input offset voltage

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ed_gops

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Hi.. I found in an IEEE conference paper that the input offset voltage of a basic two stage CMOS differential amplifier as given two pics bellow. Can any one please explain me how the input offset voltage formula can be derived from the given circuit and what dose the Δ(W/L) indicate and how to calculate it. . Thank you.
 

Hi ed_gops,

the delta(W/L) and delta(Vth) are random variables. Due to random physical effects during manufacturing, such as random dopant fluctuation (RDF) and line edge roughness (LER), every transistor has a slightly different Vth and L than its neighbors. This difference causes offset in a differential pair.
The formula in your picture calculates the offset for one differential pair given the values of the random variables.
The statistics of offset can be calculated from the formula: the mean value of offset is 0, the variance depends linearly on the variance of delta(W/L) and delta(Vth). These variances depend on the area of the devices by Pelgrom's area law.

Regards,
Michael
 

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