The influence of the reverse Early effect on the performance of bandgap references

In the literature three key-parameters are commonly used for the design of bipolar bandgap references: E
_G
(bandgap energy), I
_S
(saturation current) and X
_TI
(exponent of the temperature behavior of I
_S
). This paper shows that four key parameters exist: these three and V
_AR
,the reverse Early voltage. This parameter models the influence of the base-width modulation at the base-emitter junction on the collector current. A general expression for the error in the output voltage caused by the reverse Early effect is derived and a comparison is made with other errors.