Effect of bandgap energy temperature dependence on thermal coefficient of bandgap reference voltage

In this paper the equations of basic bandgap reference (BGR) voltage circuits are reconstructed considering dependency of bandgap energy (E_g) to absolute temperature. Notice that previous works all consider E_g as a constant, independent of temperature variations. Dependence of bandgap energy to absolute temperature is firstly approximated by a second-degree polynomial using Lagrangian interpolating polynomial method in temperature range of 2°C to 92°C. Then the simplified polynomial is used to calculate the modified thermal coefficient (TC) of the base-emitter voltage (V_BE) in BJT transistors. Accurate analysis of the resulted equations reveals that the TC of V_BE must be corrected to -1.7mV/°K at 27°C ambient temperature which has been formerly reported about -1.5mV/°K ([2], [5]), -2mV/°K ([3], [9], [10]) and -2.2mV/°K ([4], [8]) where E_g was assumed as a temperature-independent constant. More important, TC of V_BE is derived to be -1.5mV/°K at 92°C rather than previously reported, -1.2mV/°K, a 20% error originated from constant E_g assumption.