offset voltage and CMRR for diff pair

[jordan76]

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

 

[lavitaebelle]

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

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

CMRR = Adm/Acm = 2*gm/g

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.

 

[jordan76]

Hi lavitaebelle,

Thanks for your reply!

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

regards,
jordan76

 

[jinxingsun]

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