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# offset voltage and CMRR for diff pair

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#### jordan76

##### Full Member level 3
Hi

As can be seen from the attached figure, there is an equation for a differential pair:
Vos*CMRR=Itail/Gtail

Could you explain how this is derived? Thanks in advance!

regards,
jordan76

Here the equation is regarding CMRR and Overdrive voltage and not offset voltage.

Acm(common mode gain) = R*g/2

gm = 2Id/Vov

Here Vov = Vgs-Vth

Substituting,

Vov*CMRR = 4Id/g

Theres a factor of 2 difference from your answer. That may be due to the definition of CMRR in a different way.

If sizes of the two transistors and the resistors are the same there is no systematic offset. Random offset is a statistical quantity and is not deterministic in an equation like this. It will contain mean error(which would be zero for matched condition) and variance/std deviation.

Hi lavitaebelle,

I still wonder whether there does exist any relationship between offset voltage and CMRR. Any inputs on that are welcome! Thanks!

regards,
jordan76

The CMRR can be regarded as the change in input offset voltage that results from a unit change in common-mode input voltage.

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