDF below:
View attachment Acm-Calculation.pdf