Sub-$\mu$W Auto-Calibration Bandgap Voltage Reference With 1$\sigma$ Inaccuracy of $\pm$0.12% Within $-$40 $^\circ$C to 120 $^\circ$C

This article presents an auto-calibration technique for current-based bandgap voltage references (BGRs), based on a digitally-assisted auto-calibration loop for calibration cost reduction. We first present a theoretical study of the process variation induced $V_{\rm{EB}}$ and $\Delta V_{\text{EB}}$ variations in the BJT, which contribute to residual errors in the reference voltage ( $V_{\rm{REF}}$ ) and its temperature coefficient (TC) after applying conventional one-point trimming. Based on the study, we further propose an automatic one-point trimming methodology using a current digital-to-analog converter (IDAC), which can simultaneously relax the $\textit{V}_{\rm{EB}}$ and $\Delta V_{\rm{EB}}$ variations, resulting in a small drift in both $V_{\rm{REF}}$ and its TC after calibration. Fabricated in 65 nm standard CMOS, the proposed auto-calibrated BGR achieves a measured TC of 22.3 ppm/ $^{\circ}$ C at 1.2 V supply within $-$ 40 $^{\circ}$ C to 120 $^{\circ}$ C. The line regulation is 1.26 mV/V or 0.13%/V from 1.2 to 2.5 V. Based on ten-chip measurement results, the achieved $\sigma$ / $\mu$ variation in $V_{\rm{REF}}$ improves from $\pm$ 0.53% to $\pm$ 0.12% within the entire temperature spectrum after applying the proposed auto-calibration technique at 27 $^{\circ}$ C.