Nonideality consideration for high-precision amplifiers-analysis of random common-mode rejection ratio

Nonideal factors which play a key role in performance and yield in high-precision applications of operational amplifiers are rigorously investigated. The combined effects of both deterministic and statistical parameters must be incorporated. The statistical characteristics of the common-mode rejection ratio (CMRR) and the offset of two-stage CMOS op-amps are investigated. The op-amp errors associated with finite open-loop gains, finite CMRRs, and nonzero offset voltages are analyzed. It is shown that the random common-mode gain as determined by the mismatch of paired devices is comparable to the deterministic common-mode gain. It is shown that the probability density function of the CMRR is distributed similarly to that of a Gaussian random variable, but the mean is finite and the symmetry is skewed somewhat, as contrasted with the probability density function of the offset voltage which has a Gaussian distribution with zero mean. It is also shown that a nonideal finite CMRR can actually reduce the op-amp errors caused by a finite open-loop gain