Mathematical formulation of restrictions for the design of low voltage bandgap references

nowadays the qualities more looked for in the design of bandgap references are the low potential of the reference and the low value of its coefficient of temperature, being these parameters more favorable in curvature corrected bandgap references. the design parameters of bandgap references depend on the value of the potential of reference vref; nevertheless, in the reported designs there are not paid attention to conditions that limit the attainable value of vref. in this work the mathematical formulation of the restrictions that really limit the attainable value of the reference potential is presented in order that the design of a curvature corrected bandgap reference can be realizable.