The input offset voltage arises as a result of the unavoidable mismatches Present in the input
differential stage inside the op amp. In later chapters (in particular Chapters 8 and 12) we shall
study this topic in detail. Here, however, our concern is to investigate the effect of VOS on the operation
of closed-loop op-amp circuits. Toward that end, we note that general-purpose op amps
exhibit VOS in the range of 1 mV to 5 mV. Also, the value of VOS depends on temperature. The opamp
data sheets usually specify typical and maximum values for VOS at room temperature as well
as the temperature coefficient of VOS (usually in μV/°C). They do not, however, specify the
polarity of VOS because the component mismatches that give rise to VOS are obviously not known a
priori; different units of the same op-amp type may exhibit either a positive or a negative VOS.
To analyze the effect of VOS on the operation of op-amp circuits, we need a circuit model
for the op amp with input offset voltage. Such a model is shown in Fig. 2.28. It consists of a